citation_id stringlengths 89 93 | source_paper_id float64 2.1k 2.11k | cited_paper_id float64 2.1k 2.11k | source_body_item_id stringlengths 23 23 | body_item_order int64 0 1.84k | source_section stringlengths 1 211 ⌀ | source_sec_number stringclasses 284
values | source_sec_type stringclasses 3
values | citation_marker stringlengths 49 49 | span_start int64 0 95.3k | span_end int64 49 95.3k | reference_id stringlengths 57 57 | raw_source_paragraph stringlengths 51 244k | paragraph_with_target_marker stringlengths 14 242k | context_c1_sentence stringlengths 12 2.77k | context_c2_paragraph stringlengths 14 242k | context_c3_window stringlengths 110 242k | context_c3_component_body_item_ids stringlengths 47 71 | context_c4_section_aware stringlengths 110 242k | context_c4_raw_section_title stringlengths 1 211 ⌀ | candidate_atomic_passage_count int64 0 1.3k | candidate_contextual_passage_count int64 0 1.23k | candidate_total_atomic_passage_count int64 1 1.3k | candidate_total_contextual_passage_count int64 0 1.23k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2101.00098__body_000013__cite_0013__start_1576__ref_4f73c48736ce5f7ea6122853ea73b71c90f21940 | 2,101.00098 | 2,108.13004 | 2101.00098__body_000013 | 13 | Single-View 3D Reconstruction | 3 | subsection | {{cite:4f73c48736ce5f7ea6122853ea73b71c90f21940}} | 1,576 | 1,625 | 2101.00098__ref__4f73c48736ce5f7ea6122853ea73b71c90f21940 | Single-view 3D reconstruction aims at generating the 3D model of an object based on a single 2D projection of it.
Currently, deep Convolutional Neural Networks (ConvNets) based methods have achieved the highest accuracy in various benchmarks by using both low-level image cues, e.g., texture, and high-level semantic inf... | Single-view 3D reconstruction aims at generating the 3D model of an object based on a single 2D projection of it.
Currently, deep Convolutional Neural Networks (ConvNets) based methods have achieved the highest accuracy in various benchmarks by using both low-level image cues, e.g., texture, and high-level semantic inf... | A few existing work <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT> explored teeth reconstruction from X-ray, however, they either targeted at single tooth or worked with synthesized images only, which cannot serve our propose of patient-specific modeling and demonstration. | Single-view 3D reconstruction aims at generating the 3D model of an object based on a single 2D projection of it.
Currently, deep Convolutional Neural Networks (ConvNets) based methods have achieved the highest accuracy in various benchmarks by using both low-level image cues, e.g., texture, and high-level semantic inf... | CAD tools have been widely applied in dentistry to improve the design of dental restorations, e.g. crowns, dental implants and orthodontic appliances <OTHER_CIT>, <OTHER_CIT>.
Specifically, models of patients' oral cavity are created from digital 3D scanning, based on which dentists produce a virtual design of restorat... | 2101.00098__body_000012|2101.00098__body_000013|2101.00098__body_000014 | [SECTION] Single-View 3D Reconstruction
[CONTEXT]
CAD tools have been widely applied in dentistry to improve the design of dental restorations, e.g. crowns, dental implants and orthodontic appliances <OTHER_CIT>, <OTHER_CIT>.
Specifically, models of patients' oral cavity are created from digital 3D scanning, based on ... | Single-View 3D Reconstruction | 21 | 4 | 21 | 4 |
2101.00318__body_000000__cite_0001__start_190__ref_bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6 | 2,101.00318 | 2,101.00316 | 2101.00318__body_000000 | 0 | Introduction | 1 | section | {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}} | 190 | 239 | 2101.00318__ref__bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6 | The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains {{cite:1acfae6bca3fdb27d8d59584061ffec7f03f6dbf}}, {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}, {{cite:80f1542b4f6be99c38124cf8d89f12c46f726db2}}, {{cite:f7f967ce275cef99377c2... | The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose to align the marginal distributio... | The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. | The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose to align the marginal distributio... | The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose to align the marginal distributio... | 2101.00318__body_000000|2101.00318__body_000001 | [SECTION] Introduction
[CONTEXT]
The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose... | Introduction | 47 | 33 | 47 | 33 |
2101.00318__body_000007__cite_0004__start_713__ref_afc677dcb24bfbd1086d38328af76b63147eca49 | 2,101.00318 | 2,101.00317 | 2101.00318__body_000007 | 7 | Related Work | 2 | section | {{cite:afc677dcb24bfbd1086d38328af76b63147eca49}} | 713 | 762 | 2101.00318__ref__afc677dcb24bfbd1086d38328af76b63147eca49 | In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis {{cite:d50524f3e7c6b16647d8937c77673179f212f5e1}}, {{cite:72d97836bc394a2fe9a10425616c367d56dd91dc}}, {{cite:ee125d0add2d5b4c2e8662674bf596030716d8af}}. Deep lear... | In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and then fed into a prediction model into... | The effectiveness of deep learning has been demonstrated in many computer vision tasks, such as classification, detection, and segmentation <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. | In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and then fed into a prediction model into... | We propose to adaptively explore the subtype-wise conditional and label shifts in UDA without the subtype labels, and explicitly enforce the subtype-aware compactness.
We systematically investigate the cases with or without the prior information on subtype numbers. Our reliability-path based sub-graph scheme can effec... | 2101.00318__body_000006|2101.00318__body_000007|2101.00318__body_000008 | [SECTION] Related Work
[CONTEXT]
We propose to adaptively explore the subtype-wise conditional and label shifts in UDA without the subtype labels, and explicitly enforce the subtype-aware compactness.
We systematically investigate the cases with or without the prior information on subtype numbers. Our reliability-pat... | Related Work | 38 | 18 | 38 | 18 |
2101.00318__body_000008__cite_0004__start_401__ref_bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6 | 2,101.00318 | 2,101.00316 | 2101.00318__body_000008 | 8 | Related Work | 2 | section | {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}} | 401 | 450 | 2101.00318__ref__bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6 | Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications {{cite:8983ec628ed591cd40b890b1fbdb99b426b44ec2}}, {{cite:635670ba2af89d8ec96efc078523d4ce21c1b367}}, {{cite:880f4a590226730f16fbdab70c42d1262fcb329c}}. To counter this, UDA... | Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <TARGET_CIT>, which aims to match covariate shift (i.e., only {{formula... | To counter this, UDA has gradually become popular <OTHER_CIT>, <TARGET_CIT>, which aims to match covariate shift (i.e., only {{formula:180c5693-c3ba-462a-a8d9-a2697cac2adb}} shift). | Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <TARGET_CIT>, which aims to match covariate shift (i.e., only {{formula... | In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and then fed into a prediction model into... | 2101.00318__body_000007|2101.00318__body_000008|2101.00318__body_000009 | [SECTION] Related Work
[CONTEXT]
In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and the... | Related Work | 47 | 33 | 47 | 33 |
2101.00318__body_000009__cite_0001__start_123__ref_bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6 | 2,101.00318 | 2,101.00316 | 2101.00318__body_000009 | 9 | Related Work | 2 | section | {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}} | 123 | 172 | 2101.00318__ref__bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6 | Recently, pseudo labels of a target domain have been widely used in UDA {{cite:f7f967ce275cef99377c211e705a86701255ac7d}}, {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}. The pseudo labels are used to estimate target class centers {{cite:df8bc75366f50351459e663e50d0e779e13bb912}}, and the results are enforced to mat... | Recently, pseudo labels of a target domain have been widely used in UDA <OTHER_CIT>, <TARGET_CIT>. The pseudo labels are used to estimate target class centers <OTHER_CIT>, and the results are enforced to match the source class centers. Contrastive Adaptation Network <OTHER_CIT> is proposed to estimate contrastive domai... | Recently, pseudo labels of a target domain have been widely used in UDA <OTHER_CIT>, <TARGET_CIT>. | Recently, pseudo labels of a target domain have been widely used in UDA <OTHER_CIT>, <TARGET_CIT>. The pseudo labels are used to estimate target class centers <OTHER_CIT>, and the results are enforced to match the source class centers. Contrastive Adaptation Network <OTHER_CIT> is proposed to estimate contrastive domai... | Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <OTHER_CIT>, which aims to match covariate shift (i.e., only {{formula:... | 2101.00318__body_000008|2101.00318__body_000009|2101.00318__body_000010 | [SECTION] Related Work
[CONTEXT]
Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <OTHER_CIT>, which aims to match cova... | Related Work | 47 | 33 | 47 | 33 |
2101.00554__body_000029__cite_0004__start_333__ref_faa977effe6d97463e6555c0f15b8cd95d3f5478 | 2,101.00554 | 2,103.09959 | 2101.00554__body_000029 | 29 | Discussion | 4 | section | {{cite:faa977effe6d97463e6555c0f15b8cd95d3f5478}} | 333 | 382 | 2101.00554__ref__faa977effe6d97463e6555c0f15b8cd95d3f5478 | The present approach can be extended to enforce physical constraints and properties {{cite:4ef32b9d307ee1ede0bffc475a658dc16d0f3eaf}}, {{cite:df5f49a88cac2d1ff898a179117f072a4d245888}}, {{cite:d79ccb85d3c4d51dfaea989591d2fd080e552f50}}, {{cite:1e0fb6dc211228badc19d12f59934dc2dad3bca6}}.
For example, evolutional deep ne... | The present approach can be extended to enforce physical constraints and properties <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>.
For example, evolutional deep neural network <TARGET_CIT> has been able to enforce the divergence free constraint for incompressible flow.
Another possible extension is the constructio... | For example, evolutional deep neural network <TARGET_CIT> has been able to enforce the divergence free constraint for incompressible flow. | The present approach can be extended to enforce physical constraints and properties <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>.
For example, evolutional deep neural network <TARGET_CIT> has been able to enforce the divergence free constraint for incompressible flow.
Another possible extension is the constructio... | Since CNNs have a large collection of toolsets from the image processing community, the present reconstruction approach is significant from the point of view of merging image processing with sensor data analytics.
This perspective now allows engineers and scientists to move through the wealth of local and global measur... | 2101.00554__body_000028|2101.00554__body_000029|2101.00554__body_000030 | [SECTION] Discussion
[CONTEXT]
Since CNNs have a large collection of toolsets from the image processing community, the present reconstruction approach is significant from the point of view of merging image processing with sensor data analytics.
This perspective now allows engineers and scientists to move through the w... | Discussion | 94 | 66 | 94 | 66 |
2101.00781__body_000020__cite_0002__start_700__ref_59a56bbc07457c008eb7195144de915f16217459 | 2,101.00781 | 2,101.04849 | 2101.00781__body_000020 | 20 | Metric Learning for Recommendation | 2 | subsection | {{cite:59a56bbc07457c008eb7195144de915f16217459}} | 700 | 749 | 2101.00781__ref__59a56bbc07457c008eb7195144de915f16217459 | The pioneering work CML {{cite:e8affa40d3bd960293739b9730861caa2b93bde8}} learns a joint user-item metric space for capturing fine-grained user preference. It minimizes the distance between each user-item interaction in Euclidean space, i.e., {{formula:6701411e-0715-4e54-8610-fae56dcc9082}} , where {{formula:bb300fc4-9... | The pioneering work CML <OTHER_CIT> learns a joint user-item metric space for capturing fine-grained user preference. It minimizes the distance between each user-item interaction in Euclidean space, i.e., {{formula:6701411e-0715-4e54-8610-fae56dcc9082}} , where {{formula:bb300fc4-99a8-4801-8090-08a95703c669}} and {{fo... | PMLAM <TARGET_CIT> is presented to generate adaptive margins for the training triples in the metric space. | The pioneering work CML <OTHER_CIT> learns a joint user-item metric space for capturing fine-grained user preference. It minimizes the distance between each user-item interaction in Euclidean space, i.e., {{formula:6701411e-0715-4e54-8610-fae56dcc9082}} , where {{formula:bb300fc4-99a8-4801-8090-08a95703c669}} and {{fo... | The goal of metric learning is to learn a distance metric that assigns smaller distances between similar pairs, and larger distances between dissimilar pairs. Metric learning has also been adopted in recommender systems <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT> to address the issue that inner product similarity violates t... | 2101.00781__body_000019|2101.00781__body_000020|2101.00781__body_000021 | [SECTION] Metric Learning for Recommendation
[CONTEXT]
The goal of metric learning is to learn a distance metric that assigns smaller distances between similar pairs, and larger distances between dissimilar pairs. Metric learning has also been adopted in recommender systems <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT> to ad... | Metric Learning for Recommendation | 83 | 53 | 83 | 53 |
2101.01484__body_000003__cite_0000__start_422__ref_61fafec3862656e9796f4cde22c8a1569c4b5492 | 2,101.01484 | 2,103.04479 | 2101.01484__body_000003 | 3 | Introduction | 1 | section | {{cite:61fafec3862656e9796f4cde22c8a1569c4b5492}} | 422 | 471 | 2101.01484__ref__61fafec3862656e9796f4cde22c8a1569c4b5492 | The flexible and cost-effective wireless backhaul has become an attractive alternative to wired backhaul for small cell networks. However, wireless backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature of wireless channels. Therefore, the issue of secure backhaul links has aroused wide interest... | The flexible and cost-effective wireless backhaul has become an attractive alternative to wired backhaul for small cell networks. However, wireless backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature of wireless channels. Therefore, the issue of secure backhaul links has aroused wide interest... | Considering unreliable wireless backhaul connections, the authors in <TARGET_CIT> investigated the secrecy performance of cooperative single carrier HetNets. | The flexible and cost-effective wireless backhaul has become an attractive alternative to wired backhaul for small cell networks. However, wireless backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature of wireless channels. Therefore, the issue of secure backhaul links has aroused wide interest... | For the transmission security of wireless links from the EC servers to the users, the existing physical layer secure (PLS) mechanism, which has been studied intensively and extensively <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, is sufficient. However, the PLS mechanism is complicated because it could ensure th... | 2101.01484__body_000002|2101.01484__body_000003|2101.01484__body_000004 | [SECTION] Introduction
[CONTEXT]
For the transmission security of wireless links from the EC servers to the users, the existing physical layer secure (PLS) mechanism, which has been studied intensively and extensively <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, is sufficient. However, the PLS mechanism is comp... | Introduction | 151 | 114 | 151 | 114 |
2101.01369__body_000005__cite_0000__start_213__ref_e2598720f43c44d89e6c5febd43b99e169e8454e | 2,101.01369 | 2,101.01369 | 2101.01369__body_000005 | 5 | Introduction | 1 | section | {{cite:e2598720f43c44d89e6c5febd43b99e169e8454e}} | 213 | 262 | 2101.01369__ref__e2598720f43c44d89e6c5febd43b99e169e8454e | To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver {{cite:e2598720f43c44d89e6c5febd43b99e169e8454e}}. We have numerically compared the performance of the SDSD... | To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver <TARGET_CIT>. We have numerically compared the performance of the SDSD and SDJD receivers in the case of pe... | To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver <TARGET_CIT>. | To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver <TARGET_CIT>. We have numerically compared the performance of the SDSD and SDJD receivers in the case of pe... | This paper shows that the SDSD receiver can be used to improve the BER performance of either CD or ED receiver in IBCs, under perfect channel estimation. However, the SDSD receiver requires to implement both the CD and ED receivers, which lead to complicated hardware design for implanted devices. Additionally, the maxi... | 2101.01369__body_000004|2101.01369__body_000005|2101.01369__body_000006 | [SECTION] Introduction
[CONTEXT]
This paper shows that the SDSD receiver can be used to improve the BER performance of either CD or ED receiver in IBCs, under perfect channel estimation. However, the SDSD receiver requires to implement both the CD and ED receivers, which lead to complicated hardware design for implant... | Introduction | 101 | 71 | 101 | 71 |
2101.01890__body_000007__cite_0000__start_272__ref_6d34e089f18e7434db18f5f7e023a81c003e408b | 2,101.0189 | 2,101.00193 | 2101.01890__body_000007 | 7 | Introduction | 1 | section | {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}} | 272 | 321 | 2101.01890__ref__6d34e089f18e7434db18f5f7e023a81c003e408b | In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}... | In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel <TARGET_CIT>. In particular, the correction term... | With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel <TARGET_CIT>. | In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel <TARGET_CIT>. In particular, the correction term... | {{formula:26f67d1f-7de9-4c65-a49c-5edd98a23f82}}
In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the seq... | 2101.01890__body_000006|2101.01890__body_000007|2101.01890__body_000008 | [SECTION] Introduction
[CONTEXT]
{{formula:26f67d1f-7de9-4c65-a49c-5edd98a23f82}}
In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary wit... | Introduction | 116 | 99 | 116 | 99 |
2101.01890__body_000230__cite_0000__start_191__ref_6d34e089f18e7434db18f5f7e023a81c003e408b | 2,101.0189 | 2,101.00193 | 2101.01890__body_000230 | 230 | Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants | 9 | section | {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}} | 191 | 240 | 2101.01890__ref__6d34e089f18e7434db18f5f7e023a81c003e408b | Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}.
| Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
| Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>. | Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
| Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index
{{formula:3868943e-b7e1-4697-82b0-38b923109c13}} is well-defined for {{formula:2f6defca-477d-488f-af20-4bea67ddb80e}}
For {{formula:abe... | 2101.01890__body_000229|2101.01890__body_000230|2101.01890__body_000231 | [SECTION] Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants
[CONTEXT]
Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index
{{formula:3868943e-b7e1-4697-82b0-38b923109... | Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants | 116 | 99 | 116 | 99 |
2101.01890__body_000319__cite_0000__start_191__ref_6d34e089f18e7434db18f5f7e023a81c003e408b | 2,101.0189 | 2,101.00193 | 2101.01890__body_000319 | 319 | Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants | 9 | section | {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}} | 191 | 240 | 2101.01890__ref__6d34e089f18e7434db18f5f7e023a81c003e408b | Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}.
| Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
| Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>. | Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
| Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index
{{formula:3868943e-b7e1-4697-82b0-38b923109c13}} is well-defined for {{formula:2f6defca-477d-488f-af20-4bea67ddb80e}}
For {{formula:abe... | 2101.01890__body_000318|2101.01890__body_000319 | [SECTION] Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants
[CONTEXT]
Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index
{{formula:3868943e-b7e1-4697-82b0-38b923109... | Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants | 116 | 99 | 116 | 99 |
2101.02162__body_000018__cite_0003__start_2019__ref_f48e25a1fee8e81e446aecb88f279dd85c11ec4e | 2,101.02162 | 2,101.03352 | 2101.02162__body_000018 | 18 | Electronic structure | 3 | subsection | {{cite:f48e25a1fee8e81e446aecb88f279dd85c11ec4e}} | 2,019 | 2,068 | 2101.02162__ref__f48e25a1fee8e81e446aecb88f279dd85c11ec4e | The electronic band structure and density of states (DOS) within GGA+{{formula:4dd2897c-873a-46d3-bd22-60e472601a4c}}
are depicted in Fig. REF . The electronic band structure
shows two key features: a Dirac cone at the {{formula:5ab0572b-bd48-4bec-bb14-6800566ca25e}} point
and the existence of two flat-bands at {{form... | The electronic band structure and density of states (DOS) within GGA+{{formula:4dd2897c-873a-46d3-bd22-60e472601a4c}}
are depicted in Fig. REF . The electronic band structure
shows two key features: a Dirac cone at the {{formula:5ab0572b-bd48-4bec-bb14-6800566ca25e}} point
and the existence of two flat-bands at {{form... | Within this
understanding, it is clear that an increase of {{formula:ef366ab4-c604-4d60-a0a5-11f4cb4fb049}} will force the
electrons into a more localized state implying an increased effect
of the atomic SOC <TARGET_CIT>, <OTHER_CIT>.
{{figure:e8434a24-7baf-420d-a118-5ca615b77a7d}} | The electronic band structure and density of states (DOS) within GGA+{{formula:4dd2897c-873a-46d3-bd22-60e472601a4c}}
are depicted in Fig. REF . The electronic band structure
shows two key features: a Dirac cone at the {{formula:5ab0572b-bd48-4bec-bb14-6800566ca25e}} point
and the existence of two flat-bands at {{form... | The {{formula:dfd0b54b-4b92-4cc2-b2b9-0bffd6f63d0a}} , {{formula:2e89334d-6cb7-4fd4-9e1a-a8c7d515002e}} and {{formula:30c096fe-248d-4a22-b2ee-457f07c99d74}} values were found to be {{formula:5dbb8b54-2552-4372-a753-78c669a70864}}
meV, {{formula:a63e6d03-6101-46ef-ad79-a55557a7fdc5}} meV and {{formula:48fe4cd8-b1c5-... | 2101.02162__body_000017|2101.02162__body_000018|2101.02162__body_000019 | [SECTION] Electronic structure
[CONTEXT]
The {{formula:dfd0b54b-4b92-4cc2-b2b9-0bffd6f63d0a}} , {{formula:2e89334d-6cb7-4fd4-9e1a-a8c7d515002e}} and {{formula:30c096fe-248d-4a22-b2ee-457f07c99d74}} values were found to be {{formula:5dbb8b54-2552-4372-a753-78c669a70864}}
meV, {{formula:a63e6d03-6101-46ef-ad79-a55557... | Electronic structure | 27 | 5 | 27 | 5 |
2101.02161__body_000061__cite_0003__start_2173__ref_fe3c100a31a4e7906fb7f23137fbe45f930bed45 | 2,101.02161 | 2,101.02169 | 2101.02161__body_000061 | 61 | Results and Discussion | 4 | section | {{cite:fe3c100a31a4e7906fb7f23137fbe45f930bed45}} | 2,173 | 2,222 | 2101.02161__ref__fe3c100a31a4e7906fb7f23137fbe45f930bed45 | We would like to first discuss briefly about the previous calculated values of {{formula:61ae4ace-899c-48cf-ac1c-4971808450ca}} in both the Cl{{formula:eb54ef2d-b508-4e5d-a934-9c10e111a811}} and Au{{formula:e9a0dd66-eba2-4dcc-9f68-d671f78bd1e1}} ions to understand the need
of doing new theoretical results by includi... | We would like to first discuss briefly about the previous calculated values of {{formula:61ae4ace-899c-48cf-ac1c-4971808450ca}} in both the Cl{{formula:eb54ef2d-b508-4e5d-a934-9c10e111a811}} and Au{{formula:e9a0dd66-eba2-4dcc-9f68-d671f78bd1e1}} ions to understand the need
of doing new theoretical results by includi... | There are three major limitations of this calculation: (i) It uses NR theory,
however, later theoretical studies have exhibited quite large relativistic effects in the determination of {{formula:b4a8067f-589f-4be1-9cd5-56ce4d858201}} values of the negative ions
<OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>. | We would like to first discuss briefly about the previous calculated values of {{formula:61ae4ace-899c-48cf-ac1c-4971808450ca}} in both the Cl{{formula:eb54ef2d-b508-4e5d-a934-9c10e111a811}} and Au{{formula:e9a0dd66-eba2-4dcc-9f68-d671f78bd1e1}} ions to understand the need
of doing new theoretical results by includi... | with the orbital quantum number {{formula:0a48c188-2eab-4b33-9fde-c605ab7b29b8}} of the system, {{formula:471305d6-c6d0-43b2-b193-df09226e3e6c}} , {{formula:b24dc853-3c26-4216-98b4-177d2e08fac5}} , and the exponential integral {{formula:fc406c9c-f428-4ec2-8411-6af5003a819d}} .
