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0705.3360.pdf | 0 | # The Road to Quantum Artificial Intelligence
Kyriakos N. Sgarbas
Wire Communications Lab., Dept. of Electrical and Computer Engineering,
University of Patras, GR-26500, Patras, Greece
E-mail: sgarbas $$@$$ upatras.gr
# Abstract
This paper overviews the basic principles and recent advances in the emerging field of
... | <h1>The Road to Quantum Artificial Intelligence</h1>
<p>Kyriakos N. Sgarbas</p>
<p>Wire Communications Lab., Dept. of Electrical and Computer Engineering,
University of Patras, GR-26500, Patras, Greece
E-mail: sgarbas $$@$$ upatras.gr</p>
<h1>Abstract</h1>
<p>This paper overviews the basic principles and recent advance... | [{"type": "title", "coordinates": [80, 77, 401, 99], "content": "The Road to Quantum Artificial Intelligence", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [187, 124, 293, 138], "content": "Kyriakos N. Sgarbas", "block_type": "text", "index": 2}, {"type": "text", "coordinates": [74, 150, 407, 188... | [{"type": "text", "coordinates": [79, 82, 400, 98], "content": "The Road to Quantum Artificial Intelligence", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [186, 124, 295, 140], "content": "Kyriakos N. Sgarbas", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [73, 149, 408, 165], "content": "Wir... | [] | [{"type": "inline", "coordinates": [248, 176, 257, 186], "content": "@", "caption": ""}] | [] | [481.0, 680.0] | [{"type": "text", "text": "The Road to Quantum Artificial Intelligence ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Kyriakos N. Sgarbas ", "page_idx": 0}, {"type": "text", "text": "Wire Communications Lab., Dept. of Electrical and Computer Engineering, University of Patras, GR-26500, Patras, Greece E-m... | [{"category_id": 0, "poly": [223.13665771484375, 216.29258728027344, 1116.9342041015625, 216.29258728027344, 1116.9342041015625, 275.70941162109375, 223.13665771484375, 275.70941162109375], "score": 0.999996542930603}, {"category_id": 1, "poly": [522.5202026367188, 345.6185607910156, 817.049072265625, 345.6185607910156... | {"preproc_blocks": [{"type": "title", "bbox": [80, 77, 401, 99], "lines": [{"bbox": [79, 82, 400, 98], "spans": [{"bbox": [79, 82, 400, 98], "score": 1.0, "content": "The Road to Quantum Artificial Intelligence", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [187, 124, 293, 138], "lines": [{"bbo... | ./arxiv_full_mineru_outputs_20/images/0705.3360_0.png | images/0705.3360_0.png | |
0705.3360.pdf | 1 | more details the reader is advised to read [Karafyllidis (2005a)], [Gruska (1999)] or
[Nielsen & Chuang (2000)].
# 2. Quantum Computation Basics
The quantum analog of a bit is called a quantum bit or qubit. Its physical implementa-
tion can be the energy state of an electron in an atom, the polarization of a photon, ... | <p>more details the reader is advised to read [Karafyllidis (2005a)], [Gruska (1999)] or
[Nielsen & Chuang (2000)].</p>
<h1>2. Quantum Computation Basics</h1>
<p>The quantum analog of a bit is called a quantum bit or qubit. Its physical implementa-
tion can be the energy state of an electron in an atom, the polarizatio... | [{"type": "text", "coordinates": [49, 78, 432, 105], "content": "more details the reader is advised to read [Karafyllidis (2005a)], [Gruska (1999)] or\n[Nielsen & Chuang (2000)].", "block_type": "text", "index": 1}, {"type": "title", "coordinates": [49, 117, 240, 132], "content": "2. Quantum Computation Basics", "block... | [{"type": "text", "coordinates": [50, 79, 431, 94], "content": "more details the reader is advised to read [Karafyllidis (2005a)], [Gruska (1999)] or", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [50, 92, 175, 107], "content": "[Nielsen & Chuang (2000)].", "score": 1.0, "index": 2}, {"type": "text", "coo... | [] | [{"type": "block", "coordinates": [166, 241, 321, 275], "content": "", "caption": ""}, {"type": "block", "coordinates": [89, 359, 390, 394], "content": "", "caption": ""}, {"type": "block", "coordinates": [84, 497, 398, 518], "content": "", "caption": ""}, {"type": "inline", "coordinates": [395, 176, 411, 190], "conten... | [] | [481.0, 680.0] | [{"type": "text", "text": "", "page_idx": 1}, {"type": "text", "text": "2. Quantum Computation Basics ", "text_level": 1, "page_idx": 1}, {"type": "text", "text": "The quantum analog of a bit is called a quantum bit or qubit. Its physical implementation can be the energy state of an electron in an atom, the polarizatio... | [{"category_id": 2, "poly": [140.89581298828125, 146.8037567138672, 194.87283325195312, 146.8037567138672, 194.87283325195312, 176.54458618164062, 140.89581298828125, 176.54458618164062], "score": 0.9999951720237732}, {"category_id": 8, "poly": [465.86785888671875, 672.9063110351562, 897.3070068359375, 672.906311035156... | {"preproc_blocks": [{"type": "text", "bbox": [49, 78, 432, 105], "lines": [{"bbox": [50, 79, 431, 94], "spans": [{"bbox": [50, 79, 431, 94], "score": 1.0, "content": "more details the reader is advised to read [Karafyllidis (2005a)], [Gruska (1999)] or", "type": "text"}], "index": 0}, {"bbox": [50, 92, 175, 107], "span... | ./arxiv_full_mineru_outputs_20/images/0705.3360_1.png | images/0705.3360_1.png | |
0705.3360.pdf | 2 | quantum register remain in superposition until they are measured (intentionally or
not). At the time of measurement the state of the register collapses (or is resolved) to
one of its basis states randomly, according to the probability assigned to that state.
It is not necessary to measure every single qubit of a quant... | <p>quantum register remain in superposition until they are measured (intentionally or
not). At the time of measurement the state of the register collapses (or is resolved) to
one of its basis states randomly, according to the probability assigned to that state.</p>
<p>It is not necessary to measure every single qubit o... | [{"type": "text", "coordinates": [49, 78, 432, 117], "content": "quantum register remain in superposition until they are measured (intentionally or\nnot). At the time of measurement the state of the register collapses (or is resolved) to\none of its basis states randomly, according to the probability assigned to that s... | [{"type": "text", "coordinates": [50, 80, 431, 93], "content": "quantum register remain in superposition until they are measured (intentionally or", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [50, 92, 430, 105], "content": "not). At the time of measurement the state of the register collapses (or is reso... | [] | [{"type": "block", "coordinates": [130, 154, 356, 187], "content": "", "caption": ""}, {"type": "inline", "coordinates": [105, 210, 142, 224], "content": "|00000>", "caption": ""}, {"type": "inline", "coordinates": [148, 211, 183, 223], "content": "|10000>", "caption": ""}, {"type": "inline", "coordinates": [205, 210, ... | [] | [481.0, 680.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "It is not necessary to measure every single qubit of a quantum register in order to trigger its collapse to a basis state. For example, consider this case: ", "page_idx": 2}, {"type": "equation", "text": "$$\n\\left|\\mathbf{Q}_{s}\\right\\rangle\\... | [{"category_id": 2, "poly": [1145.6666259765625, 147.40145874023438, 1196.4783935546875, 147.40145874023438, 1196.4783935546875, 177.17152404785156, 1145.6666259765625, 177.17152404785156], "score": 0.9999982714653015}, {"category_id": 1, "poly": [137.08303833007812, 1522.686279296875, 1203.3995361328125, 1522.68627929... | {"preproc_blocks": [{"type": "text", "bbox": [49, 78, 432, 117], "lines": [{"bbox": [50, 80, 431, 93], "spans": [{"bbox": [50, 80, 431, 93], "score": 1.0, "content": "quantum register remain in superposition until they are measured (intentionally or", "type": "text"}], "index": 0}, {"bbox": [50, 92, 430, 105], "spans":... | ./arxiv_full_mineru_outputs_20/images/0705.3360_2.png | images/0705.3360_2.png | |
0705.3360.pdf | 3 | computation is eventually reduced to a series of basic operations to some qubits of a
quantum register; this is what quantum gates do.
Quantum gates are the basic computation components for QC. They are very different
from gates in classical computation systems. Quantum gates are not circuits with
input and output; th... | <p>computation is eventually reduced to a series of basic operations to some qubits of a
quantum register; this is what quantum gates do.</p>
<p>Quantum gates are the basic computation components for QC. They are very different
from gates in classical computation systems. Quantum gates are not circuits with
input and o... | [{"type": "text", "coordinates": [50, 79, 431, 104], "content": "computation is eventually reduced to a series of basic operations to some qubits of a\nquantum register; this is what quantum gates do.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [50, 110, 432, 161], "content": "Quantum gates are... | [{"type": "text", "coordinates": [51, 81, 430, 93], "content": "computation is eventually reduced to a series of basic operations to some qubits of a", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [51, 94, 264, 106], "content": "quantum register; this is what quantum gates do.", "score": 1.0, "index": 2},... | [] | [{"type": "inline", "coordinates": [412, 310, 428, 323], "content": "|1>", "caption": ""}, {"type": "inline", "coordinates": [171, 374, 186, 387], "content": "|1>", "caption": ""}, {"type": "inline", "coordinates": [355, 413, 371, 426], "content": "|1>", "caption": ""}, {"type": "inline", "coordinates": [397, 452, 412,... | [] | [481.0, 680.0] | [{"type": "text", "text": "", "page_idx": 3}, {"type": "text", "text": "Quantum gates are the basic computation components for QC. They are very different from gates in classical computation systems. Quantum gates are not circuits with input and output; they are operators over a quantum register. These operators are al... | [{"category_id": 2, "poly": [141.12033081054688, 148.28504943847656, 192.39727783203125, 148.28504943847656, 192.39727783203125, 176.3029327392578, 141.12033081054688, 176.3029327392578], "score": 0.9999963641166687}, {"category_id": 1, "poly": [195.24951171875, 1452.72802734375, 1200.7587890625, 1452.72802734375, 1200... | {"preproc_blocks": [{"type": "text", "bbox": [50, 79, 431, 104], "lines": [{"bbox": [51, 81, 430, 93], "spans": [{"bbox": [51, 81, 430, 93], "score": 1.0, "content": "computation is eventually reduced to a series of basic operations to some qubits of a", "type": "text"}], "index": 0}, {"bbox": [51, 94, 264, 106], "span... | ./arxiv_full_mineru_outputs_20/images/0705.3360_3.png | images/0705.3360_3.png | |
0705.3360.pdf | 4 | the intended result. This is called probability amplitude amplification [Gruska
(1999)].
Grover’s Algorithm: It searches $$\scriptstyle\mathbf{N}=2^{\ n}$$ items superimposed on a quantum
register of n qubits using a certain state as a search key. It is able to search an
unordered set of items in $$O\big(\sqrt{N}\big)$... | <p>the intended result. This is called probability amplitude amplification [Gruska
(1999)].
Grover’s Algorithm: It searches $$\scriptstyle\mathbf{N}=2^{\ n}$$ items superimposed on a quantum
register of n qubits using a certain state as a search key. It is able to search an
unordered set of items in $$O\big(\sqrt{N}\bi... | [{"type": "text", "coordinates": [69, 79, 432, 265], "content": "the intended result. This is called probability amplitude amplification [Gruska\n(1999)].\nGrover\u2019s Algorithm: It searches $$\\scriptstyle\\mathbf{N}=2^{\\ n}$$ items superimposed on a quantum\nregister of n qubits using a certain state as a search k... | [{"type": "text", "coordinates": [85, 79, 431, 92], "content": "the intended result. This is called probability amplitude amplification [Gruska", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 93, 123, 105], "content": "(1999)].", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [85, 105, 238... | [] | [{"type": "inline", "coordinates": [239, 105, 265, 116], "content": "\\scriptstyle\\mathbf{N}=2^{\\ n}", "caption": ""}, {"type": "inline", "coordinates": [199, 128, 236, 149], "content": "O\\big(\\sqrt{N}\\big)", "caption": ""}, {"type": "inline", "coordinates": [218, 150, 247, 162], "content": "(Q F T)", "caption": "... | [] | [481.0, 680.0] | [{"type": "text", "text": "the intended result. This is called probability amplitude amplification [Gruska (1999)]. \nGrover\u2019s Algorithm: It searches $\\scriptstyle\\mathbf{N}=2^{\\ n}$ items superimposed on a quantum register of n qubits using a certain state as a search key. It is able to search an unordered s... | [{"category_id": 2, "poly": [1145.6829833984375, 147.68580627441406, 1197.993408203125, 147.68580627441406, 1197.993408203125, 176.22019958496094, 1145.6829833984375, 176.22019958496094], "score": 0.9999959468841553}, {"category_id": 0, "poly": [140.22885131835938, 769.6986083984375, 747.452880859375, 769.6986083984375... | {"preproc_blocks": [{"type": "text", "bbox": [69, 79, 432, 265], "lines": [{"bbox": [85, 79, 431, 92], "spans": [{"bbox": [85, 79, 431, 92], "score": 1.0, "content": "the intended result. This is called probability amplitude amplification [Gruska", "type": "text"}], "index": 0}, {"bbox": [85, 93, 123, 105], "spans": [{... | ./arxiv_full_mineru_outputs_20/images/0705.3360_4.png | images/0705.3360_4.png | |
0705.3360.pdf | 5 | Grover’s algorithm [Grover (1997)] and its variations are ideal for efficient content-
addressable search and information retrieval from large collections of raw data. The
principle of probability amplitude amplification that guides these processes can be
relaxed for approximate pattern matching as well, thus facilitat... | <p>Grover’s algorithm [Grover (1997)] and its variations are ideal for efficient content-
addressable search and information retrieval from large collections of raw data. The
principle of probability amplitude amplification that guides these processes can be
relaxed for approximate pattern matching as well, thus facili... | [{"type": "text", "coordinates": [50, 79, 431, 205], "content": "Grover\u2019s algorithm [Grover (1997)] and its variations are ideal for efficient content-\naddressable search and information retrieval from large collections of raw data. The\nprinciple of probability amplitude amplification that guides these processes... | [{"type": "text", "coordinates": [51, 80, 430, 92], "content": "Grover\u2019s algorithm [Grover (1997)] and its variations are ideal for efficient content-", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [51, 93, 430, 105], "content": "addressable search and information retrieval from large collections of ... | [] | [{"type": "inline", "coordinates": [74, 193, 84, 204], "content": "2^{\\mathrm{n}}", "caption": ""}] | [] | [481.0, 680.0] | [{"type": "text", "text": "Grover\u2019s algorithm [Grover (1997)] and its variations are ideal for efficient contentaddressable search and information retrieval from large collections of raw data. The principle of probability amplitude amplification that guides these processes can be relaxed for approximate pattern ma... | [{"category_id": 1, "poly": [141.4107666015625, 220.2403564453125, 1199.1956787109375, 220.2403564453125, 1199.1956787109375, 570.8997802734375, 141.4107666015625, 570.8997802734375], "score": 0.9999964237213135}, {"category_id": 1, "poly": [141.23822021484375, 1200.6922607421875, 1200.5079345703125, 1200.6922607421875... | {"preproc_blocks": [{"type": "text", "bbox": [50, 79, 431, 205], "lines": [{"bbox": [51, 80, 430, 92], "spans": [{"bbox": [51, 80, 430, 92], "score": 1.0, "content": "Grover\u2019s algorithm [Grover (1997)] and its variations are ideal for efficient content-", "type": "text"}], "index": 0}, {"bbox": [51, 93, 430, 105],... | ./arxiv_full_mineru_outputs_20/images/0705.3360_5.png | images/0705.3360_5.png | |
0705.3360.pdf | 6 | cooperation [Miakisz et al. (2006)] and coordination games [Huberman & Hogg
(2003)], simulating economic systems [Chen et al. (2002)] and human behavior
[Mendes (2005)]. It is interesting that in some cases the quantum solution can be
derived as an extension to the classical one [Huberman & Hogg (2003)], thus
enabling ... | <p>cooperation [Miakisz et al. (2006)] and coordination games [Huberman & Hogg
(2003)], simulating economic systems [Chen et al. (2002)] and human behavior
[Mendes (2005)]. It is interesting that in some cases the quantum solution can be
derived as an extension to the classical one [Huberman & Hogg (2003)], thus
enabli... | [{"type": "text", "coordinates": [49, 78, 432, 244], "content": "cooperation [Miakisz et al. (2006)] and coordination games [Huberman & Hogg\n(2003)], simulating economic systems [Chen et al. (2002)] and human behavior\n[Mendes (2005)]. It is interesting that in some cases the quantum solution can be\nderived as an ext... | [{"type": "text", "coordinates": [49, 79, 431, 93], "content": "cooperation [Miakisz et al. (2006)] and coordination games [Huberman & Hogg", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [50, 91, 432, 106], "content": "(2003)], simulating economic systems [Chen et al. (2002)] and human behavior", "score":... | [] | [] | [] | [481.0, 680.0] | [{"type": "text", "text": "", "page_idx": 6}, {"type": "text", "text": "The last comment on modeling human behavior seems to lead to the philosophical question of whether the human brain performs some kind of quantum computation [Miakisz et al. (2006)] or not [Penrose (1997)], a question that has been used to argue aga... | [{"category_id": 0, "poly": [140.0205535888672, 1552.326171875, 366.07598876953125, 1552.326171875, 366.07598876953125, 1597.0377197265625, 140.0205535888672, 1597.0377197265625], "score": 0.9999988079071045}, {"category_id": 1, "poly": [139.34336853027344, 1199.7967529296875, 1202.3323974609375, 1199.7967529296875, 12... | {"preproc_blocks": [{"type": "text", "bbox": [49, 78, 432, 244], "lines": [{"bbox": [49, 79, 431, 93], "spans": [{"bbox": [49, 79, 431, 93], "score": 1.0, "content": "cooperation [Miakisz et al. (2006)] and coordination games [Huberman & Hogg", "type": "text"}], "index": 0}, {"bbox": [50, 91, 432, 106], "spans": [{"bbo... | ./arxiv_full_mineru_outputs_20/images/0705.3360_6.png | images/0705.3360_6.png | |
0705.3360.pdf | 7 | a very narrow choice of recent papers and research directions. For a lengthier
overview on QC applications to Computational Intelligence see [Perkowski (2005)].
The ideas presented here were inevitably vague and outlined, since quantum
computers are still not available for implementation purposes. The hardware for
qua... | <p>a very narrow choice of recent papers and research directions. For a lengthier
overview on QC applications to Computational Intelligence see [Perkowski (2005)].</p>
<p>The ideas presented here were inevitably vague and outlined, since quantum
computers are still not available for implementation purposes. The hardwar... | [{"type": "text", "coordinates": [50, 79, 430, 104], "content": "a very narrow choice of recent papers and research directions. For a lengthier\noverview on QC applications to Computational Intelligence see [Perkowski (2005)].", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [50, 110, 431, 275], "co... | [{"type": "text", "coordinates": [49, 79, 431, 94], "content": "a very narrow choice of recent papers and research directions. For a lengthier", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [50, 93, 422, 106], "content": "overview on QC applications to Computational Intelligence see [Perkowski (2005)].", ... | [] | [] | [] | [481.0, 680.0] | [{"type": "text", "text": "", "page_idx": 7}, {"type": "text", "text": "The ideas presented here were inevitably vague and outlined, since quantum computers are still not available for implementation purposes. The hardware for quantum registers is still in infancy due to the obstacle of decoherence which is very diffic... | [{"category_id": 0, "poly": [141.0516815185547, 798.3380737304688, 318.3129577636719, 798.3380737304688, 318.3129577636719, 841.2073364257812, 141.0516815185547, 841.2073364257812], "score": 0.9999984502792358}, {"category_id": 2, "poly": [139.8741912841797, 148.084228515625, 193.52337646484375, 148.084228515625, 193.5... | {"preproc_blocks": [{"type": "text", "bbox": [50, 79, 430, 104], "lines": [{"bbox": [49, 79, 431, 94], "spans": [{"bbox": [49, 79, 431, 94], "score": 1.0, "content": "a very narrow choice of recent papers and research directions. For a lengthier", "type": "text"}], "index": 0}, {"bbox": [50, 93, 422, 106], "spans": [{"... | ./arxiv_full_mineru_outputs_20/images/0705.3360_7.png | images/0705.3360_7.png | |
0705.3360.pdf | 8 | Karafyllidis, I.G. (2005a), Quantum Computers – Basic Principles, Klidarithmos,
Athens (in Greek).
Karafyllidis, I.G. (2005b), Quantum Computer Simulator Based on the Circuit Model
of Quantum Computation, IEEE Trans.Circ.& Syst.-I, vol.52, no.8, pp.1590-1596.
Mendes, R.V. (2005), The Quantum Ultimatum Game, Quan... | <p>Karafyllidis, I.G. (2005a), Quantum Computers – Basic Principles, Klidarithmos,
Athens (in Greek).
Karafyllidis, I.G. (2005b), Quantum Computer Simulator Based on the Circuit Model
of Quantum Computation, IEEE Trans.Circ.& Syst.-I, vol.52, no.8, pp.1590-1596.
Mendes, R.V. (2005), The Quantum Ultimatum Game, Q... | [{"type": "text", "coordinates": [50, 79, 433, 446], "content": "Karafyllidis, I.G. (2005a), Quantum Computers \u2013 Basic Principles, Klidarithmos,\nAthens (in Greek).\nKarafyllidis, I.G. (2005b), Quantum Computer Simulator Based on the Circuit Model\nof Quantum Computation, IEEE Trans.Circ.& Syst.-I, vol.52, no.8, p... | [{"type": "text", "coordinates": [49, 79, 431, 94], "content": "Karafyllidis, I.G. (2005a), Quantum Computers \u2013 Basic Principles, Klidarithmos,", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [64, 92, 148, 105], "content": "Athens (in Greek).", "score": 1.0, "index": 2}, {"type": "text", "coordinates"... | [] | [{"type": "inline", "coordinates": [103, 206, 111, 215], "content": "\\risingdotseq", "caption": ""}] | [] | [481.0, 680.0] | [{"type": "text", "text": "", "page_idx": 8}] | [{"category_id": 2, "poly": [1144.7769775390625, 146.99856567382812, 1198.39306640625, 146.99856567382812, 1198.39306640625, 177.5880584716797, 1144.7769775390625, 177.5880584716797], "score": 0.9999961256980896}, {"category_id": 2, "poly": [140.13031005859375, 147.15817260742188, 398.97406005859375, 147.15817260742188... | {"preproc_blocks": [{"type": "text", "bbox": [50, 79, 433, 446], "lines": [{"bbox": [49, 79, 431, 94], "spans": [{"bbox": [49, 79, 431, 94], "score": 1.0, "content": "Karafyllidis, I.G. (2005a), Quantum Computers \u2013 Basic Principles, Klidarithmos,", "type": "text"}], "index": 0}, {"bbox": [64, 92, 148, 105], "spans... | ./arxiv_full_mineru_outputs_20/images/0705.3360_8.png | images/0705.3360_8.png | |
0705.0734.pdf | 0 | # Soft constraint abstraction based on semiring
homomorphism ∗
Sanjiang Li and Mingsheng Ying †
Department of Computer Science and Technology
Tsinghua University, Beijing 100084, China
# Abstract
The semiring-based constraint satisfaction problems (semiring CSPs),
proposed by Bistarelli, Montanari and Rossi [3], is ... | <h1>Soft constraint abstraction based on semiring
homomorphism ∗</h1>
<p>Sanjiang Li and Mingsheng Ying †
Department of Computer Science and Technology
Tsinghua University, Beijing 100084, China</p>
<h1>Abstract</h1>
<p>The semiring-based constraint satisfaction problems (semiring CSPs),
proposed by Bistarelli, Montana... | [{"type": "title", "coordinates": [147, 163, 463, 202], "content": "Soft constraint abstraction based on semiring\nhomomorphism \u2217", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [177, 217, 433, 259], "content": "Sanjiang Li and Mingsheng Ying \u2020\nDepartment of Computer Science and Technol... | [{"type": "text", "coordinates": [148, 160, 463, 182], "content": "Soft constraint abstraction based on semiring", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [248, 185, 357, 202], "content": "homomorphism", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [359, 186, 367, 193], "content": "\u22... | [] | [{"type": "inline", "coordinates": [282, 412, 289, 416], "content": "\\alpha", "caption": ""}, {"type": "inline", "coordinates": [354, 410, 361, 416], "content": "P", "caption": ""}, {"type": "inline", "coordinates": [384, 410, 390, 416], "content": "S", "caption": ""}, {"type": "inline", "coordinates": [405, 410, 408,... | [] | [612.0, 792.0] | [{"type": "text", "text": "Soft constraint abstraction based on semiring homomorphism \u2217 ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Sanjiang Li and Mingsheng Ying \u2020 Department of Computer Science and Technology Tsinghua University, Beijing 100084, China ", "page_idx": 0}, {"type": "text", "t... | [{"category_id": 1, "poly": [439.8004455566406, 859.0845336914062, 1257.0494384765625, 859.0845336914062, 1257.0494384765625, 1070.8519287109375, 439.8004455566406, 1070.8519287109375], "score": 0.9999934434890747}, {"category_id": 0, "poly": [409.37213134765625, 453.36798095703125, 1286.7987060546875, 453.367980957031... | {"preproc_blocks": [{"type": "title", "bbox": [147, 163, 463, 202], "lines": [{"bbox": [148, 160, 463, 182], "spans": [{"bbox": [148, 160, 463, 182], "score": 1.0, "content": "Soft constraint abstraction based on semiring", "type": "text"}], "index": 0}, {"bbox": [248, 185, 367, 202], "spans": [{"bbox": [248, 185, 357,... | ./arxiv_full_mineru_outputs_20/images/0705.0734_0.png | images/0705.0734_0.png | |
0705.0734.pdf | 1 | Compared with classical CSPs, SCSPs are usually more difficult to process
and to solve. This is mainly resulted by the complexity of the underlying semir-
ing structure. Thus working on a simplified version of the given problem would
be worthwhile. Given a concrete SCSP, the idea is to get an abstract one by
changing t... | <p>Compared with classical CSPs, SCSPs are usually more difficult to process
and to solve. This is mainly resulted by the complexity of the underlying semir-
ing structure. Thus working on a simplified version of the given problem would
be worthwhile. Given a concrete SCSP, the idea is to get an abstract one by
changin... | [{"type": "text", "coordinates": [133, 125, 478, 233], "content": "Compared with classical CSPs, SCSPs are usually more difficult to process\nand to solve. This is mainly resulted by the complexity of the underlying semir-\ning structure. Thus working on a simplified version of the given problem would\nbe worthwhile. G... | [{"type": "text", "coordinates": [147, 126, 478, 138], "content": "Compared with classical CSPs, SCSPs are usually more difficult to process", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [132, 137, 477, 151], "content": "and to solve. This is mainly resulted by the complexity of the underlying semir-", "... | [] | [{"type": "inline", "coordinates": [459, 247, 467, 254], "content": "P", "caption": ""}, {"type": "inline", "coordinates": [196, 259, 203, 267], "content": "S", "caption": ""}, {"type": "inline", "coordinates": [228, 257, 235, 267], "content": "\\widetilde{S}", "caption": ""}, {"type": "inline", "coordinates": [425, 25... | [] | [612.0, 792.0] | [{"type": "text", "text": "Compared with classical CSPs, SCSPs are usually more difficult to process and to solve. This is mainly resulted by the complexity of the underlying semiring structure. Thus working on a simplified version of the given problem would be worthwhile. Given a concrete SCSP, the idea is to get an a... | [{"category_id": 1, "poly": [370.0018005371094, 348.0356140136719, 1328.955810546875, 348.0356140136719, 1328.955810546875, 648.9075317382812, 370.0018005371094, 648.9075317382812], "score": 0.9999966621398926}, {"category_id": 1, "poly": [370.5669860839844, 649.1851806640625, 1328.84375, 649.1851806640625, 1328.84375,... | {"preproc_blocks": [{"type": "text", "bbox": [133, 125, 478, 233], "lines": [{"bbox": [147, 126, 478, 138], "spans": [{"bbox": [147, 126, 478, 138], "score": 1.0, "content": "Compared with classical CSPs, SCSPs are usually more difficult to process", "type": "text"}], "index": 0}, {"bbox": [132, 137, 477, 151], "spans"... | ./arxiv_full_mineru_outputs_20/images/0705.0734_1.png | images/0705.0734_1.png | |
0705.0734.pdf | 2 | an optimal solution of the abstract problem, what we can say about optimal
solutions of the concrete problem. Conclusions are given in the final section.