{{table:63a9e284-9c28-4f9d-b177-c49abf346... | 2101.02161__body_000060|2101.02161__body_000061|2101.02161__body_000062 | [SECTION] Results and Discussion
[CONTEXT]
with the orbital quantum number {{formula:0a48c188-2eab-4b33-9fde-c605ab7b29b8}} of the system, {{formula:471305d6-c6d0-43b2-b193-df09226e3e6c}} , {{formula:b24dc853-3c26-4216-98b4-177d2e08fac5}} , and the exponential integral {{formula:fc406c9c-f428-4ec2-8411-6af5003a819d}}... | Results and Discussion | 34 | 0 | 35 | 0 |
2101.02420__body_000009__cite_0002__start_274__ref_28b1e5ac3687aee2ebb56a84790717ee689d41f9 | 2,101.0242 | 2,101.08435 | 2101.02420__body_000009 | 9 | Related Works | 1 | subsection | {{cite:28b1e5ac3687aee2ebb56a84790717ee689d41f9}} | 274 | 323 | 2101.02420__ref__28b1e5ac3687aee2ebb56a84790717ee689d41f9 | With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies {{cite:0bac1ec62384252319ffabaacd581aa10d24a311}}, {{cite:87e438eeee958ef13f5a3148842e3d762801ccdf}}, {{cite:28b1e5ac3687aee2ebb56a84790717ee689d41f... | With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. Regarding the ILS problem, researchers have proposed a deep learning based SD (DL-SD) algorithm... | With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. | With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. Regarding the ILS problem, researchers have proposed a deep learning based SD (DL-SD) algorithm... | Attempts that employ best-first search (BeFS) or stack algorithms to overcome the drawbacks of DFS and BrFS have been investigated in the literature <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Among these variants, A* like BeFS is the most promising variant wh... | 2101.02420__body_000008|2101.02420__body_000009|2101.02420__body_000010 | [SECTION] Related Works
[CONTEXT]
Attempts that employ best-first search (BeFS) or stack algorithms to overcome the drawbacks of DFS and BrFS have been investigated in the literature <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Among these variants, A* like Be... | Related Works | 86 | 51 | 86 | 51 |
2101.02931__body_000003__cite_0003__start_2821__ref_7c521c2435aba614111e633170861b7e2461fefa | 2,101.02931 | 2,101.02931 | 2101.02931__body_000003 | 3 | Our contribution | 1 | subsection | {{cite:7c521c2435aba614111e633170861b7e2461fefa}} | 2,821 | 2,870 | 2101.02931__ref__7c521c2435aba614111e633170861b7e2461fefa | In this paper, we also take a Bayesian approach, viewing the unknowns as random variables and tackling the problem as one of Bayesian modeling and inference . The idea is again (as in BTD-HIRLS)
to impose column sparsity jointly on the factors in a hierarchical, two-level manner. This is achieved through a Bayesian hie... | In this paper, we also take a Bayesian approach, viewing the unknowns as random variables and tackling the problem as one of Bayesian modeling and inference . The idea is again (as in BTD-HIRLS)
to impose column sparsity jointly on the factors in a hierarchical, two-level manner. This is achieved through a Bayesian hie... | A preliminary version can be found in <TARGET_CIT>. | In this paper, we also take a Bayesian approach, viewing the unknowns as random variables and tackling the problem as one of Bayesian modeling and inference . The idea is again (as in BTD-HIRLS)
to impose column sparsity jointly on the factors in a hierarchical, two-level manner. This is achieved through a Bayesian hie... | where {{formula:57b0f811-f25e-4a7c-93cd-45396fcea60b}} is an {{formula:7849c8b9-6add-42f7-9dd4-e43d9b3f9404}} matrix of rank {{formula:e83ad186-37ba-409f-84f6-65e7ff98eeb5}} , {{formula:23dc6257-196f-4048-980f-8a04107661c7}} is a nonzero column {{formula:2ba0f658-6fd6-4d07-9a8d-c230dd525a51}} -vector and {{formula:9... | 2101.02931__body_000002|2101.02931__body_000003|2101.02931__body_000004 | [SECTION] Our contribution
[CONTEXT]
where {{formula:57b0f811-f25e-4a7c-93cd-45396fcea60b}} is an {{formula:7849c8b9-6add-42f7-9dd4-e43d9b3f9404}} matrix of rank {{formula:e83ad186-37ba-409f-84f6-65e7ff98eeb5}} , {{formula:23dc6257-196f-4048-980f-8a04107661c7}} is a nonzero column {{formula:2ba0f658-6fd6-4d07-9a8d-... | Our contribution | 17 | 11 | 17 | 11 |
2101.02811__body_000579__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c | 2,101.02811 | 2,102.11702 | 2101.02811__body_000579 | 579 | Free abelian groups of finite rank | 1 | subsection | {{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}} | 752 | 801 | 2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>. | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul... | 2101.02811__body_000578|2101.02811__body_000579|2101.02811__body_000580 | [SECTION] Free abelian groups of finite rank
[CONTEXT]
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-8... | Free abelian groups of finite rank | 12 | 0 | 13 | 0 |
2101.02811__body_001127__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c | 2,101.02811 | 2,102.11702 | 2101.02811__body_001127 | 1,127 | Free abelian groups of finite rank | 1 | subsection | {{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}} | 752 | 801 | 2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>. | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul... | 2101.02811__body_001126|2101.02811__body_001127|2101.02811__body_001128 | [SECTION] Free abelian groups of finite rank
[CONTEXT]
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-8... | Free abelian groups of finite rank | 12 | 0 | 13 | 0 |
2101.02811__body_001611__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c | 2,101.02811 | 2,102.11702 | 2101.02811__body_001611 | 1,611 | Free abelian groups of finite rank | 1 | subsection | {{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}} | 752 | 801 | 2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>. | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul... | 2101.02811__body_001610|2101.02811__body_001611|2101.02811__body_001612 | [SECTION] Free abelian groups of finite rank
[CONTEXT]
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-8... | Free abelian groups of finite rank | 12 | 0 | 13 | 0 |
2101.02811__body_001842__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c | 2,101.02811 | 2,102.11702 | 2101.02811__body_001842 | 1,842 | Free abelian groups of finite rank | 1 | subsection | {{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}} | 752 | 801 | 2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>. | Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}}
is the set of all rotations, translations, and scalings of a fixed tr... | Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul... | 2101.02811__body_001841|2101.02811__body_001842|2101.02811__body_001843 | [SECTION] Free abelian groups of finite rank
[CONTEXT]
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} .
Now we turn to a specific example where the configurations have a simple geometric description.
For the Gaussian integers ({{formula:d7e7471a-9932-4186-8... | Free abelian groups of finite rank | 12 | 0 | 13 | 0 |
2101.02979__body_000008__cite_0000__start_732__ref_1e3610b704e450dd00eb73bbd6c71c750571207a | 2,101.02979 | 2,101.0297 | 2101.02979__body_000008 | 8 | null | -1 | null | {{cite:1e3610b704e450dd00eb73bbd6c71c750571207a}} | 732 | 781 | 2101.02979__ref__1e3610b704e450dd00eb73bbd6c71c750571207a | Figure REF shows the measured {{formula:d55d77ab-bbb4-4b72-be1e-7ca6ac0ed429}} of Nd{{formula:83c2193b-7ea2-41ca-b1bc-9d06aacd36f9}} Ni{{formula:9f023efc-9a8d-4e2b-bfa9-e1c971e7ffe8}} O{{formula:978cdb62-a154-4fb2-994e-6ba46cafe2d1}} up to 50 000 {{formula:4c3da5b6-0dac-4e64-8ab3-563ecd3cad05}} at several represent... | Figure REF shows the measured {{formula:d55d77ab-bbb4-4b72-be1e-7ca6ac0ed429}} of Nd{{formula:83c2193b-7ea2-41ca-b1bc-9d06aacd36f9}} Ni{{formula:9f023efc-9a8d-4e2b-bfa9-e1c971e7ffe8}} O{{formula:978cdb62-a154-4fb2-994e-6ba46cafe2d1}} up to 50 000 {{formula:4c3da5b6-0dac-4e64-8ab3-563ecd3cad05}} at several represent... | Below the phonon bands, {{formula:15fe2c07-46f0-46ad-b622-7ee75327a71f}} approaches a constant that is much lower than unity, which is the prototypical optical response of an insulator <TARGET_CIT>. | Figure REF shows the measured {{formula:d55d77ab-bbb4-4b72-be1e-7ca6ac0ed429}} of Nd{{formula:83c2193b-7ea2-41ca-b1bc-9d06aacd36f9}} Ni{{formula:9f023efc-9a8d-4e2b-bfa9-e1c971e7ffe8}} O{{formula:978cdb62-a154-4fb2-994e-6ba46cafe2d1}} up to 50 000 {{formula:4c3da5b6-0dac-4e64-8ab3-563ecd3cad05}} at several represent... | High-purity polycrystalline samples of Nd{{formula:6466b8a3-1d5d-4d47-b65c-cdfdb309ff5c}} Ni{{formula:f356ad7e-bb13-4b37-93df-4b8785bb1e19}} O{{formula:2125e10b-de83-42ec-9459-bf7e7c6a81dd}} were obtained by reacting Nd{{formula:9e801391-f463-4a39-88c1-79435d1d38f3}} Ni{{formula:ac8449f6-7ff5-41af-b4af-3730ef4d218b}} ... | 2101.02979__body_000007|2101.02979__body_000008|2101.02979__body_000009 | High-purity polycrystalline samples of Nd{{formula:6466b8a3-1d5d-4d47-b65c-cdfdb309ff5c}} Ni{{formula:f356ad7e-bb13-4b37-93df-4b8785bb1e19}} O{{formula:2125e10b-de83-42ec-9459-bf7e7c6a81dd}} were obtained by reacting Nd{{formula:9e801391-f463-4a39-88c1-79435d1d38f3}} Ni{{formula:ac8449f6-7ff5-41af-b4af-3730ef4d218b}} ... | null | 25 | 0 | 26 | 0 |
2101.03574__body_000004__cite_0001__start_678__ref_82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e | 2,101.03574 | 2,102.08349 | 2101.03574__body_000004 | 4 | Our results. | 1.0.0.1 | null | {{cite:82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e}} | 678 | 727 | 2101.03574__ref__82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e |
First, in Sec. , we consider the absolute retracts of bipartite graphs and some important subclasses of the latter. We observe that in the square of such graph {{formula:a016faf5-2800-46cc-b665-31afbc9ca6ee}} , its two partite sets induce Helly graphs. This result complements the known relations between Helly graphs a... |
First, in Sec. , we consider the absolute retracts of bipartite graphs and some important subclasses of the latter. We observe that in the square of such graph {{formula:a016faf5-2800-46cc-b665-31afbc9ca6ee}} , its two partite sets induce Helly graphs. This result complements the known relations between Helly graphs a... | Recently <TARGET_CIT>, we announced an {{formula:27e9758f-c21b-45dc-ac42-7b4d4bc10f76}} -time algorithm in order to compute all the eccentricities in a Helly graph. |
First, in Sec. , we consider the absolute retracts of bipartite graphs and some important subclasses of the latter. We observe that in the square of such graph {{formula:a016faf5-2800-46cc-b665-31afbc9ca6ee}} , its two partite sets induce Helly graphs. This result complements the known relations between Helly graphs a... | In this paper, we prove new structural and algorithmic properties of the absolute retracts of various hereditary graph classes, such as: bipartite graphs, {{formula:8be6ad9b-1611-492b-92c0-46875c65e95f}} -chromatic graphs (for any {{formula:30114bdc-e381-4c78-b34c-543583bf1d48}} ), split graphs and planar graphs. Our f... | 2101.03574__body_000003|2101.03574__body_000004|2101.03574__body_000005 | [SECTION] Our results.
[CONTEXT]
In this paper, we prove new structural and algorithmic properties of the absolute retracts of various hereditary graph classes, such as: bipartite graphs, {{formula:8be6ad9b-1611-492b-92c0-46875c65e95f}} -chromatic graphs (for any {{formula:30114bdc-e381-4c78-b34c-543583bf1d48}} ), spl... | Our results. | 108 | 84 | 108 | 84 |
2101.03574__body_000167__cite_0001__start_232__ref_82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e | 2,101.03574 | 2,102.08349 | 2101.03574__body_000167 | 167 | Large-diameter case. | 3.3.0.9 | null | {{cite:82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e}} | 232 | 281 | 2101.03574__ref__82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e | A function is called unimodal if every local minimum is also a global minimum. It is known that the eccentricity function of a Helly graph is unimodal {{cite:a72e8ee8d5a641e307c99623f2e2ca9426c326bc}}, and this property got used in {{cite:82bbd9cda0d3e4dddb92ea309e2ab4163adfb79e}} in order to compute all the eccentrici... | A function is called unimodal if every local minimum is also a global minimum. It is known that the eccentricity function of a Helly graph is unimodal <OTHER_CIT>, and this property got used in <TARGET_CIT> in order to compute all the eccentricities in this graph class in subquadratic time. Next, we prove that a simila... | It is known that the eccentricity function of a Helly graph is unimodal <OTHER_CIT>, and this property got used in <TARGET_CIT> in order to compute all the eccentricities in this graph class in subquadratic time. | A function is called unimodal if every local minimum is also a global minimum. It is known that the eccentricity function of a Helly graph is unimodal <OTHER_CIT>, and this property got used in <TARGET_CIT> in order to compute all the eccentricities in this graph class in subquadratic time. Next, we prove that a simila... | If {{formula:ee6fa6ee-d92d-415b-9ef7-8cef5914395e}} then, {{formula:6f0fd867-2c21-4763-8f0e-a409dbf59047}} . Otherwise, {{formula:d3be9ad3-ed80-4d77-ac5b-4e57bc835b46}} . By Theorem REF , for any {{formula:51a65f64-e207-4712-955a-8010f93e1a27}} there exists a neighbour {{formula:eaa8f210-27f5-4a61-98c1-8323b7b28c8f}}... | 2101.03574__body_000166|2101.03574__body_000167|2101.03574__body_000168 | [SECTION] Large-diameter case.
[CONTEXT]
If {{formula:ee6fa6ee-d92d-415b-9ef7-8cef5914395e}} then, {{formula:6f0fd867-2c21-4763-8f0e-a409dbf59047}} . Otherwise, {{formula:d3be9ad3-ed80-4d77-ac5b-4e57bc835b46}} . By Theorem REF , for any {{formula:51a65f64-e207-4712-955a-8010f93e1a27}} there exists a neighbour {{form... | Large-diameter case. | 108 | 84 | 108 | 84 |
2101.03642__body_000000__cite_0032__start_3078__ref_831b2c49cf1cafe2cd953865c94e9592e95cd3cc | 2,101.03642 | 2,103.1504 | 2101.03642__body_000000 | 0 | Introduction | 1 | section | {{cite:831b2c49cf1cafe2cd953865c94e9592e95cd3cc}} | 3,078 | 3,127 | 2101.03642__ref__831b2c49cf1cafe2cd953865c94e9592e95cd3cc | Maxwell Electrodynamics is a highly successful theory to describe properties of the electromagnetic interaction at
both the classical and the quantum length scales. Photon-photon scattering in Quantum Electrodynamics (QED)
motivates the study of non-linear extensions of the Maxwell Electrodynamics (MED), and phenomena ... | Maxwell Electrodynamics is a highly successful theory to describe properties of the electromagnetic interaction at
both the classical and the quantum length scales. Photon-photon scattering in Quantum Electrodynamics (QED)
motivates the study of non-linear extensions of the Maxwell Electrodynamics (MED), and phenomena ... | Furthermore, a number of new phenomena in Cosmology and black-hole physics have been reported in connection with non-linear extensions of electrodynamic systems coupled to gravity <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>. | Maxwell Electrodynamics is a highly successful theory to describe properties of the electromagnetic interaction at
both the classical and the quantum length scales. Photon-photon scattering in Quantum Electrodynamics (QED)
motivates the study of non-linear extensions of the Maxwell Electrodynamics (MED), and phenomena ... | Maxwell Electrodynamics is a highly successful theory to describe properties of the electromagnetic interaction at
both the classical and the quantum length scales. Photon-photon scattering in Quantum Electrodynamics (QED)
motivates the study of non-linear extensions of the Maxwell Electrodynamics (MED), and phenomena ... | 2101.03642__body_000000|2101.03642__body_000001 | [SECTION] Introduction
[CONTEXT]
Maxwell Electrodynamics is a highly successful theory to describe properties of the electromagnetic interaction at
both the classical and the quantum length scales. Photon-photon scattering in Quantum Electrodynamics (QED)
motivates the study of non-linear extensions of the Maxwell Ele... | Introduction | 51 | 38 | 51 | 38 |
2101.03640__body_000013__cite_0006__start_722__ref_66471eae0451341fed64df02c00ea628b7d91ef7 | 2,101.0364 | 2,105.12117 | 2101.03640__body_000013 | 13 | Introduction and main results | 1 | section | {{cite:66471eae0451341fed64df02c00ea628b7d91ef7}} | 722 | 771 | 2101.03640__ref__66471eae0451341fed64df02c00ea628b7d91ef7 | Starting from the groundbreaking work of De Lellis and Székelyhidi Jr. {{cite:a510b53582f2f38b0d76acbf755c3ac23693b6ec}}, there has been much development in applications of the convex integration method in connection with the Euler and Navier-Stokes equations; see the survey papers {{cite:c99e1bc203d39662e73eb5ffe158df... | Starting from the groundbreaking work of De Lellis and Székelyhidi Jr. <OTHER_CIT>, there has been much development in applications of the convex integration method in connection with the Euler and Navier-Stokes equations; see the survey papers <OTHER_CIT>, <OTHER_CIT>. Buckmaster and Vicol <OTHER_CIT> recently proved ... | Buckmaster and Vicol <OTHER_CIT> recently proved the nonuniqueness of weak solutions of the 3D evolutionary Navier-Stokes equations with finite energy using the convex integration method; see also <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT> for related works. | Starting from the groundbreaking work of De Lellis and Székelyhidi Jr. <OTHER_CIT>, there has been much development in applications of the convex integration method in connection with the Euler and Navier-Stokes equations; see the survey papers <OTHER_CIT>, <OTHER_CIT>. Buckmaster and Vicol <OTHER_CIT> recently proved ... | One related question is whether {{formula:90eb3abc-2477-49d8-bc2f-980575d02bcc}} weak solutions of (REF ) are regular. An affirmative answer is classical in dimensions {{formula:5a815efc-2d8d-448f-83ea-227443c5cf75}} , 3. The case {{formula:2084227a-8fdf-42d5-98d0-945993bf2075}} was proved by Gerhardt <OTHER_CIT>. Gi... | 2101.03640__body_000012|2101.03640__body_000013|2101.03640__body_000014 | [SECTION] Introduction and main results
[CONTEXT]
One related question is whether {{formula:90eb3abc-2477-49d8-bc2f-980575d02bcc}} weak solutions of (REF ) are regular. An affirmative answer is classical in dimensions {{formula:5a815efc-2d8d-448f-83ea-227443c5cf75}} , 3. The case {{formula:2084227a-8fdf-42d5-98d0-945... | Introduction and main results | 296 | 270 | 296 | 270 |
2101.03698__body_000000__cite_0001__start_264__ref_977cc0c3ac45850b2b87d8c14587973e3a412f3f | 2,101.03698 | 2,104.0618 | 2101.03698__body_000000 | 0 | Introduction | 1 | section | {{cite:977cc0c3ac45850b2b87d8c14587973e3a412f3f}} | 264 | 313 | 2101.03698__ref__977cc0c3ac45850b2b87d8c14587973e3a412f3f | Spatial point processes are stochastic processes which model random locations of points in space, such as random locations of trees in a forest, locations of disease cases, earthquake occurrences and crime events {{cite:4a5f23acd71ca515c1c24c1c81b00393882966da}}, {{cite:977cc0c3ac45850b2b87d8c14587973e3a412f3f}}, {{cit... | Spatial point processes are stochastic processes which model random locations of points in space, such as random locations of trees in a forest, locations of disease cases, earthquake occurrences and crime events <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. To understand the arrangement of points, the intensity function is ... | Spatial point processes are stochastic processes which model random locations of points in space, such as random locations of trees in a forest, locations of disease cases, earthquake occurrences and crime events <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. | Spatial point processes are stochastic processes which model random locations of points in space, such as random locations of trees in a forest, locations of disease cases, earthquake occurrences and crime events <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. To understand the arrangement of points, the intensity function is ... | Spatial point processes are stochastic processes which model random locations of points in space, such as random locations of trees in a forest, locations of disease cases, earthquake occurrences and crime events <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. To understand the arrangement of points, the intensity function is ... | 2101.03698__body_000000|2101.03698__body_000001 | [SECTION] Introduction
[CONTEXT]
Spatial point processes are stochastic processes which model random locations of points in space, such as random locations of trees in a forest, locations of disease cases, earthquake occurrences and crime events <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. To understand the arrangement of ... | Introduction | 70 | 46 | 70 | 46 |
2101.03984__body_000015__cite_0002__start_764__ref_efe72dfc4ef65a89d829334148ac0b003ef62a70 | 2,101.03984 | 2,103.13863 | 2101.03984__body_000015 | 15 | Introduction | 1 | section | {{cite:efe72dfc4ef65a89d829334148ac0b003ef62a70}} | 764 | 813 | 2101.03984__ref__efe72dfc4ef65a89d829334148ac0b003ef62a70 | We also compute the real Fourier–Mukai transform
of (co)associative cycles in {{formula:bee506c4-e9de-4a20-bcf0-57a3a4e22ea9}} -manifolds.
This makes us confirm the definition of
deformed Donaldson–Thomas connections
for a manifold with a {{formula:a992d0ff-1caf-46e1-ae55-698941eaf165}} -structure introduced by Lee and... | We also compute the real Fourier–Mukai transform
of (co)associative cycles in {{formula:bee506c4-e9de-4a20-bcf0-57a3a4e22ea9}} -manifolds.
This makes us confirm the definition of
deformed Donaldson–Thomas connections
for a manifold with a {{formula:a992d0ff-1caf-46e1-ae55-698941eaf165}} -structure introduced by Lee and... | In <TARGET_CIT>, we show them
and dDT connections for {{formula:21845818-d066-462d-a80a-f793d7b25ff3}} - and {{formula:cb7be958-6e61-48f8-be4c-1f806a0c5381}} -manifolds
minimize a kind of the volume functional, which is called the Dirac-Born-Infeld (DBI) action in physics. | We also compute the real Fourier–Mukai transform
of (co)associative cycles in {{formula:bee506c4-e9de-4a20-bcf0-57a3a4e22ea9}} -manifolds.
This makes us confirm the definition of
deformed Donaldson–Thomas connections
for a manifold with a {{formula:a992d0ff-1caf-46e1-ae55-698941eaf165}} -structure introduced by Lee and... | In this paper, we post some evidences showing that Definition REF
we suggest for a {{formula:6cc44c7a-d7f4-4280-aed7-a3f9fd06be78}} -manifold
is compatible with dDT connections for a {{formula:fd51982b-7448-46ef-bc9a-e407033de5a3}} -manifold and
dHYM connections for a Calabi-Yau 4-manifold
in Lemmas REF and REF .
W... | 2101.03984__body_000014|2101.03984__body_000015|2101.03984__body_000016 | [SECTION] Introduction
[CONTEXT]
In this paper, we post some evidences showing that Definition REF
we suggest for a {{formula:6cc44c7a-d7f4-4280-aed7-a3f9fd06be78}} -manifold
is compatible with dDT connections for a {{formula:fd51982b-7448-46ef-bc9a-e407033de5a3}} -manifold and
dHYM connections for a Calabi-Yau 4-man... | Introduction | 315 | 270 | 315 | 270 |
2101.03984__body_000084__cite_0001__start_211__ref_efe72dfc4ef65a89d829334148ac0b003ef62a70 | 2,101.03984 | 2,103.13863 | 2101.03984__body_000084 | 84 | The real Fourier–Mukai transform for coassociative {{formula:29f31f22-98cc-4b5f-98e3-c0dd7bf43258}} -fibrations | 4 | section | {{cite:efe72dfc4ef65a89d829334148ac0b003ef62a70}} | 211 | 260 | 2101.03984__ref__efe72dfc4ef65a89d829334148ac0b003ef62a70 | Before going further, we rewrite the associator equality
{{cite:191f822675e303a619e517a4c58731699a389232}}.
This is very useful because
Lemma REF implies an identity that will hold in more general settings.
In {{cite:efe72dfc4ef65a89d829334148ac0b003ef62a70}}, we show that it indeed holds generally.
Using this, we see... | Before going further, we rewrite the associator equality
<OTHER_CIT>.
This is very useful because
Lemma REF implies an identity that will hold in more general settings.
In <TARGET_CIT>, we show that it indeed holds generally.
Using this, we see that dDT connections for {{formula:b6b8f235-77e2-4843-b9cb-59afd4bc71b2}} ... | In <TARGET_CIT>, we show that it indeed holds generally. | Before going further, we rewrite the associator equality
<OTHER_CIT>.
This is very useful because
Lemma REF implies an identity that will hold in more general settings.
In <TARGET_CIT>, we show that it indeed holds generally.
Using this, we see that dDT connections for {{formula:b6b8f235-77e2-4843-b9cb-59afd4bc71b2}} ... | Since {{formula:31994926-f1b2-49d2-9251-457e3f2c26b7}} is obvious and the converse holds by <OTHER_CIT>,
(2) and (3) are equivalent.
We show the equivalence of (1) and (3).
By Lemma REF ,
{{formula:cec4559f-0f84-4589-b2e4-34d9cb108037}} is associative with an appropriate orientation if and only if
{{formula:6fda366a-... | 2101.03984__body_000083|2101.03984__body_000084|2101.03984__body_000085 | [SECTION] The real Fourier–Mukai transform for coassociative {{formula:29f31f22-98cc-4b5f-98e3-c0dd7bf43258}} -fibrations
[CONTEXT]
Since {{formula:31994926-f1b2-49d2-9251-457e3f2c26b7}} is obvious and the converse holds by <OTHER_CIT>,
(2) and (3) are equivalent.
We show the equivalence of (1) and (3).
By Lemma REF ... | The real Fourier–Mukai transform for coassociative {{formula:29f31f22-98cc-4b5f-98e3-c0dd7bf43258}} -fibrations | 315 | 270 | 315 | 270 |
2101.03984__body_000084__cite_0002__start_570__ref_efe72dfc4ef65a89d829334148ac0b003ef62a70 | 2,101.03984 | 2,103.13863 | 2101.03984__body_000084 | 84 | The real Fourier–Mukai transform for coassociative {{formula:29f31f22-98cc-4b5f-98e3-c0dd7bf43258}} -fibrations | 4 | section | {{cite:efe72dfc4ef65a89d829334148ac0b003ef62a70}} | 570 | 619 | 2101.03984__ref__efe72dfc4ef65a89d829334148ac0b003ef62a70 | Before going further, we rewrite the associator equality
{{cite:191f822675e303a619e517a4c58731699a389232}}.