# 2 Semiring Constraint Satisfaction Problem
In this section we introduce several basic notions used in this paper. In par-
ticular, we give a brief summary of the ... | <p>an optimal solution of the abstract problem, what we can say about optimal
solutions of the concrete problem. Conclusions are given in the final section.</p>
<h1>2 Semiring Constraint Satisfaction Problem</h1>
<p>In this section we introduce several basic notions used in this paper. In par-
ticular, we give a brief ... | [{"type": "text", "coordinates": [132, 125, 479, 150], "content": "an optimal solution of the abstract problem, what we can say about optimal\nsolutions of the concrete problem. Conclusions are given in the final section.", "block_type": "text", "index": 1}, {"type": "title", "coordinates": [132, 168, 455, 183], "conte... | [{"type": "text", "coordinates": [133, 127, 477, 137], "content": "an optimal solution of the abstract problem, what we can say about optimal", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [133, 138, 466, 150], "content": "solutions of the concrete problem. Conclusions are given in the final section.", "s... | [] | [{"type": "inline", "coordinates": [457, 276, 477, 286], "content": "\\textit{S}=", "caption": ""}, {"type": "inline", "coordinates": [133, 288, 191, 298], "content": "\\langle S,+,\\times,\\mathbf{0},\\mathbf{1}\\rangle", "caption": ""}, {"type": "inline", "coordinates": [158, 308, 164, 316], "content": "S", "caption"... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "2 Semiring Constraint Satisfaction Problem ", "text_level": 1, "page_idx": 2}, {"type": "text", "text": "In this section we introduce several basic notions used in this paper. In particular, we give a brief summary of the theory of c-semiring based... | [{"category_id": 0, "poly": [369.7678527832031, 708.6898803710938, 642.2720336914062, 708.6898803710938, 642.2720336914062, 746.333984375, 369.7678527832031, 746.333984375], "score": 0.9999784827232361}, {"category_id": 1, "poly": [368.1904602050781, 535.0653686523438, 1330.03466796875, 535.0653686523438, 1330.03466796... | {"preproc_blocks": [{"type": "text", "bbox": [132, 125, 479, 150], "lines": [{"bbox": [133, 127, 477, 137], "spans": [{"bbox": [133, 127, 477, 137], "score": 1.0, "content": "an optimal solution of the abstract problem, what we can say about optimal", "type": "text"}], "index": 0}, {"bbox": [133, 138, 466, 150], "spans... | ./arxiv_full_mineru_outputs_20/images/0705.0734_2.png | images/0705.0734_2.png | |
0705.0734.pdf | 3 | # 2.2 Semiring homomorphism
Definition 2.2 (homomorphism). A mapping $$\psi$$ from semiring $$\langle S,+,\times,\,\mathbf{0},\,\mathbf{1}\rangle$$
to semiring $$\langle\widetilde{S},\widetilde{+},\widetilde{\times},\widetilde{\mathbf{0}},\widetilde{\mathbf{1}}\rangle$$ is said to be a semiring homomorphism if for any... | <h1>2.2 Semiring homomorphism</h1>
<p>Definition 2.2 (homomorphism). A mapping $$\psi$$ from semiring $$\langle S,+,\times,\,\mathbf{0},\,\mathbf{1}\rangle$$
to semiring $$\langle\widetilde{S},\widetilde{+},\widetilde{\times},\widetilde{\mathbf{0}},\widetilde{\mathbf{1}}\rangle$$ is said to be a semiring homomorphism i... | [{"type": "title", "coordinates": [132, 124, 313, 138], "content": "2.2 Semiring homomorphism", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [132, 143, 478, 181], "content": "Definition 2.2 (homomorphism). A mapping $$\\psi$$ from semiring $$\\langle S,+,\\times,\\,\\mathbf{0},\\,\\mathbf{1}\\ran... | [{"type": "text", "coordinates": [133, 125, 310, 138], "content": "2.2 Semiring homomorphism", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [132, 144, 340, 157], "content": "Definition 2.2 (homomorphism). A mapping ", "score": 1.0, "index": 2}, {"type": "inline_equation", "coordinates": [340, 146, 347, 15... | [] | [{"type": "inline", "coordinates": [340, 146, 347, 155], "content": "\\psi", "caption": ""}, {"type": "inline", "coordinates": [415, 145, 477, 156], "content": "\\langle S,+,\\times,\\,\\mathbf{0},\\,\\mathbf{1}\\rangle", "caption": ""}, {"type": "inline", "coordinates": [187, 156, 247, 169], "content": "\\langle\\wide... | [] | [612.0, 792.0] | [{"type": "text", "text": "2.2 Semiring homomorphism ", "text_level": 1, "page_idx": 3}, {"type": "text", "text": "Definition 2.2 (homomorphism). A mapping $\\psi$ from semiring $\\langle S,+,\\times,\\,\\mathbf{0},\\,\\mathbf{1}\\rangle$ to semiring $\\langle\\widetilde{S},\\widetilde{+},\\widetilde{\\times},\\widetil... | [{"category_id": 1, "poly": [366.1998596191406, 1765.7568359375, 1332.96826171875, 1765.7568359375, 1332.96826171875, 1868.6942138671875, 366.1998596191406, 1868.6942138671875], "score": 0.9999894499778748}, {"category_id": 1, "poly": [367.91314697265625, 1643.9259033203125, 1330.4671630859375, 1643.9259033203125, 1330... | {"preproc_blocks": [{"type": "title", "bbox": [132, 124, 313, 138], "lines": [{"bbox": [133, 125, 310, 138], "spans": [{"bbox": [133, 125, 310, 138], "score": 1.0, "content": "2.2 Semiring homomorphism", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [132, 143, 478, 181], "lines": [{"bbox": [132,... | ./arxiv_full_mineru_outputs_20/images/0705.0734_3.png | images/0705.0734_3.png | |
0705.0734.pdf | 4 | Definition 2.5 (constraints [3]). Given a constraint system $$C S\,=\,\langle S,D,V\rangle$$ ,
where $$S=\langle S,+,\times,\mathbf{0},\mathbf{1}\rangle$$ , a constraint over $$C S$$ is a pair $$\langle{\mathsf{d e f}},{\mathsf{c o n}}\rangle$$ where
• con is a finite subset of $$V$$ , called the type of the constrain... | <p>Definition 2.5 (constraints [3]). Given a constraint system $$C S\,=\,\langle S,D,V\rangle$$ ,
where $$S=\langle S,+,\times,\mathbf{0},\mathbf{1}\rangle$$ , a constraint over $$C S$$ is a pair $$\langle{\mathsf{d e f}},{\mathsf{c o n}}\rangle$$ where</p>
<p>• con is a finite subset of $$V$$ , called the type of the ... | [{"type": "text", "coordinates": [131, 125, 478, 150], "content": "Definition 2.5 (constraints [3]). Given a constraint system $$C S\\,=\\,\\langle S,D,V\\rangle$$ ,\nwhere $$S=\\langle S,+,\\times,\\mathbf{0},\\mathbf{1}\\rangle$$ , a constraint over $$C S$$ is a pair $$\\langle{\\mathsf{d e f}},{\\mathsf{c o n}}\\ran... | [{"type": "text", "coordinates": [132, 126, 404, 139], "content": "Definition 2.5 (constraints [3]). Given a constraint system ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [405, 127, 474, 137], "content": "C S\\,=\\,\\langle S,D,V\\rangle", "score": 0.94, "index": 2}, {"type": "text", "coord... | [] | [{"type": "inline", "coordinates": [405, 127, 474, 137], "content": "C S\\,=\\,\\langle S,D,V\\rangle", "caption": ""}, {"type": "inline", "coordinates": [162, 139, 241, 150], "content": "S=\\langle S,+,\\times,\\mathbf{0},\\mathbf{1}\\rangle", "caption": ""}, {"type": "inline", "coordinates": [323, 140, 338, 147], "co... | [] | [612.0, 792.0] | [{"type": "text", "text": "Definition 2.5 (constraints [3]). Given a constraint system $C S\\,=\\,\\langle S,D,V\\rangle$ , where $S=\\langle S,+,\\times,\\mathbf{0},\\mathbf{1}\\rangle$ , a constraint over $C S$ is a pair $\\langle{\\mathsf{d e f}},{\\mathsf{c o n}}\\rangle$ where ", "page_idx": 4}, {"type": "text", "... | [{"category_id": 1, "poly": [387.6406555175781, 936.89990234375, 1330.7852783203125, 936.89990234375, 1330.7852783203125, 1090.6220703125, 387.6406555175781, 1090.6220703125], "score": 0.9999644160270691}, {"category_id": 1, "poly": [407.6069641113281, 429.59283447265625, 1328.8619384765625, 429.59283447265625, 1328.86... | {"preproc_blocks": [{"type": "text", "bbox": [131, 125, 478, 150], "lines": [{"bbox": [132, 126, 477, 139], "spans": [{"bbox": [132, 126, 404, 139], "score": 1.0, "content": "Definition 2.5 (constraints [3]). Given a constraint system ", "type": "text"}, {"bbox": [405, 127, 474, 137], "score": 0.94, "content": "C S\\,=... | ./arxiv_full_mineru_outputs_20/images/0705.0734_4.png | images/0705.0734_4.png | |
0705.0734.pdf | 5 | Definition 2.9 (projection [3]). Given a constraint $$c=\langle{\mathsf{d e f}},{\mathsf{c o n}}\rangle$$ and a subset
$$I$$ of $$V$$ , the projection of $$c$$ over $$I$$ , denoted by $$c\,\sqrt{\phantom{}_{\!\;\!I}}\,\phantom{}_{\!\;\!I}$$ , is the constraint $$\langle\mathsf{d e f}^{\prime},\mathsf{c o n}^{\prime}\ra... | <p>Definition 2.9 (projection [3]). Given a constraint $$c=\langle{\mathsf{d e f}},{\mathsf{c o n}}\rangle$$ and a subset
$$I$$ of $$V$$ , the projection of $$c$$ over $$I$$ , denoted by $$c\,\sqrt{\phantom{}_{\!\;\!I}}\,\phantom{}_{\!\;\!I}$$ , is the constraint $$\langle\mathsf{d e f}^{\prime},\mathsf{c o n}^{\prime}... | [{"type": "text", "coordinates": [132, 124, 478, 186], "content": "Definition 2.9 (projection [3]). Given a constraint $$c=\\langle{\\mathsf{d e f}},{\\mathsf{c o n}}\\rangle$$ and a subset\n$$I$$ of $$V$$ , the projection of $$c$$ over $$I$$ , denoted by $$c\\,\\sqrt{\\phantom{}_{\\!\\;\\!I}}\\,\\phantom{}_{\\!\\;\\!I... | [{"type": "text", "coordinates": [132, 126, 362, 138], "content": "Definition 2.9 (projection [3]). Given a constraint ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [362, 127, 419, 137], "content": "c=\\langle{\\mathsf{d e f}},{\\mathsf{c o n}}\\rangle", "score": 0.93, "index": 2}, {"type": "... | [] | [{"type": "block", "coordinates": [246, 257, 364, 275], "content": "", "caption": ""}, {"type": "block", "coordinates": [265, 519, 348, 573], "content": "", "caption": ""}, {"type": "block", "coordinates": [203, 635, 408, 649], "content": "", "caption": ""}, {"type": "inline", "coordinates": [362, 127, 419, 137], "cont... | [] | [612.0, 792.0] | [{"type": "text", "text": "Definition 2.9 (projection [3]). Given a constraint $c=\\langle{\\mathsf{d e f}},{\\mathsf{c o n}}\\rangle$ and a subset $I$ of $V$ , the projection of $c$ over $I$ , denoted by $c\\,\\sqrt{\\phantom{}_{\\!\\;\\!I}}\\,\\phantom{}_{\\!\\;\\!I}$ , is the constraint $\\langle\\mathsf{d e f}^{\\p... | [{"category_id": 0, "poly": [368.6676330566406, 1007.0328979492188, 1249.357421875, 1007.0328979492188, 1249.357421875, 1050.9937744140625, 368.6676330566406, 1050.9937744140625], "score": 0.9999961853027344}, {"category_id": 8, "poly": [680.5737915039062, 717.3754272460938, 1017.4440307617188, 717.3754272460938, 1017.... | {"preproc_blocks": [{"type": "text", "bbox": [132, 124, 478, 186], "lines": [{"bbox": [132, 126, 478, 138], "spans": [{"bbox": [132, 126, 362, 138], "score": 1.0, "content": "Definition 2.9 (projection [3]). Given a constraint ", "type": "text"}, {"bbox": [362, 127, 419, 137], "score": 0.93, "content": "c=\\langle{\\ma... | ./arxiv_full_mineru_outputs_20/images/0705.0734_5.png | images/0705.0734_5.png | |
0705.0734.pdf | 6 | Theorem 3.1. Let $$\alpha$$ be a mapping from $$c$$ -semiring $$S$$ to $$c$$ -semiring $$\widetilde{S}$$ such
that $$\alpha({\bf0})\,=\,\mathrm{\bf0}$$ , $$\alpha(\mathbf{1})\,=\,\widetilde{\mathbf{1}}$$ . Suppose $$D$$ contains more than two elements and
$$k=|c o n|>0$$ . Then $$\alpha$$ preserves problem ordering if ... | <p>Theorem 3.1. Let $$\alpha$$ be a mapping from $$c$$ -semiring $$S$$ to $$c$$ -semiring $$\widetilde{S}$$ such
that $$\alpha({\bf0})\,=\,\mathrm{\bf0}$$ , $$\alpha(\mathbf{1})\,=\,\widetilde{\mathbf{1}}$$ . Suppose $$D$$ contains more than two elements and
$$k=|c o n|>0$$ . Then $$\alpha$$ preserves problem ordering ... | [{"type": "text", "coordinates": [132, 124, 479, 186], "content": "Theorem 3.1. Let $$\\alpha$$ be a mapping from $$c$$ -semiring $$S$$ to $$c$$ -semiring $$\\widetilde{S}$$ such\nthat $$\\alpha({\\bf0})\\,=\\,\\mathrm{\\bf0}$$ , $$\\alpha(\\mathbf{1})\\,=\\,\\widetilde{\\mathbf{1}}$$ . Suppose $$D$$ contains more than... | [{"type": "text", "coordinates": [132, 125, 224, 139], "content": "Theorem 3.1. Let ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [224, 130, 231, 135], "content": "\\alpha", "score": 0.76, "index": 2}, {"type": "text", "coordinates": [231, 125, 323, 139], "content": " be a mapping from ", "sc... | [] | [{"type": "block", "coordinates": [199, 291, 410, 330], "content": "", "caption": ""}, {"type": "block", "coordinates": [162, 382, 448, 397], "content": "", "caption": ""}, {"type": "block", "coordinates": [202, 469, 407, 508], "content": "", "caption": ""}, {"type": "block", "coordinates": [161, 549, 448, 563], "conte... | [] | [612.0, 792.0] | [{"type": "text", "text": "Theorem 3.1. Let $\\alpha$ be a mapping from $c$ -semiring $S$ to $c$ -semiring $\\widetilde{S}$ such that $\\alpha({\\bf0})\\,=\\,\\mathrm{\\bf0}$ , $\\alpha(\\mathbf{1})\\,=\\,\\widetilde{\\mathbf{1}}$ . Suppose $D$ contains more than two elements and $k=|c o n|>0$ . Then $\\alpha$ preserve... | [{"category_id": 8, "poly": [691.0866088867188, 1773.3367919921875, 1011.998291015625, 1773.3367919921875, 1011.998291015625, 1814.762451171875, 691.0866088867188, 1814.762451171875], "score": 0.9999911189079285}, {"category_id": 1, "poly": [368.70733642578125, 1647.875244140625, 1328.503173828125, 1647.875244140625, 1... | {"preproc_blocks": [{"type": "text", "bbox": [132, 124, 479, 186], "lines": [{"bbox": [132, 125, 480, 139], "spans": [{"bbox": [132, 125, 224, 139], "score": 1.0, "content": "Theorem 3.1. Let ", "type": "text"}, {"bbox": [224, 130, 231, 135], "score": 0.76, "content": "\\alpha", "type": "inline_equation", "height": 5, ... | ./arxiv_full_mineru_outputs_20/images/0705.0734_6.png | images/0705.0734_6.png | |
0705.0734.pdf | 7 | # 4 Mappings preserving optimal solutions
In this section we discuss when a translation preserves optimal solutions, i.e.
when all optimal solutions of the concrete problem are also optimal in the ab-
stract problem.
Definition 4.1. Let $$\alpha:S\rightarrow{\widetilde{S}}$$ be a mapping between two c-semirings. We
s... | <h1>4 Mappings preserving optimal solutions</h1>
<p>In this section we discuss when a translation preserves optimal solutions, i.e.
when all optimal solutions of the concrete problem are also optimal in the ab-
stract problem.</p>
<p>Definition 4.1. Let $$\alpha:S\rightarrow{\widetilde{S}}$$ be a mapping between two c-... | [{"type": "title", "coordinates": [132, 123, 433, 138], "content": "4 Mappings preserving optimal solutions", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [133, 147, 477, 183], "content": "In this section we discuss when a translation preserves optimal solutions, i.e.\nwhen all optimal solutions ... | [{"type": "text", "coordinates": [134, 126, 143, 134], "content": "4", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [154, 123, 433, 140], "content": "Mappings preserving optimal solutions", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [132, 148, 476, 159], "content": "In this section we disc... | [] | [{"type": "block", "coordinates": [235, 288, 375, 301], "content": "", "caption": ""}, {"type": "block", "coordinates": [143, 446, 453, 479], "content": "", "caption": ""}, {"type": "block", "coordinates": [195, 571, 415, 604], "content": "", "caption": ""}, {"type": "block", "coordinates": [218, 621, 392, 645], "conte... | [] | [612.0, 792.0] | [{"type": "text", "text": "4 Mappings preserving optimal solutions ", "text_level": 1, "page_idx": 7}, {"type": "text", "text": "In this section we discuss when a translation preserves optimal solutions, i.e. when all optimal solutions of the concrete problem are also optimal in the abstract problem. ", "page_idx": 7},... | [{"category_id": 1, "poly": [369.03717041015625, 1703.3397216796875, 422.1773376464844, 1703.3397216796875, 422.1773376464844, 1733.4847412109375, 369.03717041015625, 1733.4847412109375], "score": 0.9999978542327881}, {"category_id": 8, "poly": [653.7136840820312, 799.5702514648438, 1048.551025390625, 799.5702514648438... | {"preproc_blocks": [{"type": "title", "bbox": [132, 123, 433, 138], "lines": [{"bbox": [134, 123, 433, 140], "spans": [{"bbox": [134, 126, 143, 134], "score": 1.0, "content": "4", "type": "text"}, {"bbox": [154, 123, 433, 140], "score": 1.0, "content": "Mappings preserving optimal solutions", "type": "text"}], "index":... | ./arxiv_full_mineru_outputs_20/images/0705.0734_7.png | images/0705.0734_7.png | |
0705.0734.pdf | 8 | for the value of $$t$$ in $$P$$ . Now since
entreating Equation 5, we have $$u<\!s\ v$$ . This contradicts the assumption that $$t$$
is optimal in $$P$$ with value $$u$$ .
On the other hand, suppose that $$\alpha$$ preserves optimal solutions. By con-
tradiction, suppose Equation 5 doesn’t hold. That is, we have some... | <p>for the value of $$t$$ in $$P$$ . Now since</p>
<p>entreating Equation 5, we have $$u<\!s\ v$$ . This contradicts the assumption that $$t$$
is optimal in $$P$$ with value $$u$$ .</p>
<p>On the other hand, suppose that $$\alpha$$ preserves optimal solutions. By con-
tradiction, suppose Equation 5 doesn’t hold. That i... | [{"type": "interline_equation", "coordinates": [274, 145, 336, 179], "content": "", "block_type": "interline_equation", "index": 1}, {"type": "text", "coordinates": [132, 188, 282, 199], "content": "for the value of $$t$$ in $$P$$ . Now since", "block_type": "text", "index": 2}, {"type": "interline_equation", "coordina... | [{"type": "interline_equation", "coordinates": [274, 145, 336, 179], "content": "v=\\sum_{i=1}^{n}\\prod_{j=1}^{m}v_{i j}", "score": 0.92, "index": 1}, {"type": "text", "coordinates": [132, 187, 202, 199], "content": "for the value of ", "score": 1.0, "index": 2}, {"type": "inline_equation", "coordinates": [202, 189, 2... | [] | [{"type": "block", "coordinates": [274, 145, 336, 179], "content": "", "caption": ""}, {"type": "block", "coordinates": [193, 206, 416, 230], "content": "", "caption": ""}, {"type": "block", "coordinates": [173, 308, 437, 333], "content": "", "caption": ""}, {"type": "block", "coordinates": [158, 391, 444, 430], "conte... | [] | [612.0, 792.0] | [{"type": "equation", "text": "$$\nv=\\sum_{i=1}^{n}\\prod_{j=1}^{m}v_{i j}\n$$", "text_format": "latex", "page_idx": 8}, {"type": "text", "text": "for the value of $t$ in $P$ . Now since ", "page_idx": 8}, {"type": "equation", "text": "$$\n\\widetilde{\\sum}_{i=1}^{n}\\widetilde{\\prod}_{j=1}^{m}\\alpha(u_{i j})=\\wid... | [{"category_id": 8, "poly": [761.2239379882812, 406.74029541015625, 934.9337158203125, 406.74029541015625, 934.9337158203125, 497.477783203125, 761.2239379882812, 497.477783203125], "score": 0.9999984502792358}, {"category_id": 1, "poly": [368.7708435058594, 522.4937744140625, 784.671875, 522.4937744140625, 784.671875,... | {"preproc_blocks": [{"type": "interline_equation", "bbox": [274, 145, 336, 179], "lines": [{"bbox": [274, 145, 336, 179], "spans": [{"bbox": [274, 145, 336, 179], "score": 0.92, "content": "v=\\sum_{i=1}^{n}\\prod_{j=1}^{m}v_{i j}", "type": "interline_equation"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [13... | ./arxiv_full_mineru_outputs_20/images/0705.0734_8.png | images/0705.0734_8.png | |
0705.0734.pdf | 9 | The next lemma shows that $$\alpha$$ preserves optimal solutions only if it is a
semiring homomorphism.
Lemma 4.3. Let $$\alpha$$ be a mapping from $$c$$ -semiring $$S$$ to $$c$$ -semiring $$\widetilde{S}$$ such that
$$\alpha(\mathbf{0})=\tilde{\mathbf{0}},\ \alpha(\mathbf{1})=\tilde{\mathbf{1}}$$ . Suppose $$\alpha:S... | <p>The next lemma shows that $$\alpha$$ preserves optimal solutions only if it is a
semiring homomorphism.</p>
<p>Lemma 4.3. Let $$\alpha$$ be a mapping from $$c$$ -semiring $$S$$ to $$c$$ -semiring $$\widetilde{S}$$ such that
$$\alpha(\mathbf{0})=\tilde{\mathbf{0}},\ \alpha(\mathbf{1})=\tilde{\mathbf{1}}$$ . Suppose $... | [{"type": "text", "coordinates": [133, 126, 478, 149], "content": "The next lemma shows that $$\\alpha$$ preserves optimal solutions only if it is a\nsemiring homomorphism.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [132, 154, 478, 190], "content": "Lemma 4.3. Let $$\\alpha$$ be a mapping from... | [{"type": "text", "coordinates": [147, 126, 279, 138], "content": "The next lemma shows that ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [280, 130, 286, 135], "content": "\\alpha", "score": 0.88, "index": 2}, {"type": "text", "coordinates": [287, 126, 479, 138], "content": " preserves optim... | [] | [{"type": "block", "coordinates": [181, 343, 428, 356], "content": "", "caption": ""}, {"type": "block", "coordinates": [171, 370, 438, 384], "content": "", "caption": ""}, {"type": "block", "coordinates": [211, 527, 397, 550], "content": "", "caption": ""}, {"type": "block", "coordinates": [142, 570, 468, 603], "conte... | [] | [612.0, 792.0] | [{"type": "text", "text": "The next lemma shows that $\\alpha$ preserves optimal solutions only if it is a semiring homomorphism. ", "page_idx": 9}, {"type": "text", "text": "Lemma 4.3. Let $\\alpha$ be a mapping from $c$ -semiring $S$ to $c$ -semiring $\\widetilde{S}$ such that $\\alpha(\\mathbf{0})=\\tilde{\\mathbf{0... | [{"category_id": 8, "poly": [692.4064331054688, 1735.6934814453125, 997.9283447265625, 1735.6934814453125, 997.9283447265625, 1828.2525634765625, 692.4064331054688, 1828.2525634765625], "score": 0.9999969005584717}, {"category_id": 2, "poly": [836.39453125, 1930.7962646484375, 865.160888671875, 1930.7962646484375, 865.... | {"preproc_blocks": [{"type": "text", "bbox": [133, 126, 478, 149], "lines": [{"bbox": [147, 126, 479, 138], "spans": [{"bbox": [147, 126, 279, 138], "score": 1.0, "content": "The next lemma shows that ", "type": "text"}, {"bbox": [280, 130, 286, 135], "score": 0.88, "content": "\\alpha", "type": "inline_equation", "hei... | ./arxiv_full_mineru_outputs_20/images/0705.0734_9.png | images/0705.0734_9.png | |
0705.0734.pdf | 10 | # 5 Computing concrete optimal solutions from
abstract ones
In the above section, we investigated conditions under which all optimal solu-
tions of concrete problem can be related precisely to those of abstract problem.
There are often situations where it suffices to find some optimal solutions or sim-
ply a good appr... | <h1>5 Computing concrete optimal solutions from
abstract ones</h1>
<p>In the above section, we investigated conditions under which all optimal solu-
tions of concrete problem can be related precisely to those of abstract problem.
There are often situations where it suffices to find some optimal solutions or sim-
ply a ... | [{"type": "title", "coordinates": [132, 122, 477, 155], "content": "5 Computing concrete optimal solutions from\nabstract ones", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [133, 165, 477, 237], "content": "In the above section, we investigated conditions under which all optimal solu-\ntions of ... | [{"type": "text", "coordinates": [133, 124, 142, 137], "content": "5", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [157, 123, 477, 139], "content": "Computing concrete optimal solutions from", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [157, 141, 252, 156], "content": "abstract ones", "sc... | [] | [{"type": "block", "coordinates": [220, 344, 390, 377], "content": "", "caption": ""}, {"type": "block", "coordinates": [217, 447, 393, 479], "content": "", "caption": ""}, {"type": "block", "coordinates": [160, 506, 450, 538], "content": "", "caption": ""}, {"type": "block", "coordinates": [210, 591, 399, 604], "conte... | [] | [612.0, 792.0] | [{"type": "text", "text": "5 Computing concrete optimal solutions from abstract ones ", "text_level": 1, "page_idx": 10}, {"type": "text", "text": "In the above section, we investigated conditions under which all optimal solutions of concrete problem can be related precisely to those of abstract problem. There are ofte... | [{"category_id": 8, "poly": [751.1357421875, 1794.5816650390625, 937.5807495117188, 1794.5816650390625, 937.5807495117188, 1885.3446044921875, 751.1357421875, 1885.3446044921875], "score": 0.999998927116394}, {"category_id": 8, "poly": [610.0521850585938, 954.5721435546875, 1085.382080078125, 954.5721435546875, 1085.38... | {"preproc_blocks": [{"type": "title", "bbox": [132, 122, 477, 155], "lines": [{"bbox": [133, 123, 477, 139], "spans": [{"bbox": [133, 124, 142, 137], "score": 1.0, "content": "5", "type": "text"}, {"bbox": [157, 123, 477, 139], "score": 1.0, "content": "Computing concrete optimal solutions from", "type": "text"}], "ind... | ./arxiv_full_mineru_outputs_20/images/0705.0734_10.png | images/0705.0734_10.png | |
0705.0734.pdf | 11 | Now we show $$\alpha(\overline{{v}})\leq_{\widetilde{S}}\widetilde{v}$$ .
By $$v<\!s\;\overline{{v}}$$ , we have $$\alpha(v)\leq_{\widetilde{S}}\alpha(\overline{{v}})$$ . Then
where the last term, $$\tilde{\overline{{v}}}$$ , is the value of $$t$$ in $$\alpha(P)$$ . Now since $$t$$ is optimal in $$\alpha(P)$$ ,
we hav... | <p>Now we show $$\alpha(\overline{{v}})\leq_{\widetilde{S}}\widetilde{v}$$ .
By $$v<\!s\;\overline{{v}}$$ , we have $$\alpha(v)\leq_{\widetilde{S}}\alpha(\overline{{v}})$$ . Then</p>
<p>where the last term, $$\tilde{\overline{{v}}}$$ , is the value of $$t$$ in $$\alpha(P)$$ . Now since $$t$$ is optimal in $$\alpha(P)$$... | [{"type": "text", "coordinates": [133, 126, 326, 151], "content": "Now we show $$\\alpha(\\overline{{v}})\\leq_{\\widetilde{S}}\\widetilde{v}$$ .\nBy $$v<\\!s\\;\\overline{{v}}$$ , we have $$\\alpha(v)\\leq_{\\widetilde{S}}\\alpha(\\overline{{v}})$$ . Then", "block_type": "text", "index": 1}, {"type": "interline_equati... | [{"type": "text", "coordinates": [132, 124, 195, 140], "content": "Now we show ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [195, 127, 239, 138], "content": "\\alpha(\\overline{{v}})\\leq_{\\widetilde{S}}\\widetilde{v}", "score": 0.93, "index": 2}, {"type": "text", "coordinates": [239, 124, ... | [] | [{"type": "block", "coordinates": [164, 158, 446, 253], "content": "", "caption": ""}, {"type": "inline", "coordinates": [195, 127, 239, 138], "content": "\\alpha(\\overline{{v}})\\leq_{\\widetilde{S}}\\widetilde{v}", "caption": ""}, {"type": "inline", "coordinates": [164, 140, 194, 149], "content": "v<\\!s\\;\\overlin... | [] | [612.0, 792.0] | [{"type": "text", "text": "Now we show $\\alpha(\\overline{{v}})\\leq_{\\widetilde{S}}\\widetilde{v}$ . By $v<\\!s\\;\\overline{{v}}$ , we have $\\alpha(v)\\leq_{\\widetilde{S}}\\alpha(\\overline{{v}})$ . Then ", "page_idx": 11}, {"type": "equation", "text": "$$\n\\begin{array}{r c l}{{\\widetilde{v}}}&{{=}}&{{{\\displ... | [{"category_id": 1, "poly": [411.0888671875, 1572.1982421875, 775.7063598632812, 1572.1982421875, 775.7063598632812, 1724.8355712890625, 411.0888671875, 1724.8355712890625], "score": 0.9999968409538269}, {"category_id": 1, "poly": [367.7666931152344, 850.723388671875, 1329.5869140625, 850.723388671875, 1329.5869140625,... | {"preproc_blocks": [{"type": "text", "bbox": [133, 126, 326, 151], "lines": [{"bbox": [132, 124, 243, 140], "spans": [{"bbox": [132, 124, 195, 140], "score": 1.0, "content": "Now we show ", "type": "text"}, {"bbox": [195, 127, 239, 138], "score": 0.93, "content": "\\alpha(\\overline{{v}})\\leq_{\\widetilde{S}}\\widetil... | ./arxiv_full_mineru_outputs_20/images/0705.0734_11.png | images/0705.0734_11.png | |
0705.0734.pdf | 12 | Theorem 5.2. Let $$\alpha:S\rightarrow{\widetilde{S}}$$ be a quasi-semiring homomorphism. Given an
SCSP $$P$$ over $$S$$ , suppose $$t\in O p t(\alpha(P))$$ has value $$\boldsymbol{v}$$ in $$P$$ and value $$\widetilde{v}$$ in $$\alpha(P)$$ .
Then there exists an optimal solution $$t$$ of $$P$$ , say with value $$\bar{v... | <p>Theorem 5.2. Let $$\alpha:S\rightarrow{\widetilde{S}}$$ be a quasi-semiring homomorphism. Given an
SCSP $$P$$ over $$S$$ , suppose $$t\in O p t(\alpha(P))$$ has value $$\boldsymbol{v}$$ in $$P$$ and value $$\widetilde{v}$$ in $$\alpha(P)$$ .
Then there exists an optimal solution $$t$$ of $$P$$ , say with value $$\ba... | [{"type": "text", "coordinates": [132, 123, 479, 174], "content": "Theorem 5.2. Let $$\\alpha:S\\rightarrow{\\widetilde{S}}$$ be a quasi-semiring homomorphism. Given an\nSCSP $$P$$ over $$S$$ , suppose $$t\\in O p t(\\alpha(P))$$ has value $$\\boldsymbol{v}$$ in $$P$$ and value $$\\widetilde{v}$$ in $$\\alpha(P)$$ .\nT... | [{"type": "text", "coordinates": [132, 124, 222, 139], "content": "Theorem 5.2. Let ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [223, 125, 269, 135], "content": "\\alpha:S\\rightarrow{\\widetilde{S}}", "score": 0.93, "index": 2}, {"type": "text", "coordinates": [270, 124, 479, 139], "conten... | [{"coordinates": [197, 234, 413, 364], "index": 15.0, "caption": "Figure 1: A counter-example", "caption_coordinates": [240, 372, 370, 385]}] | [{"type": "block", "coordinates": [235, 505, 374, 540], "content": "", "caption": ""}, {"type": "block", "coordinates": [230, 566, 379, 618], "content": "", "caption": ""}, {"type": "block", "coordinates": [223, 627, 386, 680], "content": "", "caption": ""}, {"type": "inline", "coordinates": [223, 125, 269, 135], "cont... | [] | [612.0, 792.0] | [{"type": "text", "text": "Theorem 5.2. Let $\\alpha:S\\rightarrow{\\widetilde{S}}$ be a quasi-semiring homomorphism. Given an SCSP $P$ over $S$ , suppose $t\\in O p t(\\alpha(P))$ has value $\\boldsymbol{v}$ in $P$ and value $\\widetilde{v}$ in $\\alpha(P)$ . Then there exists an optimal solution $t$ of $P$ , say with... | [{"category_id": 8, "poly": [654.7659301757812, 1406.948974609375, 1044.2076416015625, 1406.948974609375, 1044.2076416015625, 1502.6083984375, 654.7659301757812, 1502.6083984375], "score": 0.9999936819076538}, {"category_id": 1, "poly": [368.6871337890625, 1109.0634765625, 1332.05322265625, 1109.0634765625, 1332.053222... | {"preproc_blocks": [{"type": "text", "bbox": [132, 123, 479, 174], "lines": [{"bbox": [132, 124, 479, 139], "spans": [{"bbox": [132, 124, 222, 139], "score": 1.0, "content": "Theorem 5.2. Let ", "type": "text"}, {"bbox": [223, 125, 269, 135], "score": 0.93, "content": "\\alpha:S\\rightarrow{\\widetilde{S}}", "type": "i... | ./arxiv_full_mineru_outputs_20/images/0705.0734_12.png | images/0705.0734_12.png | |
0705.0734.pdf | 13 | Set $$t\,=\,(d_{2},d_{2})$$ . Clearly, $$t$$ is an optimal solution of $$\alpha(P)$$ with value $$\{{q}\}$$ in
$$\alpha(P)$$ , and value $$\Vec{\mathcal{Q}}$$ in $$P$$ . Notice that $$\bar{t}=(d_{1},d_{1})$$ is the unique optimal solution
of $$P$$ . Since $$\alpha(\{a\})=\{p\}\not\subseteq\{q\}$$ , there is no optimal ... | <p>Set $$t\,=\,(d_{2},d_{2})$$ . Clearly, $$t$$ is an optimal solution of $$\alpha(P)$$ with value $$\{{q}\}$$ in
$$\alpha(P)$$ , and value $$\Vec{\mathcal{Q}}$$ in $$P$$ . Notice that $$\bar{t}=(d_{1},d_{1})$$ is the unique optimal solution
of $$P$$ . Since $$\alpha(\{a\})=\{p\}\not\subseteq\{q\}$$ , there is no optim... | [{"type": "text", "coordinates": [131, 124, 479, 175], "content": "Set $$t\\,=\\,(d_{2},d_{2})$$ . Clearly, $$t$$ is an optimal solution of $$\\alpha(P)$$ with value $$\\{{q}\\}$$ in\n$$\\alpha(P)$$ , and value $$\\Vec{\\mathcal{Q}}$$ in $$P$$ . Notice that $$\\bar{t}=(d_{1},d_{1})$$ is the unique optimal solution\nof ... | [{"type": "text", "coordinates": [132, 126, 151, 138], "content": "Set ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [151, 127, 203, 137], "content": "t\\,=\\,(d_{2},d_{2})", "score": 0.94, "index": 2}, {"type": "text", "coordinates": [203, 126, 250, 138], "content": ". Clearly, ", "score": 1... | [] | [{"type": "block", "coordinates": [218, 384, 391, 396], "content": "", "caption": ""}, {"type": "block", "coordinates": [200, 590, 410, 621], "content": "", "caption": ""}, {"type": "inline", "coordinates": [151, 127, 203, 137], "content": "t\\,=\\,(d_{2},d_{2})", "caption": ""}, {"type": "inline", "coordinates": [251,... | [] | [612.0, 792.0] | [{"type": "text", "text": "Set $t\\,=\\,(d_{2},d_{2})$ . Clearly, $t$ is an optimal solution of $\\alpha(P)$ with value $\\{{q}\\}$ in $\\alpha(P)$ , and value $\\Vec{\\mathcal{Q}}$ in $P$ . Notice that $\\bar{t}=(d_{1},d_{1})$ is the unique optimal solution of $P$ . Since $\\alpha(\\{a\\})=\\{p\\}\\not\\subseteq\\{q\\... | [{"category_id": 9, "poly": [1291.1085205078125, 1659.42333984375, 1325.24267578125, 1659.42333984375, 1325.24267578125, 1692.2578125, 1291.1085205078125, 1692.2578125], "score": 0.9999949336051941}, {"category_id": 8, "poly": [558.8052368164062, 1641.557373046875, 1138.1263427734375, 1641.557373046875, 1138.1263427734... | {"preproc_blocks": [{"type": "text", "bbox": [131, 124, 479, 175], "lines": [{"bbox": [132, 126, 478, 138], "spans": [{"bbox": [132, 126, 151, 138], "score": 1.0, "content": "Set ", "type": "text"}, {"bbox": [151, 127, 203, 137], "score": 0.94, "content": "t\\,=\\,(d_{2},d_{2})", "type": "inline_equation", "height": 10... | ./arxiv_full_mineru_outputs_20/images/0705.0734_13.png | images/0705.0734_13.png | |
0705.0734.pdf | 14 | Proof. The sufficiency part is clear, and we now show the necessity part. Notice
that $$\alpha$$ , as a Galois connection, is monotonic. On the other hand, given $$x,y\in S$$ ,
suppose $$\alpha(x)\,\leq_{\widetilde{S}}\alpha(y)$$ . By Equation 7, we have $$x\leq_{S}y$$ . That is to say, for
any $$x,y\in S$$ , $$\alpha(... | <p>Proof. The sufficiency part is clear, and we now show the necessity part. Notice
that $$\alpha$$ , as a Galois connection, is monotonic. On the other hand, given $$x,y\in S$$ ,
suppose $$\alpha(x)\,\leq_{\widetilde{S}}\alpha(y)$$ . By Equation 7, we have $$x\leq_{S}y$$ . That is to say, for
any $$x,y\in S$$ , $$\alp... | [{"type": "text", "coordinates": [133, 156, 478, 240], "content": "Proof. The sufficiency part is clear, and we now show the necessity part. Notice\nthat $$\\alpha$$ , as a Galois connection, is monotonic. On the other hand, given $$x,y\\in S$$ ,\nsuppose $$\\alpha(x)\\,\\leq_{\\widetilde{S}}\\alpha(y)$$ . By Equation ... | [{"type": "text", "coordinates": [133, 156, 478, 169], "content": "Proof. The sufficiency part is clear, and we now show the necessity part. Notice", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [133, 169, 154, 181], "content": "that ", "score": 1.0, "index": 2}, {"type": "inline_equation", "coordinates":... | [] | [{"type": "block", "coordinates": [199, 608, 436, 639], "content": "", "caption": ""}, {"type": "inline", "coordinates": [154, 173, 161, 178], "content": "\\alpha", "caption": ""}, {"type": "inline", "coordinates": [440, 171, 474, 180], "content": "x,y\\in S", "caption": ""}, {"type": "inline", "coordinates": [171, 182... | [] | [612.0, 792.0] | [{"type": "text", "text": "Proof. The sufficiency part is clear, and we now show the necessity part. Notice that $\\alpha$ , as a Galois connection, is monotonic. On the other hand, given $x,y\\in S$ , suppose $\\alpha(x)\\,\\leq_{\\widetilde{S}}\\alpha(y)$ . By Equation 7, we have $x\\leq_{S}y$ . That is to say, for a... | [{"category_id": 8, "poly": [551.0706787109375, 1690.21142578125, 1216.8319091796875, 1690.21142578125, 1216.8319091796875, 1775.2257080078125, 551.0706787109375, 1775.2257080078125], "score": 0.9999984502792358}, {"category_id": 9, "poly": [1291.404541015625, 1713.7259521484375, 1325.820068359375, 1713.7259521484375, ... | {"preproc_blocks": [{"type": "text", "bbox": [133, 156, 478, 240], "lines": [{"bbox": [133, 156, 478, 169], "spans": [{"bbox": [133, 156, 478, 169], "score": 1.0, "content": "Proof. The sufficiency part is clear, and we now show the necessity part. Notice", "type": "text"}], "index": 0}, {"bbox": [133, 169, 477, 181], ... | ./arxiv_full_mineru_outputs_20/images/0705.0734_14.png | images/0705.0734_14.png | |
0705.0734.pdf | 15 | The next theorem shows that an aggregate compatible mapping must be a
semiring homomorphism.