This is very useful because
Lemma REF implies an identity that will hold in more general settings.
In {{cite:efe72dfc4ef65a89d829334148ac0b003ef62a70}}, we show that it indeed holds generally.
Using this, we see... | Before going further, we rewrite the associator equality
<OTHER_CIT>.
This is very useful because
Lemma REF implies an identity that will hold in more general settings.
In <OTHER_CIT>, we show that it indeed holds generally.
Using this, we see that dDT connections for {{formula:b6b8f235-77e2-4843-b9cb-59afd4bc71b2}} -... | For more details, see <TARGET_CIT>. | Before going further, we rewrite the associator equality
<OTHER_CIT>.
This is very useful because
Lemma REF implies an identity that will hold in more general settings.
In <OTHER_CIT>, we show that it indeed holds generally.
Using this, we see that dDT connections for {{formula:b6b8f235-77e2-4843-b9cb-59afd4bc71b2}} -... | Since {{formula:31994926-f1b2-49d2-9251-457e3f2c26b7}} is obvious and the converse holds by <OTHER_CIT>,
(2) and (3) are equivalent.
We show the equivalence of (1) and (3).
By Lemma REF ,
{{formula:cec4559f-0f84-4589-b2e4-34d9cb108037}} is associative with an appropriate orientation if and only if
{{formula:6fda366a-... | 2101.03984__body_000083|2101.03984__body_000084|2101.03984__body_000085 | [SECTION] The real Fourier–Mukai transform for coassociative {{formula:29f31f22-98cc-4b5f-98e3-c0dd7bf43258}} -fibrations
[CONTEXT]
Since {{formula:31994926-f1b2-49d2-9251-457e3f2c26b7}} is obvious and the converse holds by <OTHER_CIT>,
(2) and (3) are equivalent.
We show the equivalence of (1) and (3).
By Lemma REF ... | The real Fourier–Mukai transform for coassociative {{formula:29f31f22-98cc-4b5f-98e3-c0dd7bf43258}} -fibrations | 315 | 270 | 315 | 270 |
2101.03984__body_000107__cite_0001__start_311__ref_efe72dfc4ef65a89d829334148ac0b003ef62a70 | 2,101.03984 | 2,103.13863 | 2101.03984__body_000107 | 107 | The real Fourier–Mukai transform for Cayley {{formula:fdd9f834-6d08-4e20-8d70-6bfbc9d8b0b3}} -fibrations | 5 | section | {{cite:efe72dfc4ef65a89d829334148ac0b003ef62a70}} | 311 | 360 | 2101.03984__ref__efe72dfc4ef65a89d829334148ac0b003ef62a70 | Before going further, we rewrite the Cayley equality
{{cite:191f822675e303a619e517a4c58731699a389232}}.
This is very useful because
Lemma REF implies an identity that will hold in more general settings as in Lemma REF .
We show that it indeed holds generally and gives many applications. For more details, see {{cite:ef... | Before going further, we rewrite the Cayley equality
<OTHER_CIT>.
This is very useful because
Lemma REF implies an identity that will hold in more general settings as in Lemma REF .
We show that it indeed holds generally and gives many applications. For more details, see <TARGET_CIT>.
| For more details, see <TARGET_CIT>. | Before going further, we rewrite the Cayley equality
<OTHER_CIT>.
This is very useful because
Lemma REF implies an identity that will hold in more general settings as in Lemma REF .
We show that it indeed holds generally and gives many applications. For more details, see <TARGET_CIT>.
| Set
{{formula:0e24ba0b-0e8f-4058-963c-38797b2c5d7c}}
where
{{formula:2c62e983-b91c-46f0-bc3c-d61b51fdc4af}} and {{formula:a8fb8ac5-5bdc-494e-b2a3-c3dc595b7e4d}} are given by
{{formula:3493d36e-cf68-42a7-9007-a633254392b4}}
Set
{{formula:b220ae41-0080-4231-bfd1-3689235a2767}} and {{formula:1c07f60a-4a3f-483b-a6c3-c... | 2101.03984__body_000106|2101.03984__body_000107|2101.03984__body_000108 | [SECTION] The real Fourier–Mukai transform for Cayley {{formula:fdd9f834-6d08-4e20-8d70-6bfbc9d8b0b3}} -fibrations
[CONTEXT]
Set
{{formula:0e24ba0b-0e8f-4058-963c-38797b2c5d7c}}
where
{{formula:2c62e983-b91c-46f0-bc3c-d61b51fdc4af}} and {{formula:a8fb8ac5-5bdc-494e-b2a3-c3dc595b7e4d}} are given by
{{formula:3493d36... | The real Fourier–Mukai transform for Cayley {{formula:fdd9f834-6d08-4e20-8d70-6bfbc9d8b0b3}} -fibrations | 315 | 270 | 315 | 270 |
2101.03866__body_000024__cite_0000__start_36__ref_677659407cacb207dadef1a36f5a5d9b0660fbfb | 2,101.03866 | 2,101.03866 | 2101.03866__body_000024 | 24 | Introduction | 1 | section | {{cite:677659407cacb207dadef1a36f5a5d9b0660fbfb}} | 36 | 85 | 2101.03866__ref__677659407cacb207dadef1a36f5a5d9b0660fbfb | This article is the long version of {{cite:677659407cacb207dadef1a36f5a5d9b0660fbfb}}. It in particular provides full proofs for all results.
| This article is the long version of <TARGET_CIT>. It in particular provides full proofs for all results.
| This article is the long version of <TARGET_CIT>. | This article is the long version of <TARGET_CIT>. It in particular provides full proofs for all results.
| On the other hand,
deciding the emptiness problem for the corresponding models of register automata discussed above becomes more involved as the models are generalized. The overall idea of deciding emptiness tree register automata with extrema constraints is to (1) reduce to the emptiness problem for tree register auto... | 2101.03866__body_000023|2101.03866__body_000024|2101.03866__body_000025 | [SECTION] Introduction
[CONTEXT]
On the other hand,
deciding the emptiness problem for the corresponding models of register automata discussed above becomes more involved as the models are generalized. The overall idea of deciding emptiness tree register automata with extrema constraints is to (1) reduce to the emptin... | Introduction | 345 | 264 | 345 | 264 |
2101.03986__body_000000__cite_0001__start_424__ref_de057f82b98ebaf721f93dbf15056852a814cfa8 | 2,101.03986 | 2,101.03984 | 2101.03986__body_000000 | 0 | Introduction | 1 | section | {{cite:de057f82b98ebaf721f93dbf15056852a814cfa8}} | 424 | 473 | 2101.03986__ref__de057f82b98ebaf721f93dbf15056852a814cfa8 | A deformed Donaldson–Thomas connection for a manifold with a {{formula:bfc1a0ad-827b-4765-89a1-23e7b77fc629}} -structure,
which we call a {{formula:4d8e990e-3d64-41b5-b717-4a4014827bf2}} -dDT connection,
was first introduced by Lee and Leung {{cite:b40c7689397312522f4b5d94cd540f05c14697cc}}
as a mirror object of a Cayl... | A deformed Donaldson–Thomas connection for a manifold with a {{formula:bfc1a0ad-827b-4765-89a1-23e7b77fc629}} -structure,
which we call a {{formula:4d8e990e-3d64-41b5-b717-4a4014827bf2}} -dDT connection,
was first introduced by Lee and Leung <OTHER_CIT>
as a mirror object of a Cayley cycle (a Cayley submanifold with an... | In <TARGET_CIT>, we gave the following alternative definition of a {{formula:2b37dd52-46f0-4d5b-866e-f549e68a8c00}} -dDT connection
which seems to be more appropriate by carefully computing the real Fourier–Mukai transform again. | A deformed Donaldson–Thomas connection for a manifold with a {{formula:bfc1a0ad-827b-4765-89a1-23e7b77fc629}} -structure,
which we call a {{formula:4d8e990e-3d64-41b5-b717-4a4014827bf2}} -dDT connection,
was first introduced by Lee and Leung <OTHER_CIT>
as a mirror object of a Cayley cycle (a Cayley submanifold with an... | A deformed Donaldson–Thomas connection for a manifold with a {{formula:bfc1a0ad-827b-4765-89a1-23e7b77fc629}} -structure,
which we call a {{formula:4d8e990e-3d64-41b5-b717-4a4014827bf2}} -dDT connection,
was first introduced by Lee and Leung <OTHER_CIT>
as a mirror object of a Cayley cycle (a Cayley submanifold with an... | 2101.03986__body_000000|2101.03986__body_000001 | [SECTION] Introduction
[CONTEXT]
A deformed Donaldson–Thomas connection for a manifold with a {{formula:bfc1a0ad-827b-4765-89a1-23e7b77fc629}} -structure,
which we call a {{formula:4d8e990e-3d64-41b5-b717-4a4014827bf2}} -dDT connection,
was first introduced by Lee and Leung <OTHER_CIT>
as a mirror object of a Cayley c... | Introduction | 152 | 136 | 152 | 136 |
2101.03986__body_000034__cite_0001__start_62__ref_de057f82b98ebaf721f93dbf15056852a814cfa8 | 2,101.03986 | 2,101.03984 | 2101.03986__body_000034 | 34 | {{formula:0b5c3a86-19e1-46bf-97c1-384482df4084}} -geometry | 2.3 | subsection | {{cite:de057f82b98ebaf721f93dbf15056852a814cfa8}} | 62 | 111 | 2101.03986__ref__de057f82b98ebaf721f93dbf15056852a814cfa8 | Lemma 2.3 ({{cite:e8302be718fff05c3da809c1e73186e5fa18f915}}, {{cite:de057f82b98ebaf721f93dbf15056852a814cfa8}})
Let {{formula:94598f1a-0797-4296-ba42-803e1c110596}} be a unit vector.
Set {{formula:5bb889fb-aa32-432c-8b74-5c16df92691d}} , the orthogonal complement of {{formula:10f4b973-188b-4c89-b9f5-f4b1c6df1b51}} ... | Lemma 2.3 (<OTHER_CIT>, <TARGET_CIT>)
Let {{formula:94598f1a-0797-4296-ba42-803e1c110596}} be a unit vector.
Set {{formula:5bb889fb-aa32-432c-8b74-5c16df92691d}} , the orthogonal complement of {{formula:10f4b973-188b-4c89-b9f5-f4b1c6df1b51}} .
The group {{formula:03606a14-2917-46e7-9a46-66a58798ee45}} acts irreduci... | Lemma 2.3 (<OTHER_CIT>, <TARGET_CIT>)
Let {{formula:94598f1a-0797-4296-ba42-803e1c110596}} be a unit vector. | Lemma 2.3 (<OTHER_CIT>, <TARGET_CIT>)
Let {{formula:94598f1a-0797-4296-ba42-803e1c110596}} be a unit vector.
Set {{formula:5bb889fb-aa32-432c-8b74-5c16df92691d}} , the orthogonal complement of {{formula:10f4b973-188b-4c89-b9f5-f4b1c6df1b51}} .
The group {{formula:03606a14-2917-46e7-9a46-66a58798ee45}} acts irreduci... | The space {{formula:907d4a21-6b85-40b9-b4c7-82a5c8f1d4c0}} for {{formula:27c5b473-8d89-43e1-91bf-eb32995e595f}}
is explicitly given as follows.
For the explicit descriptions of the other irreducible summands,
see for example <OTHER_CIT>.
Lemma 2.3 (<OTHER_CIT>, <TARGET_CIT>)
Let {{formula:94598f1a-0797-4296-ba42-... | 2101.03986__body_000033|2101.03986__body_000034|2101.03986__body_000035 | [SECTION] {{formula:0b5c3a86-19e1-46bf-97c1-384482df4084}} -geometry
[CONTEXT]
The space {{formula:907d4a21-6b85-40b9-b4c7-82a5c8f1d4c0}} for {{formula:27c5b473-8d89-43e1-91bf-eb32995e595f}}
is explicitly given as follows.
For the explicit descriptions of the other irreducible summands,
see for example <OTHER_CIT>.
... | {{formula:0b5c3a86-19e1-46bf-97c1-384482df4084}} -geometry | 152 | 136 | 152 | 136 |
2101.03986__body_000088__cite_0001__start_356__ref_de057f82b98ebaf721f93dbf15056852a814cfa8 | 2,101.03986 | 2,101.03984 | 2101.03986__body_000088 | 88 | Some properties of {{formula:b39646e5-cfdb-47bc-b71e-d58f1244c9fb}} -dDT connections | 3 | section | {{cite:de057f82b98ebaf721f93dbf15056852a814cfa8}} | 356 | 405 | 2101.03986__ref__de057f82b98ebaf721f93dbf15056852a814cfa8 | Remark 3.2 Though the dDT connection for a {{formula:82b02086-94e5-4a11-9a14-8c3ecc554f62}} -manifold was first introduced in {{cite:b40c7689397312522f4b5d94cd540f05c14697cc}}
as a Hermitian connection {{formula:d8146b48-c513-492d-9a41-59134d43fb06}} satisfying {{formula:5db9e652-95b5-4d24-8ffb-3b8248d63cb3}} ,
we use... | Remark 3.2 Though the dDT connection for a {{formula:82b02086-94e5-4a11-9a14-8c3ecc554f62}} -manifold was first introduced in <OTHER_CIT>
as a Hermitian connection {{formula:d8146b48-c513-492d-9a41-59134d43fb06}} satisfying {{formula:5db9e652-95b5-4d24-8ffb-3b8248d63cb3}} ,
we use the definition above introduced in <T... | Remark 3.2 Though the dDT connection for a {{formula:82b02086-94e5-4a11-9a14-8c3ecc554f62}} -manifold was first introduced in <OTHER_CIT>
as a Hermitian connection {{formula:d8146b48-c513-492d-9a41-59134d43fb06}} satisfying {{formula:5db9e652-95b5-4d24-8ffb-3b8248d63cb3}} ,
we use the definition above introduced in <T... | Remark 3.2 Though the dDT connection for a {{formula:82b02086-94e5-4a11-9a14-8c3ecc554f62}} -manifold was first introduced in <OTHER_CIT>
as a Hermitian connection {{formula:d8146b48-c513-492d-9a41-59134d43fb06}} satisfying {{formula:5db9e652-95b5-4d24-8ffb-3b8248d63cb3}} ,
we use the definition above introduced in <T... | is called a deformed Donaldson–Thomas connection.
For the rest of this paper,
we call this a {{formula:a614b89d-f72c-40a8-890d-ca347a8c8fef}} -dDT connection for short.
Remark 3.2 Though the dDT connection for a {{formula:82b02086-94e5-4a11-9a14-8c3ecc554f62}} -manifold was first introduced in <OTHER_CIT>
as a Hermi... | 2101.03986__body_000087|2101.03986__body_000088|2101.03986__body_000089 | [SECTION] Some properties of {{formula:b39646e5-cfdb-47bc-b71e-d58f1244c9fb}} -dDT connections
[CONTEXT]
is called a deformed Donaldson–Thomas connection.
For the rest of this paper,
we call this a {{formula:a614b89d-f72c-40a8-890d-ca347a8c8fef}} -dDT connection for short.
Remark 3.2 Though the dDT connection for a... | Some properties of {{formula:b39646e5-cfdb-47bc-b71e-d58f1244c9fb}} -dDT connections | 152 | 136 | 152 | 136 |
2101.03986__body_000222__cite_0000__start_249__ref_d78f7126bc7e9c66b94d811d50c021a4025e770f | 2,101.03986 | 2,103.13863 | 2101.03986__body_000222 | 222 |
The induced {{formula:8b89ddcd-a98f-405e-942c-2c6a79da5630}} -structure from a {{formula:b7a4b7d0-3e63-4daa-9d64-83705e15b8b2}} -dDT connection | 1 | section | {{cite:d78f7126bc7e9c66b94d811d50c021a4025e770f}} | 249 | 298 | 2101.03986__ref__d78f7126bc7e9c66b94d811d50c021a4025e770f | for {{formula:57dc21ca-53fe-4fbe-a553-eabc0bd71032}} satisfying
{{formula:63c417ee-d55a-4698-bc40-9edb3801d0c2}} and {{formula:235f781e-ea97-487b-9f44-03801a8d781f}}
by Lemma REF .
We can also prove this by the “mirror" of the Cayley equality in {{cite:d78f7126bc7e9c66b94d811d50c021a4025e770f}}.
| for {{formula:57dc21ca-53fe-4fbe-a553-eabc0bd71032}} satisfying
{{formula:63c417ee-d55a-4698-bc40-9edb3801d0c2}} and {{formula:235f781e-ea97-487b-9f44-03801a8d781f}}
by Lemma REF .
We can also prove this by the “mirror" of the Cayley equality in <TARGET_CIT>.
| We can also prove this by the “mirror" of the Cayley equality in <TARGET_CIT>. | for {{formula:57dc21ca-53fe-4fbe-a553-eabc0bd71032}} satisfying
{{formula:63c417ee-d55a-4698-bc40-9edb3801d0c2}} and {{formula:235f781e-ea97-487b-9f44-03801a8d781f}}
by Lemma REF .
We can also prove this by the “mirror" of the Cayley equality in <TARGET_CIT>.
| Remark 1.10 Since
{{formula:27673881-2f00-4d1a-bcf2-9126b60d02ff}} ,
we see that
{{formula:562918b2-bb68-4225-b363-7419e7d7c52d}}
for {{formula:57dc21ca-53fe-4fbe-a553-eabc0bd71032}} satisfying
{{formula:63c417ee-d55a-4698-bc40-9edb3801d0c2}} and {{formula:235f781e-ea97-487b-9f44-03801a8d781f}}
by Lemma REF .
We ... | 2101.03986__body_000221|2101.03986__body_000222|2101.03986__body_000223 | [SECTION] The induced {{formula:8b89ddcd-a98f-405e-942c-2c6a79da5630}} -structure from a {{formula:b7a4b7d0-3e63-4daa-9d64-83705e15b8b2}} -dDT connection
[CONTEXT]
Remark 1.10 Since
{{formula:27673881-2f00-4d1a-bcf2-9126b60d02ff}} ,
we see that
{{formula:562918b2-bb68-4225-b363-7419e7d7c52d}}
for {{formula:57dc21ca... |
The induced {{formula:8b89ddcd-a98f-405e-942c-2c6a79da5630}} -structure from a {{formula:b7a4b7d0-3e63-4daa-9d64-83705e15b8b2}} -dDT connection | 315 | 270 | 315 | 270 |
2101.04704__body_000053__cite_0001__start_96__ref_7962dd5abe0a208bc6918855bff88a1df34b4a99 | 2,101.04704 | 2,105.09451 | 2101.04704__body_000053 | 53 | Datasets | 1 | subsubsection | {{cite:7962dd5abe0a208bc6918855bff88a1df34b4a99}} | 96 | 145 | 2101.04704__ref__7962dd5abe0a208bc6918855bff88a1df34b4a99 | We test our model on the CHAMELEON {{cite:ee8be266aaaf0078e9a3405aff764f8ea65fed6e}}, CAMO-Test {{cite:7962dd5abe0a208bc6918855bff88a1df34b4a99}} and COD10K-Test datasets {{cite:e7f82e56b3c1a8a727d35c82a6d6d5b2ba077b95}}. CHAMELEON {{cite:ee8be266aaaf0078e9a3405aff764f8ea65fed6e}} contains 76 images taken by independen... | We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <TARGET_CIT> and COD10K-Test datasets <OTHER_CIT>. CHAMELEON <OTHER_CIT> contains 76 images taken by independent photographers. These images are marked as good examples of camouflaged animals by the photographers.
CAMO <OTHER_CIT> contains both camouflaged and n... | We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <TARGET_CIT> and COD10K-Test datasets <OTHER_CIT>. | We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <TARGET_CIT> and COD10K-Test datasets <OTHER_CIT>. CHAMELEON <OTHER_CIT> contains 76 images taken by independent photographers. These images are marked as good examples of camouflaged animals by the photographers.
CAMO <OTHER_CIT> contains both camouflaged and n... | To further evaluate the performance of the proposed BASNet, we also tested it on the camouflaged object segmentation (COS) task <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Compared with salient object segmentation, COS is a relatively newer and more challenging task. Because the contrast between the camouflaged targets and ... | 2101.04704__body_000052|2101.04704__body_000053|2101.04704__body_000054 | [SECTION] Datasets
[CONTEXT]
To further evaluate the performance of the proposed BASNet, we also tested it on the camouflaged object segmentation (COS) task <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Compared with salient object segmentation, COS is a relatively newer and more challenging task. Because the contrast betwee... | Datasets | 57 | 20 | 57 | 20 |
2101.04704__body_000053__cite_0004__start_428__ref_7962dd5abe0a208bc6918855bff88a1df34b4a99 | 2,101.04704 | 2,105.09451 | 2101.04704__body_000053 | 53 | Datasets | 1 | subsubsection | {{cite:7962dd5abe0a208bc6918855bff88a1df34b4a99}} | 428 | 477 | 2101.04704__ref__7962dd5abe0a208bc6918855bff88a1df34b4a99 | We test our model on the CHAMELEON {{cite:ee8be266aaaf0078e9a3405aff764f8ea65fed6e}}, CAMO-Test {{cite:7962dd5abe0a208bc6918855bff88a1df34b4a99}} and COD10K-Test datasets {{cite:e7f82e56b3c1a8a727d35c82a6d6d5b2ba077b95}}. CHAMELEON {{cite:ee8be266aaaf0078e9a3405aff764f8ea65fed6e}} contains 76 images taken by independen... | We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <OTHER_CIT> and COD10K-Test datasets <OTHER_CIT>. CHAMELEON <OTHER_CIT> contains 76 images taken by independent photographers. These images are marked as good examples of camouflaged animals by the photographers.
CAMO <TARGET_CIT> contains both camouflaged and n... | CAMO <TARGET_CIT> contains both camouflaged and non-camouflaged subsets. | We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <OTHER_CIT> and COD10K-Test datasets <OTHER_CIT>. CHAMELEON <OTHER_CIT> contains 76 images taken by independent photographers. These images are marked as good examples of camouflaged animals by the photographers.
CAMO <TARGET_CIT> contains both camouflaged and n... | To further evaluate the performance of the proposed BASNet, we also tested it on the camouflaged object segmentation (COS) task <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Compared with salient object segmentation, COS is a relatively newer and more challenging task. Because the contrast between the camouflaged targets and ... | 2101.04704__body_000052|2101.04704__body_000053|2101.04704__body_000054 | [SECTION] Datasets
[CONTEXT]
To further evaluate the performance of the proposed BASNet, we also tested it on the camouflaged object segmentation (COS) task <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Compared with salient object segmentation, COS is a relatively newer and more challenging task. Because the contrast betwee... | Datasets | 57 | 20 | 57 | 20 |
2101.04704__body_000054__cite_0009__start_678__ref_7962dd5abe0a208bc6918855bff88a1df34b4a99 | 2,101.04704 | 2,105.09451 | 2101.04704__body_000054 | 54 | Comparison with State-of-the-Arts | 2 | subsubsection | {{cite:7962dd5abe0a208bc6918855bff88a1df34b4a99}} | 678 | 727 | 2101.04704__ref__7962dd5abe0a208bc6918855bff88a1df34b4a99 | To validate the performance of the proposed BASNet on the camouflaged object segmentation task, we compared BASNet
against 13 sate-of-the-art models, including FPN{{cite:2a58a5b861ead9ea7f035102908345ead18bf133}}, MaskRCNN{{cite:d05de6485e35007882ffb53ee1936973fe3efee5}}, PSPNet{{cite:8a3c307bba5b4d8cebdee5a6607e455c0e... | To validate the performance of the proposed BASNet on the camouflaged object segmentation task, we compared BASNet
against 13 sate-of-the-art models, including FPN<OTHER_CIT>, MaskRCNN<OTHER_CIT>, PSPNet<OTHER_CIT>, UNet++<OTHER_CIT>, PiCANet<OTHER_CIT>, MSRCN<OTHER_CIT>, PFANet<OTHER_CIT>, HTC<OTHER_CIT>, PoolNet<OTHE... | To validate the performance of the proposed BASNet on the camouflaged object segmentation task, we compared BASNet
against 13 sate-of-the-art models, including FPN<OTHER_CIT>, MaskRCNN<OTHER_CIT>, PSPNet<OTHER_CIT>, UNet++<OTHER_CIT>, PiCANet<OTHER_CIT>, MSRCN<OTHER_CIT>, PFANet<OTHER_CIT>, HTC<OTHER_CIT>, PoolNet<OTHE... | To validate the performance of the proposed BASNet on the camouflaged object segmentation task, we compared BASNet
against 13 sate-of-the-art models, including FPN<OTHER_CIT>, MaskRCNN<OTHER_CIT>, PSPNet<OTHER_CIT>, UNet++<OTHER_CIT>, PiCANet<OTHER_CIT>, MSRCN<OTHER_CIT>, PFANet<OTHER_CIT>, HTC<OTHER_CIT>, PoolNet<OTHE... | We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <OTHER_CIT> and COD10K-Test datasets <OTHER_CIT>. CHAMELEON <OTHER_CIT> contains 76 images taken by independent photographers. These images are marked as good examples of camouflaged animals by the photographers.