Theorem 6.1. Let $$\alpha:S\to{\widetilde{S}}$$ be a mapping between two totally ordered semir-
ings. Then $$\alpha$$ is aggregate compatible if and only if $$\alpha$$ is a semiring homomor-
phism.
Proof. A semiring homomorph... | <p>The next theorem shows that an aggregate compatible mapping must be a
semiring homomorphism.</p>
<p>Theorem 6.1. Let $$\alpha:S\to{\widetilde{S}}$$ be a mapping between two totally ordered semir-
ings. Then $$\alpha$$ is aggregate compatible if and only if $$\alpha$$ is a semiring homomor-
phism.</p>
<p>Proof. A sem... | [{"type": "text", "coordinates": [133, 126, 478, 150], "content": "The next theorem shows that an aggregate compatible mapping must be a\nsemiring homomorphism.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [133, 153, 478, 190], "content": "Theorem 6.1. Let $$\\alpha:S\\to{\\widetilde{S}}$$ be a ... | [{"type": "text", "coordinates": [147, 125, 479, 138], "content": "The next theorem shows that an aggregate compatible mapping must be a", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [133, 139, 243, 150], "content": "semiring homomorphism.", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [132... | [] | [{"type": "inline", "coordinates": [221, 153, 265, 163], "content": "\\alpha:S\\to{\\widetilde{S}}", "caption": ""}, {"type": "inline", "coordinates": [185, 171, 192, 176], "content": "\\alpha", "caption": ""}, {"type": "inline", "coordinates": [361, 171, 367, 176], "content": "\\alpha", "caption": ""}, {"type": "inlin... | [] | [612.0, 792.0] | [{"type": "text", "text": "The next theorem shows that an aggregate compatible mapping must be a semiring homomorphism. ", "page_idx": 15}, {"type": "text", "text": "Theorem 6.1. Let $\\alpha:S\\to{\\widetilde{S}}$ be a mapping between two totally ordered semirings. Then $\\alpha$ is aggregate compatible if and only if... | [{"category_id": 0, "poly": [370.98077392578125, 1443.1239013671875, 677.612060546875, 1443.1239013671875, 677.612060546875, 1483.6802978515625, 370.98077392578125, 1483.6802978515625], "score": 0.9999004602432251}, {"category_id": 1, "poly": [369.1455993652344, 539.7915649414062, 1331.26171875, 539.7915649414062, 1331... | {"preproc_blocks": [{"type": "text", "bbox": [133, 126, 478, 150], "lines": [{"bbox": [147, 125, 479, 138], "spans": [{"bbox": [147, 125, 479, 138], "score": 1.0, "content": "The next theorem shows that an aggregate compatible mapping must be a", "type": "text"}], "index": 0}, {"bbox": [133, 139, 243, 150], "spans": [{... | ./arxiv_full_mineru_outputs_20/images/0705.0734_15.png | images/0705.0734_15.png | |
0705.0734.pdf | 16 | # References
[1] S. Bistarelli, P. Codognet, F. Rossi, Abstracting soft constraints: Frame-
work, properties, examples, Artificial Intelligence 139 (2002) 175-211.
[2] S. Bistarelli, H. Fargier, U. Montanari, F. Rossi, T. Schiex, G. Verfaillie,
Semiring-Based CSPs and Valued CSPs: Basic Properties and Compari-
son, in... | <h1>References</h1>
<p>[1] S. Bistarelli, P. Codognet, F. Rossi, Abstracting soft constraints: Frame-
work, properties, examples, Artificial Intelligence 139 (2002) 175-211.
[2] S. Bistarelli, H. Fargier, U. Montanari, F. Rossi, T. Schiex, G. Verfaillie,
Semiring-Based CSPs and Valued CSPs: Basic Properties and Compari... | [{"type": "title", "coordinates": [132, 121, 211, 138], "content": "References", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [138, 145, 479, 650], "content": "[1] S. Bistarelli, P. Codognet, F. Rossi, Abstracting soft constraints: Frame-\nwork, properties, examples, Artificial Intelligence 139 (... | [{"type": "text", "coordinates": [132, 122, 210, 137], "content": "References", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [142, 147, 478, 162], "content": "[1] S. Bistarelli, P. Codognet, F. Rossi, Abstracting soft constraints: Frame-", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [159, 1... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "References ", "text_level": 1, "page_idx": 16}, {"type": "text", "text": "[1] S. Bistarelli, P. Codognet, F. Rossi, Abstracting soft constraints: Framework, properties, examples, Artificial Intelligence 139 (2002) 175-211. \n[2] S. Bistarelli, H. Fargier, U. Montanari, F. Rossi, T. Schiex, ... | [{"category_id": 0, "poly": [368.67193603515625, 338.4980163574219, 586.248779296875, 338.4980163574219, 586.248779296875, 385.24676513671875, 368.67193603515625, 385.24676513671875], "score": 0.9999915957450867}, {"category_id": 1, "poly": [384.6622009277344, 403.5213928222656, 1332.928466796875, 403.5213928222656, 13... | {"preproc_blocks": [{"type": "title", "bbox": [132, 121, 211, 138], "lines": [{"bbox": [132, 122, 210, 137], "spans": [{"bbox": [132, 122, 210, 137], "score": 1.0, "content": "References", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [138, 145, 479, 650], "lines": [{"bbox": [142, 147, 478, 162]... | ./arxiv_full_mineru_outputs_20/images/0705.0734_16.png | images/0705.0734_16.png | |
0705.0734.pdf | 17 | [14] T. Schiex, H. Fargier, G. Verfaillie, Valued Constraint Satisfaction Prob-
lems: Hard and Easy Problems, in: Proc. IJCAI-95, Montreal, Quebec,
Morgan Kaufmann, San Mateo, CA, 1995, pp.631-639.
[15] L. Shapiro and R. Haralick, Structural descriptions and inexact matching.
IEEE Transactions on Pattern Analysis and M... | <p>[14] T. Schiex, H. Fargier, G. Verfaillie, Valued Constraint Satisfaction Prob-
lems: Hard and Easy Problems, in: Proc. IJCAI-95, Montreal, Quebec,
Morgan Kaufmann, San Mateo, CA, 1995, pp.631-639.
[15] L. Shapiro and R. Haralick, Structural descriptions and inexact matching.
IEEE Transactions on Pattern Analysis an... | [{"type": "text", "coordinates": [136, 124, 479, 205], "content": "[14] T. Schiex, H. Fargier, G. Verfaillie, Valued Constraint Satisfaction Prob-\nlems: Hard and Easy Problems, in: Proc. IJCAI-95, Montreal, Quebec,\nMorgan Kaufmann, San Mateo, CA, 1995, pp.631-639.\n[15] L. Shapiro and R. Haralick, Structural descript... | [{"type": "text", "coordinates": [137, 126, 477, 138], "content": "[14] T. Schiex, H. Fargier, G. Verfaillie, Valued Constraint Satisfaction Prob-", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [158, 138, 477, 151], "content": "lems: Hard and Easy Problems, in: Proc. IJCAI-95, Montreal, Quebec,", "score":... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 17}] | [{"category_id": 1, "poly": [378.7882995605469, 345.73101806640625, 1332.852783203125, 345.73101806640625, 1332.852783203125, 571.1796264648438, 378.7882995605469, 571.1796264648438], "score": 0.9999865293502808}, {"category_id": 2, "poly": [834.88427734375, 1931.5997314453125, 864.1302490234375, 1931.5997314453125, 86... | {"preproc_blocks": [{"type": "text", "bbox": [136, 124, 479, 205], "lines": [{"bbox": [137, 126, 477, 138], "spans": [{"bbox": [137, 126, 477, 138], "score": 1.0, "content": "[14] T. Schiex, H. Fargier, G. Verfaillie, Valued Constraint Satisfaction Prob-", "type": "text"}], "index": 0}, {"bbox": [158, 138, 477, 151], "... | ./arxiv_full_mineru_outputs_20/images/0705.0734_17.png | images/0705.0734_17.png | |
0705.0693.pdf | 0 | # Learning to Bluff
Evan Hurwitz and Tshilidzi Marwala
Abstract— The act of bluffing confounds game designers to
this day. The very nature of bluffing is even open for debate,
adding further complication to the process of creating
intelligent virtual players that can bluff, and hence play,
realisticall... | <h1>Learning to Bluff</h1>
<p>Evan Hurwitz and Tshilidzi Marwala</p>
<p>Abstract— The act of bluffing confounds game designers to
this day. The very nature of bluffing is even open for debate,
adding further complication to the process of creating
intelligent virtual players that can bluff, and hence pla... | [{"type": "title", "coordinates": [246, 74, 367, 92], "content": "Learning to Bluff", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [223, 103, 389, 115], "content": "Evan Hurwitz and Tshilidzi Marwala", "block_type": "text", "index": 2}, {"type": "text", "coordinates": [53, 143, 300, 309], "conten... | [{"type": "text", "coordinates": [244, 75, 367, 92], "content": "Learning to Bluff", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [223, 104, 387, 115], "content": "Evan Hurwitz and Tshilidzi Marwala", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [63, 143, 299, 154], "content": "Abstract\u201... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "Learning to Bluff ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Evan Hurwitz and Tshilidzi Marwala ", "page_idx": 0}, {"type": "text", "text": "Abstract\u2014 The act of bluffing confounds game designers to this day. The very nature of bluffing is even open for debate, adding ... | [{"category_id": 2, "poly": [147.28082275390625, 1846.36328125, 833.1051025390625, 1846.36328125, 833.1051025390625, 2024.2418212890625, 147.28082275390625, 2024.2418212890625], "score": 0.9999937415122986}, {"category_id": 1, "poly": [148.4297332763672, 398.14874267578125, 833.61669921875, 398.14874267578125, 833.6166... | {"preproc_blocks": [{"type": "title", "bbox": [246, 74, 367, 92], "lines": [{"bbox": [244, 75, 367, 92], "spans": [{"bbox": [244, 75, 367, 92], "score": 1.0, "content": "Learning to Bluff", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [223, 103, 389, 115], "lines": [{"bbox": [223, 104, 387, 115... | ./arxiv_full_mineru_outputs_20/images/0705.0693_0.png | images/0705.0693_0.png | |
0705.0693.pdf | 1 | As with any optimisation system, very careful consideration
needs to be taken with regards to how the system is
structured, since the implications of these decisions can often
result in unintentional assumptions made by the system
created. With this in mind, the Lerpa Multi-Agent System
(MAS) has been designed to allow... | <p>As with any optimisation system, very careful consideration
needs to be taken with regards to how the system is
structured, since the implications of these decisions can often
result in unintentional assumptions made by the system
created. With this in mind, the Lerpa Multi-Agent System
(MAS) has been designed to al... | [{"type": "text", "coordinates": [53, 69, 300, 184], "content": "As with any optimisation system, very careful consideration\nneeds to be taken with regards to how the system is\nstructured, since the implications of these decisions can often\nresult in unintentional assumptions made by the system\ncreated. With this i... | [{"type": "text", "coordinates": [54, 71, 299, 81], "content": "As with any optimisation system, very careful consideration", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [52, 81, 300, 92], "content": "needs to be taken with regards to how the system is", "score": 1.0, "index": 2}, {"type": "text", "coord... | [{"coordinates": [100, 261, 251, 354], "index": 16.25, "caption": "Fig. 1. System interactions", "caption_coordinates": [121, 353, 231, 364]}, {"coordinates": [112, 572, 239, 665], "index": 34.25, "caption": "Fig. 2. Agent learning scheme", "caption_coordinates": [114, 670, 238, 682]}, {"coordinates": [368, 529, 512, 6... | [{"type": "inline", "coordinates": [52, 504, 79, 516], "content": "\\mathrm{TD}(\\boldsymbol{\\lambda})", "caption": ""}, {"type": "inline", "coordinates": [543, 698, 558, 710], "content": "40^{3}", "caption": ""}, {"type": "inline", "coordinates": [466, 709, 484, 722], "content": "^{40}\\mathrm{P}_{3}", "caption": ""}... | [] | [612.0, 792.0] | [{"type": "text", "text": "As with any optimisation system, very careful consideration needs to be taken with regards to how the system is structured, since the implications of these decisions can often result in unintentional assumptions made by the system created. With this in mind, the Lerpa Multi-Agent System (MAS)... | [{"category_id": 3, "poly": [313.2093811035156, 1589.1512451171875, 665.7476806640625, 1589.1512451171875, 665.7476806640625, 1847.9881591796875, 313.2093811035156, 1847.9881591796875], "score": 0.9999957084655762}, {"category_id": 3, "poly": [1024.709228515625, 1471.534912109375, 1423.1080322265625, 1471.534912109375,... | {"preproc_blocks": [{"type": "text", "bbox": [53, 69, 300, 184], "lines": [{"bbox": [54, 71, 299, 81], "spans": [{"bbox": [54, 71, 299, 81], "score": 1.0, "content": "As with any optimisation system, very careful consideration", "type": "text"}], "index": 0}, {"bbox": [52, 81, 300, 92], "spans": [{"bbox": [52, 81, 300,... | ./arxiv_full_mineru_outputs_20/images/0705.0693_1.png | images/0705.0693_1.png | |
0705.0693.pdf | 2 | scheme would in fact allow for repeated cards, and hence $$40^{3}$$
options would be available). The first thing to notice is that
only a single deck of cards is being used, hence no card can
ever be repeated in a hand. Acting on this principle, consistent
ordering of the hand means that the base dimensionality of the
... | <p>scheme would in fact allow for repeated cards, and hence $$40^{3}$$
options would be available). The first thing to notice is that
only a single deck of cards is being used, hence no card can
ever be repeated in a hand. Acting on this principle, consistent
ordering of the hand means that the base dimensionality of t... | [{"type": "text", "coordinates": [52, 52, 300, 260], "content": "scheme would in fact allow for repeated cards, and hence $$40^{3}$$\noptions would be available). The first thing to notice is that\nonly a single deck of cards is being used, hence no card can\never be repeated in a hand. Acting on this principle, consis... | [{"type": "text", "coordinates": [52, 54, 284, 66], "content": "scheme would in fact allow for repeated cards, and hence", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [284, 52, 299, 64], "content": "40^{3}", "score": 0.86, "index": 2}, {"type": "text", "coordinates": [54, 67, 300, 77], "conten... | [{"coordinates": [104, 448, 247, 541], "index": 33.25, "caption": "Fig. 4. Agent card input structure", "caption_coordinates": [107, 539, 244, 551]}] | [{"type": "block", "coordinates": [335, 588, 398, 640], "content": "", "caption": ""}, {"type": "block", "coordinates": [313, 684, 405, 696], "content": "", "caption": ""}, {"type": "block", "coordinates": [313, 720, 369, 732], "content": "", "caption": ""}, {"type": "inline", "coordinates": [284, 52, 299, 64], "conten... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "\u2022 Trump suit \u2022 Suit agent has multiple cards in (not trumps) \u2022 Suit in agent\u2019s highest singleton \u2022 Suit in agent\u2019s second-highest singleton \u2022 Suit in agent\u2019s third-highest singleton ", "page_idx": 2}, {"type"... | [{"category_id": 1, "poly": [869.327880859375, 925.6714477539062, 1552.5576171875, 925.6714477539062, 1552.5576171875, 1117.8394775390625, 869.327880859375, 1117.8394775390625], "score": 0.9999923706054688}, {"category_id": 1, "poly": [945.361328125, 1119.611083984375, 1554.0889892578125, 1119.611083984375, 1554.088989... | {"preproc_blocks": [{"type": "text", "bbox": [52, 52, 300, 260], "lines": [{"bbox": [52, 52, 299, 66], "spans": [{"bbox": [52, 54, 284, 66], "score": 1.0, "content": "scheme would in fact allow for repeated cards, and hence", "type": "text"}, {"bbox": [284, 52, 299, 64], "score": 0.86, "content": "40^{3}", "type": "inl... | ./arxiv_full_mineru_outputs_20/images/0705.0693_2.png | images/0705.0693_2.png | |
0705.0693.pdf | 3 | The internal structure of the neural network uses a standard
sigmoidal activation function [7], which is suitable for
stability issues and still allows for the freedom expected from
a neural network. The sigmoidal activations function varies
between zero and one, rather than the often-used one and
minus one, in or... | <p>The internal structure of the neural network uses a standard
sigmoidal activation function [7], which is suitable for
stability issues and still allows for the freedom expected from
a neural network. The sigmoidal activations function varies
between zero and one, rather than the often-used one and
minus one, in... | [{"type": "interline_equation", "coordinates": [53, 53, 117, 99], "content": "", "block_type": "interline_equation", "index": 1}, {"type": "text", "coordinates": [53, 111, 300, 250], "content": "The internal structure of the neural network uses a standard\nsigmoidal activation function [7], which is suitable for\n... | [{"type": "interline_equation", "coordinates": [53, 53, 117, 99], "content": "\\begin{array}{l}{B=P(O=2)}\\\\ {C=P(O=1)}\\\\ {D=P(O=-3)}\\end{array}", "score": 0.86, "index": 1}, {"type": "text", "coordinates": [64, 113, 300, 123], "content": "The internal structure of the neural network uses a standard", "score": 1.0,... | [{"coordinates": [322, 53, 549, 204], "index": 55.5, "caption": "Fig. 5. Agent performance, averaged over 40 hands", "caption_coordinates": [331, 203, 541, 214]}, {"coordinates": [331, 352, 550, 480], "index": 77.0, "caption": "Fig. 6. Agent cowardice. Averaged over 5 hands", "caption_coordinates": [341, 479, 541, 490]... | [{"type": "block", "coordinates": [53, 53, 117, 99], "content": "", "caption": ""}, {"type": "inline", "coordinates": [257, 631, 284, 642], "content": "\\mathrm{TD}(\\boldsymbol{\\lambda})", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "equation", "text": "$$\n\\begin{array}{l}{B=P(O=2)}\\\\ {C=P(O=1)}\\\\ {D=P(O=-3)}\\end{array}\n$$", "text_format": "latex", "page_idx": 3}, {"type": "text", "text": "The internal structure of the neural network uses a standard sigmoidal activation function [7], which is suitable for stability issues an... | [{"category_id": 1, "poly": [865.4581298828125, 1391.212646484375, 1556.2950439453125, 1391.212646484375, 1556.2950439453125, 1969.68359375, 865.4581298828125, 1969.68359375], "score": 0.9999923706054688}, {"category_id": 1, "poly": [865.146240234375, 752.4821166992188, 1555.4990234375, 752.4821166992188, 1555.49902343... | {"preproc_blocks": [{"type": "interline_equation", "bbox": [53, 53, 117, 99], "lines": [{"bbox": [53, 53, 117, 99], "spans": [{"bbox": [53, 53, 117, 99], "score": 0.86, "content": "\\begin{array}{l}{B=P(O=2)}\\\\ {C=P(O=1)}\\\\ {D=P(O=-3)}\\end{array}", "type": "interline_equation"}], "index": 0}], "index": 0}, {"type"... | ./arxiv_full_mineru_outputs_20/images/0705.0693_3.png | images/0705.0693_3.png | |
0705.0693.pdf | 4 | B. Parameter Optimisation
A number of parameters need to be optimised, in order to
optimise the learning of the agents. These parameters are the
learning-rate α, the memory parameter $$\uplambda$$ and the exploration
parameter ε. The multi-agent system provides a perfect
environment for this testing, since four diffe... | <p>B. Parameter Optimisation</p>
<p>A number of parameters need to be optimised, in order to
optimise the learning of the agents. These parameters are the
learning-rate α, the memory parameter $$\uplambda$$ and the exploration
parameter ε. The multi-agent system provides a perfect
environment for this testing, since f... | [{"type": "text", "coordinates": [59, 54, 176, 65], "content": "B. Parameter Optimisation", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [51, 67, 301, 298], "content": "A number of parameters need to be optimised, in order to\noptimise the learning of the agents. These parameters are the\nlearnin... | [{"type": "text", "coordinates": [60, 54, 175, 66], "content": "B. Parameter Optimisation", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [53, 69, 299, 80], "content": "A number of parameters need to be optimised, in order to", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [53, 81, 300, 92], ... | [{"coordinates": [63, 310, 288, 435], "index": 29.25, "caption": "over 30 hands", "caption_coordinates": [52, 436, 301, 460]}, {"coordinates": [331, 53, 549, 182], "index": 62.5, "caption": "playing against unpredictable opponents.", "caption_coordinates": [311, 192, 560, 230]}, {"coordinates": [340, 431, 542, 561], "i... | [{"type": "inline", "coordinates": [211, 91, 218, 101], "content": "\\uplambda", "caption": ""}, {"type": "inline", "coordinates": [154, 482, 184, 492], "content": "a=0.1", "caption": ""}, {"type": "inline", "coordinates": [188, 482, 218, 492], "content": "\\lambda=0.1", "caption": ""}, {"type": "inline", "coordinates"... | [] | [612.0, 792.0] | [{"type": "text", "text": "B. Parameter Optimisation ", "page_idx": 4}, {"type": "text", "text": "A number of parameters need to be optimised, in order to optimise the learning of the agents. These parameters are the learning-rate \u03b1, the memory parameter $\\uplambda$ and the exploration parameter \u03b5. The mult... | [{"category_id": 1, "poly": [865.7196044921875, 1640.5230712890625, 1556.1160888671875, 1640.5230712890625, 1556.1160888671875, 2027.1429443359375, 865.7196044921875, 2027.1429443359375], "score": 0.9999954104423523}, {"category_id": 1, "poly": [867.426513671875, 717.9448852539062, 1557.8389892578125, 717.9448852539062... | {"preproc_blocks": [{"type": "text", "bbox": [59, 54, 176, 65], "lines": [{"bbox": [60, 54, 175, 66], "spans": [{"bbox": [60, 54, 175, 66], "score": 1.0, "content": "B. Parameter Optimisation", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [51, 67, 301, 298], "lines": [{"bbox": [53, 69, 299, 80... | ./arxiv_full_mineru_outputs_20/images/0705.0693_4.png | images/0705.0693_4.png | |
0705.0693.pdf | 5 | achieved. This is akin to Game Theory’s “static equilibrium”
[4], as is evidenced in Fig. 10.
for one’s opponent unfavourable by representing a strong
hand, then this result shows that the agents learn each other’s
patterns well enough to factor their opponent’s strategies into
the game evaluation, something game theo... | <p>achieved. This is akin to Game Theory’s “static equilibrium”
[4], as is evidenced in Fig. 10.</p>
<p>for one’s opponent unfavourable by representing a strong
hand, then this result shows that the agents learn each other’s
patterns well enough to factor their opponent’s strategies into
the game evaluation, something ... | [{"type": "text", "coordinates": [53, 54, 299, 76], "content": "achieved. This is akin to Game Theory\u2019s \u201cstatic equilibrium\u201d\n[4], as is evidenced in Fig. 10.", "block_type": "text", "index": 1}, {"type": "image", "coordinates": [82, 76, 271, 186], "content": "", "block_type": "image", "index": 2}, {"typ... | [{"type": "text", "coordinates": [53, 54, 298, 67], "content": "achieved. This is akin to Game Theory\u2019s \u201cstatic equilibrium\u201d", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [54, 66, 174, 78], "content": "[4], as is evidenced in Fig. 10.", "score": 1.0, "index": 2}, {"type": "text", "coordina... | [{"coordinates": [82, 76, 271, 186], "index": 9.5, "caption": "", "caption_coordinates": [119, 179, 234, 190]}, {"coordinates": [75, 336, 276, 480], "index": 46.75, "caption": "Fig. 11. Agent bluffing ", "caption_coordinates": [129, 478, 224, 489]}] | [{"type": "inline", "coordinates": [331, 322, 358, 334], "content": "\\mathrm{TD}(\\boldsymbol{\\lambda})", "caption": ""}, {"type": "inline", "coordinates": [473, 498, 483, 507], "content": "\\delta^{t h}", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 5}, {"type": "image", "img_path": "images/97ee7c0fcd3c866fac4e302cc90448312687f3108faee713450b3e691bcd8f88.jpg", "img_caption": [""], "img_footnote": [], "page_idx": 5}, {"type": "text", "text": "for one\u2019s opponent unfavourable by representing a strong hand, then this resu... | [{"category_id": 0, "poly": [1138.05517578125, 1218.7125244140625, 1282.9974365234375, 1218.7125244140625, 1282.9974365234375, 1247.571044921875, 1138.05517578125, 1247.571044921875], "score": 0.9999973177909851}, {"category_id": 1, "poly": [868.6779174804688, 148.71763610839844, 1554.672119140625, 148.71763610839844, ... | {"preproc_blocks": [{"type": "text", "bbox": [53, 54, 299, 76], "lines": [{"bbox": [53, 54, 298, 67], "spans": [{"bbox": [53, 54, 298, 67], "score": 1.0, "content": "achieved. This is akin to Game Theory\u2019s \u201cstatic equilibrium\u201d", "type": "text"}], "index": 0}, {"bbox": [54, 66, 174, 78], "spans": [{"bbox"... | ./arxiv_full_mineru_outputs_20/images/0705.0693_5.png | images/0705.0693_5.png | |
0705.2235.pdf | 0 | # Response Prediction of Structural System Subject to Earthquake
Motions using Artificial Neural Network
# S. Chakraverty*, T. Marwala** , Pallavi Gupta* and Thando Tettey**
*B.P.P.P. Division, Central Building Research Institute
Roorkee-247 667, Uttaranchal, India
e-mail :sne_chak@yahoo.com
**School of Electrical ... | <h1>Response Prediction of Structural System Subject to Earthquake
Motions using Artificial Neural Network</h1>
<h1>S. Chakraverty*, T. Marwala** , Pallavi Gupta* and Thando Tettey**</h1>
<p>*B.P.P.P. Division, Central Building Research Institute
Roorkee-247 667, Uttaranchal, India
e-mail :sne_chak@yahoo.com</p>
<p>**... | [{"type": "title", "coordinates": [87, 70, 525, 113], "content": "Response Prediction of Structural System Subject to Earthquake\nMotions using Artificial Neural Network", "block_type": "title", "index": 1}, {"type": "title", "coordinates": [114, 142, 497, 160], "content": "S. Chakraverty*, T. Marwala** , Pallavi Gupt... | [{"type": "text", "coordinates": [89, 73, 522, 90], "content": "Response Prediction of Structural System Subject to Earthquake", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [174, 97, 438, 114], "content": "Motions using Artificial Neural Network", "score": 1.0, "index": 2}, {"type": "text", "coordinates"... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "Response Prediction of Structural System Subject to Earthquake Motions using Artificial Neural Network ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "S. Chakraverty\\*, T. Marwala\\*\\* , Pallavi Gupta\\* and Thando Tettey\\*\\* ", "text_level": 1, "page_idx": 0}, {"type": "te... | [{"category_id": 0, "poly": [246.4246826171875, 848.72607421875, 414.2247009277344, 848.72607421875, 414.2247009277344, 892.638916015625, 246.4246826171875, 892.638916015625], "score": 0.9999977350234985}, {"category_id": 1, "poly": [453.6440734863281, 513.7282104492188, 1253.5723876953125, 513.7282104492188, 1253.5723... | {"preproc_blocks": [{"type": "title", "bbox": [87, 70, 525, 113], "lines": [{"bbox": [89, 73, 522, 90], "spans": [{"bbox": [89, 73, 522, 90], "score": 1.0, "content": "Response Prediction of Structural System Subject to Earthquake", "type": "text"}], "index": 0}, {"bbox": [174, 97, 438, 114], "spans": [{"bbox": [174, 9... | ./arxiv_full_mineru_outputs_20/images/0705.2235_0.png | images/0705.2235_0.png | |
0705.2235.pdf | 1 | # 1 Introduction
Real earthquake ground motion at a particular building site is very complicated.
The response of a building to an earthquake is dynamic and for a dynamic
response, the building is subjected to a vibratory shaking of the base. Exactly
how a building responds is complex and depends on the amplitude and
... | <h1>1 Introduction</h1>
<p>Real earthquake ground motion at a particular building site is very complicated.
The response of a building to an earthquake is dynamic and for a dynamic
response, the building is subjected to a vibratory shaking of the base. Exactly
how a building responds is complex and depends on the ampli... | [{"type": "title", "coordinates": [89, 133, 210, 151], "content": "1 Introduction", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [88, 169, 526, 583], "content": "Real earthquake ground motion at a particular building site is very complicated.\nThe response of a building to an earthquake is dynami... | [{"type": "text", "coordinates": [90, 138, 96, 145], "content": "1", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [124, 134, 208, 149], "content": "Introduction", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [89, 173, 522, 189], "content": "Real earthquake ground motion at a particular build... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "1 Introduction ", "text_level": 1, "page_idx": 1}, {"type": "text", "text": "Real earthquake ground motion at a particular building site is very complicated. The response of a building to an earthquake is dynamic and for a dynamic response, the building is subjected to a vibratory shaking of ... | [{"category_id": 1, "poly": [245.41824340820312, 1660.7110595703125, 1460.0672607421875, 1660.7110595703125, 1460.0672607421875, 2001.521240234375, 245.41824340820312, 2001.521240234375], "score": 0.9999927282333374}, {"category_id": 1, "poly": [244.94178771972656, 470.07159423828125, 1462.6524658203125, 470.0715942382... | {"preproc_blocks": [{"type": "title", "bbox": [89, 133, 210, 151], "lines": [{"bbox": [90, 134, 208, 149], "spans": [{"bbox": [90, 138, 96, 145], "score": 1.0, "content": "1", "type": "text"}, {"bbox": [124, 134, 208, 149], "score": 1.0, "content": "Introduction", "type": "text"}], "index": 0}], "index": 0}, {"type": "... | ./arxiv_full_mineru_outputs_20/images/0705.2235_1.png | images/0705.2235_1.png | |
0705.2235.pdf | 2 | applied a counter-propagation NN to locate damage in beams and frames.