CAMO <OTHER_CIT> contains both camouflaged and no... | 2101.04704__body_000053|2101.04704__body_000054|2101.04704__body_000055 | [SECTION] Comparison with State-of-the-Arts
[CONTEXT]
We test our model on the CHAMELEON <OTHER_CIT>, CAMO-Test <OTHER_CIT> and COD10K-Test datasets <OTHER_CIT>. CHAMELEON <OTHER_CIT> contains 76 images taken by independent photographers. These images are marked as good examples of camouflaged animals by the photograp... | Comparison with State-of-the-Arts | 57 | 20 | 57 | 20 |
2101.04852__body_000034__cite_0002__start_275__ref_3b54eb2076e1e650843f748a85ab64c52a1dfd4d | 2,101.04852 | 2,101.04849 | 2101.04852__body_000034 | 34 | Adaptive and Fine-grained Regularization | 4.3 | subsection | {{cite:3b54eb2076e1e650843f748a85ab64c52a1dfd4d}} | 275 | 324 | 2101.04852__ref__3b54eb2076e1e650843f748a85ab64c52a1dfd4d | In this expression, {{formula:5bfdaed8-58a2-4845-956f-924fb8a73f29}} is the learning rate for one step of inner optimization. Related approximations have been validated in {{cite:970caa7e244f8b6a1dca1ff434177bb1f18effd4}}, {{cite:7a9150108b56ab69d649cb402a77f49c6fef9bb4}}, {{cite:3b54eb2076e1e650843f748a85ab64c52a1dfd... | In this expression, {{formula:5bfdaed8-58a2-4845-956f-924fb8a73f29}} is the learning rate for one step of inner optimization. Related approximations have been validated in <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>. Thus, we can define a proxy function to link {{formula:d8453922-ef41-4b04-8983-9c7294f43ba2}} with the out... | Related approximations have been validated in <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>. | In this expression, {{formula:5bfdaed8-58a2-4845-956f-924fb8a73f29}} is the learning rate for one step of inner optimization. Related approximations have been validated in <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>. Thus, we can define a proxy function to link {{formula:d8453922-ef41-4b04-8983-9c7294f43ba2}} with the out... | As most existing models use gradient-based methods for optimization, a simple approximation strategy with less computation is introduced as follows:
{{formula:4e1d47f3-ef20-4c89-a9f3-94708eb4203e}}
In this expression, {{formula:5bfdaed8-58a2-4845-956f-924fb8a73f29}} is the learning rate for one step of inner optimi... | 2101.04852__body_000033|2101.04852__body_000034|2101.04852__body_000035 | [SECTION] Adaptive and Fine-grained Regularization
[CONTEXT]
As most existing models use gradient-based methods for optimization, a simple approximation strategy with less computation is introduced as follows:
{{formula:4e1d47f3-ef20-4c89-a9f3-94708eb4203e}}
In this expression, {{formula:5bfdaed8-58a2-4845-956f-924... | Adaptive and Fine-grained Regularization | 83 | 53 | 83 | 53 |
2101.05113__body_000142__cite_0000__start_330__ref_cc5890d7b330c4b445d958813c993cbc45255dda | 2,101.05113 | 2,101.05113 | 2101.05113__body_000142 | 142 | Acknowledgments | -1 | section | {{cite:cc5890d7b330c4b445d958813c993cbc45255dda}} | 330 | 379 | 2101.05113__ref__cc5890d7b330c4b445d958813c993cbc45255dda | This work is supported in part by ONR under the grants N00014-18-1-2142 and N00014-19-1-2404,
by ARO under the grant W911NF-18-1-0303, and by NSF under the grants
CAREER ECCS-1818571, CCF-1806154 and CCF-1901199. A preliminary version of this paper was presented at the 2019 Asilomar Conference on Signals, Systems, and ... | This work is supported in part by ONR under the grants N00014-18-1-2142 and N00014-19-1-2404,
by ARO under the grant W911NF-18-1-0303, and by NSF under the grants
CAREER ECCS-1818571, CCF-1806154 and CCF-1901199. A preliminary version of this paper was presented at the 2019 Asilomar Conference on Signals, Systems, and ... | A preliminary version of this paper was presented at the 2019 Asilomar Conference on Signals, Systems, and Computers <TARGET_CIT>. | This work is supported in part by ONR under the grants N00014-18-1-2142 and N00014-19-1-2404,
by ARO under the grant W911NF-18-1-0303, and by NSF under the grants
CAREER ECCS-1818571, CCF-1806154 and CCF-1901199. A preliminary version of this paper was presented at the 2019 Asilomar Conference on Signals, Systems, and ... | The proof is then finished.
This work is supported in part by ONR under the grants N00014-18-1-2142 and N00014-19-1-2404,
by ARO under the grant W911NF-18-1-0303, and by NSF under the grants
CAREER ECCS-1818571, CCF-1806154 and CCF-1901199. A preliminary version of this paper was presented at the 2019 Asilomar Confer... | 2101.05113__body_000141|2101.05113__body_000142 | [SECTION] Acknowledgments
[CONTEXT]
The proof is then finished.
This work is supported in part by ONR under the grants N00014-18-1-2142 and N00014-19-1-2404,
by ARO under the grant W911NF-18-1-0303, and by NSF under the grants
CAREER ECCS-1818571, CCF-1806154 and CCF-1901199. A preliminary version of this paper was ... | Acknowledgments | 143 | 127 | 143 | 127 |
2101.05118__body_000003__cite_0008__start_996__ref_c544bb34d9d0ffa3ba7e137a0614701031f5acdb | 2,101.05118 | 2,101.03502 | 2101.05118__body_000003 | 3 | INTRODUCTION | 1 | section | {{cite:c544bb34d9d0ffa3ba7e137a0614701031f5acdb}} | 996 | 1,045 | 2101.05118__ref__c544bb34d9d0ffa3ba7e137a0614701031f5acdb | The non-correlation between the IceCube high energy neutrinos and the diffuse {{formula:cf079b5a-84d7-415b-a370-932bea55383f}} -ray background measured by the Fermi gamma-ray space telescope disfavors {{formula:fd3d92ff-e510-471f-970a-b87cd9c33c3a}} -ray bright sources as the main origin of high energy neutrinos (e.g.,... | The non-correlation between the IceCube high energy neutrinos and the diffuse {{formula:cf079b5a-84d7-415b-a370-932bea55383f}} -ray background measured by the Fermi gamma-ray space telescope disfavors {{formula:fd3d92ff-e510-471f-970a-b87cd9c33c3a}} -ray bright sources as the main origin of high energy neutrinos (e.g.,... | Chocked GRB jets (e.g., <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>; <TARGET_CIT>) and chocked jets in core collapse supernovae (CCSNe; e.g., <OTHER_CIT>; <OTHER_CIT>) have been extensively investigated as potential sources of the high energy neutrino diffuse flux. | The non-correlation between the IceCube high energy neutrinos and the diffuse {{formula:cf079b5a-84d7-415b-a370-932bea55383f}} -ray background measured by the Fermi gamma-ray space telescope disfavors {{formula:fd3d92ff-e510-471f-970a-b87cd9c33c3a}} -ray bright sources as the main origin of high energy neutrinos (e.g.,... | Various astrophysical objects and transient events were studied as possible sources of very high energy neutrinos over the years. Among the possible candidates are blazars (e.g., <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>), satuburst galaxies (e.g., <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>), magnetars... | 2101.05118__body_000002|2101.05118__body_000003|2101.05118__body_000004 | [SECTION] INTRODUCTION
[CONTEXT]
Various astrophysical objects and transient events were studied as possible sources of very high energy neutrinos over the years. Among the possible candidates are blazars (e.g., <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>; <OTHER_CIT>), satuburst galaxies (e.g., <OTHER_CIT>; <OTHER_CIT>; <O... | INTRODUCTION | 120 | 90 | 120 | 90 |
2101.05553__body_000002__cite_0001__start_260__ref_1bdfd356e20a39ec3155b2425bafc23ac097c813 | 2,101.05553 | 2,101.02169 | 2101.05553__body_000002 | 2 | Introduction | 1 | section | {{cite:1bdfd356e20a39ec3155b2425bafc23ac097c813}} | 260 | 309 | 2101.05553__ref__1bdfd356e20a39ec3155b2425bafc23ac097c813 | On physical grounds, many-body effects are expected to behave differently in ions and neutral atoms of isoelectronic systems. Among them, electron correlation effects in the negative ions are vastly different {{cite:134ab8b68ffbaeb6dec857b22134e396cf791c2d}}, {{cite:1bdfd356e20a39ec3155b2425bafc23ac097c813}} owing to t... | On physical grounds, many-body effects are expected to behave differently in ions and neutral atoms of isoelectronic systems. Among them, electron correlation effects in the negative ions are vastly different <OTHER_CIT>, <TARGET_CIT> owing to the short-range potentials that bind the outer valence electron in these ion... | On physical grounds, many-body effects are expected to behave differently in ions and neutral atoms of isoelectronic systems. Among them, electron correlation effects in the negative ions are vastly different <OTHER_CIT>, <TARGET_CIT> owing to the short-range potentials that bind the outer valence electron in these ion... | On physical grounds, many-body effects are expected to behave differently in ions and neutral atoms of isoelectronic systems. Among them, electron correlation effects in the negative ions are vastly different <OTHER_CIT>, <TARGET_CIT> owing to the short-range potentials that bind the outer valence electron in these ion... | Precise quantum many-body calculations in atoms and molecules are based on a rigorous treatment of the electron correlation effects. Although simulations of electronic structure have been performed using quantum algorithms, not much emphasis has always been placed on obtaining the correct correlation trends, mostly owi... | 2101.05553__body_000001|2101.05553__body_000002|2101.05553__body_000003 | [SECTION] Introduction
[CONTEXT]
Precise quantum many-body calculations in atoms and molecules are based on a rigorous treatment of the electron correlation effects. Although simulations of electronic structure have been performed using quantum algorithms, not much emphasis has always been placed on obtaining the corr... | Introduction | 34 | 0 | 35 | 0 |
2101.05471__body_000022__cite_0004__start_1871__ref_297a988c64ce42ab82320a20ce47332dc781b6bd | 2,101.05471 | 2,109.05109 | 2101.05471__body_000022 | 22 | Distributed Stochastic Gradient Methods | 2.4 | subsection | {{cite:297a988c64ce42ab82320a20ce47332dc781b6bd}} | 1,871 | 1,920 | 2101.05471__ref__297a988c64ce42ab82320a20ce47332dc781b6bd | Distributed stochastic gradient descent was first introduced in {{cite:af6789553ad5af7ff0d05829ed45caa5c362a307}} in the parameter-server setting. Further, in the decentralized setting, {{cite:a51af833c033552d3beb979d111aaa0ced14219d}} give the analysis on the stochastic gradient descent. All of the analysis shows that... | Distributed stochastic gradient descent was first introduced in <OTHER_CIT> in the parameter-server setting. Further, in the decentralized setting, <OTHER_CIT> give the analysis on the stochastic gradient descent. All of the analysis shows that the convergence speed will be linear to the number of workers in the parame... | Moreover, <TARGET_CIT> give an analysis of Adagrad and show the convergence speed will be linear to the number of workers. | Distributed stochastic gradient descent was first introduced in <OTHER_CIT> in the parameter-server setting. Further, in the decentralized setting, <OTHER_CIT> give the analysis on the stochastic gradient descent. All of the analysis shows that the convergence speed will be linear to the number of workers in the parame... | In practice, people usually use mini-batch stochastic gradient methods instead of single sample stochastic gradient methods or full gradient methods for faster convergence. For mini-batch SGD algorithms, <OTHER_CIT> have shown that mini-batch SGD boost {{formula:18d96244-6272-4efb-8104-3715957b0747}} convergence rate ... | 2101.05471__body_000021|2101.05471__body_000022|2101.05471__body_000023 | [SECTION] Distributed Stochastic Gradient Methods
[CONTEXT]
In practice, people usually use mini-batch stochastic gradient methods instead of single sample stochastic gradient methods or full gradient methods for faster convergence. For mini-batch SGD algorithms, <OTHER_CIT> have shown that mini-batch SGD boost {{form... | Distributed Stochastic Gradient Methods | 106 | 88 | 106 | 88 |
2101.05730__body_000029__cite_0004__start_864__ref_521c4bd3cd4ef585e3e67683f1d35ec27e403dca | 2,101.0573 | 2,102.07878 | 2101.05730__body_000029 | 29 | Single-Network Tasks | 1 | subsubsection | {{cite:521c4bd3cd4ef585e3e67683f1d35ec27e403dca}} | 864 | 913 | 2101.05730__ref__521c4bd3cd4ef585e3e67683f1d35ec27e403dca | Structural node embeddings are often used to predict the labels of nodes, when these are thought to correspond to a node's structural role in a network {{cite:d680cb5e9f051c59a82aa65647912799410b6a66}}. The problem of node classification can be modeled as a supervised machine learning problem that can be solved with an... | Structural node embeddings are often used to predict the labels of nodes, when these are thought to correspond to a node's structural role in a network <OTHER_CIT>. The problem of node classification can be modeled as a supervised machine learning problem that can be solved with any off-the-shelf downstream machine lea... | It is a common task for node embeddings <OTHER_CIT>, <TARGET_CIT>; however, the fundamental insight needed for link prediction is the proximity of the nodes (whether or not they should share an edge and be in close proximity). | Structural node embeddings are often used to predict the labels of nodes, when these are thought to correspond to a node's structural role in a network <OTHER_CIT>. The problem of node classification can be modeled as a supervised machine learning problem that can be solved with any off-the-shelf downstream machine lea... | Node embeddings may be used for a variety of downstream tasks. To evaluate the utility of various methods, we compare them based on several families of tasks which we discuss here.
Structural node embeddings are often used to predict the labels of nodes, when these are thought to correspond to a node's structural rol... | 2101.05730__body_000028|2101.05730__body_000029|2101.05730__body_000030 | [SECTION] Single-Network Tasks
[CONTEXT]
Node embeddings may be used for a variety of downstream tasks. To evaluate the utility of various methods, we compare them based on several families of tasks which we discuss here.
Structural node embeddings are often used to predict the labels of nodes, when these are though... | Single-Network Tasks | 115 | 81 | 115 | 81 |
2101.06136__body_000026__cite_0004__start_496__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000026 | 26 | Structure | 3 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 496 | 545 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | is by definition the score function and
gives a global measure of the symmetry in the system with respect to the reference structure.
The LOM and the score function has provided physical insights into a variety of systems {{cite:e30a0f793690af4d6802c03fd9a57ce39ae5955f}}, {{cite:be67b749b0b0918a4ace96afeac4094c15f4aff6... | is by definition the score function and
gives a global measure of the symmetry in the system with respect to the reference structure.
The LOM and the score function has provided physical insights into a variety of systems <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, hence they are particularly suitable also
to characterize <... | The LOM and the score function has provided physical insights into a variety of systems <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, hence they are particularly suitable also
to characterize <OTHER_CIT> and quantify <TARGET_CIT> how far
the membrane affects the water structural properties. | is by definition the score function and
gives a global measure of the symmetry in the system with respect to the reference structure.
The LOM and the score function has provided physical insights into a variety of systems <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, hence they are particularly suitable also
to characterize <... | where {{formula:d8f336f2-31d4-410a-ae47-e6f5f3f1b955}} are the Euler angles for a given orientation of the reference structure {{formula:a61f9efb-9e25-4dec-b546-f2b5ce6ffb5a}} , {{formula:1997708d-63a5-440e-b6ba-515d8a3d8dd9}} are the indices of the neighbours {{formula:0df45c53-43d5-4959-9379-5f64fb45b330}}
under t... | 2101.06136__body_000025|2101.06136__body_000026|2101.06136__body_000027 | [SECTION] Structure
[CONTEXT]
where {{formula:d8f336f2-31d4-410a-ae47-e6f5f3f1b955}} are the Euler angles for a given orientation of the reference structure {{formula:a61f9efb-9e25-4dec-b546-f2b5ce6ffb5a}} , {{formula:1997708d-63a5-440e-b6ba-515d8a3d8dd9}} are the indices of the neighbours {{formula:0df45c53-43d5-49... | Structure | 42 | 20 | 42 | 20 |
2101.06136__body_000031__cite_0000__start_9__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000031 | 31 | Structure | 3 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 9 | 58 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | We found {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} an overlap between the bulk-water distribution and that for the confined water only if between the two membrane leaflets there is enough water to reach distances as far as {{formula:0d2bb4f8-38c1-42bb-be38-c1a9e33ce56d}} nm from the membrane.
Such a remarkable... | We found <TARGET_CIT> an overlap between the bulk-water distribution and that for the confined water only if between the two membrane leaflets there is enough water to reach distances as far as {{formula:0d2bb4f8-38c1-42bb-be38-c1a9e33ce56d}} nm from the membrane.
Such a remarkable result indicates that the membrane a... | We found <TARGET_CIT> an overlap between the bulk-water distribution and that for the confined water only if between the two membrane leaflets there is enough water to reach distances as far as {{formula:0d2bb4f8-38c1-42bb-be38-c1a9e33ce56d}} nm from the membrane. | We found <TARGET_CIT> an overlap between the bulk-water distribution and that for the confined water only if between the two membrane leaflets there is enough water to reach distances as far as {{formula:0d2bb4f8-38c1-42bb-be38-c1a9e33ce56d}} nm from the membrane.
Such a remarkable result indicates that the membrane a... | Surprisingly, the two distributions do not overlap. This result indicates that the membrane perturbs the structure of water at the intermediate range of, at least, {{formula:8e8c4cff-616b-4529-8046-3f2598ae6853}} nm, considering half bin-width. This distance is much larger than that defining hydration water.
We foun... | 2101.06136__body_000030|2101.06136__body_000031|2101.06136__body_000032 | [SECTION] Structure
[CONTEXT]
Surprisingly, the two distributions do not overlap. This result indicates that the membrane perturbs the structure of water at the intermediate range of, at least, {{formula:8e8c4cff-616b-4529-8046-3f2598ae6853}} nm, considering half bin-width. This distance is much larger than that defi... | Structure | 42 | 20 | 42 | 20 |
2101.06136__body_000036__cite_0000__start_198__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000036 | 36 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 198 | 247 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | Based on the idea that the connectivity in network-forming materials governs theirs properties, we explored how the topology of the HBN changes when water is confined between phospholipid membranes {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}}.
In fact, the HBN is what differentiates water from "simple" liquids {{c... | Based on the idea that the connectivity in network-forming materials governs theirs properties, we explored how the topology of the HBN changes when water is confined between phospholipid membranes <TARGET_CIT>.
In fact, the HBN is what differentiates water from "simple" liquids <OTHER_CIT>.
| Based on the idea that the connectivity in network-forming materials governs theirs properties, we explored how the topology of the HBN changes when water is confined between phospholipid membranes <TARGET_CIT>. | Based on the idea that the connectivity in network-forming materials governs theirs properties, we explored how the topology of the HBN changes when water is confined between phospholipid membranes <TARGET_CIT>.
In fact, the HBN is what differentiates water from "simple" liquids <OTHER_CIT>.
| After some hesitant debut in the field of water <OTHER_CIT>, <OTHER_CIT>, ring statistics has been embraced more and more as a tool to study water properties, starting from its application by Martelli et al. to characterize the transformations in the bulk water HBN near the liquid-liquid critical point <OTHER_CIT>.
Sin... | 2101.06136__body_000035|2101.06136__body_000036|2101.06136__body_000037 | [SECTION] Network topology
[CONTEXT]
After some hesitant debut in the field of water <OTHER_CIT>, <OTHER_CIT>, ring statistics has been embraced more and more as a tool to study water properties, starting from its application by Martelli et al. to characterize the transformations in the bulk water HBN near the liquid-... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000040__cite_0000__start_20__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000040 | 40 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 20 | 69 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | The authors of Ref. {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} computed the probability of having a {{formula:47393cca-07fd-4d54-ae91-0c944ac28b91}} -folded ring, {{formula:7b70f178-1f0d-4004-af4f-50ec0333c48b}} , as a function of the distance {{formula:bf14cce4-b6ef-4ae6-8f7e-ebe8d069426a}} from the membrane. ... | The authors of Ref. <TARGET_CIT> computed the probability of having a {{formula:47393cca-07fd-4d54-ae91-0c944ac28b91}} -folded ring, {{formula:7b70f178-1f0d-4004-af4f-50ec0333c48b}} , as a function of the distance {{formula:bf14cce4-b6ef-4ae6-8f7e-ebe8d069426a}} from the membrane. They found that near the membrane the... | The authors of Ref. <TARGET_CIT> computed the probability of having a {{formula:47393cca-07fd-4d54-ae91-0c944ac28b91}} -folded ring, {{formula:7b70f178-1f0d-4004-af4f-50ec0333c48b}} , as a function of the distance {{formula:bf14cce4-b6ef-4ae6-8f7e-ebe8d069426a}} from the membrane. | The authors of Ref. <TARGET_CIT> computed the probability of having a {{formula:47393cca-07fd-4d54-ae91-0c944ac28b91}} -folded ring, {{formula:7b70f178-1f0d-4004-af4f-50ec0333c48b}} , as a function of the distance {{formula:bf14cce4-b6ef-4ae6-8f7e-ebe8d069426a}} from the membrane. They found that near the membrane the... | In Fig. REF we present three possible ways of defining rings in a directional network, as in the case of water. The first (Fig. REF Top) explicitly looks for the shortest ring <OTHER_CIT> starting from the molecule 1, when this molecule donates one HB, regardless whether other molecules in the ring accept or donate a... | 2101.06136__body_000039|2101.06136__body_000040|2101.06136__body_000041 | [SECTION] Network topology
[CONTEXT]
In Fig. REF we present three possible ways of defining rings in a directional network, as in the case of water. The first (Fig. REF Top) explicitly looks for the shortest ring <OTHER_CIT> starting from the molecule 1, when this molecule donates one HB, regardless whether other mo... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000043__cite_0002__start_687__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000043 | 43 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 687 | 736 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | This sudden change in {{formula:7dfc76ea-06c4-4d94-ab99-9adf7a432f3b}} , between the first and the following bins, is consistent with the results, discussed in the previous sections, demonstrating the existence of a drastic change in structure and dynamics between bound water, in the first hydration layer, and unbound ... | This sudden change in {{formula:7dfc76ea-06c4-4d94-ab99-9adf7a432f3b}} , between the first and the following bins, is consistent with the results, discussed in the previous sections, demonstrating the existence of a drastic change in structure and dynamics between bound water, in the first hydration layer, and unbound ... | Here, the border between the two regions is increased from {{formula:5cc235ac-6c13-460f-9b43-44cf01519c26}} nm <OTHER_CIT> to
{{formula:8f8a6c2a-226a-427e-9cc6-5684f6c5cf9a}} nm due to the membrane fluctuations, that are not filtered out in Ref. <TARGET_CIT>, and to the spatial resolution, i.e., the bin-size, of the ... | This sudden change in {{formula:7dfc76ea-06c4-4d94-ab99-9adf7a432f3b}} , between the first and the following bins, is consistent with the results, discussed in the previous sections, demonstrating the existence of a drastic change in structure and dynamics between bound water, in the first hydration layer, and unbound ... | All the {{formula:3581aaab-aecb-45bf-b8fd-6e0830db4c08}} calculated at larger distances, {{formula:5ab25697-cade-41d3-9e8e-484bdc021fbf}} nm, are quite different from that for the hydration water and gradually converge towards a the bulk case upon increasing {{formula:91d8084e-f979-4c24-ac21-f9bfe081c193}} . In parti... | 2101.06136__body_000042|2101.06136__body_000043|2101.06136__body_000044 | [SECTION] Network topology
[CONTEXT]
All the {{formula:3581aaab-aecb-45bf-b8fd-6e0830db4c08}} calculated at larger distances, {{formula:5ab25697-cade-41d3-9e8e-484bdc021fbf}} nm, are quite different from that for the hydration water and gradually converge towards a the bulk case upon increasing {{formula:91d8084e-f9... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000045__cite_0001__start_436__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000045 | 45 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 436 | 485 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | The quality of the HBN, in terms of broken and intact HBs, is a tool of fundamental importance to fully cast the topology of the HBN in a consistent and complete physical framework.
As a matter of fact, the presence of coordination defects affects the fluidity of water and is directly related to its capability of absor... | The quality of the HBN, in terms of broken and intact HBs, is a tool of fundamental importance to fully cast the topology of the HBN in a consistent and complete physical framework.
As a matter of fact, the presence of coordination defects affects the fluidity of water and is directly related to its capability of absor... | Therefore, the authors in Ref. <TARGET_CIT> complemented their investigation of the HBN topology with the analysis of its quality. | The quality of the HBN, in terms of broken and intact HBs, is a tool of fundamental importance to fully cast the topology of the HBN in a consistent and complete physical framework.
As a matter of fact, the presence of coordination defects affects the fluidity of water and is directly related to its capability of absor... | The HBN of bulk water is finally recovered in the bin centered at {{formula:63ce3139-ff34-48fa-a42a-433f6ae7be26}} nm away from the membrane,
i.e., for {{formula:f9413756-6f78-45c5-bd29-90579de2b7ea}} nm. Remarkably, this distance corresponds to the same at which water recovers the IRO of bulk water <OTHER_CIT>, as d... | 2101.06136__body_000044|2101.06136__body_000045|2101.06136__body_000046 | [SECTION] Network topology
[CONTEXT]
The HBN of bulk water is finally recovered in the bin centered at {{formula:63ce3139-ff34-48fa-a42a-433f6ae7be26}} nm away from the membrane,
i.e., for {{formula:f9413756-6f78-45c5-bd29-90579de2b7ea}} nm. Remarkably, this distance corresponds to the same at which water recovers t... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000050__cite_0001__start_268__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000050 | 50 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 268 | 317 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance {{cite:6bcc7abd852b18e64da30a688e1f625f018145fb}}, {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}}, a... | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance <OTHER_CIT>, <TARGET_CIT>, and with the enhanced hexagonal ring-statistics of the HBN <OTHER_CIT>, alre... | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance <OTHER_CIT>, <TARGET_CIT>, and with the enhanced hexagonal ring-statistics of the HBN <OTHER_CIT>, alre... | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance <OTHER_CIT>, <TARGET_CIT>, and with the enhanced hexagonal ring-statistics of the HBN <OTHER_CIT>, alre... | In the proximity of the membrane, the network of HBs largely deviates from that of bulk water, except for the under-coordinated configuration {{formula:2b52626a-6162-471c-9524-8ca37d060255}} .
In particular, the coordination defects
{{formula:a309e70e-8b33-43b2-be3f-a054b68de857}} and
{{formula:28771b12-d417-425b-b2ae... | 2101.06136__body_000049|2101.06136__body_000050|2101.06136__body_000051 | [SECTION] Network topology
[CONTEXT]
In the proximity of the membrane, the network of HBs largely deviates from that of bulk water, except for the under-coordinated configuration {{formula:2b52626a-6162-471c-9524-8ca37d060255}} .
In particular, the coordination defects
{{formula:a309e70e-8b33-43b2-be3f-a054b68de857}} ... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000050__cite_0002__start_378__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000050 | 50 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 378 | 427 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance {{cite:6bcc7abd852b18e64da30a688e1f625f018145fb}}, {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}}, a... | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance <OTHER_CIT>, <OTHER_CIT>, and with the enhanced hexagonal ring-statistics of the HBN <TARGET_CIT>, alre... | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance <OTHER_CIT>, <OTHER_CIT>, and with the enhanced hexagonal ring-statistics of the HBN <TARGET_CIT>, alre... | However, the small percentage of perfectly coordinated configurations, {{formula:54df87a0-687f-4d37-8b57-259da3a5b55b}} , near the membrane seems inconsistent with the higher local order observed at the same distance <OTHER_CIT>, <OTHER_CIT>, and with the enhanced hexagonal ring-statistics of the HBN <TARGET_CIT>, alre... | In the proximity of the membrane, the network of HBs largely deviates from that of bulk water, except for the under-coordinated configuration {{formula:2b52626a-6162-471c-9524-8ca37d060255}} .
In particular, the coordination defects
{{formula:a309e70e-8b33-43b2-be3f-a054b68de857}} and
{{formula:28771b12-d417-425b-b2ae... | 2101.06136__body_000049|2101.06136__body_000050|2101.06136__body_000051 | [SECTION] Network topology
[CONTEXT]
In the proximity of the membrane, the network of HBs largely deviates from that of bulk water, except for the under-coordinated configuration {{formula:2b52626a-6162-471c-9524-8ca37d060255}} .
In particular, the coordination defects
{{formula:a309e70e-8b33-43b2-be3f-a054b68de857}} ... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000053__cite_0000__start_70__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000053 | 53 | Network topology | 4 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 70 | 119 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | Away from the membrane, upon increasing the distance, Martelli et al. {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} observed a progressive enhancement of perfectly tetra-coordinated configurations (Fig. REF lower panel).
They found a progressive depletion of all coordination defects, up to recovering the bulk-wate... | Away from the membrane, upon increasing the distance, Martelli et al. <TARGET_CIT> observed a progressive enhancement of perfectly tetra-coordinated configurations (Fig. REF lower panel).
They found a progressive depletion of all coordination defects, up to recovering the bulk-water case at distance {{formula:8a6c4b98... | Away from the membrane, upon increasing the distance, Martelli et al. <TARGET_CIT> observed a progressive enhancement of perfectly tetra-coordinated configurations (Fig. REF lower panel). | Away from the membrane, upon increasing the distance, Martelli et al. <TARGET_CIT> observed a progressive enhancement of perfectly tetra-coordinated configurations (Fig. REF lower panel).
They found a progressive depletion of all coordination defects, up to recovering the bulk-water case at distance {{formula:8a6c4b98... | Second, the defects analysis includes only HBs between water molecules and do not account for the strong HBs between water molecules and the phospholipid headgroups. Instead, as discussed in the previous section <OTHER_CIT>, {{formula:dfc587f5-2b6d-4b49-a51e-293a8a8bb4f3}} of the water molecules in the first hydration... | 2101.06136__body_000052|2101.06136__body_000053|2101.06136__body_000054 | [SECTION] Network topology
[CONTEXT]
Second, the defects analysis includes only HBs between water molecules and do not account for the strong HBs between water molecules and the phospholipid headgroups. Instead, as discussed in the previous section <OTHER_CIT>, {{formula:dfc587f5-2b6d-4b49-a51e-293a8a8bb4f3}} of the ... | Network topology | 42 | 20 | 42 | 20 |
2101.06136__body_000059__cite_0000__start_29__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000059 | 59 | Conclusions and future research directions | 5 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 29 | 78 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | Furthermore, Martelli et al. {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} analyzed the IRO from the HB perspective by studying the HBN topology and its ring statistics. They found that water within {{formula:4842d611-209c-4f14-a675-3100cace5155}} nm from the average position of the fluctuating membrane has an exc... | Furthermore, Martelli et al. <TARGET_CIT> analyzed the IRO from the HB perspective by studying the HBN topology and its ring statistics. They found that water within {{formula:4842d611-209c-4f14-a675-3100cace5155}} nm from the average position of the fluctuating membrane has an excess of hexagonal and shorter rings, a... | Furthermore, Martelli et al. <TARGET_CIT> analyzed the IRO from the HB perspective by studying the HBN topology and its ring statistics. | Furthermore, Martelli et al. <TARGET_CIT> analyzed the IRO from the HB perspective by studying the HBN topology and its ring statistics. They found that water within {{formula:4842d611-209c-4f14-a675-3100cace5155}} nm from the average position of the fluctuating membrane has an excess of hexagonal and shorter rings, a... | However, we showed that the membrane interface has an effect on the structure of the hydration water at a distance almost twice as large, up to, at least, {{formula:4620b53f-92e4-4bac-951a-5fd83e0aacf9}} nm <OTHER_CIT>. We got such a result by analyzing how the water structure, and its IRO, changes by moving away from... | 2101.06136__body_000058|2101.06136__body_000059|2101.06136__body_000060 | [SECTION] Conclusions and future research directions
[CONTEXT]
However, we showed that the membrane interface has an effect on the structure of the hydration water at a distance almost twice as large, up to, at least, {{formula:4620b53f-92e4-4bac-951a-5fd83e0aacf9}} nm <OTHER_CIT>. We got such a result by analyzing h... | Conclusions and future research directions | 42 | 20 | 42 | 20 |
2101.06136__body_000060__cite_0000__start_16__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000060 | 60 | Conclusions and future research directions | 5 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 16 | 65 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | Martelli et al. {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} found also a sudden change in the HBN around {{formula:b9e833cf-0cb0-4d82-869c-7c89a3d7e63b}} nm, with a ring statistics that approaches that of bulk. This result confirms the qualitative difference between bound and unbound water {{cite:fbba47337ac72dc... | Martelli et al. <TARGET_CIT> found also a sudden change in the HBN around {{formula:b9e833cf-0cb0-4d82-869c-7c89a3d7e63b}} nm, with a ring statistics that approaches that of bulk. This result confirms the qualitative difference between bound and unbound water <OTHER_CIT>.
| Martelli et al. <TARGET_CIT> found also a sudden change in the HBN around {{formula:b9e833cf-0cb0-4d82-869c-7c89a3d7e63b}} nm, with a ring statistics that approaches that of bulk. | Martelli et al. <TARGET_CIT> found also a sudden change in the HBN around {{formula:b9e833cf-0cb0-4d82-869c-7c89a3d7e63b}} nm, with a ring statistics that approaches that of bulk. This result confirms the qualitative difference between bound and unbound water <OTHER_CIT>.
| Furthermore, Martelli et al. <OTHER_CIT> analyzed the IRO from the HB perspective by studying the HBN topology and its ring statistics. They found that water within {{formula:4842d611-209c-4f14-a675-3100cace5155}} nm from the average position of the fluctuating membrane has an excess of hexagonal and shorter rings, an... | 2101.06136__body_000059|2101.06136__body_000060|2101.06136__body_000061 | [SECTION] Conclusions and future research directions
[CONTEXT]
Furthermore, Martelli et al. <OTHER_CIT> analyzed the IRO from the HB perspective by studying the HBN topology and its ring statistics. They found that water within {{formula:4842d611-209c-4f14-a675-3100cace5155}} nm from the average position of the fluct... | Conclusions and future research directions | 42 | 20 | 42 | 20 |
2101.06136__body_000061__cite_0000__start_229__ref_d2769e83c22ba3c35201593c267a141edf8d6595 | 2,101.06136 | 2,101.06151 | 2101.06136__body_000061 | 61 | Conclusions and future research directions | 5 | section | {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}} | 229 | 278 | 2101.06136__ref__d2769e83c22ba3c35201593c267a141edf8d6595 | The analysis of the HBN ring statistics and the HBN defects
show that the membrane interface generates a perturbations in the ring statistics that extends as far as, at least, {{formula:6f964e33-b9a6-4d57-9dfd-ae30c1ac51bb}} nm {{cite:d2769e83c22ba3c35201593c267a141edf8d6595}}. These observations, therefore, corrobora... | The analysis of the HBN ring statistics and the HBN defects
show that the membrane interface generates a perturbations in the ring statistics that extends as far as, at least, {{formula:6f964e33-b9a6-4d57-9dfd-ae30c1ac51bb}} nm <TARGET_CIT>. These observations, therefore, corroborate that the water structure is affect... | The analysis of the HBN ring statistics and the HBN defects
show that the membrane interface generates a perturbations in the ring statistics that extends as far as, at least, {{formula:6f964e33-b9a6-4d57-9dfd-ae30c1ac51bb}} nm <TARGET_CIT>. | The analysis of the HBN ring statistics and the HBN defects
show that the membrane interface generates a perturbations in the ring statistics that extends as far as, at least, {{formula:6f964e33-b9a6-4d57-9dfd-ae30c1ac51bb}} nm <TARGET_CIT>. These observations, therefore, corroborate that the water structure is affect... | Martelli et al. <OTHER_CIT> found also a sudden change in the HBN around {{formula:b9e833cf-0cb0-4d82-869c-7c89a3d7e63b}} nm, with a ring statistics that approaches that of bulk. This result confirms the qualitative difference between bound and unbound water <OTHER_CIT>.
The analysis of the HBN ring statistics and t... | 2101.06136__body_000060|2101.06136__body_000061|2101.06136__body_000062 | [SECTION] Conclusions and future research directions
[CONTEXT]
Martelli et al. <OTHER_CIT> found also a sudden change in the HBN around {{formula:b9e833cf-0cb0-4d82-869c-7c89a3d7e63b}} nm, with a ring statistics that approaches that of bulk. This result confirms the qualitative difference between bound and unbound wa... | Conclusions and future research directions | 42 | 20 | 42 | 20 |
2101.06044__body_000012__cite_0000__start_155__ref_56d41c75ce33fbb4d735788fddfefc2d971cd047 | 2,101.06044 | 2,101.06044 | 2101.06044__body_000012 | 12 | INTRODUCTION | 1 | section | {{cite:56d41c75ce33fbb4d735788fddfefc2d971cd047}} | 155 | 204 | 2101.06044__ref__56d41c75ce33fbb4d735788fddfefc2d971cd047 | In our work, we overcome the above limitations by proposing the following contributions. This paper is based on our recent ION GNSS+ 2020 conference paper {{cite:56d41c75ce33fbb4d735788fddfefc2d971cd047}}.
| In our work, we overcome the above limitations by proposing the following contributions. This paper is based on our recent ION GNSS+ 2020 conference paper <TARGET_CIT>.
| This paper is based on our recent ION GNSS+ 2020 conference paper <TARGET_CIT>. | In our work, we overcome the above limitations by proposing the following contributions. This paper is based on our recent ION GNSS+ 2020 conference paper <TARGET_CIT>.
| 1
They address state estimation and integrity monitoring separately, similar to traditional RAIM approaches.
2
They accommodate camera measurements within a linear or linearizable framework such as KF, EKF, or IF and become infeasible when camera measurements are not linearizable without loss of generality.
3
There is ... | 2101.06044__body_000011|2101.06044__body_000012|2101.06044__body_000013 | [SECTION] INTRODUCTION
[CONTEXT]
1
They address state estimation and integrity monitoring separately, similar to traditional RAIM approaches.
2
They accommodate camera measurements within a linear or linearizable framework such as KF, EKF, or IF and become infeasible when camera measurements are not linearizable witho... | INTRODUCTION | 54 | 26 | 54 | 26 |
2101.06337__body_000000__cite_0001__start_275__ref_db68695ccc800d8c40e14bfde2e9e8c4a184b7e0 | 2,101.06337 | 2,101.06338 | 2101.06337__body_000000 | 0 | INTRODUCTION | 1 | section | {{cite:db68695ccc800d8c40e14bfde2e9e8c4a184b7e0}} | 275 | 324 | 2101.06337__ref__db68695ccc800d8c40e14bfde2e9e8c4a184b7e0 | The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a 21 cm neutral hydrogen intensity mapping experiment to be deployed in the Karoo Desert in South Africa {{cite:48b60f6e12cd22923312e0b5b84c8b00f0144800}}. It will consist of 1024 six-meter parabolic dishes {{cite:db68695ccc800d8c40e14bfde2e9e8c4a184b7... | The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a 21 cm neutral hydrogen intensity mapping experiment to be deployed in the Karoo Desert in South Africa <OTHER_CIT>. It will consist of 1024 six-meter parabolic dishes <TARGET_CIT>, and will map much of the southern sky over the course of four years. ... | It will consist of 1024 six-meter parabolic dishes <TARGET_CIT>, and will map much of the southern sky over the course of four years. | The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a 21 cm neutral hydrogen intensity mapping experiment to be deployed in the Karoo Desert in South Africa <OTHER_CIT>. It will consist of 1024 six-meter parabolic dishes <TARGET_CIT>, and will map much of the southern sky over the course of four years. ... | The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a 21 cm neutral hydrogen intensity mapping experiment to be deployed in the Karoo Desert in South Africa <OTHER_CIT>. It will consist of 1024 six-meter parabolic dishes <TARGET_CIT>, and will map much of the southern sky over the course of four years. ... | 2101.06337__body_000000|2101.06337__body_000001 | [SECTION] INTRODUCTION
[CONTEXT]
The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a 21 cm neutral hydrogen intensity mapping experiment to be deployed in the Karoo Desert in South Africa <OTHER_CIT>. It will consist of 1024 six-meter parabolic dishes <TARGET_CIT>, and will map much of the southern s... | INTRODUCTION | 54 | 12 | 54 | 12 |
2101.06410__body_000002__cite_0012__start_2513__ref_6a8079f8498e5f2d139ba89b84cee6340c4374b0 | 2,101.0641 | 2,101.03628 | 2101.06410__body_000002 | 2 | Introduction | 1 | section | {{cite:6a8079f8498e5f2d139ba89b84cee6340c4374b0}} | 2,513 | 2,562 | 2101.06410__ref__6a8079f8498e5f2d139ba89b84cee6340c4374b0 | In four dimensions, the first black hole solution with a scalar field as a matter field was derived by Bocharova, Bronnikov and Melnikov and independently by Bekenstein, called BBMB black hole {{cite:96823e9d7e7d6c28557cde182d498f7ca784ea82}}. The scalar field is conformally coupled to gravity, resulting to the vanishi... | In four dimensions, the first black hole solution with a scalar field as a matter field was derived by Bocharova, Bronnikov and Melnikov and independently by Bekenstein, called BBMB black hole <OTHER_CIT>. The scalar field is conformally coupled to gravity, resulting to the vanishing of scalar curvature, the metric tak... | Finally, in <TARGET_CIT> Plebanski-Demianski solutions in Quadratic gravity with conformally coupled scalar fields were investigated. | In four dimensions, the first black hole solution with a scalar field as a matter field was derived by Bocharova, Bronnikov and Melnikov and independently by Bekenstein, called BBMB black hole <OTHER_CIT>. The scalar field is conformally coupled to gravity, resulting to the vanishing of scalar curvature, the metric tak... | After the discovery of this solution, scalar fields minimally and nonminimally coupled to gravity were introduced as matter fields. In <OTHER_CIT>, <OTHER_CIT> three dimensional black holes with a conformally coupled scalar field, being regular everywhere, were discussed. After these first results other hairy black hol... | 2101.06410__body_000001|2101.06410__body_000002|2101.06410__body_000003 | [SECTION] Introduction
[CONTEXT]
After the discovery of this solution, scalar fields minimally and nonminimally coupled to gravity were introduced as matter fields. In <OTHER_CIT>, <OTHER_CIT> three dimensional black holes with a conformally coupled scalar field, being regular everywhere, were discussed. After these f... | Introduction | 49 | 34 | 49 | 34 |
2101.06379__body_000007__cite_0000__start_278__ref_d613e14c6ee7bc6fd2258be943ec3eadce219647 | 2,101.06379 | 2,101.06379 | 2101.06379__body_000007 | 7 | Introduction | 1 | section | {{cite:d613e14c6ee7bc6fd2258be943ec3eadce219647}} | 278 | 327 | 2101.06379__ref__d613e14c6ee7bc6fd2258be943ec3eadce219647 | In this paper, we propose a novel method for computing protection levels associated with a given vehicular state estimate (position and orientation) from camera image measurements and a 3D map of the environment. This work is based on our recent ION GNSS+ 2020 conference paper {{cite:d613e14c6ee7bc6fd2258be943ec3eadce2... | In this paper, we propose a novel method for computing protection levels associated with a given vehicular state estimate (position and orientation) from camera image measurements and a 3D map of the environment. This work is based on our recent ION GNSS+ 2020 conference paper <TARGET_CIT> and includes additional exper... | This work is based on our recent ION GNSS+ 2020 conference paper <TARGET_CIT> and includes additional experiments and improvements to the DNN training process. | In this paper, we propose a novel method for computing protection levels associated with a given vehicular state estimate (position and orientation) from camera image measurements and a 3D map of the environment. This work is based on our recent ION GNSS+ 2020 conference paper <TARGET_CIT> and includes additional exper... | While aleatoric uncertainty is typically modeled as the input-dependent variance in the output of the DNN <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, epistemic uncertainty relates to the DNN model and, therefore, requires further deliberation. Existing approaches approximate epistemic uncertainty by assuming a probability d... | 2101.06379__body_000006|2101.06379__body_000007|2101.06379__body_000008 | [SECTION] Introduction
[CONTEXT]
While aleatoric uncertainty is typically modeled as the input-dependent variance in the output of the DNN <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, epistemic uncertainty relates to the DNN model and, therefore, requires further deliberation. Existing approaches approximate epistemic uncer... | Introduction | 87 | 43 | 87 | 43 |
2101.06367__body_000005__cite_0003__start_1587__ref_e43397690b1737dff1a83ada47e38bf0d1be81b4 | 2,101.06367 | 2,101.06597 | 2101.06367__body_000005 | 5 | Introduction | 1 | section | {{cite:e43397690b1737dff1a83ada47e38bf0d1be81b4}} | 1,587 | 1,636 | 2101.06367__ref__e43397690b1737dff1a83ada47e38bf0d1be81b4 | All these aforementioned studies demonstrate that the flow physics past a microcylinder confined in a channel can become increasingly complex if one changes either the blockage ratio or places an additional microcylinder in it. This is primarily due to the variation of the extent of shear and extensional flow fields in... | All these aforementioned studies demonstrate that the flow physics past a microcylinder confined in a channel can become increasingly complex if one changes either the blockage ratio or places an additional microcylinder in it. This is primarily due to the variation of the extent of shear and extensional flow fields in... | Only recently <TARGET_CIT>, it has been proven that this motion is, indeed, due to the breakage of micelles downstream of the sphere using the two-species Vasquez-Cook-McKinley (VCM) model <OTHER_CIT>. | All these aforementioned studies demonstrate that the flow physics past a microcylinder confined in a channel can become increasingly complex if one changes either the blockage ratio or places an additional microcylinder in it. This is primarily due to the variation of the extent of shear and extensional flow fields in... | Apart from the influence of the blockage ratio, the placing of another microcylinder in the channel can also greatly modify the flow field in this model geometry. For example, Haward et al. <OTHER_CIT> experimentally found a significant modification in the flow field in between the two microcylinders than that seen for... | 2101.06367__body_000004|2101.06367__body_000005|2101.06367__body_000006 | [SECTION] Introduction
[CONTEXT]
Apart from the influence of the blockage ratio, the placing of another microcylinder in the channel can also greatly modify the flow field in this model geometry. For example, Haward et al. <OTHER_CIT> experimentally found a significant modification in the flow field in between the two... | Introduction | 32 | 13 | 32 | 13 |
2101.06500__body_000050__cite_0002__start_574__ref_9b67117226c8b92533e40b069d2ed39d3462df38 | 2,101.065 | 2,106.12544 | 2101.06500__body_000050 | 50 | External and internal parameters in the maximum potential intensity formulations | 3.b | subsection | {{cite:9b67117226c8b92533e40b069d2ed39d3462df38}} | 574 | 623 | 2101.06500__ref__9b67117226c8b92533e40b069d2ed39d3462df38 | For Lilly's analytical model, which is closely related to E-PI, it was established that the outflow temperature
(which Lilly himself believed was environmentally prescribed) is controlled by the interior flow of the cyclone {{cite:fe89a18436996bdb08756a7cf437d5f834036bdc}}.
Equations (REF ) and (REF ) are probably more... | For Lilly's analytical model, which is closely related to E-PI, it was established that the outflow temperature
(which Lilly himself believed was environmentally prescribed) is controlled by the interior flow of the cyclone <OTHER_CIT>.
Equations (REF ) and (REF ) are probably more transparent than, but has a similar p... | Equations (REF ) and (REF ) are probably more transparent than, but has a similar physical meaning as, <OTHER_CIT>'s Eq. (2), although explicitly demonstrating the equivalence
of different maximum potential intensity formulations may require considerable space <TARGET_CIT>. | For Lilly's analytical model, which is closely related to E-PI, it was established that the outflow temperature
(which Lilly himself believed was environmentally prescribed) is controlled by the interior flow of the cyclone <OTHER_CIT>.