KuZniar and Waszczyszyn [11] simulated the dynamic response for prefabricated
building using ANN. Elkordy et al.[12] used a back-propagation neural network
with modal shapes in the input layer to detect the simulated damage of
structures. Muhammad... | <p>applied a counter-propagation NN to locate damage in beams and frames.
KuZniar and Waszczyszyn [11] simulated the dynamic response for prefabricated
building using ANN. Elkordy et al.[12] used a back-propagation neural network
with modal shapes in the input layer to detect the simulated damage of
structures. Muham... | [{"type": "text", "coordinates": [87, 69, 525, 253], "content": "applied a counter-propagation NN to locate damage in beams and frames.\nKuZniar and Waszczyszyn [11] simulated the dynamic response for prefabricated\nbuilding using ANN. Elkordy et al.[12] used a back-propagation neural network\nwith modal shapes in the ... | [{"type": "text", "coordinates": [90, 73, 522, 86], "content": "applied a counter-propagation NN to locate damage in beams and frames.", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 92, 523, 109], "content": "KuZniar and Waszczyszyn [11] simulated the dynamic response for prefabricated", "score": 1.0... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "In the present paper, the Chamoli earthquake ground acceleration at Barkot (NE) and Uttarkashi earthquake ground acceleration recorded at Barkot (NE and NW) have been considered based on the authors' previous study [18]. From their ground accelerat... | [{"category_id": 1, "poly": [244.24134826660156, 192.71363830566406, 1460.809326171875, 192.71363830566406, 1460.809326171875, 705.3646240234375, 244.24134826660156, 705.3646240234375], "score": 0.9999949932098389}, {"category_id": 1, "poly": [242.3686065673828, 1698.7611083984375, 1462.6788330078125, 1698.761108398437... | {"preproc_blocks": [{"type": "text", "bbox": [87, 69, 525, 253], "lines": [{"bbox": [90, 73, 522, 86], "spans": [{"bbox": [90, 73, 522, 86], "score": 1.0, "content": "applied a counter-propagation NN to locate damage in beams and frames.", "type": "text"}], "index": 0}, {"bbox": [88, 92, 523, 109], "spans": [{"bbox": [... | ./arxiv_full_mineru_outputs_20/images/0705.2235_2.png | images/0705.2235_2.png | |
0705.2235.pdf | 3 | channels called connections. The general structure of the network that have
been used here is given in Fig.1. the structure consists of three layers : the input
layer, the hidden layer and the output layer. The input layer is made up of one or
more neurons or processing elements that collectively represent the informat... | <p>channels called connections. The general structure of the network that have
been used here is given in Fig.1. the structure consists of three layers : the input
layer, the hidden layer and the output layer. The input layer is made up of one or
more neurons or processing elements that collectively represent the infor... | [{"type": "text", "coordinates": [86, 69, 527, 379], "content": "channels called connections. The general structure of the network that have\nbeen used here is given in Fig.1. the structure consists of three layers : the input\nlayer, the hidden layer and the output layer. The input layer is made up of one or\nmore neu... | [{"type": "text", "coordinates": [90, 73, 523, 87], "content": "channels called connections. The general structure of the network that have", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [89, 94, 524, 109], "content": "been used here is given in Fig.1. the structure consists of three layers : the input ",... | [{"coordinates": [137, 400, 439, 719], "index": 26.5, "caption": "Input Units", "caption_coordinates": [212, 722, 273, 735]}] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 3}, {"type": "image", "img_path": "images/833ef17bd232c62476585eb54bc848919b9a5459ec41d1bb19ca9387b744152e.jpg", "img_caption": ["Output Units ", "Input Units "], "img_footnote": [], "page_idx": 3}] | [{"category_id": 3, "poly": [381.8630676269531, 1112.8297119140625, 1220.9266357421875, 1112.8297119140625, 1220.9266357421875, 1998.7496337890625, 381.8630676269531, 1998.7496337890625], "score": 0.9999906420707703}, {"category_id": 4, "poly": [590.6754760742188, 2006.5673828125, 759.4070434570312, 2006.5673828125, 75... | {"preproc_blocks": [{"type": "text", "bbox": [86, 69, 527, 379], "lines": [{"bbox": [90, 73, 523, 87], "spans": [{"bbox": [90, 73, 523, 87], "score": 1.0, "content": "channels called connections. The general structure of the network that have", "type": "text"}], "index": 0}, {"bbox": [89, 94, 524, 109], "spans": [{"bbo... | ./arxiv_full_mineru_outputs_20/images/0705.2235_3.png | images/0705.2235_3.png | |
0705.2235.pdf | 4 | # Fig.1. Layered Feedforward Neural Network
# 3 Error Back Propagation Training Algorithm (EBPTA)
Here, Error Back Propagation Training algorithm and feedforward recall with one
hidden layer has been used. In Fig. 1, Zi, $${\mathsf{P}}_{\mathrm{j}}$$ and $$\mathsf{O}_{\mathsf{k}}$$ are input, hidden and output
layer ... | <h1>Fig.1. Layered Feedforward Neural Network</h1>
<h1>3 Error Back Propagation Training Algorithm (EBPTA)</h1>
<p>Here, Error Back Propagation Training algorithm and feedforward recall with one
hidden layer has been used. In Fig. 1, Zi, $${\mathsf{P}}_{\mathrm{j}}$$ and $$\mathsf{O}_{\mathsf{k}}$$ are input, hidden an... | [{"type": "title", "coordinates": [181, 98, 432, 114], "content": "Fig.1. Layered Feedforward Neural Network", "block_type": "title", "index": 1}, {"type": "title", "coordinates": [88, 126, 476, 144], "content": "3 Error Back Propagation Training Algorithm (EBPTA)", "block_type": "title", "index": 2}, {"type": "text", ... | [{"type": "text", "coordinates": [183, 100, 429, 115], "content": "Fig.1. Layered Feedforward Neural Network", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 128, 99, 142], "content": "3", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [124, 127, 472, 145], "content": "Error Back Propagatio... | [] | [{"type": "block", "coordinates": [157, 296, 305, 314], "content": "", "caption": ""}, {"type": "block", "coordinates": [151, 362, 316, 392], "content": "", "caption": ""}, {"type": "block", "coordinates": [135, 480, 369, 533], "content": "", "caption": ""}, {"type": "block", "coordinates": [108, 581, 397, 604], "conte... | [] | [612.0, 792.0] | [{"type": "text", "text": "Fig.1. Layered Feedforward Neural Network ", "text_level": 1, "page_idx": 4}, {"type": "text", "text": "3 Error Back Propagation Training Algorithm (EBPTA) ", "text_level": 1, "page_idx": 4}, {"type": "text", "text": "Here, Error Back Propagation Training algorithm and feedforward recall with... | [{"category_id": 8, "poly": [420.2420349121094, 1010.7469482421875, 875.8907470703125, 1010.7469482421875, 875.8907470703125, 1083.8326416015625, 420.2420349121094, 1083.8326416015625], "score": 0.9999960660934448}, {"category_id": 1, "poly": [246.49916076660156, 430.7459411621094, 1456.2493896484375, 430.7459411621094... | {"preproc_blocks": [{"type": "title", "bbox": [181, 98, 432, 114], "lines": [{"bbox": [183, 100, 429, 115], "spans": [{"bbox": [183, 100, 429, 115], "score": 1.0, "content": "Fig.1. Layered Feedforward Neural Network", "type": "text"}], "index": 0}], "index": 0}, {"type": "title", "bbox": [88, 126, 476, 144], "lines": ... | ./arxiv_full_mineru_outputs_20/images/0705.2235_4.png | images/0705.2235_4.png | |
0705.2235.pdf | 5 | # 4 Response Prediction
The basic idea behind the proposed methodology is to predict the structural
response of single degree of freedom system i.e. single storey building subject to
various earthquake forces. Two cases viz without damping and with damping
have been considered for the analysis.
# Case(i) : Without da... | <h1>4 Response Prediction</h1>
<p>The basic idea behind the proposed methodology is to predict the structural
response of single degree of freedom system i.e. single storey building subject to
various earthquake forces. Two cases viz without damping and with damping
have been considered for the analysis.</p>
<h1>Case(i... | [{"type": "title", "coordinates": [90, 133, 267, 151], "content": "4 Response Prediction", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [88, 170, 524, 248], "content": "The basic idea behind the proposed methodology is to predict the structural\nresponse of single degree of freedom system i.e. si... | [{"type": "text", "coordinates": [88, 136, 98, 148], "content": "4", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [125, 134, 266, 151], "content": "Response Prediction", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [89, 173, 523, 188], "content": "The basic idea behind the proposed methodolo... | [] | [{"type": "block", "coordinates": [107, 375, 191, 389], "content": "", "caption": ""}, {"type": "block", "coordinates": [108, 521, 176, 537], "content": "", "caption": ""}, {"type": "block", "coordinates": [112, 620, 267, 655], "content": "", "caption": ""}, {"type": "inline", "coordinates": [164, 314, 173, 325], "cont... | [] | [612.0, 792.0] | [{"type": "text", "text": "4 Response Prediction ", "text_level": 1, "page_idx": 5}, {"type": "text", "text": "The basic idea behind the proposed methodology is to predict the structural response of single degree of freedom system i.e. single storey building subject to various earthquake forces. Two cases viz without d... | [{"category_id": 0, "poly": [251.93362426757812, 371.4665832519531, 741.7333374023438, 371.4665832519531, 741.7333374023438, 420.4585266113281, 251.93362426757812, 420.4585266113281], "score": 0.9999949336051941}, {"category_id": 1, "poly": [243.14231872558594, 1124.3514404296875, 648.299072265625, 1124.3514404296875, ... | {"preproc_blocks": [{"type": "title", "bbox": [90, 133, 267, 151], "lines": [{"bbox": [88, 134, 266, 151], "spans": [{"bbox": [88, 136, 98, 148], "score": 1.0, "content": "4", "type": "text"}, {"bbox": [125, 134, 266, 151], "score": 1.0, "content": "Response Prediction", "type": "text"}], "index": 0}], "index": 0}, {"t... | ./arxiv_full_mineru_outputs_20/images/0705.2235_5.png | images/0705.2235_5.png | |
0705.2235.pdf | 6 | Case (ii) : With damping
Let M be the mass of the generalized one storey structure, K the stiffness of the
structure, C the damping and $$\mathsf{x}$$ be the displacement relative to the ground then
the equation of motion may be written as:
where
$$\ddot{{\mathsf X}}=$$ Responseacceleration,
$${\dot{\mathsf{X}}}=$$ ... | <p>Case (ii) : With damping</p>
<p>Let M be the mass of the generalized one storey structure, K the stiffness of the
structure, C the damping and $$\mathsf{x}$$ be the displacement relative to the ground then
the equation of motion may be written as:</p>
<p>where</p>
<p>$$\ddot{{\mathsf X}}=$$ Responseacceleration,
$${... | [{"type": "text", "coordinates": [89, 133, 221, 148], "content": "Case (ii) : With damping", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [89, 167, 524, 224], "content": "Let M be the mass of the generalized one storey structure, K the stiffness of the\nstructure, C the damping and $$\\mathsf{x}$$... | [{"type": "text", "coordinates": [90, 134, 219, 150], "content": "Case (ii) : With damping", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 169, 522, 184], "content": "Let M be the mass of the generalized one storey structure, K the stiffness of the", "score": 1.0, "index": 2}, {"type": "text", "coordi... | [] | [{"type": "block", "coordinates": [107, 238, 213, 252], "content": "", "caption": ""}, {"type": "block", "coordinates": [94, 411, 202, 427], "content": "", "caption": ""}, {"type": "block", "coordinates": [105, 520, 339, 556], "content": "", "caption": ""}, {"type": "inline", "coordinates": [252, 191, 261, 201], "conte... | [] | [612.0, 792.0] | [{"type": "text", "text": "Case (ii) : With damping ", "page_idx": 6}, {"type": "text", "text": "Let M be the mass of the generalized one storey structure, K the stiffness of the structure, C the damping and $\\mathsf{x}$ be the displacement relative to the ground then the equation of motion may be written as: ", "page... | [{"category_id": 1, "poly": [299.9274597167969, 818.4502563476562, 705.0848388671875, 818.4502563476562, 705.0848388671875, 1012.6136474609375, 299.9274597167969, 1012.6136474609375], "score": 0.9999987483024597}, {"category_id": 1, "poly": [247.6234588623047, 1739.052490234375, 1456.5859375, 1739.052490234375, 1456.58... | {"preproc_blocks": [{"type": "text", "bbox": [89, 133, 221, 148], "lines": [{"bbox": [90, 134, 219, 150], "spans": [{"bbox": [90, 134, 219, 150], "score": 1.0, "content": "Case (ii) : With damping", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [89, 167, 524, 224], "lines": [{"bbox": [88, 169, 5... | ./arxiv_full_mineru_outputs_20/images/0705.2235_6.png | images/0705.2235_6.png | |
0705.2235.pdf | 7 | for the other problem of time period vs. maximum response the input and output
layer contain the time period and the corresponding maximum response
respectively at each interval for the particular structure.
# 5 Numerical Results and Discussions
For the present study two Indian earthquakes viz. the Chamoli Ea... | <p>for the other problem of time period vs. maximum response the input and output
layer contain the time period and the corresponding maximum response
respectively at each interval for the particular structure.</p>
<h1>5 Numerical Results and Discussions</h1>
<p>For the present study two Indian earthquakes viz.... | [{"type": "text", "coordinates": [87, 69, 526, 130], "content": "for the other problem of time period vs. maximum response the input and output\nlayer contain the time period and the corresponding maximum response\nrespectively at each interval for the particular structure.", "block_type": "text", "index": 1}, ... | [{"type": "text", "coordinates": [88, 72, 523, 88], "content": "for the other problem of time period vs. maximum response the input and output", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 93, 522, 109], "content": "layer contain the time period and the corresponding maximum response", "scor... | [] | [{"type": "inline", "coordinates": [199, 202, 313, 215], "content": "=0.16885\\ m/{\\sf s e c/s e c})", "caption": ""}, {"type": "inline", "coordinates": [88, 243, 194, 257], "content": "=0.931\\:\\:\\mathsf{m/s e c/s e c})", "caption": ""}, {"type": "inline", "coordinates": [209, 382, 243, 395], "content": "\\mathtt{o... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 7}, {"type": "text", "text": "5 Numerical Results and Discussions ", "text_level": 1, "page_idx": 7}, {"type": "text", "text": "For the present study two Indian earthquakes viz. the Chamoli Earthquake (max. ground acceleration $=0.16885\\ m/{\\sf s e c/s e c})$ at Barkot in NE ... | [{"category_id": 0, "poly": [247.100830078125, 393.9649658203125, 1017.2991943359375, 393.9649658203125, 1017.2991943359375, 450.2577209472656, 247.100830078125, 450.2577209472656], "score": 0.9999985694885254}, {"category_id": 1, "poly": [243.87551879882812, 497.847412109375, 1461.0517578125, 497.847412109375, 1461.05... | {"preproc_blocks": [{"type": "text", "bbox": [87, 69, 526, 130], "lines": [{"bbox": [88, 72, 523, 88], "spans": [{"bbox": [88, 72, 523, 88], "score": 1.0, "content": "for the other problem of time period vs. maximum response the input and output", "type": "text"}], "index": 0}, {"bbox": [88, 93, 522, 109], "spans": [{"... | ./arxiv_full_mineru_outputs_20/images/0705.2235_7.png | images/0705.2235_7.png | |
0705.2235.pdf | 8 | response data with Chamoli earthquake is trained for an example with the time
range 0 to 10.96 sec.(550 data points). Its weights are stored to find the
response for the time range 0 to 14.92 sec. (whole period) at different
percentages of the earthquake in order to test the network learning for the points
ou... | <p>response data with Chamoli earthquake is trained for an example with the time
range 0 to 10.96 sec.(550 data points). Its weights are stored to find the
response for the time range 0 to 14.92 sec. (whole period) at different
percentages of the earthquake in order to test the network learning for the points... | [{"type": "text", "coordinates": [86, 68, 526, 385], "content": "response data with Chamoli earthquake is trained for an example with the time\nrange 0 to 10.96 sec.(550 data points). Its weights are stored to find the\nresponse for the time range 0 to 14.92 sec. (whole period) at different\npercentages of th... | [{"type": "text", "coordinates": [90, 73, 521, 87], "content": "response data with Chamoli earthquake is trained for an example with the time", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 94, 523, 108], "content": "range 0 to 10.96 sec.(550 data points). Its weights are stored to find the", "score":... | [] | [{"type": "inline", "coordinates": [294, 176, 334, 190], "content": "\\scriptstyle{\\omega=0.01}", "caption": ""}, {"type": "inline", "coordinates": [464, 178, 472, 188], "content": "^{\\ast}=", "caption": ""}, {"type": "inline", "coordinates": [88, 198, 146, 212], "content": "\\mathsf{m/s e c/s e c})", "caption": ""},... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 8}, {"type": "text", "text": "The system with damping is then considered and for this, first from the ground acceleration of Chamoli Earthquake at Barkot (NE), the response is computed using Eq.(6). The obtained responses and the ground acceleration are trained by the said ANN ... | [{"category_id": 1, "poly": [241.301513671875, 191.40390014648438, 1461.942138671875, 191.40390014648438, 1461.942138671875, 1069.5789794921875, 241.301513671875, 1069.5789794921875], "score": 0.9999906420707703}, {"category_id": 1, "poly": [242.48599243164062, 1107.242431640625, 1462.901123046875, 1107.242431640625, 1... | {"preproc_blocks": [{"type": "text", "bbox": [86, 68, 526, 385], "lines": [{"bbox": [90, 73, 521, 87], "spans": [{"bbox": [90, 73, 521, 87], "score": 1.0, "content": "response data with Chamoli earthquake is trained for an example with the time", "type": "text"}], "index": 0}, {"bbox": [88, 94, 523, 108], "spans": [{"b... | ./arxiv_full_mineru_outputs_20/images/0705.2235_8.png | images/0705.2235_8.png | |
0705.2235.pdf | 9 | 6(c) $$(\omega=~0.68981$$ , damping $$=$$ 1.58033 and maximum response for $$120\%\;=$$
$$0.00910\;\mathsf{m/s e c/s e c})$$ for $$120\%$$ of earthquake acceleration.
Finally, the Uttarkashi earthquake at Barkot (NW) ground acceleration is used
with damping $$=0.05$$ , at different time periods ( $$\mathfrak{t}=1/\mat... | <p>6(c) $$(\omega=~0.68981$$ , damping $$=$$ 1.58033 and maximum response for $$120\%\;=$$
$$0.00910\;\mathsf{m/s e c/s e c})$$ for $$120\%$$ of earthquake acceleration.</p>
<p>Finally, the Uttarkashi earthquake at Barkot (NW) ground acceleration is used
with damping $$=0.05$$ , at different time periods ( $$\mathfrak{... | [{"type": "text", "coordinates": [87, 70, 525, 110], "content": "6(c) $$(\\omega=~0.68981$$ , damping $$=$$ 1.58033 and maximum response for $$120\\%\\;=$$\n$$0.00910\\;\\mathsf{m/s e c/s e c})$$ for $$120\\%$$ of earthquake acceleration.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [87, 125, 52... | [{"type": "text", "coordinates": [88, 73, 118, 88], "content": "6(c) ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [118, 72, 186, 87], "content": "(\\omega=~0.68981", "score": 0.49, "index": 2}, {"type": "text", "coordinates": [187, 73, 246, 88], "content": ", damping ", "score": 1.0, "index"... | [] | [{"type": "inline", "coordinates": [118, 72, 186, 87], "content": "(\\omega=~0.68981", "caption": ""}, {"type": "inline", "coordinates": [247, 74, 259, 85], "content": "=", "caption": ""}, {"type": "inline", "coordinates": [476, 72, 523, 86], "content": "120\\%\\;=", "caption": ""}, {"type": "inline", "coordinates": [8... | [] | [612.0, 792.0] | [{"type": "text", "text": "6(c) $(\\omega=~0.68981$ , damping $=$ 1.58033 and maximum response for $120\\%\\;=$ $0.00910\\;\\mathsf{m/s e c/s e c})$ for $120\\%$ of earthquake acceleration. ", "page_idx": 9}, {"type": "text", "text": "Finally, the Uttarkashi earthquake at Barkot (NW) ground acceleration is used with da... | [{"category_id": 1, "poly": [242.1837158203125, 348.1542053222656, 1461.874267578125, 348.1542053222656, 1461.874267578125, 979.0828247070312, 242.1837158203125, 979.0828247070312], "score": 0.9999796152114868}, {"category_id": 1, "poly": [243.35011291503906, 195.4203643798828, 1459.0714111328125, 195.4203643798828, 14... | {"preproc_blocks": [{"type": "text", "bbox": [87, 70, 525, 110], "lines": [{"bbox": [88, 72, 523, 88], "spans": [{"bbox": [88, 73, 118, 88], "score": 1.0, "content": "6(c) ", "type": "text"}, {"bbox": [118, 72, 186, 87], "score": 0.49, "content": "(\\omega=~0.68981", "type": "inline_equation", "height": 15, "width": 68... | ./arxiv_full_mineru_outputs_20/images/0705.2235_9.png | images/0705.2235_9.png | |
0705.2235.pdf | 10 | The authors would like to thank Department of Science and Technology, India for
funding and Director C.B.R.I. for giving permission to publish this paper.
# References
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representation by error propagation. In Parallel Distributed Processing... | <p>The authors would like to thank Department of Science and Technology, India for
funding and Director C.B.R.I. for giving permission to publish this paper.</p>
<h1>References</h1>
<p>[1] D.E. Rumelhart, G.E. Hinton, R.J. Williams, Learning international
representation by error propagation. In Parallel Distrib... | [{"type": "text", "coordinates": [87, 70, 524, 110], "content": "The authors would like to thank Department of Science and Technology, India for\nfunding and Director C.B.R.I. for giving permission to publish this paper.", "block_type": "text", "index": 1}, {"type": "title", "coordinates": [89, 134, 167, 151], "content... | [{"type": "text", "coordinates": [89, 73, 522, 87], "content": "The authors would like to thank Department of Science and Technology, India for", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [89, 92, 471, 109], "content": "funding and Director C.B.R.I. for giving permission to publish this paper.", "score... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "The authors would like to thank Department of Science and Technology, India for funding and Director C.B.R.I. for giving permission to publish this paper. ", "page_idx": 10}, {"type": "text", "text": "References ", "text_level": 1, "page_idx": 10}, {"type": "text", "text": "[1] D.E. Rumelha... | [{"category_id": 0, "poly": [247.42991638183594, 372.7825012207031, 465.4985046386719, 372.7825012207031, 465.4985046386719, 419.6600646972656, 247.42991638183594, 419.6600646972656], "score": 0.9999936819076538}, {"category_id": 1, "poly": [243.93246459960938, 431.4963073730469, 1459.5350341796875, 431.4963073730469, ... | {"preproc_blocks": [{"type": "text", "bbox": [87, 70, 524, 110], "lines": [{"bbox": [89, 73, 522, 87], "spans": [{"bbox": [89, 73, 522, 87], "score": 1.0, "content": "The authors would like to thank Department of Science and Technology, India for", "type": "text"}], "index": 0}, {"bbox": [89, 92, 471, 109], "spans": [{... | ./arxiv_full_mineru_outputs_20/images/0705.2235_10.png | images/0705.2235_10.png | |
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0705.2235.pdf | 12 | [{"type": "image", "coordinates": [140, 13, 448, 190], "content": "", "block_type": "image", "index": 1}, {"type": "image", "coordinates": [152, 266, 448, 441], "content": "", "block_type": "image", "index": 2}, {"type": "image", "coordinates": [156, 497, 449, 668], "content": "", "block_type": "image", "index": 3}] | [] | [{"coordinates": [140, 13, 448, 190], "index": 2.25, "caption": " 0.16885m/sec/sec", "caption_coordinates": [188, 218, 454, 243]}, {"coordinates": [152, 266, 448, 441], "index": 7.25, "caption": "Peak Acceleration : 0.9317m/sec/sec", "caption_coordinates": [170, 459, 441, 483]}, {"coordinates": [156, 497, 449, 668], "i... | [] | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/239994b493c033484c37e350a0c65cf44210c26438e78f2a9b16b284c81723ff.jpg", "img_caption": ["Fig. 2(a). Chamoli Earthquake at Barkot in NE direction Peak Acceleration $\\equiv$ 0.16885m/sec/sec "], "img_footnote": [], "page_idx": 12}, {"type": "image", "img_path": "images/f63a682bdf31... | [{"category_id": 3, "poly": [434.6166076660156, 1382.97265625, 1248.7779541015625, 1382.97265625, 1248.7779541015625, 1857.4818115234375, 434.6166076660156, 1857.4818115234375], "score": 0.999998927116394}, {"category_id": 3, "poly": [424.0379638671875, 739.9469604492188, 1244.57861328125, 739.9469604492188, 1244.57861... | {"preproc_blocks": [{"type": "image", "bbox": [140, 13, 448, 190], "blocks": [{"type": "image_body", "bbox": [140, 13, 448, 190], "group_id": 0, "lines": [{"bbox": [140, 13, 448, 190], "spans": [{"bbox": [140, 13, 448, 190], "score": 0.9999957084655762, "type": "image", "image_path": "239994b493c033484c37e350a0c65cf442... | ./arxiv_full_mineru_outputs_20/images/0705.2235_12.png | images/0705.2235_12.png | |||
0705.2235.pdf | 13 | [{"type": "image", "coordinates": [112, 32, 538, 309], "content": "", "block_type": "image", "index": 1}, {"type": "image", "coordinates": [113, 401, 538, 670], "content": "", "block_type": "image", "index": 2}] | [] | [{"coordinates": [112, 32, 538, 309], "index": 2.25, "caption": "Earthquake at Barkot (NE) for", "caption_coordinates": [120, 333, 491, 360]}, {"coordinates": [113, 401, 538, 670], "index": 7.25, "caption": "Earthquake at Barkot (NE) for", "caption_coordinates": [117, 675, 494, 702]}] | [] | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/35b21614cc162a5d97e59ba5a4ccf90dd15f6267287e4fcfae8aa0f4e0ff67ad.jpg", "img_caption": ["Fig. 3(a). $80\\%$ Response comparison Between Neural and Desired of Chamoli Earthquake at Barkot (NE) for $\\scriptstyle{\\mathsf{o}=0.01}$ "], "img_footnote": [], "page_idx": 13}, {"type": "i... | [{"category_id": 3, "poly": [314.06085205078125, 1114.9306640625, 1496.668701171875, 1114.9306640625, 1496.668701171875, 1863.63330078125, 314.06085205078125, 1863.63330078125], "score": 0.9999971389770508}, {"category_id": 3, "poly": [313.37109375, 91.49817657470703, 1496.9283447265625, 91.49817657470703, 1496.9283447... | {"preproc_blocks": [{"type": "image", "bbox": [112, 32, 538, 309], "blocks": [{"type": "image_body", "bbox": [112, 32, 538, 309], "group_id": 0, "lines": [{"bbox": [112, 32, 538, 309], "spans": [{"bbox": [112, 32, 538, 309], "score": 0.9999915957450867, "type": "image", "image_path": "35b21614cc162a5d97e59ba5a4ccf90dd1... | ./arxiv_full_mineru_outputs_20/images/0705.2235_13.png | images/0705.2235_13.png | |||
0705.2235.pdf | 14 | [{"type": "image", "coordinates": [90, 31, 522, 302], "content": "", "block_type": "image", "index": 1}, {"type": "image", "coordinates": [90, 376, 521, 649], "content": "", "block_type": "image", "index": 2}] | [] | [{"coordinates": [90, 31, 522, 302], "index": 2.25, "caption": "of Chamoli Earthquake at Barkot (NE) for ", "caption_coordinates": [129, 319, 483, 346]}, {"coordinates": [90, 376, 521, 649], "index": 7.25, "caption": "of Chamoli Earthquake at Barkot (NE) for", "caption_coordinates": [129, 662, 483, 689]}] | [] | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/ff7bd97a20a9021cd501f254d7e047d4d90600c0c8db4f889fc1ed2b4c256167.jpg", "img_caption": ["Fig. 4(a). Response Comparison Between Neural and Desired (550 points) of Chamoli Earthquake at Barkot (NE) for $\\scriptstyle{\\mathtt{o o=0.01}}$ "], "img_footnote": [], "page_idx": 14}, {"ty... | [{"category_id": 3, "poly": [251.791748046875, 87.11904907226562, 1450.8890380859375, 87.11904907226562, 1450.8890380859375, 840.0170288085938, 251.791748046875, 840.0170288085938], "score": 0.9999956488609314}, {"category_id": 3, "poly": [250.3185577392578, 1044.7945556640625, 1448.4510498046875, 1044.7945556640625, 1... | {"preproc_blocks": [{"type": "image", "bbox": [90, 31, 522, 302], "blocks": [{"type": "image_body", "bbox": [90, 31, 522, 302], "group_id": 0, "lines": [{"bbox": [90, 31, 522, 302], "spans": [{"bbox": [90, 31, 522, 302], "score": 0.9999956488609314, "type": "image", "image_path": "ff7bd97a20a9021cd501f254d7e047d4d90600... | ./arxiv_full_mineru_outputs_20/images/0705.2235_14.png | images/0705.2235_14.png | |||
0705.2235.pdf | 15 | [{"type": "image", "coordinates": [90, 33, 520, 304], "content": "", "block_type": "image", "index": 1}, {"type": "image", "coordinates": [91, 388, 520, 661], "content": "", "block_type": "image", "index": 2}] | [] | [{"coordinates": [90, 33, 520, 304], "index": 2.5, "caption": "(After training from 550 points)", "caption_coordinates": [147, 320, 468, 358]}, {"coordinates": [91, 388, 520, 661], "index": 8.5, "caption": "(After training from 550 points)", "caption_coordinates": [147, 678, 465, 715]}] | [] | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/029d7ec075dd32efcc0fddcdf2b90a43e430c6e37edefb3cb4a70b80417b2f50.jpg", "img_caption": ["Fig. 5(a). $\\pmb{120\\%}$ Response Comparison Between Neural and Desired of Chamoli Earthquake at Barkot (NE) (748 points) $\\scriptstyle{\\tt o-o-o-1}$ (After training from 550 points) "], "i... | [{"category_id": 3, "poly": [253.24671936035156, 1079.178955078125, 1444.684814453125, 1079.178955078125, 1444.684814453125, 1836.515625, 253.24671936035156, 1836.515625], "score": 0.9999974966049194}, {"category_id": 3, "poly": [251.5133514404297, 92.86186981201172, 1445.9345703125, 92.86186981201172, 1445.9345703125,... | {"preproc_blocks": [{"type": "image", "bbox": [90, 33, 520, 304], "blocks": [{"type": "image_body", "bbox": [90, 33, 520, 304], "group_id": 0, "lines": [{"bbox": [90, 33, 520, 304], "spans": [{"bbox": [90, 33, 520, 304], "score": 0.9999968409538269, "type": "image", "image_path": "029d7ec075dd32efcc0fddcdf2b90a43e430c6... | ./arxiv_full_mineru_outputs_20/images/0705.2235_15.png | images/0705.2235_15.png | |||
0705.2235.pdf | 16 | [{"type": "image", "coordinates": [155, 20, 447, 206], "content": "", "block_type": "image", "index": 1}, {"type": "image", "coordinates": [155, 253, 447, 444], "content": "", "block_type": "image", "index": 2}, {"type": "image", "coordinates": [154, 507, 447, 683], "content": "", "block_type": "image", "index": 3}] | [] | [{"coordinates": [155, 20, 447, 206], "index": 2.25, "caption": "Earthquake at Barkot (NE)with Damping", "caption_coordinates": [118, 210, 493, 235]}, {"coordinates": [155, 253, 447, 444], "index": 7.25, "caption": "Earthquake at Barkot (NE) with Damping", "caption_coordinates": [120, 448, 490, 473]}, {"coordinates": [... | [] | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/10dccda9a837088ee125cda6a0eeefa6325724270a653fe9d5aaf2249b164b91.jpg", "img_caption": ["Fig.6(a). $100\\%$ Response Comparison Between Neural and Desired of Chamoli Earthquake at Barkot (NE)with Damping "], "img_footnote": [], "page_idx": 16}, {"type": "image", "img_path": "images... | [{"category_id": 3, "poly": [430.1962585449219, 1411.041259765625, 1243.5765380859375, 1411.041259765625, 1243.5765380859375, 1898.6932373046875, 430.1962585449219, 1898.6932373046875], "score": 0.9999980926513672}, {"category_id": 3, "poly": [430.84576416015625, 704.1519775390625, 1243.58935546875, 704.1519775390625, ... | {"preproc_blocks": [{"type": "image", "bbox": [155, 20, 447, 206], "blocks": [{"type": "image_body", "bbox": [155, 20, 447, 206], "group_id": 0, "lines": [{"bbox": [155, 20, 447, 206], "spans": [{"bbox": [155, 20, 447, 206], "score": 0.999992847442627, "type": "image", "image_path": "10dccda9a837088ee125cda6a0eeefa6325... | ./arxiv_full_mineru_outputs_20/images/0705.2235_16.png | images/0705.2235_16.png | |||
0705.2235.pdf | 17 | [{"type": "image", "coordinates": [92, 47, 533, 314], "content": "", "block_type": "image", "index": 1}, {"type": "image", "coordinates": [90, 389, 535, 660], "content": "", "block_type": "image", "index": 2}] | [] | [{"coordinates": [92, 47, 533, 314], "index": 2.5, "caption": "Barkot in NW direction ( 620 points ) ", "caption_coordinates": [127, 325, 484, 363]}, {"coordinates": [90, 389, 535, 660], "index": 8.5, "caption": "Tehri in NW direction ( From weights of 620 points ) ", "caption_coordinates": [128, 673, 485, 710]}] | [] | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/ef363e0a06683216a3c247e3be84dfc91cf4cff4ebac5b969ed347b986871593.jpg", "img_caption": ["Fig. 7(a). Comparison Between Neural and Desired for time period and the corresponding maximum response of Uttarkashi earthquake at Barkot in NW direction ( 620 points ) "], "img_footnote": [],... | [{"category_id": 4, "poly": [357.9667053222656, 1871.744384765625, 1347.283203125, 1871.744384765625, 1347.283203125, 1973.642578125, 357.9667053222656, 1973.642578125], "score": 0.999994695186615}, {"category_id": 3, "poly": [252.19757080078125, 1080.97119140625, 1486.6680908203125, 1080.97119140625, 1486.668090820312... | {"preproc_blocks": [{"type": "image", "bbox": [92, 47, 533, 314], "blocks": [{"type": "image_body", "bbox": [92, 47, 533, 314], "group_id": 0, "lines": [{"bbox": [92, 47, 533, 314], "spans": [{"bbox": [92, 47, 533, 314], "score": 0.9999935030937195, "type": "image", "image_path": "ef363e0a06683216a3c247e3be84dfc91cf4cf... | ./arxiv_full_mineru_outputs_20/images/0705.2235_17.png | images/0705.2235_17.png | |||
0705.2236.pdf | 0 | # Fault Classification using Pseudomodal Energies and
Neuro-fuzzy modelling
# TSHILIDZI MARWALA, THANDO TETTEY AND SNEHASHISH
# CHAKRAVERTY
# ABSTRACT:
This paper presents a fault classification method which makes use of a Takagi-Sugeno
neuro-fuzzy model and Pseudomodal energies calculated from the vibration signal... | <h1>Fault Classification using Pseudomodal Energies and
Neuro-fuzzy modelling</h1>
<h1>TSHILIDZI MARWALA, THANDO TETTEY AND SNEHASHISH</h1>
<h1>CHAKRAVERTY</h1>
<h1>ABSTRACT:</h1>
<p>This paper presents a fault classification method which makes use of a Takagi-Sugeno
neuro-fuzzy model and Pseudomodal energies calculate... | [{"type": "title", "coordinates": [84, 89, 511, 140], "content": "Fault Classification using Pseudomodal Energies and\nNeuro-fuzzy modelling", "block_type": "title", "index": 1}, {"type": "title", "coordinates": [84, 162, 512, 180], "content": "TSHILIDZI MARWALA, THANDO TETTEY AND SNEHASHISH", "block_type": "title", "i... | [{"type": "text", "coordinates": [84, 92, 511, 111], "content": "Fault Classification using Pseudomodal Energies and", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 120, 261, 141], "content": "Neuro-fuzzy modelling", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [85, 166, 511, 180], "cont... | [] | [{"type": "inline", "coordinates": [392, 388, 430, 401], "content": "91.62\\%", "caption": ""}] | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "Fault Classification using Pseudomodal Energies and Neuro-fuzzy modelling ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "TSHILIDZI MARWALA, THANDO TETTEY AND SNEHASHISH ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "CHAKRAVERTY ", "text_level": 1, "page_idx": 0},... | [{"category_id": 1, "poly": [236.21163940429688, 717.38037109375, 1422.6712646484375, 717.38037109375, 1422.6712646484375, 1159.4283447265625, 236.21163940429688, 1159.4283447265625], "score": 0.9999871253967285}, {"category_id": 1, "poly": [236.50067138671875, 1274.823974609375, 1422.025390625, 1274.823974609375, 1422... | {"preproc_blocks": [{"type": "title", "bbox": [84, 89, 511, 140], "lines": [{"bbox": [84, 92, 511, 111], "spans": [{"bbox": [84, 92, 511, 111], "score": 1.0, "content": "Fault Classification using Pseudomodal Energies and", "type": "text"}], "index": 0}, {"bbox": [84, 120, 261, 141], "spans": [{"bbox": [84, 120, 261, 1... | ./arxiv_full_mineru_outputs_20/images/0705.2236_0.png | images/0705.2236_0.png | |
0705.2236.pdf | 1 | From the frequency domain data, and sometimes directly from the time domain, the
modal properties may be extracted. All of these domains theoretically contain similar
information but in reality this is not necessarily the case. Because the time domain data
are relatively difficult to interpret, they have not been use... | <p>From the frequency domain data, and sometimes directly from the time domain, the
modal properties may be extracted. All of these domains theoretically contain similar
information but in reality this is not necessarily the case. Because the time domain data
are relatively difficult to interpret, they have not been ... | [{"type": "text", "coordinates": [83, 99, 513, 216], "content": "From the frequency domain data, and sometimes directly from the time domain, the\nmodal properties may be extracted. All of these domains theoretically contain similar\ninformation but in reality this is not necessarily the case. Because the time domain... | [{"type": "text", "coordinates": [84, 101, 511, 114], "content": "From the frequency domain data, and sometimes directly from the time domain, the", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 116, 511, 129], "content": "modal properties may be extracted. All of these domains theoretically contain ... | [] | [{"type": "block", "coordinates": [183, 521, 362, 555], "content": "", "caption": ""}, {"type": "inline", "coordinates": [137, 568, 149, 582], "content": "a_{{\\scriptscriptstyle q}}", "caption": ""}, {"type": "inline", "coordinates": [173, 567, 184, 582], "content": "b_{q}", "caption": ""}, {"type": "inline", "coordin... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "From the frequency domain data, and sometimes directly from the time domain, the modal properties may be extracted. All of these domains theoretically contain similar information but in reality this is not necessarily the case. Because the time domain data are relatively difficult to interp... | [{"category_id": 0, "poly": [234.4219970703125, 718.037353515625, 564.198486328125, 718.037353515625, 564.198486328125, 759.1627197265625, 234.4219970703125, 759.1627197265625], "score": 0.9999966621398926}, {"category_id": 1, "poly": [233.9857635498047, 1078.135009765625, 1422.087646484375, 1078.135009765625, 1422.087... | {"preproc_blocks": [{"type": "text", "bbox": [83, 99, 513, 216], "lines": [{"bbox": [84, 101, 511, 114], "spans": [{"bbox": [84, 101, 511, 114], "score": 1.0, "content": "From the frequency domain data, and sometimes directly from the time domain, the", "type": "text"}], "index": 0}, {"bbox": [85, 116, 511, 129], "span... | ./arxiv_full_mineru_outputs_20/images/0705.2236_1.png | images/0705.2236_1.png | |
0705.2236.pdf | 2 | limited by the number of modes identified; and integrating the FRFs to obtain the
pseudomodal energies smoothes out the zero-mean noise present in the FRFs.