Equations (REF ) and (REF ) are probably more transparent than, but has a similar p... | These empirical findings have two implications. First, calculating {{formula:84230459-a88a-49c3-9b0d-ccce568cb57a}} (Table REF )
for an arbitrary environment may not be very informative: if the cyclone modifies its outflow region,
there should exist “unmodified” environments where cyclonic outflows may never happen. O... | 2101.06500__body_000049|2101.06500__body_000050|2101.06500__body_000051 | [SECTION] External and internal parameters in the maximum potential intensity formulations
[CONTEXT]
These empirical findings have two implications. First, calculating {{formula:84230459-a88a-49c3-9b0d-ccce568cb57a}} (Table REF )
for an arbitrary environment may not be very informative: if the cyclone modifies its ou... | External and internal parameters in the maximum potential intensity formulations | 288 | 227 | 288 | 227 |
2101.06500__body_000052__cite_0000__start_0__ref_9b67117226c8b92533e40b069d2ed39d3462df38 | 2,101.065 | 2,106.12544 | 2101.06500__body_000052 | 52 | External and internal parameters in the maximum potential intensity formulations | 3.b | subsection | {{cite:9b67117226c8b92533e40b069d2ed39d3462df38}} | 0 | 49 | 2101.06500__ref__9b67117226c8b92533e40b069d2ed39d3462df38 | {{cite:9b67117226c8b92533e40b069d2ed39d3462df38}} showed that conventional E-PI at the point of maximum wind corresponds to an infinitely narrow thermodynamic cycle, where the finite changes of temperature and pressure are adiabatic and where total work in the free troposphere is zero. Work of this cycle is equal to wo... | <TARGET_CIT> showed that conventional E-PI at the point of maximum wind corresponds to an infinitely narrow thermodynamic cycle, where the finite changes of temperature and pressure are adiabatic and where total work in the free troposphere is zero. Work of this cycle is equal to work at the top of the boundary layer {... | <TARGET_CIT> showed that conventional E-PI at the point of maximum wind corresponds to an infinitely narrow thermodynamic cycle, where the finite changes of temperature and pressure are adiabatic and where total work in the free troposphere is zero. | <TARGET_CIT> showed that conventional E-PI at the point of maximum wind corresponds to an infinitely narrow thermodynamic cycle, where the finite changes of temperature and pressure are adiabatic and where total work in the free troposphere is zero. Work of this cycle is equal to work at the top of the boundary layer {... | For {{formula:5f41fec0-8a75-42bd-a476-053f34e1da07}} and a realistic {{formula:ad4dccb2-49d4-48d8-83a0-4d7abc8ac52c}} , Eq. (REF ) predicts that the outflow temperature should be about one half of {{formula:c53105db-8969-43b4-ba5c-5b66cfc0595c}} , i.e., around 150 K. Such temperatures are well below the tropopause tem... | 2101.06500__body_000051|2101.06500__body_000052|2101.06500__body_000053 | [SECTION] External and internal parameters in the maximum potential intensity formulations
[CONTEXT]
For {{formula:5f41fec0-8a75-42bd-a476-053f34e1da07}} and a realistic {{formula:ad4dccb2-49d4-48d8-83a0-4d7abc8ac52c}} , Eq. (REF ) predicts that the outflow temperature should be about one half of {{formula:c53105db-8... | External and internal parameters in the maximum potential intensity formulations | 288 | 227 | 288 | 227 |
2101.06510__body_000003__cite_0020__start_2847__ref_910e9be1473785b58cc4f56958788ea755541512 | 2,101.0651 | 2,101.03628 | 2101.06510__body_000003 | 3 | Introduction | 1 | section | {{cite:910e9be1473785b58cc4f56958788ea755541512}} | 2,847 | 2,896 | 2101.06510__ref__910e9be1473785b58cc4f56958788ea755541512 | In the vacuum Einstein system, the Taub-NUT solution generalizes Schwarzschild solution to include the so-called NUT (Newman-Unti-Tamburino) parameter {{formula:4534ce8c-e442-4dc7-b7b8-3bd3aefdb18a}} . This parameter is interpreted as a “gravitomagnetic” mass in an analogy to the magnetic monopole in electromagnetic th... | In the vacuum Einstein system, the Taub-NUT solution generalizes Schwarzschild solution to include the so-called NUT (Newman-Unti-Tamburino) parameter {{formula:4534ce8c-e442-4dc7-b7b8-3bd3aefdb18a}} . This parameter is interpreted as a “gravitomagnetic” mass in an analogy to the magnetic monopole in electromagnetic th... | In a recent work <OTHER_CIT>, the authors show that the Misner string contribution to the entropy of Taub-NUT-AdS can be renormalized by introducing the Gauss-Bonnet term, and in <TARGET_CIT> the authors show how to embed the Taub-NUT solutions in general scalar-tensor theories. | In the vacuum Einstein system, the Taub-NUT solution generalizes Schwarzschild solution to include the so-called NUT (Newman-Unti-Tamburino) parameter {{formula:4534ce8c-e442-4dc7-b7b8-3bd3aefdb18a}} . This parameter is interpreted as a “gravitomagnetic” mass in an analogy to the magnetic monopole in electromagnetic th... | Despite the loss of asymptotic flatness for a magnetized spacetime containing a black hole, this solution has been considered to have some astrophysical uses especially in modeling the spacetime near rotating supermassive black hole surrounded by hot moving plasma <OTHER_CIT>. Indeed, a full comprehension for the inter... | 2101.06510__body_000002|2101.06510__body_000003|2101.06510__body_000004 | [SECTION] Introduction
[CONTEXT]
Despite the loss of asymptotic flatness for a magnetized spacetime containing a black hole, this solution has been considered to have some astrophysical uses especially in modeling the spacetime near rotating supermassive black hole surrounded by hot moving plasma <OTHER_CIT>. Indeed, ... | Introduction | 49 | 34 | 49 | 34 |
2101.06749__body_000003__cite_0003__start_515__ref_5a8e6d87a81425ae158728dfde73e2cbc4072644 | 2,101.06749 | 2,101.05795 | 2101.06749__body_000003 | 3 | Introduction | 1 | section | {{cite:5a8e6d87a81425ae158728dfde73e2cbc4072644}} | 515 | 564 | 2101.06749__ref__5a8e6d87a81425ae158728dfde73e2cbc4072644 | In the context of deep neural networks, there exist another class of methods that are composed of Restricted Boltzmann Machines (RBMs) {{cite:3756e4c729ad2184f0bbfb5567bb86cd3fe28089}}, a stochastic approach represented by a bipartite graph whose training is given by the minimization of the energy between a visible and... | In the context of deep neural networks, there exist another class of methods that are composed of Restricted Boltzmann Machines (RBMs) <OTHER_CIT>, a stochastic approach represented by a bipartite graph whose training is given by the minimization of the energy between a visible and a latent layer. Among these methods, ... | Among these methods, Deep Belief Networks (DBNs) <OTHER_CIT> and Deep Boltzmann Machines <OTHER_CIT>, <TARGET_CIT> achieved a considerable popularity in the last years due the satisfactory results over a wide variety of applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. | In the context of deep neural networks, there exist another class of methods that are composed of Restricted Boltzmann Machines (RBMs) <OTHER_CIT>, a stochastic approach represented by a bipartite graph whose training is given by the minimization of the energy between a visible and a latent layer. Among these methods, ... | The model achieved fast popularity, being applied in a wide range of applications, such as traffic surveillance <OTHER_CIT>, medicine <OTHER_CIT>, <OTHER_CIT>, and action recognition <OTHER_CIT>, to cite a few. Moreover, many works proposed different approaches using the idea of residual functions. Lin et al. <OTHER_CI... | 2101.06749__body_000002|2101.06749__body_000003|2101.06749__body_000004 | [SECTION] Introduction
[CONTEXT]
The model achieved fast popularity, being applied in a wide range of applications, such as traffic surveillance <OTHER_CIT>, medicine <OTHER_CIT>, <OTHER_CIT>, and action recognition <OTHER_CIT>, to cite a few. Moreover, many works proposed different approaches using the idea of residu... | Introduction | 56 | 31 | 56 | 31 |
2101.06865__body_000008__cite_0012__start_1668__ref_1162074e2ebefbc6b7b15c88f7b78990398bae09 | 2,101.06865 | 2,101.06742 | 2101.06865__body_000008 | 8 | Point Cloud Segmentation | 2 | null | {{cite:1162074e2ebefbc6b7b15c88f7b78990398bae09}} | 1,668 | 1,717 | 2101.06865__ref__1162074e2ebefbc6b7b15c88f7b78990398bae09 | Initial attempts for 3D point cloud segmentation {{cite:179adc62108331785b8920415935693aa8bd51e2}}, {{cite:6c3a15b056e833f3de7b4ead0a469c344a01964f}} used clustering methods to identify individual objects.
Convolutional networks using a layered 2D representation for the point cloud in bird's-eye view have also been pr... | Initial attempts for 3D point cloud segmentation <OTHER_CIT>, <OTHER_CIT> used clustering methods to identify individual objects.
Convolutional networks using a layered 2D representation for the point cloud in bird's-eye view have also been proposed <OTHER_CIT>, where the sparsity of the data can be further exploited ... | Recently, parametric continuous convolutions <TARGET_CIT> were shown to significantly improve over the state-of-the-art by reasoning directly over neighborhood graphs constructed from points with their natural coordinates in continuous domain. | Initial attempts for 3D point cloud segmentation <OTHER_CIT>, <OTHER_CIT> used clustering methods to identify individual objects.
Convolutional networks using a layered 2D representation for the point cloud in bird's-eye view have also been proposed <OTHER_CIT>, where the sparsity of the data can be further exploited ... | End-to-end trainable structured prediction techniques model dependencies between the predictions at multiple pixels <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. We draw inspiration from this to refine our segmentation results by reasoning about spatio-temporally related 3D points.
Initial attempts for 3D point cloud segme... | 2101.06865__body_000007|2101.06865__body_000008|2101.06865__body_000009 | [SECTION] Point Cloud Segmentation
[CONTEXT]
End-to-end trainable structured prediction techniques model dependencies between the predictions at multiple pixels <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. We draw inspiration from this to refine our segmentation results by reasoning about spatio-temporally related 3D point... | Point Cloud Segmentation | 59 | 29 | 59 | 29 |
2101.06865__body_000012__cite_0005__start_1119__ref_1162074e2ebefbc6b7b15c88f7b78990398bae09 | 2,101.06865 | 2,101.06742 | 2101.06865__body_000012 | 12 | Memory Networks | 6 | null | {{cite:1162074e2ebefbc6b7b15c88f7b78990398bae09}} | 1,119 | 1,168 | 2101.06865__ref__1162074e2ebefbc6b7b15c88f7b78990398bae09 | The majority of approaches utilizing memory rely on recurrent neural networks based on a long short-term memory (LSTM) {{cite:3ede27cf928315322ac6eb92dd66f2f4b73fcc3f}}, {{cite:f0880d9fb731e92f9fc930843c42998b0401e6ee}}, where the memory is represented as a 1D-vector. More recently, {{cite:c2944c61fdb4bf21cba97a2135a... | The majority of approaches utilizing memory rely on recurrent neural networks based on a long short-term memory (LSTM) <OTHER_CIT>, <OTHER_CIT>, where the memory is represented as a 1D-vector. More recently, <OTHER_CIT>, <OTHER_CIT> have shown techniques using ConvLSTMs to explicitly remember spatial information. Suc... | In contrast, our memory representation is an explicitly external 4D spatio-temporal buffer that both has a direct mapping to the real world in a local coordinate frame, as well as being compatible with the continuous convolutions <TARGET_CIT> for sparse computation in that space. | The majority of approaches utilizing memory rely on recurrent neural networks based on a long short-term memory (LSTM) <OTHER_CIT>, <OTHER_CIT>, where the memory is represented as a 1D-vector. More recently, <OTHER_CIT>, <OTHER_CIT> have shown techniques using ConvLSTMs to explicitly remember spatial information. Suc... | Building dynamically changing semantic maps is a active topic in robotics. It is crucial for the robot to complete many tasks in a dynamic evolving environment, such as navigation <OTHER_CIT>, localization <OTHER_CIT> and manipulation <OTHER_CIT>. There is a large body of work in semantic 3D reconstruction using RGB-D ... | 2101.06865__body_000011|2101.06865__body_000012|2101.06865__body_000013 | [SECTION] Memory Networks
[CONTEXT]
Building dynamically changing semantic maps is a active topic in robotics. It is crucial for the robot to complete many tasks in a dynamic evolving environment, such as navigation <OTHER_CIT>, localization <OTHER_CIT> and manipulation <OTHER_CIT>. There is a large body of work in se... | Memory Networks | 59 | 29 | 59 | 29 |
2101.06865__body_000019__cite_0000__start_651__ref_1162074e2ebefbc6b7b15c88f7b78990398bae09 | 2,101.06865 | 2,101.06742 | 2101.06865__body_000019 | 19 | Non-parametric Memory for Spatio-temporal Segmentation | 2 | subsection | {{cite:1162074e2ebefbc6b7b15c88f7b78990398bae09}} | 651 | 700 | 2101.06865__ref__1162074e2ebefbc6b7b15c88f7b78990398bae09 | Concretely, we define a dynamic graph {{formula:6b294b72-7f12-4ee4-973e-2c89b5a6cd37}} where {{formula:72c1b5e1-3c31-409f-a0a7-186b559998b2}} is the set {{formula:92eb6c2b-2997-4846-832b-5217ec3356c1}} of all historical and current 3D points, and {{formula:f400e1b6-b9df-4846-9065-158df79ecbb0}} is the set of edges ... | Concretely, we define a dynamic graph {{formula:6b294b72-7f12-4ee4-973e-2c89b5a6cd37}} where {{formula:72c1b5e1-3c31-409f-a0a7-186b559998b2}} is the set {{formula:92eb6c2b-2997-4846-832b-5217ec3356c1}} of all historical and current 3D points, and {{formula:f400e1b6-b9df-4846-9065-158df79ecbb0}} is the set of edges ... | We then use a model based on the continuous convolutions (CC) architecture <TARGET_CIT> to process each point. | Concretely, we define a dynamic graph {{formula:6b294b72-7f12-4ee4-973e-2c89b5a6cd37}} where {{formula:72c1b5e1-3c31-409f-a0a7-186b559998b2}} is the set {{formula:92eb6c2b-2997-4846-832b-5217ec3356c1}} of all historical and current 3D points, and {{formula:f400e1b6-b9df-4846-9065-158df79ecbb0}} is the set of edges ... | We propose a learned model to address the aforementioned shortcomings. The overall pipeline of our model is depicted in (Figure REF ).
We use a non-parametric memory structure to maintain our current best estimate for segmentation of aggregated point clouds. The memory stores a length {{formula:8680c3d8-c21b-4378-b0d6-... | 2101.06865__body_000018|2101.06865__body_000019|2101.06865__body_000020 | [SECTION] Non-parametric Memory for Spatio-temporal Segmentation
[CONTEXT]
We propose a learned model to address the aforementioned shortcomings. The overall pipeline of our model is depicted in (Figure REF ).
We use a non-parametric memory structure to maintain our current best estimate for segmentation of aggregated... | Non-parametric Memory for Spatio-temporal Segmentation | 59 | 29 | 59 | 29 |
2101.06852__body_000006__cite_0003__start_948__ref_cb2c92488c6cb3f5f6571b92acfe8bb136b28c2c | 2,101.06852 | 2,104.06589 | 2101.06852__body_000006 | 6 | Introduction | 1 | section | {{cite:cb2c92488c6cb3f5f6571b92acfe8bb136b28c2c}} | 948 | 997 | 2101.06852__ref__cb2c92488c6cb3f5f6571b92acfe8bb136b28c2c | To reduce the ensemble simulation cost, a breakthrough idea was presented in {{cite:10990ed6dcb2e6294d0e495c08627ca2fc230b3e}} to find a set of {{formula:56c6657c-d6d3-4c2b-82df-4221d971a0dc}} solutions of the NSEs for different initial conditions and body forces. The fundamental idea is that, at each time step, each ... | To reduce the ensemble simulation cost, a breakthrough idea was presented in <OTHER_CIT> to find a set of {{formula:56c6657c-d6d3-4c2b-82df-4221d971a0dc}} solutions of the NSEs for different initial conditions and body forces. The fundamental idea is that, at each time step, each of the {{formula:eb1dfd78-4591-46c6-a9... | This breakthrough idea has been implemented in heat conduction <OTHER_CIT>, Navier-Stokes simulations <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>, magnetohydrodynamics <OTHER_CIT>, <OTHER_CIT>, parameterized flow problems <OTHER_CIT>, and turbulence modeling <OTHER_CIT>. | To reduce the ensemble simulation cost, a breakthrough idea was presented in <OTHER_CIT> to find a set of {{formula:56c6657c-d6d3-4c2b-82df-4221d971a0dc}} solutions of the NSEs for different initial conditions and body forces. The fundamental idea is that, at each time step, each of the {{formula:eb1dfd78-4591-46c6-a9... | together with the initial and boundary conditions.
To reduce the ensemble simulation cost, a breakthrough idea was presented in <OTHER_CIT> to find a set of {{formula:56c6657c-d6d3-4c2b-82df-4221d971a0dc}} solutions of the NSEs for different initial conditions and body forces. The fundamental idea is that, at each t... | 2101.06852__body_000005|2101.06852__body_000006|2101.06852__body_000007 | [SECTION] Introduction
[CONTEXT]
together with the initial and boundary conditions.
To reduce the ensemble simulation cost, a breakthrough idea was presented in <OTHER_CIT> to find a set of {{formula:56c6657c-d6d3-4c2b-82df-4221d971a0dc}} solutions of the NSEs for different initial conditions and body forces. The f... | Introduction | 60 | 48 | 60 | 48 |
2101.07370__body_000000__cite_0001__start_657__ref_5c786c4feab08e8520ddc58ec2b0db97ff8b143e | 2,101.0737 | 2,101.08299 | 2101.07370__body_000000 | 0 | Introduction | 1 | section | {{cite:5c786c4feab08e8520ddc58ec2b0db97ff8b143e}} | 657 | 706 | 2101.07370__ref__5c786c4feab08e8520ddc58ec2b0db97ff8b143e | Segmentation in computer vision is the task of dividing an image into parts that are easier to analyse. Text lines of a handwritten document image are widely used for word segmentation, text recognition and spotting, manuscripts alignment and writer recognition. Text lines need to be provided to these applications eith... | Segmentation in computer vision is the task of dividing an image into parts that are easier to analyse. Text lines of a handwritten document image are widely used for word segmentation, text recognition and spotting, manuscripts alignment and writer recognition. Text lines need to be provided to these applications eith... | Much research in the recent years has focused on text line detection <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. | Segmentation in computer vision is the task of dividing an image into parts that are easier to analyse. Text lines of a handwritten document image are widely used for word segmentation, text recognition and spotting, manuscripts alignment and writer recognition. Text lines need to be provided to these applications eith... | Segmentation in computer vision is the task of dividing an image into parts that are easier to analyse. Text lines of a handwritten document image are widely used for word segmentation, text recognition and spotting, manuscripts alignment and writer recognition. Text lines need to be provided to these applications eith... | 2101.07370__body_000000|2101.07370__body_000001 | [SECTION] Introduction
[CONTEXT]
Segmentation in computer vision is the task of dividing an image into parts that are easier to analyse. Text lines of a handwritten document image are widely used for word segmentation, text recognition and spotting, manuscripts alignment and writer recognition. Text lines need to be p... | Introduction | 29 | 13 | 29 | 13 |
2101.07370__body_000006__cite_0004__start_638__ref_5c786c4feab08e8520ddc58ec2b0db97ff8b143e | 2,101.0737 | 2,101.08299 | 2101.07370__body_000006 | 6 | Introduction | 1 | section | {{cite:5c786c4feab08e8520ddc58ec2b0db97ff8b143e}} | 638 | 687 | 2101.07370__ref__5c786c4feab08e8520ddc58ec2b0db97ff8b143e | There are two main approaches to represent text lines: text line detection and text line extraction. Text line detection detects the lines, polylines or blobs that represent the locations of spatially aligned set of text line elements. Detected line or polyline is called a baseline {{cite:e08b57f0906c6a3e417845d0a8b58b... | There are two main approaches to represent text lines: text line detection and text line extraction. Text line detection detects the lines, polylines or blobs that represent the locations of spatially aligned set of text line elements. Detected line or polyline is called a baseline <OTHER_CIT>, <OTHER_CIT> if it joins ... | Detected blobs <TARGET_CIT> that cover the character main bodies in a text line are called text line blobs. | There are two main approaches to represent text lines: text line detection and text line extraction. Text line detection detects the lines, polylines or blobs that represent the locations of spatially aligned set of text line elements. Detected line or polyline is called a baseline <OTHER_CIT>, <OTHER_CIT> if it joins ... | A text line is a set of image elements, such as pixels or connected components. Text line components in a document image can be represented using basic geometric primitives such as points, lines, polylines, polygons or blobs. Text line representation is given as an input to other document image processing algorithms, a... | 2101.07370__body_000005|2101.07370__body_000006|2101.07370__body_000007 | [SECTION] Introduction
[CONTEXT]
A text line is a set of image elements, such as pixels or connected components. Text line components in a document image can be represented using basic geometric primitives such as points, lines, polylines, polygons or blobs. Text line representation is given as an input to other docum... | Introduction | 29 | 13 | 29 | 13 |
2101.07370__body_000008__cite_0004__start_534__ref_5c786c4feab08e8520ddc58ec2b0db97ff8b143e | 2,101.0737 | 2,101.08299 | 2101.07370__body_000008 | 8 | Introduction | 1 | section | {{cite:5c786c4feab08e8520ddc58ec2b0db97ff8b143e}} | 534 | 583 | 2101.07370__ref__5c786c4feab08e8520ddc58ec2b0db97ff8b143e | Recent deep learning methods estimate {{formula:ff3cee97-c210-455c-853c-53df375d833b}} -height of text lines using FCN and apply Line Adjacency Graphs (LAG) to post-process FCN output to split touching lines {{cite:5ad0f5b92c1c6792df0a2207898df8753b22e367}}, {{cite:ecfd68e24839d281a135a836ae7645889f3f914c}}. Renton et ... | Recent deep learning methods estimate {{formula:ff3cee97-c210-455c-853c-53df375d833b}} -height of text lines using FCN and apply Line Adjacency Graphs (LAG) to post-process FCN output to split touching lines <OTHER_CIT>, <OTHER_CIT>. Renton et al. <OTHER_CIT>, <OTHER_CIT> also use FCN to predict {{formula:d1e2a565-7dc9... | Kurar et al. <TARGET_CIT> applied FCN for challenging manuscript images with multi-skewed, multi-directed and curved handwritten text lines. | Recent deep learning methods estimate {{formula:ff3cee97-c210-455c-853c-53df375d833b}} -height of text lines using FCN and apply Line Adjacency Graphs (LAG) to post-process FCN output to split touching lines <OTHER_CIT>, <OTHER_CIT>. Renton et al. <OTHER_CIT>, <OTHER_CIT> also use FCN to predict {{formula:d1e2a565-7dc9... | Text line extraction determines the constituting pixels or the polygons around the spatially aligned text line elements. Pixel labeling assigns the same label to all the pixels of a text line <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Bounding polygon is used to enclose all the elements of a text line together with its nei... | 2101.07370__body_000007|2101.07370__body_000008|2101.07370__body_000009 | [SECTION] Introduction
[CONTEXT]
Text line extraction determines the constituting pixels or the polygons around the spatially aligned text line elements. Pixel labeling assigns the same label to all the pixels of a text line <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Bounding polygon is used to enclose all the elements of... | Introduction | 29 | 13 | 29 | 13 |
2101.07722__body_000001__cite_0000__start_804__ref_5fb3c541099d199c9434796073ca93a3de77804c | 2,101.07722 | 2,101.10691 | 2101.07722__body_000001 | 1 | Introduction | 1 | section | {{cite:5fb3c541099d199c9434796073ca93a3de77804c}} | 804 | 853 | 2101.07722__ref__5fb3c541099d199c9434796073ca93a3de77804c | The current small satellite literature lacks the whole life cycle: i.e. all aspects relating to mission planning, design, launch, operations and lessons learned. The teams either report very specific technical information of the design, or come up with mission descriptions and in-orbit results. One can barely find info... | The current small satellite literature lacks the whole life cycle: i.e. all aspects relating to mission planning, design, launch, operations and lessons learned. The teams either report very specific technical information of the design, or come up with mission descriptions and in-orbit results. One can barely find info... | We present our findings in two papers: the first one covering the technology development aspects <TARGET_CIT> whereas the present paper covers the in-orbit results and lessons learned. | The current small satellite literature lacks the whole life cycle: i.e. all aspects relating to mission planning, design, launch, operations and lessons learned. The teams either report very specific technical information of the design, or come up with mission descriptions and in-orbit results. One can barely find info... | There has been a significant increase in the design, development, launch and operation of nano and micro satellites since last two decades. A large number countries initiated their space activities and a large number of Newspace companies emerged as an outcome. A number of innovative platform subsystems, payloads and m... | 2101.07722__body_000000|2101.07722__body_000001|2101.07722__body_000002 | [SECTION] Introduction
[CONTEXT]
There has been a significant increase in the design, development, launch and operation of nano and micro satellites since last two decades. A large number countries initiated their space activities and a large number of Newspace companies emerged as an outcome. A number of innovative p... | Introduction | 84 | 38 | 84 | 38 |
2101.07722__body_000010__cite_0000__start_182__ref_5fb3c541099d199c9434796073ca93a3de77804c | 2,101.07722 | 2,101.10691 | 2101.07722__body_000010 | 10 | Mission payloads | 4 | section | {{cite:5fb3c541099d199c9434796073ca93a3de77804c}} | 182 | 231 | 2101.07722__ref__5fb3c541099d199c9434796073ca93a3de77804c | This section describes the in orbit performance of radmon, epb and aasi payloads. The thorough design approach, selection and implementation has been presented in accompanying paper {{cite:5fb3c541099d199c9434796073ca93a3de77804c}}.
| This section describes the in orbit performance of radmon, epb and aasi payloads. The thorough design approach, selection and implementation has been presented in accompanying paper <TARGET_CIT>.
| The thorough design approach, selection and implementation has been presented in accompanying paper <TARGET_CIT>. | This section describes the in orbit performance of radmon, epb and aasi payloads. The thorough design approach, selection and implementation has been presented in accompanying paper <TARGET_CIT>.
| The mission wise timeline on the commissioning and operations of each experiment is presented in Fig. REF . During leop, the first aasi picture was downloaded and radmon commissioning phase was started. As part of Aalto-1 operations, multiple aasi campaigns have been completed.
radmon operations resulted in a useful da... | 2101.07722__body_000009|2101.07722__body_000010|2101.07722__body_000011 | [SECTION] Mission payloads
[CONTEXT]
The mission wise timeline on the commissioning and operations of each experiment is presented in Fig. REF . During leop, the first aasi picture was downloaded and radmon commissioning phase was started. As part of Aalto-1 operations, multiple aasi campaigns have been completed.
rad... | Mission payloads | 84 | 38 | 84 | 38 |
2101.07722__body_000011__cite_0001__start_269__ref_5fb3c541099d199c9434796073ca93a3de77804c | 2,101.07722 | 2,101.10691 | 2101.07722__body_000011 | 11 | Radiation monitor mission | 1 | subsection | {{cite:5fb3c541099d199c9434796073ca93a3de77804c}} | 269 | 318 | 2101.07722__ref__5fb3c541099d199c9434796073ca93a3de77804c | The radmon is a small (4{{formula:3b099663-2fe3-4411-8424-3434550e6b8b}} 9{{formula:0e3a10a1-eb66-49d4-bdfb-a5ccba33f264}} 10 {{formula:ffc15835-3412-4025-9f6b-6f7e5a36b41d}} , 360 g) low-power (1 W) radiation monitor {{cite:120c844922e73ca11a0b2bdc41727cebac70023a}}, {{cite:5fb3c541099d199c9434796073ca93a3de77804c}}. ... | The radmon is a small (4{{formula:3b099663-2fe3-4411-8424-3434550e6b8b}} 9{{formula:0e3a10a1-eb66-49d4-bdfb-a5ccba33f264}} 10 {{formula:ffc15835-3412-4025-9f6b-6f7e5a36b41d}} , 360 g) low-power (1 W) radiation monitor <OTHER_CIT>, <TARGET_CIT>. The monitor detects protons and electrons employing a regular E – E analysi... | The radmon is a small (4{{formula:3b099663-2fe3-4411-8424-3434550e6b8b}} 9{{formula:0e3a10a1-eb66-49d4-bdfb-a5ccba33f264}} 10 {{formula:ffc15835-3412-4025-9f6b-6f7e5a36b41d}} , 360 g) low-power (1 W) radiation monitor <OTHER_CIT>, <TARGET_CIT>. | The radmon is a small (4{{formula:3b099663-2fe3-4411-8424-3434550e6b8b}} 9{{formula:0e3a10a1-eb66-49d4-bdfb-a5ccba33f264}} 10 {{formula:ffc15835-3412-4025-9f6b-6f7e5a36b41d}} , 360 g) low-power (1 W) radiation monitor <OTHER_CIT>, <TARGET_CIT>. The monitor detects protons and electrons employing a regular E – E analysi... | This section describes the in orbit performance of radmon, epb and aasi payloads. The thorough design approach, selection and implementation has been presented in accompanying paper <OTHER_CIT>.
The radmon is a small (4{{formula:3b099663-2fe3-4411-8424-3434550e6b8b}} 9{{formula:0e3a10a1-eb66-49d4-bdfb-a5ccba33f264}} ... | 2101.07722__body_000010|2101.07722__body_000011|2101.07722__body_000012 | [SECTION] Radiation monitor mission
[CONTEXT]
This section describes the in orbit performance of radmon, epb and aasi payloads. The thorough design approach, selection and implementation has been presented in accompanying paper <OTHER_CIT>.
The radmon is a small (4{{formula:3b099663-2fe3-4411-8424-3434550e6b8b}} 9{{... | Radiation monitor mission | 84 | 38 | 84 | 38 |
2101.07722__body_000041__cite_0006__start_753__ref_5fb3c541099d199c9434796073ca93a3de77804c | 2,101.07722 | 2,101.10691 | 2101.07722__body_000041 | 41 | Platform in-orbit performance | 5 | section | {{cite:5fb3c541099d199c9434796073ca93a3de77804c}} | 753 | 802 | 2101.07722__ref__5fb3c541099d199c9434796073ca93a3de77804c | The in-orbit performance of spacecraft platform which consisted of commercial and in house developed subsystems, is briefly presented. While the key platform subsystems were successfully commissioned, the spacecraft accomplished its mission with partial success. The design approach of platform subsystems which consiste... | The in-orbit performance of spacecraft platform which consisted of commercial and in house developed subsystems, is briefly presented. While the key platform subsystems were successfully commissioned, the spacecraft accomplished its mission with partial success. The design approach of platform subsystems which consiste... | The design approach of platform subsystems which consisted of an eps <OTHER_CIT>, an adcs <OTHER_CIT>, a gps-based navigation system <OTHER_CIT>, a uhf <OTHER_CIT> and S-band <OTHER_CIT> radios for ttc, and a Linux-based obdh <OTHER_CIT> is briefly presented in <TARGET_CIT>. | The in-orbit performance of spacecraft platform which consisted of commercial and in house developed subsystems, is briefly presented. While the key platform subsystems were successfully commissioned, the spacecraft accomplished its mission with partial success. The design approach of platform subsystems which consiste... | Not all functionalities of the imager could be verified though. The tumbling platform prevented imaging of planned targets, and the limited downlink allowed only the use of minimal spectral mode with six wavelengths. However, the tumbling platform showcased the benefits of frame-based spectral imaging, as the images in... | 2101.07722__body_000040|2101.07722__body_000041|2101.07722__body_000042 | [SECTION] Platform in-orbit performance
[CONTEXT]
Not all functionalities of the imager could be verified though. The tumbling platform prevented imaging of planned targets, and the limited downlink allowed only the use of minimal spectral mode with six wavelengths. However, the tumbling platform showcased the benefit... | Platform in-orbit performance | 84 | 38 | 84 | 38 |
2101.07722__body_000051__cite_0000__start_245__ref_5fb3c541099d199c9434796073ca93a3de77804c | 2,101.07722 | 2,101.10691 | 2101.07722__body_000051 | 51 | In-orbit performance of obdh, ttc and gps subsystems | 3 | subsection | {{cite:5fb3c541099d199c9434796073ca93a3de77804c}} | 245 | 294 | 2101.07722__ref__5fb3c541099d199c9434796073ca93a3de77804c | The commissioning of the uhf transceiver was successful since the first contact with the CubeSat was established during first pass over the ground station. The commissioning phase was met with many challenges which have been briefly detailed in {{cite:5fb3c541099d199c9434796073ca93a3de77804c}}. From the telemetry logs,... | The commissioning of the uhf transceiver was successful since the first contact with the CubeSat was established during first pass over the ground station. The commissioning phase was met with many challenges which have been briefly detailed in <TARGET_CIT>. From the telemetry logs, a radio interference in the Northern... | The commissioning phase was met with many challenges which have been briefly detailed in <TARGET_CIT>. | The commissioning of the uhf transceiver was successful since the first contact with the CubeSat was established during first pass over the ground station. The commissioning phase was met with many challenges which have been briefly detailed in <TARGET_CIT>. From the telemetry logs, a radio interference in the Northern... | It has been observed that the tle accuracy has been sufficient for most routine operations, and the use of GPS has been less frequent than expected. A sub-optimal GPS antenna placement (resulting from a compromise with solar panel placement) and satellite tumbling have caused delays in obtaining the first fix after pow... | 2101.07722__body_000050|2101.07722__body_000051|2101.07722__body_000052 | [SECTION] In-orbit performance of obdh, ttc and gps subsystems
[CONTEXT]
It has been observed that the tle accuracy has been sufficient for most routine operations, and the use of GPS has been less frequent than expected. A sub-optimal GPS antenna placement (resulting from a compromise with solar panel placement) and ... | In-orbit performance of obdh, ttc and gps subsystems | 84 | 38 | 84 | 38 |
2101.07774__body_000001__cite_0004__start_728__ref_10042fd9241e08c2a76b9a0b08da4d948b703996 | 2,101.07774 | 2,101.07783 | 2101.07774__body_000001 | 1 | Introduction | 1 | section | {{cite:10042fd9241e08c2a76b9a0b08da4d948b703996}} | 728 | 777 | 2101.07774__ref__10042fd9241e08c2a76b9a0b08da4d948b703996 | This paper investigates the application of DSE for the protection of radial portions of a microgrid (or a distribution network).
This can be a challenge in electrical grids with distributed generation on account of lack of fault current from inverter-interfaced generation {{cite:e6790e2c484b7f39b9da8d40295753efc4470fe5... | This paper investigates the application of DSE for the protection of radial portions of a microgrid (or a distribution network).
This can be a challenge in electrical grids with distributed generation on account of lack of fault current from inverter-interfaced generation <OTHER_CIT>, varying fault current between grid... | Admittance relaying has been investigated as a solution for the protection of microgrids <TARGET_CIT>, however, it has been observed to present issues with grounded-wye connected loads <OTHER_CIT>; consequently, additional relaying is necessary to prevent misoperation <OTHER_CIT>. | This paper investigates the application of DSE for the protection of radial portions of a microgrid (or a distribution network).
This can be a challenge in electrical grids with distributed generation on account of lack of fault current from inverter-interfaced generation <OTHER_CIT>, varying fault current between grid... | Dynamic state estimation (abbr. DSE) is a generalization of differential protection, which offers a reduced likelihood of misoperation, particularly in the case of assets with nonlinear characteristics (e.g., transformers that are being energized) <OTHER_CIT>. It is also useful in cases where distance protection perfor... | 2101.07774__body_000000|2101.07774__body_000001|2101.07774__body_000002 | [SECTION] Introduction
[CONTEXT]
Dynamic state estimation (abbr. DSE) is a generalization of differential protection, which offers a reduced likelihood of misoperation, particularly in the case of assets with nonlinear characteristics (e.g., transformers that are being energized) <OTHER_CIT>. It is also useful in case... | Introduction | 86 | 75 | 86 | 75 |
2101.07778__body_000004__cite_0001__start_883__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000004 | 4 | Introduction | 1 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 883 | 932 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect {{cite:0eaff349a5a626755d4d815cd5de0e504b3dce2f}}
implies that this sector should admit a global d... | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | We then show that
this condition implies that {{formula:bcaad2b0-1c0a-4e05-bd4e-2e60a02a015a}} is a Siegel bundle in the sense
of <TARGET_CIT>, i.e. a principal bundle whose structure
group is the automorphism group of an integral symplectic affine torus. | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a Lorentzian metric, {{formula:43ab5d... | 2101.07778__body_000003|2101.07778__body_000004|2101.07778__body_000005 | [SECTION] Introduction
[CONTEXT]
The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a L... | Introduction | 588 | 526 | 588 | 526 |
2101.07778__body_000004__cite_0002__start_1298__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000004 | 4 | Introduction | 1 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 1,298 | 1,347 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect {{cite:0eaff349a5a626755d4d815cd5de0e504b3dce2f}}
implies that this sector should admit a global d... | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | This process parallels the DSZ quantization of Abelian gauge theories
with manifest electromagnetic duality, developed in <TARGET_CIT>,
which depends on a Siegel system {{formula:a0cc5a51-d82f-4d4f-b615-fc3bc10851e0}} on {{formula:af35c18a-7357-4453-8cf1-72d5695afa2a}} . | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a Lorentzian metric, {{formula:43ab5d... | 2101.07778__body_000003|2101.07778__body_000004|2101.07778__body_000005 | [SECTION] Introduction
[CONTEXT]
The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a L... | Introduction | 588 | 526 | 588 | 526 |
2101.07778__body_000004__cite_0003__start_1512__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000004 | 4 | Introduction | 1 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 1,512 | 1,561 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect {{cite:0eaff349a5a626755d4d815cd5de0e504b3dce2f}}
implies that this sector should admit a global d... | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | The latter was defined
in <TARGET_CIT> as a local system of finitely-generated free
Abelian groups whose structure group reduces to a modified
Siegel modular group and which is isomorphic to {{formula:74000b6a-4ff3-47e3-9bfd-d6ac5e22d698}} upon tensorization
with {{formula:1de9358c-4f12-4645-b209-e2d012f6ea55}} over ... | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a Lorentzian metric, {{formula:43ab5d... | 2101.07778__body_000003|2101.07778__body_000004|2101.07778__body_000005 | [SECTION] Introduction
[CONTEXT]
The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a L... | Introduction | 588 | 526 | 588 | 526 |
2101.07778__body_000004__cite_0004__start_2477__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000004 | 4 | Introduction | 1 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 2,477 | 2,526 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect {{cite:0eaff349a5a626755d4d815cd5de0e504b3dce2f}}
implies that this sector should admit a global d... | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | By the results
of <TARGET_CIT>, any element of {{formula:188b9d40-3adc-433d-aa44-a5d29d150b36}} is the twisted
Chern class of a Siegel bundle defined on the total space of {{formula:f7f40cb8-b8cb-4fb4-a206-1c39b2fe4d38}} . | The description of the gauge sector in terms of field strengths {{formula:1e72133f-c05d-47a5-a133-5b42d45f3c8f}} is
unsatisfactory when coupling the theory to quantized charged
particles. Indeed, the Aharonov-Bohm effect <OTHER_CIT>
implies that this sector should admit a global description in terms of
gauge potential... | The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a Lorentzian metric, {{formula:43ab5d... | 2101.07778__body_000003|2101.07778__body_000004|2101.07778__body_000005 | [SECTION] Introduction
[CONTEXT]
The configuration space of the bosonic supergravity theory determined by
a tuple {{formula:6fd6964b-abe7-4000-90c5-5a1a7e2e3f36}} as introduced above is the set of
triples {{formula:6dbf5866-fca5-48d9-89d2-fba58bc10f35}} , where {{formula:12aa0e45-705b-4e54-a92c-97a57f1bd316}} is a L... | Introduction | 588 | 526 | 588 | 526 |
2101.07778__body_000007__cite_0002__start_689__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000007 | 7 | Introduction | 1 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 689 | 738 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | Using this geometric and gauge-theoretic formulation of bosonic supergravity,
we study its group of continuous and discrete U-duality transformations, which
we characterize through short exact sequences involving the group of automorphisms
of {{formula:5cd4a23c-d229-47cc-b5fa-ae9b9c5236bd}} and its adjoint bundle. In ... | Using this geometric and gauge-theoretic formulation of bosonic supergravity,
we study its group of continuous and discrete U-duality transformations, which
we characterize through short exact sequences involving the group of automorphisms
of {{formula:5cd4a23c-d229-47cc-b5fa-ae9b9c5236bd}} and its adjoint bundle. In ... | In this regard, we emphasize the dependence of U-duality groups on the
typeThis is a classical notion in the theory of symplectic
lattices see for instance <OTHER_CIT> or <TARGET_CIT>
for more details. of the corresponding Siegel modular group and of the
isomorphism class of the Siegel system {{formula:615e5248-de4e-4e... | Using this geometric and gauge-theoretic formulation of bosonic supergravity,
we study its group of continuous and discrete U-duality transformations, which
we characterize through short exact sequences involving the group of automorphisms
of {{formula:5cd4a23c-d229-47cc-b5fa-ae9b9c5236bd}} and its adjoint bundle. In ... | The configuration space of the DSZ quantization of bosonic supergravity
determined by {{formula:f04615b9-655a-43fb-822f-733da1c62cdb}} and {{formula:c2a82f5c-0fd3-43e4-9960-4422263b072d}} is given by triples {{formula:5411cbc3-332a-49f7-a3c2-772c792f66a1}} ,
where {{formula:e57d2991-968e-4641-9056-a377a009510a}} and... | 2101.07778__body_000006|2101.07778__body_000007|2101.07778__body_000008 | [SECTION] Introduction
[CONTEXT]
The configuration space of the DSZ quantization of bosonic supergravity
determined by {{formula:f04615b9-655a-43fb-822f-733da1c62cdb}} and {{formula:c2a82f5c-0fd3-43e4-9960-4422263b072d}} is given by triples {{formula:5411cbc3-332a-49f7-a3c2-772c792f66a1}} ,
where {{formula:e57d2991-... | Introduction | 588 | 526 | 588 | 526 |
2101.07778__body_000112__cite_0000__start_302__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000112 | 112 | The vector space of integral field strengths | 3.1 | subsection | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 302 | 351 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | For every {{formula:1eab289d-39ec-4e76-8af2-a7ea35afb496}} , the fiber {{formula:7a4c4ee0-e017-4084-a4a5-d3aec2d79e7a}} of
an integral duality bundle {{formula:4ae28824-8f48-4021-b355-520699e55516}} with
{{formula:71b414c8-3f05-4838-9347-2a42c5d6e392}} is an integral symplectic space as
defined in {{cite:df81b0aac57... | For every {{formula:1eab289d-39ec-4e76-8af2-a7ea35afb496}} , the fiber {{formula:7a4c4ee0-e017-4084-a4a5-d3aec2d79e7a}} of
an integral duality bundle {{formula:4ae28824-8f48-4021-b355-520699e55516}} with
{{formula:71b414c8-3f05-4838-9347-2a42c5d6e392}} is an integral symplectic space as
defined in <TARGET_CIT>. All ... | For every {{formula:1eab289d-39ec-4e76-8af2-a7ea35afb496}} , the fiber {{formula:7a4c4ee0-e017-4084-a4a5-d3aec2d79e7a}} of
an integral duality bundle {{formula:4ae28824-8f48-4021-b355-520699e55516}} with
{{formula:71b414c8-3f05-4838-9347-2a42c5d6e392}} is an integral symplectic space as
defined in <TARGET_CIT>. | For every {{formula:1eab289d-39ec-4e76-8af2-a7ea35afb496}} , the fiber {{formula:7a4c4ee0-e017-4084-a4a5-d3aec2d79e7a}} of
an integral duality bundle {{formula:4ae28824-8f48-4021-b355-520699e55516}} with
{{formula:71b414c8-3f05-4838-9347-2a42c5d6e392}} is an integral symplectic space as
defined in <TARGET_CIT>. All ... | consisting of a duality bundle {{formula:af6c09fd-6a59-4800-9212-b96d8057f2c3}} and a choice of Dirac system
{{formula:4b2f6cd1-76f8-4fe6-aff0-5e2a795463ec}} for {{formula:1b0c27c4-278a-4407-8d49-20038f0807ec}} is called an integral duality bundle.
For every {{formula:1eab289d-39ec-4e76-8af2-a7ea35afb496}} , the ... | 2101.07778__body_000111|2101.07778__body_000112|2101.07778__body_000113 | [SECTION] The vector space of integral field strengths
[CONTEXT]
consisting of a duality bundle {{formula:af6c09fd-6a59-4800-9212-b96d8057f2c3}} and a choice of Dirac system
{{formula:4b2f6cd1-76f8-4fe6-aff0-5e2a795463ec}} for {{formula:1b0c27c4-278a-4407-8d49-20038f0807ec}} is called an integral duality bundle.
... | The vector space of integral field strengths | 588 | 526 | 588 | 526 |
2101.07778__body_000126__cite_0000__start_147__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000126 | 126 | The vector space of integral field strengths | 3.1 | subsection | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 147 | 196 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | It can be shown that {{formula:2969a06f-c156-4c98-84d4-6a36f651f6e7}} is a full lattice in
{{formula:05831fb7-d2ef-42c9-9c9a-675196380629}} (see {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}}). Given an integral scalar-electromagnetic
bundle {{formula:4924fae6-a919-48ed-b860-6029086c8003}} , we implement DSZ quant... | It can be shown that {{formula:2969a06f-c156-4c98-84d4-6a36f651f6e7}} is a full lattice in
{{formula:05831fb7-d2ef-42c9-9c9a-675196380629}} (see <TARGET_CIT>). Given an integral scalar-electromagnetic
bundle {{formula:4924fae6-a919-48ed-b860-6029086c8003}} , we implement DSZ quantization by restricting the
configurat... | It can be shown that {{formula:2969a06f-c156-4c98-84d4-6a36f651f6e7}} is a full lattice in
{{formula:05831fb7-d2ef-42c9-9c9a-675196380629}} (see <TARGET_CIT>). | It can be shown that {{formula:2969a06f-c156-4c98-84d4-6a36f651f6e7}} is a full lattice in
{{formula:05831fb7-d2ef-42c9-9c9a-675196380629}} (see <TARGET_CIT>). Given an integral scalar-electromagnetic
bundle {{formula:4924fae6-a919-48ed-b860-6029086c8003}} , we implement DSZ quantization by restricting the
configurat... | Elements of this lattice are called integral cohomology
classes.
It can be shown that {{formula:2969a06f-c156-4c98-84d4-6a36f651f6e7}} is a full lattice in
{{formula:05831fb7-d2ef-42c9-9c9a-675196380629}} (see <TARGET_CIT>). Given an integral scalar-electromagnetic
bundle {{formula:4924fae6-a919-48ed-b860-6029086c... | 2101.07778__body_000125|2101.07778__body_000126|2101.07778__body_000127 | [SECTION] The vector space of integral field strengths
[CONTEXT]
Elements of this lattice are called integral cohomology
classes.
It can be shown that {{formula:2969a06f-c156-4c98-84d4-6a36f651f6e7}} is a full lattice in
{{formula:05831fb7-d2ef-42c9-9c9a-675196380629}} (see <TARGET_CIT>). Given an integral scalar... | The vector space of integral field strengths | 588 | 526 | 588 | 526 |
2101.07778__body_000134__cite_0000__start_246__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000134 | 134 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 246 | 295 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} for Abelian gauge
theory... | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in <TARGET_CIT> for Abelian gauge
theory. Instead of going through the detail... | This formulation can be constructed through a
step-by-step process as done in <TARGET_CIT> for Abelian gauge
theory. | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in <TARGET_CIT> for Abelian gauge
theory. Instead of going through the detail... | The arithmetic U-duality group {{formula:11f37d69-bffb-465c-a254-60176a9fa38a}} is the global
counterpart of the arithmetic U-duality group of local supergravity
normally considered in the physics literature <OTHER_CIT>, <OTHER_CIT>.
We remark that the supergravity literature seems to have considered thus far only hol... | 2101.07778__body_000133|2101.07778__body_000134|2101.07778__body_000135 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
The arithmetic U-duality group {{formula:11f37d69-bffb-465c-a254-60176a9fa38a}} is the global
counterpart of the arithmetic U-duality group of local supergravity
normally considered in the physics literature <OTHER_CIT>, <OTHER_CIT>.
We remark that t... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000134__cite_0001__start_406__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000134 | 134 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 406 | 455 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} for Abelian gauge
theory... | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in <OTHER_CIT> for Abelian gauge
theory. Instead of going through the details... | Instead of going through the details of that process, which are similar
to those in <TARGET_CIT>, we give the description of the theory in
its final form, verifying then that it satisfies the appropriate DSZ quantization
(see Theorem REF ). | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in <OTHER_CIT> for Abelian gauge
theory. Instead of going through the details... | The arithmetic U-duality group {{formula:11f37d69-bffb-465c-a254-60176a9fa38a}} is the global
counterpart of the arithmetic U-duality group of local supergravity
normally considered in the physics literature <OTHER_CIT>, <OTHER_CIT>.
We remark that the supergravity literature seems to have considered thus far only hol... | 2101.07778__body_000133|2101.07778__body_000134|2101.07778__body_000135 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
The arithmetic U-duality group {{formula:11f37d69-bffb-465c-a254-60176a9fa38a}} is the global
counterpart of the arithmetic U-duality group of local supergravity
normally considered in the physics literature <OTHER_CIT>, <OTHER_CIT>.
We remark that t... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000134__cite_0002__start_752__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000134 | 134 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 752 | 801 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} for Abelian gauge
theory... | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in <OTHER_CIT> for Abelian gauge
theory. Instead of going through the details... | The key ingredient occurring in the construction
is a Siegel bundle, a special kind of principal bundle which was introduced
and discussed in detail in <TARGET_CIT> and forms a
particular case of the more general notion of principal bundle with weakly-Abelian
structure group studied in <OTHER_CIT>, to which we refer th... | In this section we describe the geometric and gauge-theoretic formulation
of the universal bosonic sector of 4d supergravity implied by the DSZ
quantization condition. This formulation can be constructed through a
step-by-step process as done in <OTHER_CIT> for Abelian gauge
theory. Instead of going through the details... | The arithmetic U-duality group {{formula:11f37d69-bffb-465c-a254-60176a9fa38a}} is the global
counterpart of the arithmetic U-duality group of local supergravity
normally considered in the physics literature <OTHER_CIT>, <OTHER_CIT>.
We remark that the supergravity literature seems to have considered thus far only hol... | 2101.07778__body_000133|2101.07778__body_000134|2101.07778__body_000135 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
The arithmetic U-duality group {{formula:11f37d69-bffb-465c-a254-60176a9fa38a}} is the global
counterpart of the arithmetic U-duality group of local supergravity
normally considered in the physics literature <OTHER_CIT>, <OTHER_CIT>.