# Neuro-fuzzy modelling
A fuzzy inference system is a model that takes a fuzzy set as an input and performs a
composition to arrive at the output based on the co... | <p>limited by the number of modes identified; and integrating the FRFs to obtain the
pseudomodal energies smoothes out the zero-mean noise present in the FRFs.</p>
<h1>Neuro-fuzzy modelling</h1>
<p>A fuzzy inference system is a model that takes a fuzzy set as an input and performs a
composition to arrive at the output ... | [{"type": "text", "coordinates": [83, 84, 512, 114], "content": "limited by the number of modes identified; and integrating the FRFs to obtain the\npseudomodal energies smoothes out the zero-mean noise present in the FRFs.", "block_type": "text", "index": 1}, {"type": "title", "coordinates": [84, 128, 204, 143], "conte... | [{"type": "text", "coordinates": [83, 86, 512, 101], "content": "limited by the number of modes identified; and integrating the FRFs to obtain the ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 101, 458, 115], "content": "pseudomodal energies smoothes out the zero-mean noise present in the FRFs.", "... | [] | [{"type": "block", "coordinates": [209, 291, 403, 309], "content": "", "caption": ""}, {"type": "block", "coordinates": [353, 420, 440, 441], "content": "", "caption": ""}, {"type": "block", "coordinates": [237, 478, 395, 512], "content": "", "caption": ""}, {"type": "block", "coordinates": [228, 564, 397, 627], "conte... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "Neuro-fuzzy modelling ", "text_level": 1, "page_idx": 2}, {"type": "text", "text": "A fuzzy inference system is a model that takes a fuzzy set as an input and performs a composition to arrive at the output based on the concepts of fuzzy set theory,... | [{"category_id": 8, "poly": [637.3903198242188, 1573.8046875, 1101.441650390625, 1573.8046875, 1101.441650390625, 1743.1895751953125, 637.3903198242188, 1743.1895751953125], "score": 0.9999980330467224}, {"category_id": 8, "poly": [662.12451171875, 1335.854248046875, 1095.0382080078125, 1335.854248046875, 1095.03820800... | {"preproc_blocks": [{"type": "text", "bbox": [83, 84, 512, 114], "lines": [{"bbox": [83, 86, 512, 101], "spans": [{"bbox": [83, 86, 512, 101], "score": 1.0, "content": "limited by the number of modes identified; and integrating the FRFs to obtain the ", "type": "text"}], "index": 0}, {"bbox": [84, 101, 458, 115], "span... | ./arxiv_full_mineru_outputs_20/images/0705.2236_2.png | images/0705.2236_2.png | |
0705.2236.pdf | 3 | 1. Fuzzy rules may be extracted from expert knowledge and used to create an initial
model. The parameters of the model can then be fine tuned using data collected
from the operational system being modelled.
2. The number of rules can be determined from collected numerical data using a
model selection technique. The p... | <p>1. Fuzzy rules may be extracted from expert knowledge and used to create an initial
model. The parameters of the model can then be fine tuned using data collected
from the operational system being modelled.
2. The number of rules can be determined from collected numerical data using a
model selection technique. Th... | [{"type": "text", "coordinates": [101, 84, 514, 173], "content": "1. Fuzzy rules may be extracted from expert knowledge and used to create an initial\nmodel. The parameters of the model can then be fine tuned using data collected\nfrom the operational system being modelled.\n2. The number of rules can be determined f... | [{"type": "text", "coordinates": [102, 86, 512, 101], "content": "1. Fuzzy rules may be extracted from expert knowledge and used to create an initial ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [119, 101, 511, 115], "content": "model. The parameters of the model can then be fine tuned using data coll... | [] | [{"type": "inline", "coordinates": [225, 374, 247, 386], "content": "0\\mathrm{Hz}", "caption": ""}, {"type": "inline", "coordinates": [421, 416, 454, 430], "content": "100\\mathrm{Hz}", "caption": ""}, {"type": "inline", "coordinates": [352, 431, 387, 444], "content": "300\\mathrm{Hz}", "caption": ""}, {"type": "inlin... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "1. Fuzzy rules may be extracted from expert knowledge and used to create an initial model. The parameters of the model can then be fine tuned using data collected from the operational system being modelled. \n2. The number of rules can be determined from collected numerical data using a m... | [{"category_id": 1, "poly": [229.60104370117188, 1677.5645751953125, 1425.9573974609375, 1677.5645751953125, 1425.9573974609375, 2081.281005859375, 229.60104370117188, 2081.281005859375], "score": 0.999993085861206}, {"category_id": 1, "poly": [282.38922119140625, 235.05059814453125, 1427.88134765625, 235.0505981445312... | {"preproc_blocks": [{"type": "text", "bbox": [101, 84, 514, 173], "lines": [{"bbox": [102, 86, 512, 101], "spans": [{"bbox": [102, 86, 512, 101], "score": 1.0, "content": "1. Fuzzy rules may be extracted from expert knowledge and used to create an initial ", "type": "text"}], "index": 0}, {"bbox": [119, 101, 511, 115]... | ./arxiv_full_mineru_outputs_20/images/0705.2236_3.png | images/0705.2236_3.png | |
0705.2236.pdf | 4 | Each cylinder is measured three times under different boundary conditions by
changing the orientation of a rectangular sponge inserted inside the cylinder. The number
of sets of measurements taken for undamaged population is 60 (20 cylinders X 3 for
different boundary conditions).
The impulse and response data are pro... | <p>Each cylinder is measured three times under different boundary conditions by
changing the orientation of a rectangular sponge inserted inside the cylinder. The number
of sets of measurements taken for undamaged population is 60 (20 cylinders X 3 for
different boundary conditions).</p>
<p>The impulse and response dat... | [{"type": "text", "coordinates": [83, 84, 513, 142], "content": "Each cylinder is measured three times under different boundary conditions by\nchanging the orientation of a rectangular sponge inserted inside the cylinder. The number\nof sets of measurements taken for undamaged population is 60 (20 cylinders X 3 for\ndi... | [{"type": "text", "coordinates": [101, 86, 511, 101], "content": "Each cylinder is measured three times under different boundary conditions by", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 101, 511, 116], "content": "changing the orientation of a rectangular sponge inserted inside the cylinder. The ... | [{"coordinates": [181, 447, 417, 626], "index": 34.5, "caption": "Figure 1: A schematic diagram illustrating the set up of the experiment.", "caption_coordinates": [124, 633, 471, 648]}] | [{"type": "inline", "coordinates": [379, 215, 415, 228], "content": "1.22\\mathrm{Hz}", "caption": ""}, {"type": "inline", "coordinates": [415, 230, 433, 242], "content": "6\\%", "caption": ""}, {"type": "inline", "coordinates": [208, 388, 228, 400], "content": "\\textrm{X}2", "caption": ""}] | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "Each cylinder is measured three times under different boundary conditions by changing the orientation of a rectangular sponge inserted inside the cylinder. The number of sets of measurements taken for undamaged population is 60 (20 cylinders X 3 for different boundary conditions). ", "page_id... | [{"category_id": 4, "poly": [344.74664306640625, 1760.47705078125, 1308.577392578125, 1760.47705078125, 1308.577392578125, 1800.829833984375, 344.74664306640625, 1800.829833984375], "score": 0.9999966025352478}, {"category_id": 3, "poly": [502.41046142578125, 1244.031005859375, 1159.1702880859375, 1244.031005859375, 11... | {"preproc_blocks": [{"type": "text", "bbox": [83, 84, 513, 142], "lines": [{"bbox": [101, 86, 511, 101], "spans": [{"bbox": [101, 86, 511, 101], "score": 1.0, "content": "Each cylinder is measured three times under different boundary conditions by", "type": "text"}], "index": 0}, {"bbox": [85, 101, 511, 116], "spans": ... | ./arxiv_full_mineru_outputs_20/images/0705.2236_4.png | images/0705.2236_4.png | |
0705.2236.pdf | 5 | optimum number of rules in the model has been determined by evaluating models with
between one and ten fuzzy rules. The optimum number of rules is found to be four as it
gives a low prediction error together with a small standard deviation. The remaining
parameters of the neuro-fuzzy model are optimised using a combina... | <p>optimum number of rules in the model has been determined by evaluating models with
between one and ten fuzzy rules. The optimum number of rules is found to be four as it
gives a low prediction error together with a small standard deviation. The remaining
parameters of the neuro-fuzzy model are optimised using a comb... | [{"type": "text", "coordinates": [84, 85, 512, 158], "content": "optimum number of rules in the model has been determined by evaluating models with\nbetween one and ten fuzzy rules. The optimum number of rules is found to be four as it\ngives a low prediction error together with a small standard deviation. The remainin... | [{"type": "text", "coordinates": [85, 87, 512, 101], "content": "optimum number of rules in the model has been determined by evaluating models with ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [83, 100, 512, 116], "content": "between one and ten fuzzy rules. The optimum number of rules is found to be f... | [] | [{"type": "block", "coordinates": [127, 336, 352, 366], "content": "", "caption": ""}, {"type": "block", "coordinates": [210, 393, 309, 408], "content": "", "caption": ""}, {"type": "block", "coordinates": [211, 437, 313, 452], "content": "", "caption": ""}, {"type": "inline", "coordinates": [472, 477, 479, 486], "cont... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "", "page_idx": 5}, {"type": "text", "text": "Threshold determination ", "text_level": 1, "page_idx": 5}, {"type": "text", "text": "For a given input set, the neuro-fuzzy model gives an output of three decision values [x, y, z]. A correct classification must give the correct values of x, y and... | [{"category_id": 8, "poly": [586.5618286132812, 1091.9931640625, 860.3316040039062, 1091.9931640625, 860.3316040039062, 1136.156005859375, 586.5618286132812, 1136.156005859375], "score": 0.9999982714653015}, {"category_id": 8, "poly": [589.9351806640625, 1210.417724609375, 872.0121459960938, 1210.417724609375, 872.0121... | {"preproc_blocks": [{"type": "text", "bbox": [84, 85, 512, 158], "lines": [{"bbox": [85, 87, 512, 101], "spans": [{"bbox": [85, 87, 512, 101], "score": 1.0, "content": "optimum number of rules in the model has been determined by evaluating models with ", "type": "text"}], "index": 0}, {"bbox": [83, 100, 512, 116], "spa... | ./arxiv_full_mineru_outputs_20/images/0705.2236_5.png | images/0705.2236_5.png | |
0705.2236.pdf | 6 | expensive, is useful especially in the cases where modelling data is very limited.
Moreover, it has been shown that not only is the leave-one-out cross validation
generalisation estimate is a better measure, the worst-case error of this estimate is not
much worse than that of the training error estimate [8]. In our wor... | <p>expensive, is useful especially in the cases where modelling data is very limited.
Moreover, it has been shown that not only is the leave-one-out cross validation
generalisation estimate is a better measure, the worst-case error of this estimate is not
much worse than that of the training error estimate [8]. In our ... | [{"type": "text", "coordinates": [84, 85, 512, 171], "content": "expensive, is useful especially in the cases where modelling data is very limited.\nMoreover, it has been shown that not only is the leave-one-out cross validation\ngeneralisation estimate is a better measure, the worst-case error of this estimate is not\... | [{"type": "text", "coordinates": [85, 87, 510, 100], "content": "expensive, is useful especially in the cases where modelling data is very limited.", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 101, 510, 115], "content": "Moreover, it has been shown that not only is the leave-one-out cross validatio... | [{"coordinates": [186, 463, 399, 645], "index": 32.5, "caption": "trained neural network used by Marwala [2].", "caption_coordinates": [83, 679, 512, 710]}] | [] | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "", "page_idx": 6}, {"type": "text", "text": "RESULTS AND DISCUSSIONS ", "text_level": 1, "page_idx": 6}, {"type": "text", "text": "The classification result is assessed using the leave-one-out cross validation process described above. The performance of the TS neuro-fuzzy model is illustrated... | [{"category_id": 1, "poly": [234.984375, 237.14938354492188, 1422.8521728515625, 237.14938354492188, 1422.8521728515625, 477.208251953125, 234.984375, 477.208251953125], "score": 0.9999942779541016}, {"category_id": 3, "poly": [517.8548583984375, 1288.9334716796875, 1109.6368408203125, 1288.9334716796875, 1109.63684082... | {"preproc_blocks": [{"type": "text", "bbox": [84, 85, 512, 171], "lines": [{"bbox": [85, 87, 510, 100], "spans": [{"bbox": [85, 87, 510, 100], "score": 1.0, "content": "expensive, is useful especially in the cases where modelling data is very limited.", "type": "text"}], "index": 0}, {"bbox": [84, 101, 510, 115], "span... | ./arxiv_full_mineru_outputs_20/images/0705.2236_6.png | images/0705.2236_6.png | |
0705.2236.pdf | 7 | In this paper, pseudomodal properties obtained from the FRF have been calculated from
vibration signal measured from a population of cylindrical shells. These properties have
been used as inputs into a TS neuro-fuzzy model. A model selection process reveals that
the optimum number of fuzzy rules for accurate classifica... | <p>In this paper, pseudomodal properties obtained from the FRF have been calculated from
vibration signal measured from a population of cylindrical shells. These properties have
been used as inputs into a TS neuro-fuzzy model. A model selection process reveals that
the optimum number of fuzzy rules for accurate classif... | [{"type": "text", "coordinates": [83, 84, 513, 186], "content": "In this paper, pseudomodal properties obtained from the FRF have been calculated from\nvibration signal measured from a population of cylindrical shells. These properties have\nbeen used as inputs into a TS neuro-fuzzy model. A model selection process rev... | [{"type": "text", "coordinates": [84, 86, 512, 101], "content": "In this paper, pseudomodal properties obtained from the FRF have been calculated from ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 102, 511, 115], "content": "vibration signal measured from a population of cylindrical shells. These p... | [] | [{"type": "inline", "coordinates": [270, 157, 308, 170], "content": "91.42\\%", "caption": ""}, {"type": "inline", "coordinates": [243, 560, 260, 572], "content": "{10}^{\\mathrm{th}}", "caption": ""}] | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "In this paper, pseudomodal properties obtained from the FRF have been calculated from vibration signal measured from a population of cylindrical shells. These properties have been used as inputs into a TS neuro-fuzzy model. A model selection process reveals that the optimum number of fuzzy ru... | [{"category_id": 1, "poly": [232.20553588867188, 234.04356384277344, 1425.8946533203125, 234.04356384277344, 1425.8946533203125, 517.6708374023438, 232.20553588867188, 517.6708374023438], "score": 0.9999926090240479}, {"category_id": 0, "poly": [234.9279327392578, 831.750244140625, 464.7436828613281, 831.750244140625, ... | {"preproc_blocks": [{"type": "text", "bbox": [83, 84, 513, 186], "lines": [{"bbox": [84, 86, 512, 101], "spans": [{"bbox": [84, 86, 512, 101], "score": 1.0, "content": "In this paper, pseudomodal properties obtained from the FRF have been calculated from ", "type": "text"}], "index": 0}, {"bbox": [85, 102, 511, 115], "... | ./arxiv_full_mineru_outputs_20/images/0705.2236_7.png | images/0705.2236_7.png | |
0705.0197.pdf | 0 | # FAULT CLASSIFICATION IN CYLINDERS USING MULTI-
LAYER PERCEPTRONS, SUPPORT VECTOR MACHINES AND
GUASSIAN MIXTURE MODELS
Tshilidzi Marwalaa, Unathi Maholaa and Snehashish Chakravertyb
$$\pmb{a}$$ School of Electrical and Information Engineering
University of the Witwatersrand Private Bag x 3 Wits 2050 South Africa
e-m... | <h1>FAULT CLASSIFICATION IN CYLINDERS USING MULTI-
LAYER PERCEPTRONS, SUPPORT VECTOR MACHINES AND
GUASSIAN MIXTURE MODELS</h1>
<p>Tshilidzi Marwalaa, Unathi Maholaa and Snehashish Chakravertyb</p>
<p>$$\pmb{a}$$ School of Electrical and Information Engineering
University of the Witwatersrand Private Bag x 3 Wits 2050 S... | [{"type": "title", "coordinates": [93, 70, 502, 121], "content": "FAULT CLASSIFICATION IN CYLINDERS USING MULTI-\nLAYER PERCEPTRONS, SUPPORT VECTOR MACHINES AND\nGUASSIAN MIXTURE MODELS", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [125, 135, 470, 150], "content": "Tshilidzi Marwalaa, Unathi Mah... | [{"type": "text", "coordinates": [107, 74, 488, 86], "content": "FAULT CLASSIFICATION IN CYLINDERS USING MULTI-", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [94, 91, 500, 103], "content": "LAYER PERCEPTRONS, SUPPORT VECTOR MACHINES AND", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [194, 1... | [] | [{"type": "inline", "coordinates": [175, 152, 180, 163], "content": "\\pmb{a}", "caption": ""}, {"type": "inline", "coordinates": [169, 335, 193, 348], "content": "98\\%", "caption": ""}, {"type": "inline", "coordinates": [283, 335, 308, 348], "content": "94\\%", "caption": ""}, {"type": "inline", "coordinates": [130, ... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "FAULT CLASSIFICATION IN CYLINDERS USING MULTILAYER PERCEPTRONS, SUPPORT VECTOR MACHINES AND GUASSIAN MIXTURE MODELS ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Tshilidzi Marwalaa, Unathi Maholaa and Snehashish Chakravertyb ", "page_idx": 0}, {"type": "text", "text": "$\\pmb{... | [{"category_id": 1, "poly": [342.505615234375, 414.2729187011719, 1315.544677734375, 414.2729187011719, 1315.544677734375, 653.5216674804688, 342.505615234375, 653.5216674804688], "score": 0.9999967813491821}, {"category_id": 1, "poly": [235.11875915527344, 1420.1273193359375, 1420.7510986328125, 1420.1273193359375, 14... | {"preproc_blocks": [{"type": "title", "bbox": [93, 70, 502, 121], "lines": [{"bbox": [107, 74, 488, 86], "spans": [{"bbox": [107, 74, 488, 86], "score": 1.0, "content": "FAULT CLASSIFICATION IN CYLINDERS USING MULTI-", "type": "text"}], "index": 0}, {"bbox": [94, 91, 500, 103], "spans": [{"bbox": [94, 91, 500, 103], "s... | ./arxiv_full_mineru_outputs_20/images/0705.0197_0.png | images/0705.0197_0.png | |
0705.0197.pdf | 1 | shells [2,3,4]. The importance of fault identification process in a population of
nominally identical structures is particularly important in areas such as the automated
manufacturing process in the assembly line. Thus far various forms of neural networks
such as MLP and Bayesian neural networks have been successfull... | <p>shells [2,3,4]. The importance of fault identification process in a population of
nominally identical structures is particularly important in areas such as the automated
manufacturing process in the assembly line. Thus far various forms of neural networks
such as MLP and Bayesian neural networks have been successf... | [{"type": "text", "coordinates": [84, 70, 512, 199], "content": "shells [2,3,4]. The importance of fault identification process in a population of\nnominally identical structures is particularly important in areas such as the automated\nmanufacturing process in the assembly line. Thus far various forms of neural netw... | [{"type": "text", "coordinates": [84, 72, 513, 87], "content": "shells [2,3,4]. The importance of fault identification process in a population of ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 87, 512, 101], "content": "nominally identical structures is particularly important in areas such as the a... | [] | [{"type": "block", "coordinates": [84, 425, 324, 464], "content": "", "caption": ""}, {"type": "block", "coordinates": [84, 682, 212, 703], "content": "", "caption": ""}, {"type": "inline", "coordinates": [116, 471, 136, 489], "content": "\\mathbf{W}_{\\mathrm{ji}}^{(1)}", "caption": ""}, {"type": "inline", "coordinate... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "", "page_idx": 1}, {"type": "text", "text": "This paper is organized as follows: neural networks, SVMs and GMMs are summarized, experiment performed is discussed and results as well as conclusions are discussed. ", "page_idx": 1}, {"type": "text", "text": "2. NEURAL NETWORKS ", "text_level": ... | [{"category_id": 1, "poly": [234.27764892578125, 197.02883911132812, 1423.5198974609375, 197.02883911132812, 1423.5198974609375, 554.3274536132812, 234.27764892578125, 554.3274536132812], "score": 0.9999954104423523}, {"category_id": 9, "poly": [1314.706787109375, 1218.9315185546875, 1359.408935546875, 1218.93151855468... | {"preproc_blocks": [{"type": "text", "bbox": [84, 70, 512, 199], "lines": [{"bbox": [84, 72, 513, 87], "spans": [{"bbox": [84, 72, 513, 87], "score": 1.0, "content": "shells [2,3,4]. The importance of fault identification process in a population of ", "type": "text"}], "index": 0}, {"bbox": [84, 87, 512, 101], "spans"... | ./arxiv_full_mineru_outputs_20/images/0705.0197_1.png | images/0705.0197_1.png | |
0705.0197.pdf | 2 | where $$\mathrm{h}\in\mathrm{N}^{+}$$ is the Vapnik-Chervonenkis (VC) dimension of $$\mathrm{f}\!\in\!\mathrm{F}$$ and $$\updelta>0$$ holds true
for all δ. The VC dimension of a function class $$\mathrm{F}$$ is defined as the largest number $$_\mathrm{h}$$ of
points that can be separated in all possible ways using func... | <p>where $$\mathrm{h}\in\mathrm{N}^{+}$$ is the Vapnik-Chervonenkis (VC) dimension of $$\mathrm{f}\!\in\!\mathrm{F}$$ and $$\updelta>0$$ holds true
for all δ. The VC dimension of a function class $$\mathrm{F}$$ is defined as the largest number $$_\mathrm{h}$$ of
points that can be separated in all possible ways using f... | [{"type": "interline_equation", "coordinates": [84, 70, 304, 113], "content": "", "block_type": "interline_equation", "index": 1}, {"type": "text", "coordinates": [83, 115, 513, 172], "content": "where $$\\mathrm{h}\\in\\mathrm{N}^{+}$$ is the Vapnik-Chervonenkis (VC) dimension of $$\\mathrm{f}\\!\\in\\!\\mathrm{F}$$ a... | [{"type": "interline_equation", "coordinates": [84, 70, 304, 113], "content": "\\mathrm{R}[\\mathrm{f}]=\\mathrm{R}[\\mathrm{f}]_{\\mathrm{emp}}+\\sqrt{\\left.\\mathrm{h}(\\mathrm{in}\\,\\frac{2\\mathrm{n}}{\\mathrm{h}}+1)-\\mathrm{ln}(8/4)\\right\\rangle_{\\mathrm{n}}}^{\\prime}", "score": 0.59, "index": 1}, {"type": ... | [{"coordinates": [145, 279, 392, 461], "index": 12.75, "caption": ".[13]", "caption_coordinates": [83, 463, 514, 521]}] | [{"type": "block", "coordinates": [84, 70, 304, 113], "content": "", "caption": ""}, {"type": "block", "coordinates": [84, 172, 214, 204], "content": "", "caption": ""}, {"type": "block", "coordinates": [84, 220, 301, 238], "content": "", "caption": ""}, {"type": "block", "coordinates": [85, 649, 222, 664], "content": ... | [] | [595.219970703125, 842.0] | [{"type": "equation", "text": "$$\n\\mathrm{R}[\\mathrm{f}]=\\mathrm{R}[\\mathrm{f}]_{\\mathrm{emp}}+\\sqrt{\\left.\\mathrm{h}(\\mathrm{in}\\,\\frac{2\\mathrm{n}}{\\mathrm{h}}+1)-\\mathrm{ln}(8/4)\\right\\rangle_{\\mathrm{n}}}^{\\prime}\n$$", "text_format": "latex", "page_idx": 2}, {"type": "text", "text": "where $\\ma... | [{"category_id": 8, "poly": [240.40264892578125, 1993.679931640625, 419.4319152832031, 1993.679931640625, 419.4319152832031, 2069.587646484375, 240.40264892578125, 2069.587646484375], "score": 0.9999997019767761}, {"category_id": 8, "poly": [235.44248962402344, 1803.4287109375, 618.8136596679688, 1803.4287109375, 618.8... | {"preproc_blocks": [{"type": "interline_equation", "bbox": [84, 70, 304, 113], "lines": [{"bbox": [84, 70, 304, 113], "spans": [{"bbox": [84, 70, 304, 113], "score": 0.59, "content": "\\mathrm{R}[\\mathrm{f}]=\\mathrm{R}[\\mathrm{f}]_{\\mathrm{emp}}+\\sqrt{\\left.\\mathrm{h}(\\mathrm{in}\\,\\frac{2\\mathrm{n}}{\\mathrm... | ./arxiv_full_mineru_outputs_20/images/0705.0197_2.png | images/0705.0197_2.png | |
0705.0197.pdf | 3 | However, assuming that we can only access the feature space using only dot products,
equation 7 is transformed into a dual optimization problem by introducing Lagrangian
multipliers $${\mathfrak{a}}_{\mathrm{i}}{\mathrm{i}}=1,\;2,\;...,\;{\mathrm{n}}$$ and doing some minimisation, maximisation and saddle
point property... | <p>However, assuming that we can only access the feature space using only dot products,
equation 7 is transformed into a dual optimization problem by introducing Lagrangian
multipliers $${\mathfrak{a}}_{\mathrm{i}}{\mathrm{i}}=1,\;2,\;...,\;{\mathrm{n}}$$ and doing some minimisation, maximisation and saddle
point prope... | [{"type": "text", "coordinates": [84, 71, 512, 128], "content": "However, assuming that we can only access the feature space using only dot products,\nequation 7 is transformed into a dual optimization problem by introducing Lagrangian\nmultipliers $${\\mathfrak{a}}_{\\mathrm{i}}{\\mathrm{i}}=1,\\;2,\\;...,\\;{\\mathrm... | [{"type": "text", "coordinates": [84, 71, 510, 87], "content": "However, assuming that we can only access the feature space using only dot products,", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 87, 510, 101], "content": "equation 7 is transformed into a dual optimization problem by introducing Lagr... | [] | [{"type": "block", "coordinates": [85, 128, 265, 161], "content": "", "caption": ""}, {"type": "block", "coordinates": [85, 182, 179, 227], "content": "", "caption": ""}, {"type": "block", "coordinates": [83, 269, 269, 340], "content": "", "caption": ""}, {"type": "block", "coordinates": [84, 369, 303, 385], "content":... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "However, assuming that we can only access the feature space using only dot products, equation 7 is transformed into a dual optimization problem by introducing Lagrangian multipliers ${\\mathfrak{a}}_{\\mathrm{i}}{\\mathrm{i}}=1,\\;2,\\;...,\\;{\\mathrm{n}}$ and doing some minimisation, maximi... | [{"category_id": 9, "poly": [1315.5850830078125, 828.2252807617188, 1359.3095703125, 828.2252807617188, 1359.3095703125, 863.4547119140625, 1315.5850830078125, 863.4547119140625], "score": 0.9999914169311523}, {"category_id": 9, "poly": [1316.322509765625, 1185.2427978515625, 1376.21484375, 1185.2427978515625, 1376.214... | {"preproc_blocks": [{"type": "text", "bbox": [84, 71, 512, 128], "lines": [{"bbox": [84, 71, 510, 87], "spans": [{"bbox": [84, 71, 510, 87], "score": 1.0, "content": "However, assuming that we can only access the feature space using only dot products,", "type": "text"}], "index": 0}, {"bbox": [84, 87, 510, 101], "spans... | ./arxiv_full_mineru_outputs_20/images/0705.0197_3.png | images/0705.0197_3.png | |
0705.0197.pdf | 4 | the EM algorithm is used since it has reasonable fast computational time when
compared to other algorithms. The EM algorithm finds the optimum model parameters
by iteratively refining GMM parameters to increase the likelihood of the estimated
model for the given fault feature modal vector. For the EM equations for trai... | <p>the EM algorithm is used since it has reasonable fast computational time when
compared to other algorithms. The EM algorithm finds the optimum model parameters
by iteratively refining GMM parameters to increase the likelihood of the estimated
model for the given fault feature modal vector. For the EM equations for t... | [{"type": "text", "coordinates": [84, 70, 512, 169], "content": "the EM algorithm is used since it has reasonable fast computational time when\ncompared to other algorithms. The EM algorithm finds the optimum model parameters\nby iteratively refining GMM parameters to increase the likelihood of the estimated\nmodel for... | [{"type": "text", "coordinates": [84, 72, 510, 85], "content": "the EM algorithm is used since it has reasonable fast computational time when", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 87, 512, 100], "content": "compared to other algorithms. The EM algorithm finds the optimum model parameters ", ... | [] | [{"type": "block", "coordinates": [84, 169, 212, 202], "content": "", "caption": ""}, {"type": "block", "coordinates": [85, 247, 186, 280], "content": "", "caption": ""}, {"type": "block", "coordinates": [84, 294, 350, 326], "content": "", "caption": ""}, {"type": "inline", "coordinates": [389, 205, 474, 218], "content... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "", "page_idx": 4}, {"type": "equation", "text": "$$\n\\hat{\\mathbf{s}}\\!=\\!\\arg\\operatorname*{max}_{\\mathrm{1\\leqf\\leqF}}\\sum_{\\mathrm{k=l}}^{\\mathrm{K}}\\!\\log\\mathrm{p(x_{\\mathrm{k}}\\mid\\lambda_{\\mathrm{f}})}\n$$", "text_format": "latex", "page_idx": 4}, {"type": "text", "t... | [{"category_id": 8, "poly": [236.37704467773438, 695.2887573242188, 517.1423950195312, 695.2887573242188, 517.1423950195312, 778.10009765625, 236.37704467773438, 778.10009765625], "score": 0.999996542930603}, {"category_id": 8, "poly": [232.93252563476562, 821.719482421875, 971.5743408203125, 821.719482421875, 971.5743... | {"preproc_blocks": [{"type": "text", "bbox": [84, 70, 512, 169], "lines": [{"bbox": [84, 72, 510, 85], "spans": [{"bbox": [84, 72, 510, 85], "score": 1.0, "content": "the EM algorithm is used since it has reasonable fast computational time when", "type": "text"}], "index": 0}, {"bbox": [84, 87, 512, 100], "spans": [{"b... | ./arxiv_full_mineru_outputs_20/images/0705.0197_4.png | images/0705.0197_4.png | |
0705.0197.pdf | 5 | where [M], [C] and [K] are the mass, damping and stiffness matrices respectively, and
$$\{{\mathbf X}\}$$ , $$\{{\mathbf X^{\prime}}\}$$ and $$\{{X^{\prime\prime}}\}$$ are the displacement, velocity and acceleration vectors,
respectively, while {F} is the applied force vector. If equation 17 is transformed into
... | <p>where [M], [C] and [K] are the mass, damping and stiffness matrices respectively, and
$$\{{\mathbf X}\}$$ , $$\{{\mathbf X^{\prime}}\}$$ and $$\{{X^{\prime\prime}}\}$$ are the displacement, velocity and acceleration vectors,
respectively, while {F} is the applied force vector. If equation 17 is transformed in... | [{"type": "text", "coordinates": [83, 87, 512, 146], "content": "where [M], [C] and [K] are the mass, damping and stiffness matrices respectively, and\n$$\\{{\\mathbf X}\\}$$ , $$\\{{\\mathbf X^{\\prime}}\\}$$ and $$\\{{X^{\\prime\\prime}}\\}$$ are the displacement, velocity and acceleration vectors,\nrespectivel... | [{"type": "text", "coordinates": [85, 89, 511, 102], "content": "where [M], [C] and [K] are the mass, damping and stiffness matrices respectively, and", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [84, 102, 105, 116], "content": "\\{{\\mathbf X}\\}", "score": 0.49, "index": 2}, {"type": "text"... | [{"coordinates": [127, 478, 466, 702], "index": 23.25, "caption": "accelerometer, substructures, fault position and supporting sponge.", "caption_coordinates": [109, 722, 486, 749]}] | [{"type": "block", "coordinates": [85, 145, 252, 164], "content": "", "caption": ""}, {"type": "inline", "coordinates": [84, 102, 105, 116], "content": "\\{{\\mathbf X}\\}", "caption": ""}, {"type": "inline", "coordinates": [116, 102, 140, 116], "content": "\\{{\\mathbf X^{\\prime}}\\}", "caption": ""}, {"type": "inlin... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "where [M], [C] and [K] are the mass, damping and stiffness matrices respectively, and $\\{{\\mathbf X}\\}$ , $\\{{\\mathbf X^{\\prime}}\\}$ and $\\{{X^{\\prime\\prime}}\\}$ are the displacement, velocity and acceleration vectors, respectively, while {F} is the applied force vector. If ... | [{"category_id": 1, "poly": [234.6791229248047, 467.92218017578125, 1425.390380859375, 467.92218017578125, 1425.390380859375, 690.5120239257812, 234.6791229248047, 690.5120239257812], "score": 0.9999892115592957}, {"category_id": 3, "poly": [354.818603515625, 1328.517333984375, 1294.75146484375, 1328.517333984375, 1294... | {"preproc_blocks": [{"type": "text", "bbox": [83, 87, 512, 146], "lines": [{"bbox": [85, 89, 511, 102], "spans": [{"bbox": [85, 89, 511, 102], "score": 1.0, "content": "where [M], [C] and [K] are the mass, damping and stiffness matrices respectively, and", "type": "text"}], "index": 0}, {"bbox": [84, 102, 512, 118], "s... | ./arxiv_full_mineru_outputs_20/images/0705.0197_5.png | images/0705.0197_5.png | |
0705.0197.pdf | 6 | For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given
the identity [0 0 0], indicating that there are no faults in any of the three substructures.
The second type of fault is a one-fault-scenario, where a hole may be located in any of
the three substructures. Three possible on... | <p>For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given
the identity [0 0 0], indicating that there are no faults in any of the three substructures.
The second type of fault is a one-fault-scenario, where a hole may be located in any of
the three substructures. Three possible... | [{"type": "text", "coordinates": [84, 71, 512, 213], "content": "For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given\nthe identity [0 0 0], indicating that there are no faults in any of the three substructures.\nThe second type of fault is a one-fault-scenario, where a hole m... | [{"type": "text", "coordinates": [83, 72, 510, 86], "content": "For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 87, 509, 99], "content": "the identity [0 0 0], indicating that there are no faults in any of ... | [] | [{"type": "inline", "coordinates": [490, 114, 511, 127], "content": "[0\\,0", "caption": ""}, {"type": "inline", "coordinates": [490, 185, 511, 198], "content": "[0\\,0", "caption": ""}, {"type": "inline", "coordinates": [428, 256, 447, 268], "content": "\\times\\,3", "caption": ""}, {"type": "inline", "coordinates": [... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given the identity [0 0 0], indicating that there are no faults in any of the three substructures. The second type of fault is a one-fault-scenario, where a hole may be located in any of the three substr... | [{"category_id": 1, "poly": [235.1701202392578, 197.56771850585938, 1423.1878662109375, 197.56771850585938, 1423.1878662109375, 592.3051147460938, 235.1701202392578, 592.3051147460938], "score": 0.9999942183494568}, {"category_id": 1, "poly": [235.0725860595703, 1351.6007080078125, 1422.263671875, 1351.6007080078125, 1... | {"preproc_blocks": [{"type": "text", "bbox": [84, 71, 512, 213], "lines": [{"bbox": [83, 72, 510, 86], "spans": [{"bbox": [83, 72, 510, 86], "score": 1.0, "content": "For one cylinder the first type of fault is a zero-fault scenario. This type of fault is given", "type": "text"}], "index": 0}, {"bbox": [85, 87, 509, 9... | ./arxiv_full_mineru_outputs_20/images/0705.0197_6.png | images/0705.0197_6.png | |
0705.0197.pdf | 7 | by the total number of cases can be misleading. This is the case if the fault cases
classified incorrectly are those from the less numerous cases. To remedy this situation a
measure of accuracy called geometrical accuracy (GA) is used and defined as:
where $$\Pi$$ is the product, $$\mathsf{c}_{\mathrm{n}}$$ is the nu... | <p>by the total number of cases can be misleading. This is the case if the fault cases
classified incorrectly are those from the less numerous cases. To remedy this situation a
measure of accuracy called geometrical accuracy (GA) is used and defined as:</p>
<p>where $$\Pi$$ is the product, $$\mathsf{c}_{\mathrm{n}}$$ ... | [{"type": "text", "coordinates": [83, 70, 512, 113], "content": "by the total number of cases can be misleading. This is the case if the fault cases\nclassified incorrectly are those from the less numerous cases. To remedy this situation a\nmeasure of accuracy called geometrical accuracy (GA) is used and defined as:",... | [{"type": "text", "coordinates": [84, 72, 511, 86], "content": "by the total number of cases can be misleading. This is the case if the fault cases", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 87, 511, 100], "content": "classified incorrectly are those from the less numerous cases. To remedy this ... | [] | [{"type": "block", "coordinates": [84, 113, 172, 150], "content": "", "caption": ""}, {"type": "inline", "coordinates": [118, 151, 131, 165], "content": "\\Pi", "caption": ""}, {"type": "inline", "coordinates": [207, 154, 219, 165], "content": "\\mathsf{c}_{\\mathrm{n}}", "caption": ""}, {"type": "inline", "coordinates... | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "", "page_idx": 7}, {"type": "equation", "text": "$$\n\\mathrm{GA}={\\sqrt{\\frac{\\prod\\mathbf{c}_{1}...\\mathbf{c}_{\\mathrm{n}}}{\\prod\\mathbf{q}_{1}...\\mathbf{q}_{\\mathrm{n}}}}}\n$$", "text_format": "latex", "page_idx": 7}, {"type": "text", "text": "where $\\Pi$ is the product, $\\math... | [{"category_id": 8, "poly": [234.7801055908203, 320.52593994140625, 472.77239990234375, 320.52593994140625, 472.77239990234375, 417.29901123046875, 234.7801055908203, 417.29901123046875], "score": 0.9999973177909851}, {"category_id": 6, "poly": [821.9614868164062, 1087.270751953125, 937.527099609375, 1087.270751953125,... | {"preproc_blocks": [{"type": "text", "bbox": [83, 70, 512, 113], "lines": [{"bbox": [84, 72, 511, 86], "spans": [{"bbox": [84, 72, 511, 86], "score": 1.0, "content": "by the total number of cases can be misleading. This is the case if the fault cases", "type": "text"}], "index": 0}, {"bbox": [85, 87, 511, 100], "spans... | ./arxiv_full_mineru_outputs_20/images/0705.0197_7.png | images/0705.0197_7.png | |
0705.0197.pdf | 8 | Actual
# 8. CONCLUSIONS
In this paper GMM and SVM were introduced to classify faults in a population of
cylindrical shells and compared to the MLP. The GMM was observed to give more
accurate results than the SVM, which was in turn observed to give more accurate results
than the MLP.
# REFERENCE
[1] S.W. Doebling, ... | <p>Actual</p>
<h1>8. CONCLUSIONS</h1>
<p>In this paper GMM and SVM were introduced to classify faults in a population of
cylindrical shells and compared to the MLP. The GMM was observed to give more
accurate results than the SVM, which was in turn observed to give more accurate results
than the MLP.</p>
<h1>REFERENCE<... | [{"type": "table", "coordinates": [121, 132, 507, 270], "content": "", "block_type": "table", "index": 1}, {"type": "text", "coordinates": [87, 196, 115, 207], "content": "Actual", "block_type": "text", "index": 2}, {"type": "title", "coordinates": [84, 298, 186, 310], "content": "8. CONCLUSIONS", "block_type": "title"... | [{"type": "text", "coordinates": [87, 195, 116, 207], "content": "Actual ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [85, 299, 184, 310], "content": "8. CONCLUSIONS", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [84, 313, 512, 327], "content": "In this paper GMM and SVM were introduced t... | [] | [] | [] | [595.219970703125, 842.0] | [{"type": "table", "img_path": "images/1642ed32e52e40207cfad994cf54963ca0c8da8f2c17c98c61c5da865d1e529a.jpg", "table_caption": ["Table 4. The confusion matrix obtained when the GMM network is used for fault classification ", "Predicted "], "table_footnote": [], "page_idx": 8}, {"type": "text", "text": "Actual ", "page_... | [{"category_id": 5, "poly": [336.6766357421875, 367.46563720703125, 1407.988525390625, 367.46563720703125, 1407.988525390625, 751.6536865234375, 336.6766357421875, 751.6536865234375], "score": 0.9999882578849792}, {"category_id": 1, "poly": [233.16262817382812, 1891.761962890625, 1422.2542724609375, 1891.761962890625, ... | {"preproc_blocks": [{"type": "table", "bbox": [121, 132, 507, 270], "blocks": [{"type": "table_caption", "bbox": [83, 91, 512, 105], "group_id": 0, "lines": [{"bbox": [83, 92, 512, 107], "spans": [{"bbox": [83, 92, 512, 107], "score": 1.0, "content": "Table 4. The confusion matrix obtained when the GMM network is used ... | ./arxiv_full_mineru_outputs_20/images/0705.0197_8.png | images/0705.0197_8.png | |
0705.0197.pdf | 9 | Materials & Structures, 10: 540-547, 2001.
[10] S. Haykin. Neural networks. Prentice-Hall, Inc, New York, USA, 1995.
[11] G.E. Hinton. Learning translation invariant recognition in massively parallel
networks. Proceedings PARLE Conference on Parallel Architectures and
Languages, 1-13, 1987.
[12] M. Møller.... | <p>Materials & Structures, 10: 540-547, 2001.</p>
<p>[10] S. Haykin. Neural networks. Prentice-Hall, Inc, New York, USA, 1995.
[11] G.E. Hinton. Learning translation invariant recognition in massively parallel
networks. Proceedings PARLE Conference on Parallel Architectures and
Languages, 1-13, 1987.
[12] M... | [{"type": "text", "coordinates": [104, 71, 317, 84], "content": "Materials & Structures, 10: 540-547, 2001.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [83, 83, 515, 541], "content": "[10] S. Haykin. Neural networks. Prentice-Hall, Inc, New York, USA, 1995.\n[11] G.E. Hinton. Learning transl... | [{"type": "text", "coordinates": [106, 73, 314, 85], "content": "Materials & Structures, 10: 540-547, 2001.", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [83, 87, 451, 100], "content": "[10] S. Haykin. Neural networks. Prentice-Hall, Inc, New York, USA, 1995.", "score": 1.0, "index": 2}, {"type": "text",... | [] | [] | [] | [595.219970703125, 842.0] | [{"type": "text", "text": "Materials & Structures, 10: 540-547, 2001. ", "page_idx": 9}, {"type": "text", "text": "[10] S. Haykin. Neural networks. Prentice-Hall, Inc, New York, USA, 1995. \n[11] G.E. Hinton. Learning translation invariant recognition in massively parallel networks. Proceedings PARLE Conferen... | [{"category_id": 1, "poly": [290.40264892578125, 199.3874969482422, 880.125732421875, 199.3874969482422, 880.125732421875, 234.88267517089844, 290.40264892578125, 234.88267517089844], "score": 0.9996790289878845}, {"category_id": 1, "poly": [230.68255615234375, 232.2093505859375, 1429.487548828125, 232.2093505859375, 1... | {"preproc_blocks": [{"type": "text", "bbox": [104, 71, 317, 84], "lines": [{"bbox": [106, 73, 314, 85], "spans": [{"bbox": [106, 73, 314, 85], "score": 1.0, "content": "Materials & Structures, 10: 540-547, 2001.", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [83, 83, 515, 541], "lines": [{"bbox... | ./arxiv_full_mineru_outputs_20/images/0705.0197_9.png | images/0705.0197_9.png | |
0704.3515.pdf | 0 | # Comparing Robustness of Pairwise and Multiclass Neural-Network Systems for Face
Recognition
J. Uglov, V. Schetinin, C. Maple
Computing and Information System Department, University of Bedfordshire, Luton, UK
Abstract. Noise, corruptions and variations in face images can seriously hurt the
performance of face recogn... | <h1>Comparing Robustness of Pairwise and Multiclass Neural-Network Systems for Face
Recognition</h1>
<p>J. Uglov, V. Schetinin, C. Maple
Computing and Information System Department, University of Bedfordshire, Luton, UK</p>
<p>Abstract. Noise, corruptions and variations in face images can seriously hurt the
performance... | [{"type": "title", "coordinates": [85, 86, 525, 113], "content": "Comparing Robustness of Pairwise and Multiclass Neural-Network Systems for Face\nRecognition", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [90, 127, 521, 156], "content": "J. Uglov, V. Schetinin, C. Maple\nComputing and Informatio... | [{"type": "text", "coordinates": [88, 87, 524, 102], "content": "Comparing Robustness of Pairwise and Multiclass Neural-Network Systems for Face", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [273, 101, 337, 115], "content": "Recognition", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [224, 1... | [] | [{"type": "inline", "coordinates": [135, 596, 146, 606], "content": "m", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "Comparing Robustness of Pairwise and Multiclass Neural-Network Systems for Face Recognition ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "J. Uglov, V. Schetinin, C. Maple Computing and Information System Department, University of Bedfordshire, Luton, UK ", "page_idx": 0}, {"ty... | [{"category_id": 1, "poly": [234.16387939453125, 968.216796875, 1467.108642578125, 968.216796875, 1467.108642578125, 1198.4161376953125, 234.16387939453125, 1198.4161376953125], "score": 0.9999861717224121}, {"category_id": 1, "poly": [234.70945739746094, 1728.680908203125, 1467.9669189453125, 1728.680908203125, 1467.9... | {"preproc_blocks": [{"type": "title", "bbox": [85, 86, 525, 113], "lines": [{"bbox": [88, 87, 524, 102], "spans": [{"bbox": [88, 87, 524, 102], "score": 1.0, "content": "Comparing Robustness of Pairwise and Multiclass Neural-Network Systems for Face", "type": "text"}], "index": 0}, {"bbox": [273, 101, 337, 115], "spans... | ./arxiv_full_mineru_outputs_20/images/0704.3515_0.png | images/0704.3515_0.png | |
0704.3515.pdf | 1 | noise components drawn from a Gaussian density function with zero mean and the standard
deviation alpha $$=0.5$$ .
From this plot we can observe that the noise components corrupt the boundary of the
given classes, and therefore the performance of a face recognition system can be affected.
From these plots we can also ... | <p>noise components drawn from a Gaussian density function with zero mean and the standard
deviation alpha $$=0.5$$ .</p>
<p>From this plot we can observe that the noise components corrupt the boundary of the
given classes, and therefore the performance of a face recognition system can be affected.
From these plots we ... | [{"type": "text", "coordinates": [84, 85, 528, 112], "content": "noise components drawn from a Gaussian density function with zero mean and the standard\ndeviation alpha $$=0.5$$ .", "block_type": "text", "index": 1}, {"type": "image", "coordinates": [124, 114, 490, 300], "content": "", "block_type": "image", "index": ... | [{"type": "text", "coordinates": [83, 86, 527, 100], "content": "noise components drawn from a Gaussian density function with zero mean and the standard", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 101, 159, 115], "content": "deviation alpha", "score": 1.0, "index": 2}, {"type": "inline_equation", ... | [{"coordinates": [124, 114, 490, 300], "index": 4.5, "caption": ".", "caption_coordinates": [85, 305, 526, 345]}] | [{"type": "inline", "coordinates": [159, 99, 186, 111], "content": "=0.5", "caption": ""}, {"type": "inline", "coordinates": [272, 497, 282, 509], "content": "C", "caption": ""}, {"type": "inline", "coordinates": [490, 497, 528, 510], "content": "C^{*}(C-", "caption": ""}, {"type": "inline", "coordinates": [222, 525, 2... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 1}, {"type": "image", "img_path": "images/88b03dfb0a285c2aea902daabfc64d56feef5df9969a365c032d20312b0d6fa4.jpg", "img_caption": ["Fig. 1. An example of scattering the samples drawn from the four classes for alpha $=0$ (the left side) and alpha $=0.5$ (the right side) in a plane... | [{"category_id": 1, "poly": [234.76177978515625, 1000.7554321289062, 1467.8995361328125, 1000.7554321289062, 1467.8995361328125, 1193.353515625, 234.76177978515625, 1193.353515625], "score": 0.9999958872795105}, {"category_id": 1, "poly": [233.72918701171875, 1461.7738037109375, 1468.143310546875, 1461.7738037109375, 1... | {"preproc_blocks": [{"type": "text", "bbox": [84, 85, 528, 112], "lines": [{"bbox": [83, 86, 527, 100], "spans": [{"bbox": [83, 86, 527, 100], "score": 1.0, "content": "noise components drawn from a Gaussian density function with zero mean and the standard", "type": "text"}], "index": 0}, {"bbox": [84, 99, 189, 115], "... | ./arxiv_full_mineru_outputs_20/images/0704.3515_1.png | images/0704.3515_1.png | |
0704.3515.pdf | 2 | Now we can combine hyperplanes $$f_{1/2},\ f_{1/3}$$ and $$f_{2/3}$$ to build up the new dividing
hyperplanes $$g_{1},g_{2}$$ , and $$g_{3}$$ . The first hyperplane $$g_{1}$$ combines the functions $$f_{1/2}$$ and $$f_{1/3}$$ so that
$$g_{1}=f_{1/2}+f_{1/3}$$ . These functions are taken with weights of 1.0 because both... | <p>Now we can combine hyperplanes $$f_{1/2},\ f_{1/3}$$ and $$f_{2/3}$$ to build up the new dividing
hyperplanes $$g_{1},g_{2}$$ , and $$g_{3}$$ . The first hyperplane $$g_{1}$$ combines the functions $$f_{1/2}$$ and $$f_{1/3}$$ so that
$$g_{1}=f_{1/2}+f_{1/3}$$ . These functions are taken with weights of 1.0 because b... | [{"type": "image", "coordinates": [224, 85, 385, 217], "content": "", "block_type": "image", "index": 1}, {"type": "text", "coordinates": [82, 275, 528, 346], "content": "Now we can combine hyperplanes $$f_{1/2},\\ f_{1/3}$$ and $$f_{2/3}$$ to build up the new dividing\nhyperplanes $$g_{1},g_{2}$$ , and $$g_{3}$$ . The... | [{"type": "text", "coordinates": [93, 274, 280, 291], "content": "Now we can combine hyperplanes", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [280, 275, 321, 289], "content": "f_{1/2},\\ f_{1/3}", "score": 0.71, "index": 2}, {"type": "text", "coordinates": [321, 274, 348, 291], "content": " a... | [{"coordinates": [224, 85, 385, 217], "index": 6.75, "caption": ".", "caption_coordinates": [98, 232, 511, 262]}, {"coordinates": [214, 465, 394, 603], "index": 31.25, "caption": " classes.", "caption_coordinates": [129, 615, 480, 630]}] | [{"type": "inline", "coordinates": [280, 275, 321, 289], "content": "f_{1/2},\\ f_{1/3}", "caption": ""}, {"type": "inline", "coordinates": [348, 275, 366, 289], "content": "f_{2/3}", "caption": ""}, {"type": "inline", "coordinates": [144, 291, 172, 303], "content": "g_{1},g_{2}", "caption": ""}, {"type": "inline", "co... | [] | [612.0, 792.0] | [{"type": "image", "img_path": "images/7ebd99546b53f94c9f0a469ce0cec0a5a6d84db958e0a599ebddced2b0d10779.jpg", "img_caption": ["Fig. 2. Hyperplanes $f_{1/2},f_{1/3}$ and $f_{2/3}$ learnt to divide the following pairs of classes: $\\Omega_{1}$ versus $\\Omega_{2},\\Omega_{1}$ versus $\\Omega_{3}$ , and $\\Omega_{2}$ vers... | [{"category_id": 4, "poly": [360.89385986328125, 1709.16845703125, 1333.6923828125, 1709.16845703125, 1333.6923828125, 1752.4078369140625, 360.89385986328125, 1752.4078369140625], "score": 0.9999966621398926}, {"category_id": 4, "poly": [272.82086181640625, 646.2789306640625, 1420.633056640625, 646.2789306640625, 1420.... | {"preproc_blocks": [{"type": "image", "bbox": [224, 85, 385, 217], "blocks": [{"type": "image_body", "bbox": [224, 85, 385, 217], "group_id": 0, "lines": [{"bbox": [224, 85, 385, 217], "spans": [{"bbox": [224, 85, 385, 217], "score": 0.9999920129776001, "type": "image", "image_path": "7ebd99546b53f94c9f0a469ce0cec0a5a6... | ./arxiv_full_mineru_outputs_20/images/0704.3515_2.png | images/0704.3515_2.png | |
0704.3515.pdf | 3 | # 4. Experiments
The goal of our experiments is to compare the robustness of the proposed pairwise and
standard multiclass neural-network systems on the Cambridge ORL face image data set [5]
(in a full paper, the experiments will run on different face image data sets). To estimate the
robustness we add noise component... | <h1>4. Experiments</h1>
<p>The goal of our experiments is to compare the robustness of the proposed pairwise and
standard multiclass neural-network systems on the Cambridge ORL face image data set [5]
(in a full paper, the experiments will run on different face image data sets). To estimate the
robustness we add noise ... | [{"type": "title", "coordinates": [84, 86, 163, 100], "content": "4. Experiments", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [84, 113, 529, 196], "content": "The goal of our experiments is to compare the robustness of the proposed pairwise and\nstandard multiclass neural-network systems on the... | [{"type": "text", "coordinates": [84, 86, 163, 100], "content": "4. Experiments", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [84, 115, 528, 128], "content": "The goal of our experiments is to compare the robustness of the proposed pairwise and", "score": 1.0, "index": 2}, {"type": "text", "coordinates":... | [{"coordinates": [131, 384, 472, 654], "index": 17.25, "caption": "intervals, respectively.", "caption_coordinates": [96, 668, 513, 696]}] | [{"type": "inline", "coordinates": [405, 340, 433, 353], "content": "=0.0", "caption": ""}, {"type": "inline", "coordinates": [188, 354, 214, 367], "content": "2.0\\%", "caption": ""}, {"type": "inline", "coordinates": [290, 354, 318, 367], "content": "=1.1", "caption": ""}, {"type": "inline", "coordinates": [450, 354,... | [] | [612.0, 792.0] | [{"type": "text", "text": "4. Experiments ", "text_level": 1, "page_idx": 3}, {"type": "text", "text": "The goal of our experiments is to compare the robustness of the proposed pairwise and standard multiclass neural-network systems on the Cambridge ORL face image data set [5] (in a full paper, the experiments will run... | [{"category_id": 0, "poly": [234.946044921875, 240.58377075195312, 454.1318359375, 240.58377075195312, 454.1318359375, 277.87359619140625, 234.946044921875, 277.87359619140625], "score": 0.9999979734420776}, {"category_id": 1, "poly": [233.93106079101562, 906.0654296875, 1467.08837890625, 906.0654296875, 1467.088378906... | {"preproc_blocks": [{"type": "title", "bbox": [84, 86, 163, 100], "lines": [{"bbox": [84, 86, 163, 100], "spans": [{"bbox": [84, 86, 163, 100], "score": 1.0, "content": "4. Experiments", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [84, 113, 529, 196], "lines": [{"bbox": [84, 115, 528, 128], "s... | ./arxiv_full_mineru_outputs_20/images/0704.3515_3.png | images/0704.3515_3.png | |
0704.3515.pdf | 4 | # 5. Conclusion
We have proposed a pairwise neural-network system for face recognition in order to reduce
the negative effect of noise and corruptions in face images. Within such a classification
scheme we expect that the improvement in the performance can be achieved on the base of
our observation that boundaries bet... | <h1>5. Conclusion</h1>
<p>We have proposed a pairwise neural-network system for face recognition in order to reduce
the negative effect of noise and corruptions in face images. Within such a classification
scheme we expect that the improvement in the performance can be achieved on the base of
our observation that bound... | [{"type": "title", "coordinates": [83, 86, 154, 99], "content": "5. Conclusion", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [84, 113, 528, 184], "content": "We have proposed a pairwise neural-network system for face recognition in order to reduce\nthe negative effect of noise and corruptions in... | [{"type": "text", "coordinates": [83, 86, 154, 99], "content": "5. Conclusion", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [83, 112, 527, 129], "content": "We have proposed a pairwise neural-network system for face recognition in order to reduce", "score": 1.0, "index": 2}, {"type": "text", "coordinates... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "5. Conclusion ", "text_level": 1, "page_idx": 4}, {"type": "text", "text": "We have proposed a pairwise neural-network system for face recognition in order to reduce the negative effect of noise and corruptions in face images. Within such a classification scheme we expect that the improvement... | [{"category_id": 0, "poly": [232.5265655517578, 877.7357177734375, 428.3000183105469, 877.7357177734375, 428.3000183105469, 912.9336547851562, 232.5265655517578, 912.9336547851562], "score": 0.9999979734420776}, {"category_id": 0, "poly": [233.31787109375, 241.20245361328125, 429.20294189453125, 241.20245361328125, 429... | {"preproc_blocks": [{"type": "title", "bbox": [83, 86, 154, 99], "lines": [{"bbox": [83, 86, 154, 99], "spans": [{"bbox": [83, 86, 154, 99], "score": 1.0, "content": "5. Conclusion", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [84, 113, 528, 184], "lines": [{"bbox": [83, 112, 527, 129], "spans... | ./arxiv_full_mineru_outputs_20/images/0704.3515_4.png | images/0704.3515_4.png | |
0705.1244.pdf | 0 | # Evolving Symbolic Controllers
Nicolas Godzik $$^{1}$$ , Marc Schoenauer $$^{1}$$ , and Mich`ele Sebag $$^2$$
$$^{1}$$ Projet Fractales, INRIA Rocquencourt, France
$$^2$$ LRI, Universite´ Paris-Sud, France
Published in G. Raidl et al., eds, Applications of Evolutionary Computing,
pp 638-650, LNCS 2611, Springer Ver... | <h1>Evolving Symbolic Controllers</h1>
<p>Nicolas Godzik $$^{1}$$ , Marc Schoenauer $$^{1}$$ , and Mich`ele Sebag $$^2$$</p>
<p>$$^{1}$$ Projet Fractales, INRIA Rocquencourt, France
$$^2$$ LRI, Universite´ Paris-Sud, France</p>
<p>Published in G. Raidl et al., eds, Applications of Evolutionary Computing,
pp 638-650, LN... | [{"type": "title", "coordinates": [199, 114, 415, 128], "content": "Evolving Symbolic Controllers", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [183, 152, 430, 162], "content": "Nicolas Godzik $$^{1}$$ , Marc Schoenauer $$^{1}$$ , and Mich`ele Sebag $$^2$$", "block_type": "text", "index": 2}, {"... | [{"type": "text", "coordinates": [200, 114, 414, 129], "content": "Evolving Symbolic Controllers", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [183, 151, 249, 164], "content": "Nicolas Godzik", "score": 1.0, "index": 2}, {"type": "inline_equation", "coordinates": [249, 152, 253, 161], "content": "^{1}", ... | [] | [{"type": "inline", "coordinates": [249, 152, 253, 161], "content": "^{1}", "caption": ""}, {"type": "inline", "coordinates": [335, 152, 339, 161], "content": "^{1}", "caption": ""}, {"type": "inline", "coordinates": [426, 152, 431, 161], "content": "^2", "caption": ""}, {"type": "inline", "coordinates": [208, 173, 212... | [] | [612.0, 792.0] | [{"type": "text", "text": "Evolving Symbolic Controllers ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Nicolas Godzik $^{1}$ , Marc Schoenauer $^{1}$ , and Mich\\`ele Sebag $^2$ $^{1}$ Projet Fractales, INRIA Rocquencourt, France $^2$ LRI, Universite\u00b4 Paris-Sud, France ", "page_idx": 0}, {"type": "... | [{"category_id": 1, "poly": [452.2422790527344, 685.4462890625, 1255.550537109375, 685.4462890625, 1255.550537109375, 990.607177734375, 452.2422790527344, 990.607177734375], "score": 0.9999966621398926}, {"category_id": 1, "poly": [509.7530517578125, 423.2669982910156, 1197.20556640625, 423.2669982910156, 1197.20556640... | {"preproc_blocks": [{"type": "title", "bbox": [199, 114, 415, 128], "lines": [{"bbox": [200, 114, 414, 129], "spans": [{"bbox": [200, 114, 414, 129], "score": 1.0, "content": "Evolving Symbolic Controllers", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [183, 152, 430, 162], "lines": [{"bbox": [... | ./arxiv_full_mineru_outputs_20/images/0705.1244_0.png | images/0705.1244_0.png | |
0705.1244.pdf | 1 | mechanism should be used all along the complexity path, leading from primitive
tasks to simple tasks, and from simple tasks to more complex behaviors.
One reason for the lack of intelligibility is that the language of the controllers
consists in low-level orders to the robot actuators (e.g. speeds of the right and
lef... | <p>mechanism should be used all along the complexity path, leading from primitive
tasks to simple tasks, and from simple tasks to more complex behaviors.</p>
<p>One reason for the lack of intelligibility is that the language of the controllers
consists in low-level orders to the robot actuators (e.g. speeds of the righ... | [{"type": "text", "coordinates": [134, 117, 482, 140], "content": "mechanism should be used all along the complexity path, leading from primitive\ntasks to simple tasks, and from simple tasks to more complex behaviors.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [134, 141, 481, 225], "content":... | [{"type": "text", "coordinates": [133, 117, 481, 130], "content": "mechanism should be used all along the complexity path, leading from primitive", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [135, 130, 451, 141], "content": "tasks to simple tasks, and from simple tasks to more complex behaviors.", "scor... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 1}, {"type": "text", "text": "One reason for the lack of intelligibility is that the language of the controllers consists in low-level orders to the robot actuators (e.g. speeds of the right and left motors). Using instead hand-coded basic behaviors (e.g. forward, turn left or ... | [{"category_id": 1, "poly": [371.71563720703125, 1585.80908203125, 1340.53271484375, 1585.80908203125, 1340.53271484375, 1851.02880859375, 371.71563720703125, 1851.02880859375], "score": 0.9999939203262329}, {"category_id": 1, "poly": [373.2875061035156, 985.1033325195312, 1340.161376953125, 985.1033325195312, 1340.161... | {"preproc_blocks": [{"type": "text", "bbox": [134, 117, 482, 140], "lines": [{"bbox": [133, 117, 481, 130], "spans": [{"bbox": [133, 117, 481, 130], "score": 1.0, "content": "mechanism should be used all along the complexity path, leading from primitive", "type": "text"}], "index": 0}, {"bbox": [135, 130, 451, 141], "s... | ./arxiv_full_mineru_outputs_20/images/0705.1244_1.png | images/0705.1244_1.png | |
0705.1244.pdf | 2 | or away from it). The robot must hence learn from the first epoch the state of
that random variable, and act accordingly in the following epochs.
The controller architecture is designed manually in the original experience,
whereas evolution has complete freedom in its recent remake [16]. Moreover,
Tuci et al. use no e... | <p>or away from it). The robot must hence learn from the first epoch the state of
that random variable, and act accordingly in the following epochs.</p>
<p>The controller architecture is designed manually in the original experience,
whereas evolution has complete freedom in its recent remake [16]. Moreover,
Tuci et al.... | [{"type": "text", "coordinates": [134, 118, 482, 140], "content": "or away from it). The robot must hence learn from the first epoch the state of\nthat random variable, and act accordingly in the following epochs.", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [134, 142, 481, 200], "content": "The... | [{"type": "text", "coordinates": [134, 118, 481, 128], "content": "or away from it). The robot must hence learn from the first epoch the state of", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [133, 129, 424, 142], "content": "that random variable, and act accordingly in the following epochs.", "score": 1... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "The controller architecture is designed manually in the original experience, whereas evolution has complete freedom in its recent remake [16]. Moreover, Tuci et al. use no explicit reinforcement. Nevertheless, the results obtained by this recent ap... | [{"category_id": 1, "poly": [373.1041564941406, 895.6410522460938, 1338.440185546875, 895.6410522460938, 1338.440185546875, 1157.5609130859375, 373.1041564941406, 1157.5609130859375], "score": 0.99998939037323}, {"category_id": 0, "poly": [372.6412658691406, 1216.1171875, 766.1827392578125, 1216.1171875, 766.1827392578... | {"preproc_blocks": [{"type": "text", "bbox": [134, 118, 482, 140], "lines": [{"bbox": [134, 118, 481, 128], "spans": [{"bbox": [134, 118, 481, 128], "score": 1.0, "content": "or away from it). The robot must hence learn from the first epoch the state of", "type": "text"}], "index": 0}, {"bbox": [133, 129, 424, 142], "s... | ./arxiv_full_mineru_outputs_20/images/0705.1244_2.png | images/0705.1244_2.png | |
0705.1244.pdf | 3 | continuous parameter (e.g. speed of forward displacement, or turning angle for
left and right actions).
The proposed symbolic controller has eight outputs with values in $$[0,1]$$ : the
first four outputs are used to specify which action will be executed, namely action
$$i$$ , with $$i=A r g m a x(o u t p u t(j),j=1..... | <p>continuous parameter (e.g. speed of forward displacement, or turning angle for
left and right actions).</p>
<p>The proposed symbolic controller has eight outputs with values in $$[0,1]$$ : the
first four outputs are used to specify which action will be executed, namely action
$$i$$ , with $$i=A r g m a x(o u t p u t... | [{"type": "text", "coordinates": [134, 117, 481, 140], "content": "continuous parameter (e.g. speed of forward displacement, or turning angle for\nleft and right actions).", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [134, 141, 482, 200], "content": "The proposed symbolic controller has eight ou... | [{"type": "text", "coordinates": [133, 115, 481, 130], "content": "continuous parameter (e.g. speed of forward displacement, or turning angle for", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [134, 129, 233, 142], "content": "left and right actions).", "score": 1.0, "index": 2}, {"type": "text", "coordin... | [] | [{"type": "inline", "coordinates": [440, 142, 460, 153], "content": "[0,1]", "caption": ""}, {"type": "inline", "coordinates": [134, 167, 138, 174], "content": "i", "caption": ""}, {"type": "inline", "coordinates": [166, 166, 306, 176], "content": "i=A r g m a x(o u t p u t(j),j=1..4)", "caption": ""}, {"type": "inline... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 3}, {"type": "text", "text": "The proposed symbolic controller has eight outputs with values in $[0,1]$ : the first four outputs are used to specify which action will be executed, namely action $i$ , with $i=A r g m a x(o u t p u t(j),j=1..4)$ . Output $i+4$ then gives the asso... | [{"category_id": 1, "poly": [371.0531005859375, 730.9566040039062, 1340.63623046875, 730.9566040039062, 1340.63623046875, 1095.58056640625, 371.0531005859375, 1095.58056640625], "score": 0.9999923706054688}, {"category_id": 1, "poly": [372.2391662597656, 1096.3486328125, 1339.1883544921875, 1096.3486328125, 1339.188354... | {"preproc_blocks": [{"type": "text", "bbox": [134, 117, 481, 140], "lines": [{"bbox": [133, 115, 481, 130], "spans": [{"bbox": [133, 115, 481, 130], "score": 1.0, "content": "continuous parameter (e.g. speed of forward displacement, or turning angle for", "type": "text"}], "index": 0}, {"bbox": [134, 129, 233, 142], "s... | ./arxiv_full_mineru_outputs_20/images/0705.1244_3.png | images/0705.1244_3.png | |
0705.1244.pdf | 4 | other selection and replacement procedures, multi-objective optimization, and
even other paradigms like Evolution Strategies and Genetic Programming. How-
ever, all experiments presented here use as controllers Neural Networks (NNs)
with fixed topology. The genotype is hence the vector of the (real-valued) weights
of t... | <p>other selection and replacement procedures, multi-objective optimization, and
even other paradigms like Evolution Strategies and Genetic Programming. How-
ever, all experiments presented here use as controllers Neural Networks (NNs)
with fixed topology. The genotype is hence the vector of the (real-valued) weights
o... | [{"type": "text", "coordinates": [134, 116, 481, 225], "content": "other selection and replacement procedures, multi-objective optimization, and\neven other paradigms like Evolution Strategies and Genetic Programming. How-\never, all experiments presented here use as controllers Neural Networks (NNs)\nwith fixed topolo... | [{"type": "text", "coordinates": [134, 117, 481, 129], "content": "other selection and replacement procedures, multi-objective optimization, and", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [134, 130, 481, 141], "content": "even other paradigms like Evolution Strategies and Genetic Programming. How-", "... | [] | [{"type": "inline", "coordinates": [287, 166, 315, 176], "content": "[-1,1]", "caption": ""}, {"type": "inline", "coordinates": [315, 463, 448, 476], "content": "\\begin{array}{r}{\\sum_{e p o c h}\\sum_{t}|V(t)|(1-\\sqrt{\\delta V(t)})}\\end{array}", "caption": ""}, {"type": "inline", "coordinates": [134, 477, 154, 48... | [] | [612.0, 792.0] | [{"type": "text", "text": "other selection and replacement procedures, multi-objective optimization, and even other paradigms like Evolution Strategies and Genetic Programming. However, all experiments presented here use as controllers Neural Networks (NNs) with fixed topology. The genotype is hence the vector of the (... | [{"category_id": 1, "poly": [373.1298522949219, 322.9550476074219, 1337.76806640625, 322.9550476074219, 1337.76806640625, 626.0546875, 373.1298522949219, 626.0546875], "score": 0.999995231628418}, {"category_id": 0, "poly": [373.7934265136719, 807.883544921875, 1200.812744140625, 807.883544921875, 1200.812744140625, 84... | {"preproc_blocks": [{"type": "text", "bbox": [134, 116, 481, 225], "lines": [{"bbox": [134, 117, 481, 129], "spans": [{"bbox": [134, 117, 481, 129], "score": 1.0, "content": "other selection and replacement procedures, multi-objective optimization, and", "type": "text"}], "index": 0}, {"bbox": [134, 130, 481, 141], "sp... | ./arxiv_full_mineru_outputs_20/images/0705.1244_4.png | images/0705.1244_4.png | |
0705.1244.pdf | 5 | Nevertheless, in order to definitely avoid this loophole, the fitness is modified
in such a way that it increases only when the robot moves forward (sum of both
motor speeds positive) .
This modification does not alter the ranking of the controllers: the Symbolic
Controller still outperforms the Classical Controller. ... | <p>Nevertheless, in order to definitely avoid this loophole, the fitness is modified
in such a way that it increases only when the robot moves forward (sum of both
motor speeds positive) .</p>
<p>This modification does not alter the ranking of the controllers: the Symbolic
Controller still outperforms the Classical Con... | [{"type": "text", "coordinates": [134, 116, 481, 152], "content": "Nevertheless, in order to definitely avoid this loophole, the fitness is modified\nin such a way that it increases only when the robot moves forward (sum of both\nmotor speeds positive) .", "block_type": "text", "index": 1}, {"type": "text", "coordinate... | [{"type": "text", "coordinates": [149, 117, 480, 129], "content": "Nevertheless, in order to definitely avoid this loophole, the fitness is modified", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [133, 129, 480, 141], "content": "in such a way that it increases only when the robot moves forward (sum of bo... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "Nevertheless, in order to definitely avoid this loophole, the fitness is modified in such a way that it increases only when the robot moves forward (sum of both motor speeds positive) . ", "page_idx": 5}, {"type": "text", "text": "This modification does not alter the ranking of the controller... | [{"category_id": 0, "poly": [371.45977783203125, 813.353759765625, 962.8286743164062, 813.353759765625, 962.8286743164062, 847.048583984375, 371.45977783203125, 847.048583984375], "score": 0.999997615814209}, {"category_id": 5, "poly": [414.23187255859375, 584.08740234375, 865.7515869140625, 584.08740234375, 865.751586... | {"preproc_blocks": [{"type": "text", "bbox": [134, 116, 481, 152], "lines": [{"bbox": [149, 117, 480, 129], "spans": [{"bbox": [149, 117, 480, 129], "score": 1.0, "content": "Nevertheless, in order to definitely avoid this loophole, the fitness is modified", "type": "text"}], "index": 0}, {"bbox": [133, 129, 480, 141],... | ./arxiv_full_mineru_outputs_20/images/0705.1244_5.png | images/0705.1244_5.png | |
0705.1244.pdf | 6 | – Stop. This behavior is evolved to minimize the speed of the center of mass of
the robot. Note that a very small number of generations is needed to get the
perfect behavior, but that all evolved Stop behaviors in fact rotate rapidly
with inverse speeds on both motors.
– Area sweeping. The arena is divided in small squ... | <p>– Stop. This behavior is evolved to minimize the speed of the center of mass of
the robot. Note that a very small number of generations is needed to get the
perfect behavior, but that all evolved Stop behaviors in fact rotate rapidly
with inverse speeds on both motors.
– Area sweeping. The arena is divided in small ... | [{"type": "text", "coordinates": [139, 116, 482, 189], "content": "\u2013 Stop. This behavior is evolved to minimize the speed of the center of mass of\nthe robot. Note that a very small number of generations is needed to get the\nperfect behavior, but that all evolved Stop behaviors in fact rotate rapidly\nwith invers... | [{"type": "text", "coordinates": [141, 118, 482, 128], "content": "\u2013 Stop. This behavior is evolved to minimize the speed of the center of mass of", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [150, 129, 480, 141], "content": "the robot. Note that a very small number of generations is needed to get ... | [{"coordinates": [134, 456, 477, 577], "index": 26.25, "caption": "energy experiments.", "caption_coordinates": [132, 588, 482, 610]}] | [{"type": "inline", "coordinates": [455, 328, 477, 335], "content": "F O R", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "\u2013 Stop. This behavior is evolved to minimize the speed of the center of mass of the robot. Note that a very small number of generations is needed to get the perfect behavior, but that all evolved Stop behaviors in fact rotate rapidly with inverse speeds on both motors. \u2013 Area sweepi... | [{"category_id": 3, "poly": [372.47418212890625, 1269.4052734375, 1326.8265380859375, 1269.4052734375, 1326.8265380859375, 1603.5264892578125, 372.47418212890625, 1603.5264892578125], "score": 0.9999942779541016}, {"category_id": 1, "poly": [372.0342712402344, 873.2529296875, 1339.666259765625, 873.2529296875, 1339.666... | {"preproc_blocks": [{"type": "text", "bbox": [139, 116, 482, 189], "lines": [{"bbox": [141, 118, 482, 128], "spans": [{"bbox": [141, 118, 482, 128], "score": 1.0, "content": "\u2013 Stop. This behavior is evolved to minimize the speed of the center of mass of", "type": "text"}], "index": 0}, {"bbox": [150, 129, 480, 14... | ./arxiv_full_mineru_outputs_20/images/0705.1244_6.png | images/0705.1244_6.png | |
0705.1244.pdf | 7 | # 6.3 Results
The statistics over 10 independent runs can be seen on Figure 1. Three criteria
can be used to compare the performances of the 4 architectures: the best overall
performance, the variance of the results, and how rapidly good performances are
obtained. The sensitivity and generalization abilities of the re... | <h1>6.3 Results</h1>
<p>The statistics over 10 independent runs can be seen on Figure 1. Three criteria
can be used to compare the performances of the 4 architectures: the best overall
performance, the variance of the results, and how rapidly good performances are
obtained. The sensitivity and generalization abilities ... | [{"type": "title", "coordinates": [133, 130, 198, 140], "content": "6.3 Results", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [134, 151, 481, 209], "content": "The statistics over 10 independent runs can be seen on Figure 1. Three criteria\ncan be used to compare the performances of the 4 archit... | [{"type": "text", "coordinates": [133, 130, 151, 140], "content": "6.3", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [158, 129, 198, 141], "content": "Results", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [134, 151, 481, 162], "content": "The statistics over 10 independent runs can be seen... | [] | [{"type": "inline", "coordinates": [134, 237, 176, 244], "content": "6442\\pm28", "caption": ""}, {"type": "inline", "coordinates": [266, 297, 313, 304], "content": "6044\\pm316", "caption": ""}, {"type": "inline", "coordinates": [257, 308, 276, 316], "content": "95\\%", "caption": ""}, {"type": "inline", "coordinates"... | [] | [612.0, 792.0] | [{"type": "text", "text": "6.3 Results ", "text_level": 1, "page_idx": 7}, {"type": "text", "text": "The statistics over 10 independent runs can be seen on Figure 1. Three criteria can be used to compare the performances of the 4 architectures: the best overall performance, the variance of the results, and how rapidly ... | [{"category_id": 1, "poly": [373.77117919921875, 1419.3909912109375, 1338.96240234375, 1419.3909912109375, 1338.96240234375, 1682.5631103515625, 373.77117919921875, 1682.5631103515625], "score": 0.9999730587005615}, {"category_id": 1, "poly": [372.9428405761719, 586.056396484375, 1338.607666015625, 586.056396484375, 13... | {"preproc_blocks": [{"type": "title", "bbox": [133, 130, 198, 140], "lines": [{"bbox": [133, 129, 198, 141], "spans": [{"bbox": [133, 130, 151, 140], "score": 1.0, "content": "6.3", "type": "text"}, {"bbox": [158, 129, 198, 141], "score": 1.0, "content": "Results", "type": "text"}], "index": 0}], "index": 0}, {"type": ... | ./arxiv_full_mineru_outputs_20/images/0705.1244_7.png | images/0705.1244_7.png | |
0705.1244.pdf | 8 | when they see the light, they turn using the stop behavior (that consists in fast
rotation), and then go to the light using the obstacle avoidance. However, once
on the recharge area, they use the stop until the energy level is back over $$90\%$$ .
Investigating deeper, it appears that the speeds of the light followin... | <p>when they see the light, they turn using the stop behavior (that consists in fast
rotation), and then go to the light using the obstacle avoidance. However, once
on the recharge area, they use the stop until the energy level is back over $$90\%$$ .</p>
<p>Investigating deeper, it appears that the speeds of the light... | [{"type": "text", "coordinates": [134, 117, 482, 152], "content": "when they see the light, they turn using the stop behavior (that consists in fast\nrotation), and then go to the light using the obstacle avoidance. However, once\non the recharge area, they use the stop until the energy level is back over $$90\\%$$ .",... | [{"type": "text", "coordinates": [134, 117, 481, 129], "content": "when they see the light, they turn using the stop behavior (that consists in fast", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [134, 130, 481, 141], "content": "rotation), and then go to the light using the obstacle avoidance. However, o... | [{"coordinates": [135, 501, 477, 620], "index": 29.5, "caption": "useless behaviors are available.", "caption_coordinates": [133, 632, 481, 665]}] | [{"type": "inline", "coordinates": [457, 142, 475, 151], "content": "90\\%", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "when they see the light, they turn using the stop behavior (that consists in fast rotation), and then go to the light using the obstacle avoidance. However, once on the recharge area, they use the stop until the energy level is back over $90\\%$ . ", "page_idx": 8}, {"type": "text", "text": "... | [{"category_id": 4, "poly": [371.08880615234375, 1757.112548828125, 1337.943115234375, 1757.112548828125, 1337.943115234375, 1848.797119140625, 371.08880615234375, 1848.797119140625], "score": 0.9999958872795105}, {"category_id": 3, "poly": [375.5875549316406, 1393.4261474609375, 1325.591064453125, 1393.4261474609375, ... | {"preproc_blocks": [{"type": "text", "bbox": [134, 117, 482, 152], "lines": [{"bbox": [134, 117, 481, 129], "spans": [{"bbox": [134, 117, 481, 129], "score": 1.0, "content": "when they see the light, they turn using the stop behavior (that consists in fast", "type": "text"}], "index": 0}, {"bbox": [134, 130, 481, 141],... | ./arxiv_full_mineru_outputs_20/images/0705.1244_8.png | images/0705.1244_8.png | |
0705.1244.pdf | 9 | # 6.5 Generalization
Several other experiments were performed in order to test the generalization
abilities of the resulting controllers. The $$10\times4$$ best controllers obtained in the
experiments above were tested in new experimental environments.
First, some obstacles were added in the environment (the arena wa... | <h1>6.5 Generalization</h1>
<p>Several other experiments were performed in order to test the generalization
abilities of the resulting controllers. The $$10\times4$$ best controllers obtained in the
experiments above were tested in new experimental environments.</p>
<p>First, some obstacles were added in the environmen... | [{"type": "title", "coordinates": [134, 128, 234, 137], "content": "6.5 Generalization", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [134, 146, 481, 181], "content": "Several other experiments were performed in order to test the generalization\nabilities of the resulting controllers. The $$10\\t... | [{"type": "text", "coordinates": [133, 127, 150, 137], "content": "6.5", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [159, 127, 234, 137], "content": "Generalization", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [135, 147, 481, 158], "content": "Several other experiments were performed in ... | [] | [{"type": "inline", "coordinates": [313, 161, 340, 168], "content": "10\\times4", "caption": ""}, {"type": "inline", "coordinates": [245, 315, 263, 324], "content": "10\\%", "caption": ""}, {"type": "inline", "coordinates": [276, 363, 302, 372], "content": "12.5\\%", "caption": ""}, {"type": "inline", "coordinates": [3... | [] | [612.0, 792.0] | [{"type": "text", "text": "6.5 Generalization ", "text_level": 1, "page_idx": 9}, {"type": "text", "text": "Several other experiments were performed in order to test the generalization abilities of the resulting controllers. The $10\\times4$ best controllers obtained in the experiments above were tested in new experime... | [{"category_id": 1, "poly": [372.7351989746094, 1671.1400146484375, 1337.6419677734375, 1671.1400146484375, 1337.6419677734375, 1767.8780517578125, 372.7351989746094, 1767.8780517578125], "score": 0.9999784231185913}, {"category_id": 1, "poly": [373.5752258300781, 1272.5911865234375, 1338.7652587890625, 1272.5911865234... | {"preproc_blocks": [{"type": "title", "bbox": [134, 128, 234, 137], "lines": [{"bbox": [133, 127, 234, 137], "spans": [{"bbox": [133, 127, 150, 137], "score": 1.0, "content": "6.5", "type": "text"}, {"bbox": [159, 127, 234, 137], "score": 1.0, "content": "Generalization", "type": "text"}], "index": 0}], "index": 0}, {"... | ./arxiv_full_mineru_outputs_20/images/0705.1244_9.png | images/0705.1244_9.png | |
0705.1244.pdf | 10 | test for controllers evolved using a simulator is of course to be applied on the real
robot. This is on-going work, and the first experiments, applied to the obsta-
cle avoidance behaviors, have confirmed the good performance of the symbolic
controllers in any environment.
# 7 Discussion and Perspectives
The main con... | <p>test for controllers evolved using a simulator is of course to be applied on the real
robot. This is on-going work, and the first experiments, applied to the obsta-
cle avoidance behaviors, have confirmed the good performance of the symbolic
controllers in any environment.</p>
<h1>7 Discussion and Perspectives</h1>
... | [{"type": "text", "coordinates": [133, 116, 482, 165], "content": "test for controllers evolved using a simulator is of course to be applied on the real\nrobot. This is on-going work, and the first experiments, applied to the obsta-\ncle avoidance behaviors, have confirmed the good performance of the symbolic\ncontroll... | [{"type": "text", "coordinates": [133, 117, 480, 128], "content": "test for controllers evolved using a simulator is of course to be applied on the real", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [133, 129, 480, 141], "content": "robot. This is on-going work, and the first experiments, applied to the ... | [] | [{"type": "inline", "coordinates": [411, 511, 424, 519], "content": "\\varepsilon\\%", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 10}, {"type": "text", "text": "7 Discussion and Perspectives ", "text_level": 1, "page_idx": 10}, {"type": "text", "text": "The main contribution of this work is to propose some compromise between the pure black box approach where evolution is supposed to evolve everything from... | [{"category_id": 1, "poly": [367.9959716796875, 1550.005859375, 1342.14111328125, 1550.005859375, 1342.14111328125, 1853.3359375, 367.9959716796875, 1853.3359375], "score": 0.9999946355819702}, {"category_id": 1, "poly": [369.7119445800781, 1013.1080322265625, 1341.1546630859375, 1013.1080322265625, 1341.1546630859375,... | {"preproc_blocks": [{"type": "text", "bbox": [133, 116, 482, 165], "lines": [{"bbox": [133, 117, 480, 128], "spans": [{"bbox": [133, 117, 480, 128], "score": 1.0, "content": "test for controllers evolved using a simulator is of course to be applied on the real", "type": "text"}], "index": 0}, {"bbox": [133, 129, 480, 1... | ./arxiv_full_mineru_outputs_20/images/0705.1244_10.png | images/0705.1244_10.png | |
0705.1244.pdf | 11 | Alternatives for the overall architecture will also be looked for. One crucial
issue in autonomous robotics is the adaptivity of the controller. Several architec-
tures have been proposed in that direction (see [13] and references herein) and
will be tried, like for instance the idea of auto-teaching networks.
Finally... | <p>Alternatives for the overall architecture will also be looked for. One crucial
issue in autonomous robotics is the adaptivity of the controller. Several architec-
tures have been proposed in that direction (see [13] and references herein) and
will be tried, like for instance the idea of auto-teaching networks.</p>
<... | [{"type": "text", "coordinates": [132, 116, 482, 164], "content": "Alternatives for the overall architecture will also be looked for. One crucial\nissue in autonomous robotics is the adaptivity of the controller. Several architec-\ntures have been proposed in that direction (see [13] and references herein) and\nwill be... | [{"type": "text", "coordinates": [149, 117, 480, 128], "content": "Alternatives for the overall architecture will also be looked for. One crucial", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [134, 130, 480, 141], "content": "issue in autonomous robotics is the adaptivity of the controller. Several archi... | [] | [{"type": "inline", "coordinates": [222, 559, 264, 568], "content": "1995\\_{\\mathsf{Z}}^{n d}", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "Alternatives for the overall architecture will also be looked for. One crucial issue in autonomous robotics is the adaptivity of the controller. Several architectures have been proposed in that direction (see [13] and references herein) and will be tried, like for instance the idea of auto-te... | [{"category_id": 0, "poly": [373.1834716796875, 644.7802124023438, 551.2296142578125, 644.7802124023438, 551.2296142578125, 684.1874389648438, 373.1834716796875, 684.1874389648438], "score": 0.9999698400497437}, {"category_id": 1, "poly": [369.2083435058594, 323.3550109863281, 1340.7943115234375, 323.3550109863281, 134... | {"preproc_blocks": [{"type": "text", "bbox": [132, 116, 482, 164], "lines": [{"bbox": [149, 117, 480, 128], "spans": [{"bbox": [149, 117, 480, 128], "score": 1.0, "content": "Alternatives for the overall architecture will also be looked for. One crucial", "type": "text"}], "index": 0}, {"bbox": [134, 130, 480, 141], "s... | ./arxiv_full_mineru_outputs_20/images/0705.1244_11.png | images/0705.1244_11.png | |
0705.0761.pdf | 0 | # Bayesian Approach to Neuro-Rough Models for Modelling HIV
Tshilidzi Marwala and Bodie Crossingham
University of the Witwatersrand
Private Bag x3
Wits, 2050
South Africa
e-mail: t.marwala@ee.wits.ac.za
This paper proposes a new neuro-rough model for modelling the risk of HIV from
demographic data. The model is formu... | <h1>Bayesian Approach to Neuro-Rough Models for Modelling HIV</h1>
<p>Tshilidzi Marwala and Bodie Crossingham
University of the Witwatersrand
Private Bag x3
Wits, 2050
South Africa
e-mail: t.marwala@ee.wits.ac.za</p>
<p>This paper proposes a new neuro-rough model for modelling the risk of HIV from
demographic data. The... | [{"type": "title", "coordinates": [149, 71, 461, 87], "content": "Bayesian Approach to Neuro-Rough Models for Modelling HIV", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [175, 78, 449, 251], "content": "Tshilidzi Marwala and Bodie Crossingham\nUniversity of the Witwatersrand\nPrivate Bag x3\nWit... | [{"type": "text", "coordinates": [150, 72, 459, 88], "content": "Bayesian Approach to Neuro-Rough Models for Modelling HIV", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [202, 100, 408, 115], "content": "Tshilidzi Marwala and Bodie Crossingham", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [... | [] | [{"type": "inline", "coordinates": [151, 403, 175, 415], "content": "62\\%", "caption": ""}, {"type": "inline", "coordinates": [254, 403, 277, 415], "content": "58\\%", "caption": ""}, {"type": "inline", "coordinates": [409, 431, 433, 443], "content": "62\\%", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "Bayesian Approach to Neuro-Rough Models for Modelling HIV ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Tshilidzi Marwala and Bodie Crossingham \nUniversity of the Witwatersrand \nPrivate Bag x3 \nWits, 2050 \nSouth Africa \ne-mail: t.marwala@ee.wits.ac.za ", "page_i... | [{"category_id": 0, "poly": [248.8660888671875, 1657.875732421875, 434.0453796386719, 1657.875732421875, 434.0453796386719, 1695.5452880859375, 248.8660888671875, 1695.5452880859375], "score": 0.9999994039535522}, {"category_id": 1, "poly": [246.9416961669922, 1502.185302734375, 1390.278076171875, 1502.185302734375, 13... | {"preproc_blocks": [{"type": "title", "bbox": [149, 71, 461, 87], "lines": [{"bbox": [150, 72, 459, 88], "spans": [{"bbox": [150, 72, 459, 88], "score": 1.0, "content": "Bayesian Approach to Neuro-Rough Models for Modelling HIV", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [175, 78, 449, 251],... | ./arxiv_full_mineru_outputs_20/images/0705.0761_0.png | images/0705.0761_0.png | |
0705.0761.pdf | 1 | given input parameters but are not sufficiently transparent to allow the extraction of
linguistic rules that govern the predictions they make. Consequently, they are called
‘black-box’ tools because they do not give a transparent view of the rules that govern the
relationships that make predictions possible.
Rough set... | <p>given input parameters but are not sufficiently transparent to allow the extraction of
linguistic rules that govern the predictions they make. Consequently, they are called
‘black-box’ tools because they do not give a transparent view of the rules that govern the
relationships that make predictions possible.</p>
<p>... | [{"type": "text", "coordinates": [88, 70, 524, 169], "content": "given input parameters but are not sufficiently transparent to allow the extraction of\nlinguistic rules that govern the predictions they make. Consequently, they are called\n\u2018black-box\u2019 tools because they do not give a transparent view of the r... | [{"type": "text", "coordinates": [88, 73, 524, 87], "content": "given input parameters but are not sufficiently transparent to allow the extraction of ", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [90, 101, 522, 116], "content": "linguistic rules that govern the predictions they make. Consequently, they... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 1}, {"type": "text", "text": "Rough set theory (RST) was introduced by Pawlak (1991) and is a mathematical tool, which deals with vagueness and uncertainty, and is based on set of rules, which are in terms of linguistic variables. Rough sets are of fundamental importance to co... | [{"category_id": 1, "poly": [245.2900390625, 196.89511108398438, 1457.52587890625, 196.89511108398438, 1457.52587890625, 471.1237487792969, 245.2900390625, 471.1237487792969], "score": 0.9999980330467224}, {"category_id": 1, "poly": [245.16552734375, 1654.563720703125, 1456.99609375, 1654.563720703125, 1456.99609375, 1... | {"preproc_blocks": [{"type": "text", "bbox": [88, 70, 524, 169], "lines": [{"bbox": [88, 73, 524, 87], "spans": [{"bbox": [88, 73, 524, 87], "score": 1.0, "content": "given input parameters but are not sufficiently transparent to allow the extraction of ", "type": "text"}], "index": 0}, {"bbox": [90, 101, 522, 116], "s... | ./arxiv_full_mineru_outputs_20/images/0705.0761_1.png | images/0705.0761_1.png | |
0705.0761.pdf | 2 | sufficient for determining the relationship in complex cases such as between the
demographic variables and their respective outcomes, as is the case for the application
under consideration in this paper.
Greco et al. (2006) generalised the original idea of rough sets and introduced variable
precision rough set, which ... | <p>sufficient for determining the relationship in complex cases such as between the
demographic variables and their respective outcomes, as is the case for the application
under consideration in this paper.</p>
<p>Greco et al. (2006) generalised the original idea of rough sets and introduced variable
precision rough se... | [{"type": "text", "coordinates": [87, 71, 524, 141], "content": "sufficient for determining the relationship in complex cases such as between the\ndemographic variables and their respective outcomes, as is the case for the application\nunder consideration in this paper.", "block_type": "text", "index": 1}, {"type": "te... | [{"type": "text", "coordinates": [88, 72, 523, 88], "content": "sufficient for determining the relationship in complex cases such as between the", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 100, 523, 116], "content": "demographic variables and their respective outcomes, as is the case for the appli... | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 2}, {"type": "text", "text": "Greco et al. (2006) generalised the original idea of rough sets and introduced variable precision rough set, which is based on the concept of relative and absolute rough membership. The Bayesian framework is a tool that can be used to extend this a... | [{"category_id": 1, "poly": [244.172607421875, 197.9323272705078, 1457.20263671875, 197.9323272705078, 1457.20263671875, 393.91595458984375, 244.172607421875, 393.91595458984375], "score": 0.9999974966049194}, {"category_id": 1, "poly": [244.53829956054688, 1271.4544677734375, 1457.5218505859375, 1271.4544677734375, 14... | {"preproc_blocks": [{"type": "text", "bbox": [87, 71, 524, 141], "lines": [{"bbox": [88, 72, 523, 88], "spans": [{"bbox": [88, 72, 523, 88], "score": 1.0, "content": "sufficient for determining the relationship in complex cases such as between the", "type": "text"}], "index": 0}, {"bbox": [88, 100, 523, 116], "spans": ... | ./arxiv_full_mineru_outputs_20/images/0705.0761_2.png | images/0705.0761_2.png | |
0705.0761.pdf | 3 | # Rough Set Theory
Rough set theory deals with the approximation of sets that are difficult to describe with
the available information (Orhn and Rowland, 2006). It deals predominantly with the
classification of imprecise, uncertain or incomplete information. Some concepts that are
fundamental to RST theory are given i... | <h1>Rough Set Theory</h1>
<p>Rough set theory deals with the approximation of sets that are difficult to describe with
the available information (Orhn and Rowland, 2006). It deals predominantly with the
classification of imprecise, uncertain or incomplete information. Some concepts that are
fundamental to RST theory ar... | [{"type": "title", "coordinates": [89, 72, 183, 87], "content": "Rough Set Theory", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [88, 97, 525, 251], "content": "Rough set theory deals with the approximation of sets that are difficult to describe with\nthe available information (Orhn and Rowland, ... | [{"type": "text", "coordinates": [89, 72, 183, 88], "content": "Rough Set Theory", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [89, 101, 522, 115], "content": "Rough set theory deals with the approximation of sets that are difficult to describe with", "score": 1.0, "index": 2}, {"type": "text", "coordina... | [] | [{"type": "inline", "coordinates": [383, 642, 435, 655], "content": "\\Lambda=(U,A)", "caption": ""}, {"type": "inline", "coordinates": [476, 642, 487, 653], "content": "U", "caption": ""}, {"type": "inline", "coordinates": [510, 642, 519, 653], "content": "A", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "Rough Set Theory ", "text_level": 1, "page_idx": 3}, {"type": "text", "text": "Rough set theory deals with the approximation of sets that are difficult to describe with the available information (Orhn and Rowland, 2006). It deals predominantly with the classification of imprecise, uncertain o... | [{"category_id": 1, "poly": [245.62083435058594, 1701.234619140625, 1457.447021484375, 1701.234619140625, 1457.447021484375, 1912.8673095703125, 245.62083435058594, 1912.8673095703125], "score": 0.9999946355819702}, {"category_id": 1, "poly": [245.298583984375, 1242.6846923828125, 1458.1422119140625, 1242.6846923828125... | {"preproc_blocks": [{"type": "title", "bbox": [89, 72, 183, 87], "lines": [{"bbox": [89, 72, 183, 88], "spans": [{"bbox": [89, 72, 183, 88], "score": 1.0, "content": "Rough Set Theory", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [88, 97, 525, 251], "lines": [{"bbox": [89, 101, 522, 115], "spa... | ./arxiv_full_mineru_outputs_20/images/0705.0761_3.png | images/0705.0761_3.png | |
0705.0761.pdf | 4 | and Peszek, 2003). For every attribute $$a$$ an element of $$A$$ , we associate a set $$V_{a}$$ , of its
values, where $$V_{a}$$ is called the value set of $$a$$ .
Any subset $$B$$ of $$A$$ determines a binary relation $$I(B)$$ on $$U$$ , which is called an
indiscernibility relation. The main concept of rough set theo... | <p>and Peszek, 2003). For every attribute $$a$$ an element of $$A$$ , we associate a set $$V_{a}$$ , of its
values, where $$V_{a}$$ is called the value set of $$a$$ .</p>
<p>Any subset $$B$$ of $$A$$ determines a binary relation $$I(B)$$ on $$U$$ , which is called an
indiscernibility relation. The main concept of rough... | [{"type": "text", "coordinates": [87, 70, 525, 115], "content": "and Peszek, 2003). For every attribute $$a$$ an element of $$A$$ , we associate a set $$V_{a}$$ , of its\nvalues, where $$V_{a}$$ is called the value set of $$a$$ .", "block_type": "text", "index": 1}, {"type": "interline_equation", "coordinates": [88, 12... | [{"type": "text", "coordinates": [90, 74, 284, 87], "content": "and Peszek, 2003). For every attribute ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [284, 75, 292, 84], "content": "a", "score": 0.69, "index": 2}, {"type": "text", "coordinates": [292, 74, 367, 87], "content": " an element of"... | [] | [{"type": "block", "coordinates": [88, 127, 139, 141], "content": "", "caption": ""}, {"type": "block", "coordinates": [89, 687, 213, 702], "content": "", "caption": ""}, {"type": "inline", "coordinates": [284, 75, 292, 84], "content": "a", "caption": ""}, {"type": "inline", "coordinates": [368, 73, 377, 84], "content"... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 4}, {"type": "equation", "text": "$$\na\\!\\cdot{\\cal U}\\!\\!\\to V_{a}\n$$", "text_format": "latex", "page_idx": 4}, {"type": "text", "text": "Any subset $B$ of $A$ determines a binary relation $I(B)$ on $U$ , which is called an indiscernibility relation. The main concept of... | [{"category_id": 1, "poly": [243.96261596679688, 195.81240844726562, 1459.4013671875, 195.81240844726562, 1459.4013671875, 320.7054748535156, 243.96261596679688, 320.7054748535156], "score": 0.9999963641166687}, {"category_id": 1, "poly": [241.51869201660156, 426.0172119140625, 1461.202392578125, 426.0172119140625, 146... | {"preproc_blocks": [{"type": "text", "bbox": [87, 70, 525, 115], "lines": [{"bbox": [90, 73, 523, 87], "spans": [{"bbox": [90, 74, 284, 87], "score": 1.0, "content": "and Peszek, 2003). For every attribute ", "type": "text"}, {"bbox": [284, 75, 292, 84], "score": 0.69, "content": "a", "type": "inline_equation", "height... | ./arxiv_full_mineru_outputs_20/images/0705.0761_4.png | images/0705.0761_4.png | |
0705.0761.pdf | 5 | The upper approximation is defined as the collection of cases whose equivalence classes
are at least partially contained in the set of cases we want to approximate. The upper
approximation of set $$X$$ is denoted $$\overline{{B}}X$$ and is mathematically represented as:
It is through these lower and upper approximatio... | <p>The upper approximation is defined as the collection of cases whose equivalence classes
are at least partially contained in the set of cases we want to approximate. The upper
approximation of set $$X$$ is denoted $$\overline{{B}}X$$ and is mathematically represented as:</p>
<p>It is through these lower and upper app... | [{"type": "text", "coordinates": [87, 70, 524, 144], "content": "The upper approximation is defined as the collection of cases whose equivalence classes\nare at least partially contained in the set of cases we want to approximate. The upper\napproximation of set $$X$$ is denoted $$\\overline{{B}}X$$ and is mathematical... | [{"type": "text", "coordinates": [90, 73, 522, 87], "content": "The upper approximation is defined as the collection of cases whose equivalence classes", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 100, 522, 117], "content": "are at least partially contained in the set of cases we want to approximat... | [] | [{"type": "block", "coordinates": [90, 157, 234, 174], "content": "", "caption": ""}, {"type": "block", "coordinates": [89, 501, 173, 538], "content": "", "caption": ""}, {"type": "inline", "coordinates": [190, 131, 200, 141], "content": "X", "caption": ""}, {"type": "inline", "coordinates": [255, 128, 273, 142], "cont... | [] | [612.0, 792.0] | [{"type": "text", "text": "The upper approximation is defined as the collection of cases whose equivalence classes are at least partially contained in the set of cases we want to approximate. The upper approximation of set $X$ is denoted $\\overline{{B}}X$ and is mathematically represented as: ", "page_idx": 5}, {"type... | [{"category_id": 8, "poly": [249.46653747558594, 1398.9647216796875, 480.76025390625, 1398.9647216796875, 480.76025390625, 1498.481201171875, 249.46653747558594, 1498.481201171875], "score": 0.9999997019767761}, {"category_id": 1, "poly": [243.97305297851562, 195.4812469482422, 1457.000244140625, 195.4812469482422, 145... | {"preproc_blocks": [{"type": "text", "bbox": [87, 70, 524, 144], "lines": [{"bbox": [90, 73, 522, 87], "spans": [{"bbox": [90, 73, 522, 87], "score": 1.0, "content": "The upper approximation is defined as the collection of cases whose equivalence classes", "type": "text"}], "index": 0}, {"bbox": [88, 100, 522, 117], "s... | ./arxiv_full_mineru_outputs_20/images/0705.0761_5.png | images/0705.0761_5.png | |
0705.0761.pdf | 6 | the number of cases in the upper approximation (where $$0\!\leq\!\alpha_{_p}(X)\!\leq\!1)$$ and can be
written as:
Rough Sets Formulation
The process of modeling the rough set can be broken down into five stages. The first
stage would be to select the data while the second stage involves pre-processing the data
to en... | <p>the number of cases in the upper approximation (where $$0\!\leq\!\alpha_{_p}(X)\!\leq\!1)$$ and can be
written as:</p>
<p>Rough Sets Formulation</p>
<p>The process of modeling the rough set can be broken down into five stages. The first
stage would be to select the data while the second stage involves pre-processing... | [{"type": "text", "coordinates": [87, 71, 525, 119], "content": "the number of cases in the upper approximation (where $$0\\!\\leq\\!\\alpha_{_p}(X)\\!\\leq\\!1)$$ and can be\nwritten as:", "block_type": "text", "index": 1}, {"type": "interline_equation", "coordinates": [90, 131, 161, 171], "content": "", "block_type":... | [{"type": "text", "coordinates": [88, 73, 385, 90], "content": "the number of cases in the upper approximation (where ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [385, 73, 458, 89], "content": "0\\!\\leq\\!\\alpha_{_p}(X)\\!\\leq\\!1)", "score": 0.91, "index": 2}, {"type": "text", "coordina... | [] | [{"type": "block", "coordinates": [90, 131, 161, 171], "content": "", "caption": ""}, {"type": "block", "coordinates": [89, 686, 172, 702], "content": "", "caption": ""}, {"type": "inline", "coordinates": [385, 73, 458, 89], "content": "0\\!\\leq\\!\\alpha_{_p}(X)\\!\\leq\\!1)", "caption": ""}, {"type": "inline", "coor... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 6}, {"type": "equation", "text": "$$\n\\alpha_{p}(X)\\!=\\!\\frac{\\left|\\underline{{B}}X\\right|}{\\left|\\overline{{B}}X\\right|}\n$$", "text_format": "latex", "page_idx": 6}, {"type": "text", "text": "Rough Sets Formulation ", "page_idx": 6}, {"type": "text", "text": "The p... | [{"category_id": 1, "poly": [243.47877502441406, 199.53604125976562, 1459.13525390625, 199.53604125976562, 1459.13525390625, 331.6428527832031, 243.47877502441406, 331.6428527832031], "score": 0.9999987483024597}, {"category_id": 8, "poly": [249.7255401611328, 371.1877136230469, 449.1656188964844, 371.1877136230469, 44... | {"preproc_blocks": [{"type": "text", "bbox": [87, 71, 525, 119], "lines": [{"bbox": [88, 73, 523, 90], "spans": [{"bbox": [88, 73, 385, 90], "score": 1.0, "content": "the number of cases in the upper approximation (where ", "type": "text"}, {"bbox": [385, 73, 458, 89], "score": 0.91, "content": "0\\!\\leq\\!\\alpha_{_p... | ./arxiv_full_mineru_outputs_20/images/0705.0761_6.png | images/0705.0761_6.png | |
0705.0761.pdf | 7 | where $$\gamma$$ is the output, $$G_{x}$$ is the granulisation of the input space into high, low, medium
etc, $$N_{r}$$ is the number of rules and $$R$$ is the rules. So for a given nature of granulisation, the
rough set model will be able to give the optimal number and nature of rules and the
accuracy of prediction. T... | <p>where $$\gamma$$ is the output, $$G_{x}$$ is the granulisation of the input space into high, low, medium
etc, $$N_{r}$$ is the number of rules and $$R$$ is the rules. So for a given nature of granulisation, the
rough set model will be able to give the optimal number and nature of rules and the
accuracy of prediction... | [{"type": "text", "coordinates": [88, 70, 525, 227], "content": "where $$\\gamma$$ is the output, $$G_{x}$$ is the granulisation of the input space into high, low, medium\netc, $$N_{r}$$ is the number of rules and $$R$$ is the rules. So for a given nature of granulisation, the\nrough set model will be able to give the ... | [{"type": "text", "coordinates": [90, 73, 123, 89], "content": "where ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [123, 74, 132, 86], "content": "\\gamma", "score": 0.29, "index": 2}, {"type": "text", "coordinates": [132, 73, 203, 89], "content": " is the output, ", "score": 1.0, "index": 3... | [] | [{"type": "block", "coordinates": [90, 487, 188, 521], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 635, 162, 652], "content": "", "caption": ""}, {"type": "inline", "coordinates": [123, 74, 132, 86], "content": "\\gamma", "caption": ""}, {"type": "inline", "coordinates": [203, 73, 217, 85], "co... | [] | [612.0, 792.0] | [{"type": "text", "text": "where $\\gamma$ is the output, $G_{x}$ is the granulisation of the input space into high, low, medium etc, $N_{r}$ is the number of rules and $R$ is the rules. So for a given nature of granulisation, the rough set model will be able to give the optimal number and nature of rules and the accur... | [{"category_id": 1, "poly": [245.94424438476562, 197.19680786132812, 1459.088134765625, 197.19680786132812, 1459.088134765625, 633.0250854492188, 245.94424438476562, 633.0250854492188], "score": 0.9999971389770508}, {"category_id": 1, "poly": [244.6377716064453, 1498.6038818359375, 1457.586669921875, 1498.6038818359375... | {"preproc_blocks": [{"type": "text", "bbox": [88, 70, 525, 227], "lines": [{"bbox": [90, 73, 522, 89], "spans": [{"bbox": [90, 73, 123, 89], "score": 1.0, "content": "where ", "type": "text"}, {"bbox": [123, 74, 132, 86], "score": 0.29, "content": "\\gamma", "type": "inline_equation", "height": 12, "width": 9}, {"bbox"... | ./arxiv_full_mineru_outputs_20/images/0705.0761_7.png | images/0705.0761_7.png | |
0705.0761.pdf | 8 | $$2007^{\mathrm{a}})$$ . The output of the second layer is obtained by transforming the activation of the
second hidden layer using the second layer weights. Given the output of the hidden layer
$$z_{j}$$ in equation 8, the output of unit $$\mathbf{k}$$ may be written as:
Similarly, equation 9 may be transformed into ... | <p>$$2007^{\mathrm{a}})$$ . The output of the second layer is obtained by transforming the activation of the
second hidden layer using the second layer weights. Given the output of the hidden layer
$$z_{j}$$ in equation 8, the output of unit $$\mathbf{k}$$ may be written as:</p>
<p>Similarly, equation 9 may be transfor... | [{"type": "text", "coordinates": [88, 69, 524, 142], "content": "$$2007^{\\mathrm{a}})$$ . The output of the second layer is obtained by transforming the activation of the\nsecond hidden layer using the second layer weights. Given the output of the hidden layer\n$$z_{j}$$ in equation 8, the output of unit $$\\mathbf{k}... | [{"type": "inline_equation", "coordinates": [88, 72, 120, 85], "content": "2007^{\\mathrm{a}})", "score": 0.67, "index": 1}, {"type": "text", "coordinates": [120, 72, 522, 88], "content": ". The output of the second layer is obtained by transforming the activation of the", "score": 1.0, "index": 2}, {"type": "text", "c... | [] | [{"type": "block", "coordinates": [90, 154, 193, 189], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 259, 162, 276], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 373, 315, 411], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 679, 360, 717], "content":... | [] | [612.0, 792.0] | [{"type": "text", "text": "$2007^{\\mathrm{a}})$ . The output of the second layer is obtained by transforming the activation of the second hidden layer using the second layer weights. Given the output of the hidden layer $z_{j}$ in equation 8, the output of unit $\\mathbf{k}$ may be written as: ", "page_idx": 8}, {"typ... | [{"category_id": 1, "poly": [244.68699645996094, 194.31314086914062, 1457.2291259765625, 194.31314086914062, 1457.2291259765625, 394.5774841308594, 244.68699645996094, 394.5774841308594], "score": 0.999997615814209}, {"category_id": 8, "poly": [250.9894561767578, 433.00634765625, 541.4808959960938, 433.00634765625, 541... | {"preproc_blocks": [{"type": "text", "bbox": [88, 69, 524, 142], "lines": [{"bbox": [88, 72, 522, 88], "spans": [{"bbox": [88, 72, 120, 85], "score": 0.67, "content": "2007^{\\mathrm{a}})", "type": "inline_equation", "height": 13, "width": 32}, {"bbox": [120, 72, 522, 88], "score": 1.0, "content": ". The output of the ... | ./arxiv_full_mineru_outputs_20/images/0705.0761_8.png | images/0705.0761_8.png | |
0705.0761.pdf | 9 | The biases in equation 12 may be absorbed into the weights by including extra input
variables set permanently to 1 making $$x_{O}{=}\;l$$ and $$z o\!=\!I$$ , to give:
The function $$\mathrm{f}_{\mathrm{outer}}(\cdot)$$ may be logistic, linear, or sigmoid while $$\mathrm{f}_{\mathrm{inner}}$$ is a hyperbolic tangent
fu... | <p>The biases in equation 12 may be absorbed into the weights by including extra input
variables set permanently to 1 making $$x_{O}{=}\;l$$ and $$z o\!=\!I$$ , to give:</p>
<p>The function $$\mathrm{f}_{\mathrm{outer}}(\cdot)$$ may be logistic, linear, or sigmoid while $$\mathrm{f}_{\mathrm{inner}}$$ is a hyperbolic t... | [{"type": "text", "coordinates": [89, 71, 523, 114], "content": "The biases in equation 12 may be absorbed into the weights by including extra input\nvariables set permanently to 1 making $$x_{O}{=}\\;l$$ and $$z o\\!=\\!I$$ , to give:", "block_type": "text", "index": 1}, {"type": "interline_equation", "coordinates": [... | [{"type": "text", "coordinates": [88, 72, 523, 89], "content": "The biases in equation 12 may be absorbed into the weights by including extra input", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [89, 100, 273, 116], "content": "variables set permanently to 1 making", "score": 1.0, "index": 2}, {"type": "i... | [{"coordinates": [91, 261, 393, 592], "index": 15, "caption": "", "caption_coordinates": []}] | [{"type": "block", "coordinates": [90, 126, 308, 165], "content": "", "caption": ""}, {"type": "inline", "coordinates": [274, 100, 302, 113], "content": "x_{O}{=}\\;l", "caption": ""}, {"type": "inline", "coordinates": [324, 100, 351, 113], "content": "z o\\!=\\!I", "caption": ""}, {"type": "inline", "coordinates": [15... | [] | [612.0, 792.0] | [{"type": "text", "text": "The biases in equation 12 may be absorbed into the weights by including extra input variables set permanently to 1 making $x_{O}{=}\\;l$ and $z o\\!=\\!I$ , to give: ", "page_idx": 9}, {"type": "equation", "text": "$$\ny_{k}=f_{o u t e r}\\Bigg(\\sum_{j=0}^{M}\\gamma_{k}(G_{x},R,N_{r})_{k j}f... | [{"category_id": 1, "poly": [247.25563049316406, 197.87835693359375, 1454.5308837890625, 197.87835693359375, 1454.5308837890625, 317.6243591308594, 247.25563049316406, 317.6243591308594], "score": 0.9999977946281433}, {"category_id": 1, "poly": [246.72703552246094, 498.2884521484375, 1456.70361328125, 498.2884521484375... | {"preproc_blocks": [{"type": "text", "bbox": [89, 71, 523, 114], "lines": [{"bbox": [88, 72, 523, 89], "spans": [{"bbox": [88, 72, 523, 89], "score": 1.0, "content": "The biases in equation 12 may be absorbed into the weights by including extra input", "type": "text"}], "index": 0}, {"bbox": [89, 100, 394, 116], "spans... | ./arxiv_full_mineru_outputs_20/images/0705.0761_9.png | images/0705.0761_9.png | |
0705.0761.pdf | 10 | Bayesian training on rough sets
The Bayesian framework can be written as in (Marwala, $$2007^{\mathrm{a,b}}$$ ; Bishop, 2006):
The parameter $$P(M\mid D)$$ is the probability of the rough set model given the observed
data, $$P(D\,|\,M)$$ is the probability of the data given the assumed rough set model also
called the... | <p>Bayesian training on rough sets</p>
<p>The Bayesian framework can be written as in (Marwala, $$2007^{\mathrm{a,b}}$$ ; Bishop, 2006):</p>
<p>The parameter $$P(M\mid D)$$ is the probability of the rough set model given the observed
data, $$P(D\,|\,M)$$ is the probability of the data given the assumed rough set model ... | [{"type": "text", "coordinates": [89, 72, 246, 85], "content": "Bayesian training on rough sets", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [89, 98, 478, 114], "content": "The Bayesian framework can be written as in (Marwala, $$2007^{\\mathrm{a,b}}$$ ; Bishop, 2006):", "block_type": "text", "in... | [{"type": "text", "coordinates": [90, 73, 244, 86], "content": "Bayesian training on rough sets", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 99, 361, 114], "content": "The Bayesian framework can be written as in (Marwala,", "score": 1.0, "index": 2}, {"type": "inline_equation", "coordinates": [361,... | [] | [{"type": "block", "coordinates": [90, 126, 325, 200], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 390, 358, 423], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 439, 385, 484], "content": "", "caption": ""}, {"type": "block", "coordinates": [90, 667, 253, 706], "content":... | [] | [612.0, 792.0] | [{"type": "text", "text": "Bayesian training on rough sets ", "page_idx": 10}, {"type": "text", "text": "The Bayesian framework can be written as in (Marwala, $2007^{\\mathrm{a,b}}$ ; Bishop, 2006): ", "page_idx": 10}, {"type": "equation", "text": "$$\nP(M\\mid D)\\,{=}\\,{\\frac{P(D\\mid M)\\,p(M)}{p(D)}}\\;\\;\\;{\\m... | [{"category_id": 1, "poly": [245.1343231201172, 594.0044555664062, 1459.3663330078125, 594.0044555664062, 1459.3663330078125, 1048.4259033203125, 245.1343231201172, 1048.4259033203125], "score": 0.9999968409538269}, {"category_id": 1, "poly": [247.7950439453125, 273.4060363769531, 1329.099365234375, 273.4060363769531, ... | {"preproc_blocks": [{"type": "text", "bbox": [89, 72, 246, 85], "lines": [{"bbox": [90, 73, 244, 86], "spans": [{"bbox": [90, 73, 244, 86], "score": 1.0, "content": "Bayesian training on rough sets", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [89, 98, 478, 114], "lines": [{"bbox": [88, 98, 47... | ./arxiv_full_mineru_outputs_20/images/0705.0761_10.png | images/0705.0761_10.png | |
0705.0761.pdf | 11 | where $$\boldsymbol{z}_{2}$$ is the normalisation constant and $$\beta$$ is the hyperparameter of the network
weights. The posterior probability of the model given the observed data is thus:
where $$z$$ is the normalisation constant and $$\alpha$$ is the hyperparameter of the number of rules.
Since the number and the ... | <p>where $$\boldsymbol{z}_{2}$$ is the normalisation constant and $$\beta$$ is the hyperparameter of the network
weights. The posterior probability of the model given the observed data is thus:</p>
<p>where $$z$$ is the normalisation constant and $$\alpha$$ is the hyperparameter of the number of rules.
Since the number... | [{"type": "text", "coordinates": [88, 71, 523, 118], "content": "where $$\\boldsymbol{z}_{2}$$ is the normalisation constant and $$\\beta$$ is the hyperparameter of the network\nweights. The posterior probability of the model given the observed data is thus:", "block_type": "text", "index": 1}, {"type": "interline_equa... | [{"type": "text", "coordinates": [88, 73, 125, 89], "content": "where ", "score": 1.0, "index": 1}, {"type": "inline_equation", "coordinates": [126, 75, 136, 87], "content": "\\boldsymbol{z}_{2}", "score": 0.81, "index": 2}, {"type": "text", "coordinates": [137, 73, 313, 89], "content": "is the normalisation constant a... | [] | [{"type": "block", "coordinates": [89, 129, 342, 169], "content": "", "caption": ""}, {"type": "inline", "coordinates": [126, 75, 136, 87], "content": "\\boldsymbol{z}_{2}", "caption": ""}, {"type": "inline", "coordinates": [313, 73, 324, 87], "content": "\\beta", "caption": ""}, {"type": "inline", "coordinates": [122,... | [] | [612.0, 792.0] | [{"type": "text", "text": "where $\\boldsymbol{z}_{2}$ is the normalisation constant and $\\beta$ is the hyperparameter of the network weights. The posterior probability of the model given the observed data is thus: ", "page_idx": 11}, {"type": "equation", "text": "$$\nP(M\\mid D)\\!=\\!{\\frac{1}{z}}\\mathrm{exp}\\Big... | [{"category_id": 1, "poly": [244.785888671875, 199.64501953125, 1455.383056640625, 199.64501953125, 1455.383056640625, 328.6825256347656, 244.785888671875, 328.6825256347656], "score": 0.9999987483024597}, {"category_id": 1, "poly": [244.68077087402344, 511.83514404296875, 1456.7183837890625, 511.83514404296875, 1456.7... | {"preproc_blocks": [{"type": "text", "bbox": [88, 71, 523, 118], "lines": [{"bbox": [88, 73, 524, 89], "spans": [{"bbox": [88, 73, 125, 89], "score": 1.0, "content": "where ", "type": "text"}, {"bbox": [126, 75, 136, 87], "score": 0.81, "content": "\\boldsymbol{z}_{2}", "type": "inline_equation", "height": 12, "width":... | ./arxiv_full_mineru_outputs_20/images/0705.0761_11.png | images/0705.0761_11.png | |
0705.0761.pdf | 12 | equation 18. From equation 18 and by following the rules of probability theory, the
distribution of the output parameter, $$y_{.}$$ , is written as (Marwala, $$2007^{\mathrm{b}})$$ ):
Equation 19 depends on equation 18, and is difficult to solve analytically due to relatively
high dimension of the combined granule a... | <p>equation 18. From equation 18 and by following the rules of probability theory, the
distribution of the output parameter, $$y_{.}$$ , is written as (Marwala, $$2007^{\mathrm{b}})$$ ):</p>
<p>Equation 19 depends on equation 18, and is difficult to solve analytically due to relatively
high dimension of the combined ... | [{"type": "text", "coordinates": [87, 70, 525, 115], "content": "equation 18. From equation 18 and by following the rules of probability theory, the\ndistribution of the output parameter, $$y_{.}$$ , is written as (Marwala, $$2007^{\\mathrm{b}})$$ ):", "block_type": "text", "index": 1}, {"type": "interline_equation",... | [{"type": "text", "coordinates": [89, 73, 523, 88], "content": "equation 18. From equation 18 and by following the rules of probability theory, the", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [88, 99, 264, 115], "content": "distribution of the output parameter,", "score": 1.0, "index": 2}, {"type": "... | [] | [{"type": "block", "coordinates": [90, 126, 277, 148], "content": "", "caption": ""}, {"type": "block", "coordinates": [89, 251, 179, 289], "content": "", "caption": ""}, {"type": "block", "coordinates": [155, 612, 360, 641], "content": "", "caption": ""}, {"type": "inline", "coordinates": [264, 103, 272, 113], "conten... | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 12}, {"type": "equation", "text": "$$\np(y\\mid x,D)\\!=\\!\\int p(y\\mid x,M)p(M\\mid D)d M\n$$", "text_format": "latex", "page_idx": 12}, {"type": "text", "text": "Equation 19 depends on equation 18, and is difficult to solve analytically due to relatively high dimension of t... | [{"category_id": 1, "poly": [242.34934997558594, 195.16021728515625, 1459.158447265625, 195.16021728515625, 1459.158447265625, 319.5987548828125, 242.34934997558594, 319.5987548828125], "score": 0.9999975562095642}, {"category_id": 1, "poly": [244.04141235351562, 448.42144775390625, 1457.275390625, 448.42144775390625, ... | {"preproc_blocks": [{"type": "text", "bbox": [87, 70, 525, 115], "lines": [{"bbox": [89, 73, 523, 88], "spans": [{"bbox": [89, 73, 523, 88], "score": 1.0, "content": "equation 18. From equation 18 and by following the rules of probability theory, the", "type": "text"}], "index": 0}, {"bbox": [88, 98, 428, 115], "span... | ./arxiv_full_mineru_outputs_20/images/0705.0761_12.png | images/0705.0761_12.png | |
0705.0761.pdf | 13 | Basically the steps described above may be summarised as follows:
Step 1: Randomly generate the granule weight vector $$\langle g w\rangle_{n}$$
Step 2: Calculate the posterior probability $$p_{n}$$ using equation 18 and vector $$\langle g w\rangle_{n}$$
Step 3: Introduce random changes to vector $$\langle g w\rangl... | <p>Basically the steps described above may be summarised as follows:</p>
<p>Step 1: Randomly generate the granule weight vector $$\langle g w\rangle_{n}$$</p>
<p>Step 2: Calculate the posterior probability $$p_{n}$$ using equation 18 and vector $$\langle g w\rangle_{n}$$</p>
<p>Step 3: Introduce random changes to vecto... | [{"type": "text", "coordinates": [88, 71, 417, 86], "content": "Basically the steps described above may be summarised as follows:", "block_type": "text", "index": 1}, {"type": "text", "coordinates": [88, 100, 380, 114], "content": "Step 1: Randomly generate the granule weight vector $$\\langle g w\\rangle_{n}$$", "bloc... | [{"type": "text", "coordinates": [89, 73, 415, 87], "content": "Basically the steps described above may be summarised as follows:", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [89, 100, 348, 115], "content": "Step 1: Randomly generate the granule weight vector", "score": 1.0, "index": 2}, {"type": "inlin... | [] | [{"type": "inline", "coordinates": [348, 100, 378, 114], "content": "\\langle g w\\rangle_{n}", "caption": ""}, {"type": "inline", "coordinates": [293, 129, 306, 141], "content": "p_{n}", "caption": ""}, {"type": "inline", "coordinates": [448, 127, 478, 141], "content": "\\langle g w\\rangle_{n}", "caption": ""}, {"typ... | [] | [612.0, 792.0] | [{"type": "text", "text": "Basically the steps described above may be summarised as follows: ", "page_idx": 13}, {"type": "text", "text": "Step 1: Randomly generate the granule weight vector $\\langle g w\\rangle_{n}$ ", "page_idx": 13}, {"type": "text", "text": "Step 2: Calculate the posterior probability $p_{n}$ usin... | [{"category_id": 1, "poly": [241.32264709472656, 961.8753662109375, 1465.666259765625, 961.8753662109375, 1465.666259765625, 1933.111328125, 241.32264709472656, 1933.111328125], "score": 0.999936580657959}, {"category_id": 0, "poly": [245.97633361816406, 891.0084838867188, 912.707275390625, 891.0084838867188, 912.70727... | {"preproc_blocks": [{"type": "text", "bbox": [88, 71, 417, 86], "lines": [{"bbox": [89, 73, 415, 87], "spans": [{"bbox": [89, 73, 415, 87], "score": 1.0, "content": "Basically the steps described above may be summarised as follows:", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [88, 100, 380, 1... | ./arxiv_full_mineru_outputs_20/images/0705.0761_13.png | images/0705.0761_13.png |
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