We remark that t... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000137__cite_0000__start_98__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000137 | 137 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 98 | 147 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | is the standard symplectic lattice of type {{formula:5831f1d8-db9c-476b-9938-3ca50a42539a}} (see {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}}). Moreover, {{formula:bf04e7e8-58e1-4a46-9d4f-6768ea3e216e}} coincides with the
group of affine symplectomorphisms of the {{formula:3ad96fe5-1229-4336-885c-5cb396460604}} ... | is the standard symplectic lattice of type {{formula:5831f1d8-db9c-476b-9938-3ca50a42539a}} (see <TARGET_CIT>). Moreover, {{formula:bf04e7e8-58e1-4a46-9d4f-6768ea3e216e}} coincides with the
group of affine symplectomorphisms of the {{formula:3ad96fe5-1229-4336-885c-5cb396460604}} -dimensional
symplectic torus {{formu... | is the standard symplectic lattice of type {{formula:5831f1d8-db9c-476b-9938-3ca50a42539a}} (see <TARGET_CIT>). | is the standard symplectic lattice of type {{formula:5831f1d8-db9c-476b-9938-3ca50a42539a}} (see <TARGET_CIT>). Moreover, {{formula:bf04e7e8-58e1-4a46-9d4f-6768ea3e216e}} coincides with the
group of affine symplectomorphisms of the {{formula:3ad96fe5-1229-4336-885c-5cb396460604}} -dimensional
symplectic torus {{formu... | The modified Siegel modular group {{formula:7dc9fae3-998a-4526-abed-18b370d99604}}
coincides with the automorphism group of the standard integral
symplectic space {{formula:176c1406-025a-4255-ab13-62e1904b9212}} of type
{{formula:9fbf1066-81e1-4b45-b545-0fa7ac45cb5a}} , where {{formula:2e0d7cdf-1aee-4b83-88e6-76b561d... | 2101.07778__body_000136|2101.07778__body_000137|2101.07778__body_000138 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
The modified Siegel modular group {{formula:7dc9fae3-998a-4526-abed-18b370d99604}}
coincides with the automorphism group of the standard integral
symplectic space {{formula:176c1406-025a-4255-ab13-62e1904b9212}} of type
{{formula:9fbf1066-81e1-4b45-... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000139__cite_0000__start_403__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000139 | 139 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 403 | 452 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | Let {{formula:06caeebd-ab76-45f7-9bd2-87499115057d}} be a scalar bundle with submersion
{{formula:beef4e33-0468-41a7-bd78-820e26c7a353}} and consider a Siegel bundle {{formula:7a202310-f973-4e81-9c81-3930539421b5}} of
rank {{formula:fefdd143-3aab-4476-91b3-6631b3719575}} and type {{formula:08480017-5081-4dee-88cd-4... | Let {{formula:06caeebd-ab76-45f7-9bd2-87499115057d}} be a scalar bundle with submersion
{{formula:beef4e33-0468-41a7-bd78-820e26c7a353}} and consider a Siegel bundle {{formula:7a202310-f973-4e81-9c81-3930539421b5}} of
rank {{formula:fefdd143-3aab-4476-91b3-6631b3719575}} and type {{formula:08480017-5081-4dee-88cd-4... | As shown in
<TARGET_CIT>, the adjoint bundle of {{formula:7f3a21f2-f4e8-4f31-8b21-6420dd0a6d1a}} admits a
natural structure of integral duality bundle of type {{formula:a3bd6a12-7d9c-4431-abed-a9474486bb6a}} which we
denote by {{formula:11e57605-fce1-49f8-b39f-7f2da85986cf}} . | Let {{formula:06caeebd-ab76-45f7-9bd2-87499115057d}} be a scalar bundle with submersion
{{formula:beef4e33-0468-41a7-bd78-820e26c7a353}} and consider a Siegel bundle {{formula:7a202310-f973-4e81-9c81-3930539421b5}} of
rank {{formula:fefdd143-3aab-4476-91b3-6631b3719575}} and type {{formula:08480017-5081-4dee-88cd-4... | Definition 4.1 A Siegel bundle {{formula:9d129e38-79bf-4dff-97b0-3ccaba0f55b0}} of rank {{formula:b5f39bb3-0087-4c34-acab-5f963bb975cb}} and type {{formula:63ab4dbb-db76-41ce-bad5-15140951ec97}} on {{formula:1b5190af-a543-426f-9329-e745bd704710}} is a principal bundle defined on {{formula:caa33002-5d51-420c-92d3-c2... | 2101.07778__body_000138|2101.07778__body_000139|2101.07778__body_000140 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
Definition 4.1 A Siegel bundle {{formula:9d129e38-79bf-4dff-97b0-3ccaba0f55b0}} of rank {{formula:b5f39bb3-0087-4c34-acab-5f963bb975cb}} and type {{formula:63ab4dbb-db76-41ce-bad5-15140951ec97}} on {{formula:1b5190af-a543-426f-9329-e745bd704710}} ... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000139__cite_0001__start_1053__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000139 | 139 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 1,053 | 1,102 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | Let {{formula:06caeebd-ab76-45f7-9bd2-87499115057d}} be a scalar bundle with submersion
{{formula:beef4e33-0468-41a7-bd78-820e26c7a353}} and consider a Siegel bundle {{formula:7a202310-f973-4e81-9c81-3930539421b5}} of
rank {{formula:fefdd143-3aab-4476-91b3-6631b3719575}} and type {{formula:08480017-5081-4dee-88cd-4... | Let {{formula:06caeebd-ab76-45f7-9bd2-87499115057d}} be a scalar bundle with submersion
{{formula:beef4e33-0468-41a7-bd78-820e26c7a353}} and consider a Siegel bundle {{formula:7a202310-f973-4e81-9c81-3930539421b5}} of
rank {{formula:fefdd143-3aab-4476-91b3-6631b3719575}} and type {{formula:08480017-5081-4dee-88cd-4... | Given such
a taming, the pair {{formula:0c351b3a-d051-45ae-a25f-f05730ca7d76}} is called a (positively) polarized
Siegel bundle (cf. <TARGET_CIT>, <OTHER_CIT>). | Let {{formula:06caeebd-ab76-45f7-9bd2-87499115057d}} be a scalar bundle with submersion
{{formula:beef4e33-0468-41a7-bd78-820e26c7a353}} and consider a Siegel bundle {{formula:7a202310-f973-4e81-9c81-3930539421b5}} of
rank {{formula:fefdd143-3aab-4476-91b3-6631b3719575}} and type {{formula:08480017-5081-4dee-88cd-4... | Definition 4.1 A Siegel bundle {{formula:9d129e38-79bf-4dff-97b0-3ccaba0f55b0}} of rank {{formula:b5f39bb3-0087-4c34-acab-5f963bb975cb}} and type {{formula:63ab4dbb-db76-41ce-bad5-15140951ec97}} on {{formula:1b5190af-a543-426f-9329-e745bd704710}} is a principal bundle defined on {{formula:caa33002-5d51-420c-92d3-c2... | 2101.07778__body_000138|2101.07778__body_000139|2101.07778__body_000140 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
Definition 4.1 A Siegel bundle {{formula:9d129e38-79bf-4dff-97b0-3ccaba0f55b0}} of rank {{formula:b5f39bb3-0087-4c34-acab-5f963bb975cb}} and type {{formula:63ab4dbb-db76-41ce-bad5-15140951ec97}} on {{formula:1b5190af-a543-426f-9329-e745bd704710}} ... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000141__cite_0000__start_861__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000141 | 141 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 861 | 910 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | Let {{formula:d5e4bc11-20ce-434d-8b32-dd7852b434b9}} be the affine space of connections
on {{formula:59740369-4ad7-42e5-a456-6a56551b8192}} . Elements of this space are invariant one-forms
on {{formula:060ef44f-51aa-4256-91af-1abbc47f2e56}} mapping the fundamental vector fields of {{formula:89f8ee0a-2229-4084-9054-cd... | Let {{formula:d5e4bc11-20ce-434d-8b32-dd7852b434b9}} be the affine space of connections
on {{formula:59740369-4ad7-42e5-a456-6a56551b8192}} . Elements of this space are invariant one-forms
on {{formula:060ef44f-51aa-4256-91af-1abbc47f2e56}} mapping the fundamental vector fields of {{formula:89f8ee0a-2229-4084-9054-cd... | This bundle-valued 2-form is
{{formula:a93205f4-053f-4752-93bb-a00ed27e8fd3}} -closed by the Bianchi identity since (by the results
of <TARGET_CIT>, <OTHER_CIT>) all connections on
{{formula:8ef7fd62-efe3-4baa-951f-ad23e71224f6}} induce the same connection on {{formula:9458ff7d-1083-4556-bfa6-311cdb133ead}} , which
co... | Let {{formula:d5e4bc11-20ce-434d-8b32-dd7852b434b9}} be the affine space of connections
on {{formula:59740369-4ad7-42e5-a456-6a56551b8192}} . Elements of this space are invariant one-forms
on {{formula:060ef44f-51aa-4256-91af-1abbc47f2e56}} mapping the fundamental vector fields of {{formula:89f8ee0a-2229-4084-9054-cd... | Given a scalar section
{{formula:453b5074-2619-4a7a-b936-c1a498467067}} , we denote by {{formula:0cd88aeb-8834-4abf-8971-62d095742ae0}} the pullback of
{{formula:9e6bda50-91d8-40d3-8629-4d1551d9acf4}} by {{formula:af3e627f-8f96-4416-a3d1-2afe865b9403}} , which becomes a Siegel bundle over {{formula:e7dda6d9-4c4e-447a... | 2101.07778__body_000140|2101.07778__body_000141|2101.07778__body_000142 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
Given a scalar section
{{formula:453b5074-2619-4a7a-b936-c1a498467067}} , we denote by {{formula:0cd88aeb-8834-4abf-8971-62d095742ae0}} the pullback of
{{formula:9e6bda50-91d8-40d3-8629-4d1551d9acf4}} by {{formula:af3e627f-8f96-4416-a3d1-2afe865b940... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000146__cite_0000__start_165__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000146 | 146 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 165 | 214 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | Connections {{formula:5dcbd78a-1526-49ae-835d-33b9b438f073}} satisfying equation (REF ) will
be called polarized self-dual, following the terminology introduced in
{{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} in the context of Abelian gauge theory.
| Connections {{formula:5dcbd78a-1526-49ae-835d-33b9b438f073}} satisfying equation (REF ) will
be called polarized self-dual, following the terminology introduced in
<TARGET_CIT> in the context of Abelian gauge theory.
| Connections {{formula:5dcbd78a-1526-49ae-835d-33b9b438f073}} satisfying equation (REF ) will
be called polarized self-dual, following the terminology introduced in
<TARGET_CIT> in the context of Abelian gauge theory. | Connections {{formula:5dcbd78a-1526-49ae-835d-33b9b438f073}} satisfying equation (REF ) will
be called polarized self-dual, following the terminology introduced in
<TARGET_CIT> in the context of Abelian gauge theory.
| The Einstein equations:
{{formula:1915fdb8-b974-48b5-8309-f55da5366dba}}
The scalar equations:
{{formula:0a95f4a2-2753-4a1f-9bcd-2ec1c7c7e7e8}}
The Maxwell equations:
{{formula:e105877c-df8f-485e-bca9-905ffb33ddf8}}
whose set of solutions we denote by {{formula:5367c8ab-d834-400b-82da-bf810a29f53e}} .
Connecti... | 2101.07778__body_000145|2101.07778__body_000146|2101.07778__body_000147 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
The Einstein equations:
{{formula:1915fdb8-b974-48b5-8309-f55da5366dba}}
The scalar equations:
{{formula:0a95f4a2-2753-4a1f-9bcd-2ec1c7c7e7e8}}
The Maxwell equations:
{{formula:e105877c-df8f-485e-bca9-905ffb33ddf8}}
whose set of solutions we deno... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000150__cite_0000__start_511__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000150 | 150 | The DSZ quantization of 4d bosonic supergravity | 4 | section | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 511 | 560 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | Theorem 4.5
Let {{formula:425ea924-c808-4c40-bbad-d5e9530f5975}} be an integral
scalar-electromagnetic bundle of type {{formula:b57e900d-6ad7-4b2c-8c3d-8e673f1324a9}} . For every framed integral
configuration space {{formula:27cac9c0-8198-4e68-a328-e8a105362392}} there exists a vertically polarized
Siegel bundle {{f... | Theorem 4.5
Let {{formula:425ea924-c808-4c40-bbad-d5e9530f5975}} be an integral
scalar-electromagnetic bundle of type {{formula:b57e900d-6ad7-4b2c-8c3d-8e673f1324a9}} . For every framed integral
configuration space {{formula:27cac9c0-8198-4e68-a328-e8a105362392}} there exists a vertically polarized
Siegel bundle {{f... | For every framed integral
configuration space {{formula:27cac9c0-8198-4e68-a328-e8a105362392}} there exists a vertically polarized
Siegel bundle {{formula:2d528cfd-1258-47fa-ade0-c639ce378a94}} on {{formula:05fa6620-fe20-4722-aed1-b1a0e38600bc}} such that {{formula:a0f2bc67-495e-412e-a09b-2f2c644bb76d}}
and the twi... | Theorem 4.5
Let {{formula:425ea924-c808-4c40-bbad-d5e9530f5975}} be an integral
scalar-electromagnetic bundle of type {{formula:b57e900d-6ad7-4b2c-8c3d-8e673f1324a9}} . For every framed integral
configuration space {{formula:27cac9c0-8198-4e68-a328-e8a105362392}} there exists a vertically polarized
Siegel bundle {{f... | These differ from the usual Yang-Mills equations since {{formula:94657cd2-20f5-42b5-bbcb-1bf883a83dfe}}
involves both electric and magnetic degrees of freedom while the
equations themselves involve the pulled-back taming {{formula:e5573956-9ae2-4d84-8b18-f5ddef53653d}} .
Theorem 4.5
Let {{formula:425ea924-c808-4c40... | 2101.07778__body_000149|2101.07778__body_000150|2101.07778__body_000151 | [SECTION] The DSZ quantization of 4d bosonic supergravity
[CONTEXT]
These differ from the usual Yang-Mills equations since {{formula:94657cd2-20f5-42b5-bbcb-1bf883a83dfe}}
involves both electric and magnetic degrees of freedom while the
equations themselves involve the pulled-back taming {{formula:e5573956-9ae2-4d84-... | The DSZ quantization of 4d bosonic supergravity | 588 | 526 | 588 | 526 |
2101.07778__body_000185__cite_0000__start_545__ref_df81b0aac57ba02f9b65043bfbc02898429ae472 | 2,101.07778 | 2,101.07236 | 2101.07778__body_000185 | 185 | Rank zero scalar bundle | 5.2 | subsection | {{cite:df81b0aac57ba02f9b65043bfbc02898429ae472}} | 545 | 594 | 2101.07778__ref__df81b0aac57ba02f9b65043bfbc02898429ae472 | reduces to an isomorphism of groups {{formula:1ec5b2b9-0142-4010-a5d3-66ca77be2692}} where
{{formula:91a86738-d2b3-4bb0-9ce2-f03853d176cb}} is a polarized Siegel bundle over {{formula:0f5e877e-1d60-4c18-a2d0-0c775b0c64ff}} . Therefore, the gauge U-duality
group reduces to the gauge group of the Siegel bundle underlyi... | reduces to an isomorphism of groups {{formula:1ec5b2b9-0142-4010-a5d3-66ca77be2692}} where
{{formula:91a86738-d2b3-4bb0-9ce2-f03853d176cb}} is a polarized Siegel bundle over {{formula:0f5e877e-1d60-4c18-a2d0-0c775b0c64ff}} . Therefore, the gauge U-duality
group reduces to the gauge group of the Siegel bundle underlyi... | This corresponds, in fact, with the electromagnetic gauge duality
group of the abelian gauge theory determined by {{formula:53e35afd-ea24-48a1-8b88-1075bc5244fd}} as explained in
detail in <TARGET_CIT>. | reduces to an isomorphism of groups {{formula:1ec5b2b9-0142-4010-a5d3-66ca77be2692}} where
{{formula:91a86738-d2b3-4bb0-9ce2-f03853d176cb}} is a polarized Siegel bundle over {{formula:0f5e877e-1d60-4c18-a2d0-0c775b0c64ff}} . Therefore, the gauge U-duality
group reduces to the gauge group of the Siegel bundle underlyi... | Let {{formula:9d33b3e6-ede7-44e0-a89f-30aa396b7bf9}} be the rank zero scalar bundle, that is, {{formula:7c6d1c29-bc47-4be8-8d78-861efacd084f}} , {{formula:876f86ab-9f82-49b3-8eca-352383ce13f7}} is the identity map, {{formula:fa3d36ac-2241-4782-8e71-8aaa2ee9832a}} is canonically identified with the tangent
bundle of ... | 2101.07778__body_000184|2101.07778__body_000185|2101.07778__body_000186 | [SECTION] Rank zero scalar bundle
[CONTEXT]
Let {{formula:9d33b3e6-ede7-44e0-a89f-30aa396b7bf9}} be the rank zero scalar bundle, that is, {{formula:7c6d1c29-bc47-4be8-8d78-861efacd084f}} , {{formula:876f86ab-9f82-49b3-8eca-352383ce13f7}} is the identity map, {{formula:fa3d36ac-2241-4782-8e71-8aaa2ee9832a}} is canon... | Rank zero scalar bundle | 588 | 526 | 588 | 526 |
2101.07783__body_000000__cite_0010__start_1406__ref_0477f1960b70c229009abdde3560f3f7d121e58b | 2,101.07783 | 2,101.07774 | 2101.07783__body_000000 | 0 | Introduction | 1 | section | {{cite:0477f1960b70c229009abdde3560f3f7d121e58b}} | 1,406 | 1,455 | 2101.07783__ref__0477f1960b70c229009abdde3560f3f7d121e58b | In their recent paper, McDermott et al. {{cite:2ba564e93ef8d3a77ed3657553e922833015d66c}} evaluated issues with microgrid protection. They highlighted the underlying difficulties, which include the lack of fault current from inverter-interfaced generation {{cite:67013b75420d4150115ad503d45152747a32bb63}}, the varying f... | In their recent paper, McDermott et al. <OTHER_CIT> evaluated issues with microgrid protection. They highlighted the underlying difficulties, which include the lack of fault current from inverter-interfaced generation <OTHER_CIT>, the varying fault current between grid-connected and islanded modes <OTHER_CIT>, the pote... | Barnes et al. <TARGET_CIT> identified dynamic state estimation for the protection of radial portions of microgrids; however, there is a potential for sensitivity to initial conditions, particularly at the delta-connected load models. | In their recent paper, McDermott et al. <OTHER_CIT> evaluated issues with microgrid protection. They highlighted the underlying difficulties, which include the lack of fault current from inverter-interfaced generation <OTHER_CIT>, the varying fault current between grid-connected and islanded modes <OTHER_CIT>, the pote... | In their recent paper, McDermott et al. <OTHER_CIT> evaluated issues with microgrid protection. They highlighted the underlying difficulties, which include the lack of fault current from inverter-interfaced generation <OTHER_CIT>, the varying fault current between grid-connected and islanded modes <OTHER_CIT>, the pote... | 2101.07783__body_000000|2101.07783__body_000001 | [SECTION] Introduction
[CONTEXT]
In their recent paper, McDermott et al. <OTHER_CIT> evaluated issues with microgrid protection. They highlighted the underlying difficulties, which include the lack of fault current from inverter-interfaced generation <OTHER_CIT>, the varying fault current between grid-connected and is... | Introduction | 81 | 68 | 81 | 68 |
2101.08057__body_000117__cite_0000__start_314__ref_13fbc277d73e648ca8b39f66616a71ceb0371c19 | 2,101.08057 | 2,101.09081 | 2101.08057__body_000117 | 117 | Convergence Analysis | 4 | section | {{cite:13fbc277d73e648ca8b39f66616a71ceb0371c19}} | 314 | 363 | 2101.08057__ref__13fbc277d73e648ca8b39f66616a71ceb0371c19 | (c) Lemmas 3.5, 4.1, 4.2 and Theorem 4.4 can be obtained when {{formula:74672389-124c-4a63-9ff7-581e236a9010}} pseudo-monotone and weakly sequentially continuous (i.e., for all {{formula:443da6b1-c907-4c25-95fa-f29b080e4af5}} ,
{{formula:1ddc4600-9c43-4f7b-b5c0-a0f2dc7cd01f}} ). The reader can see, for example, {{cite... | (c) Lemmas 3.5, 4.1, 4.2 and Theorem 4.4 can be obtained when {{formula:74672389-124c-4a63-9ff7-581e236a9010}} pseudo-monotone and weakly sequentially continuous (i.e., for all {{formula:443da6b1-c907-4c25-95fa-f29b080e4af5}} ,
{{formula:1ddc4600-9c43-4f7b-b5c0-a0f2dc7cd01f}} ). The reader can see, for example, <TARGE... | The reader can see, for example, <TARGET_CIT>.{{formula:d2db5f63-a97e-4067-8761-5e6484df593a}} | (c) Lemmas 3.5, 4.1, 4.2 and Theorem 4.4 can be obtained when {{formula:74672389-124c-4a63-9ff7-581e236a9010}} pseudo-monotone and weakly sequentially continuous (i.e., for all {{formula:443da6b1-c907-4c25-95fa-f29b080e4af5}} ,
{{formula:1ddc4600-9c43-4f7b-b5c0-a0f2dc7cd01f}} ). The reader can see, for example, <TARGE... | (b) In finite-dimensional spaces, Theorem REF holds when {{formula:164aa730-4316-420f-ab36-1b93ef567c52}} is monotone and continuous.
(c) Lemmas 3.5, 4.1, 4.2 and Theorem 4.4 can be obtained when {{formula:74672389-124c-4a63-9ff7-581e236a9010}} pseudo-monotone and weakly sequentially continuous (i.e., for all {{fo... | 2101.08057__body_000116|2101.08057__body_000117|2101.08057__body_000118 | [SECTION] Convergence Analysis
[CONTEXT]
(b) In finite-dimensional spaces, Theorem REF holds when {{formula:164aa730-4316-420f-ab36-1b93ef567c52}} is monotone and continuous.
(c) Lemmas 3.5, 4.1, 4.2 and Theorem 4.4 can be obtained when {{formula:74672389-124c-4a63-9ff7-581e236a9010}} pseudo-monotone and weakly s... | Convergence Analysis | 168 | 160 | 168 | 160 |
2101.08012__body_000000__cite_0030__start_2376__ref_a8693951b9fbc330a876214b0564654bd3f40213 | 2,101.08012 | 2,101.06869 | 2101.08012__body_000000 | 0 | Introduction | 1 | section | {{cite:a8693951b9fbc330a876214b0564654bd3f40213}} | 2,376 | 2,425 | 2101.08012__ref__a8693951b9fbc330a876214b0564654bd3f40213 | Recently, the North American Nanohertz Observatory for Gravitational Wave
(NANOGrav) Collaboration {{cite:6233864c0cc712ec9fb7b580bb867b45a5f422bc}} has reported an
analysis of 12.5-year pulsar timing array (PTA) data. According to the
analysis {{cite:6233864c0cc712ec9fb7b580bb867b45a5f422bc}}, a possible evidence is f... | Recently, the North American Nanohertz Observatory for Gravitational Wave
(NANOGrav) Collaboration <OTHER_CIT> has reported an
analysis of 12.5-year pulsar timing array (PTA) data. According to the
analysis <OTHER_CIT>, a possible evidence is found for a
stochastic common-spectrum process which may be interpreted as a
... | Although
the observational results need further analyses, such as a joint analysis
with data from the other PTA collaborations (such as EPTA and
PPTA) <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, the potentiality of its being a
stochastic GW background (SGWB) signal has aroused keen interest of
theorists <OTHER_CIT>, <OTHER_... | Recently, the North American Nanohertz Observatory for Gravitational Wave
(NANOGrav) Collaboration <OTHER_CIT> has reported an
analysis of 12.5-year pulsar timing array (PTA) data. According to the
analysis <OTHER_CIT>, a possible evidence is found for a
stochastic common-spectrum process which may be interpreted as a
... | Recently, the North American Nanohertz Observatory for Gravitational Wave
(NANOGrav) Collaboration <OTHER_CIT> has reported an
analysis of 12.5-year pulsar timing array (PTA) data. According to the
analysis <OTHER_CIT>, a possible evidence is found for a
stochastic common-spectrum process which may be interpreted as a
... | 2101.08012__body_000000|2101.08012__body_000001 | [SECTION] Introduction
[CONTEXT]
Recently, the North American Nanohertz Observatory for Gravitational Wave
(NANOGrav) Collaboration <OTHER_CIT> has reported an
analysis of 12.5-year pulsar timing array (PTA) data. According to the
analysis <OTHER_CIT>, a possible evidence is found for a
stochastic common-spectrum proc... | Introduction | 27 | 0 | 28 | 0 |
2101.08117__body_000003__cite_0003__start_875__ref_7979208e803ba7ab95dc2c00ac608e3e58b112ad | 2,101.08117 | 2,101.01828 | 2101.08117__body_000003 | 3 | I. Introduction | 1 | section | {{cite:7979208e803ba7ab95dc2c00ac608e3e58b112ad}} | 875 | 924 | 2101.08117__ref__7979208e803ba7ab95dc2c00ac608e3e58b112ad | For attractive bosons, which is the case for axions, one lacks positive pressure and consequently the condensate formed at subcritical temperatures is prone to fragmentation {{cite:b6afa174d35194c3ddd7079398c63669231d945b}}. The only possibility for sustaining the macroscopic homogeneous core is to consider the case of... | For attractive bosons, which is the case for axions, one lacks positive pressure and consequently the condensate formed at subcritical temperatures is prone to fragmentation <OTHER_CIT>. The only possibility for sustaining the macroscopic homogeneous core is to consider the case of ultra-light particles. Achieving macr... | The detailed analysis of phenomenological implications of such a scenario was performed in <OTHER_CIT> (see <TARGET_CIT> for recent numerical simulations of the structure formation). | For attractive bosons, which is the case for axions, one lacks positive pressure and consequently the condensate formed at subcritical temperatures is prone to fragmentation <OTHER_CIT>. The only possibility for sustaining the macroscopic homogeneous core is to consider the case of ultra-light particles. Achieving macr... | An interesting version of self-interacting dark matter was considered in <OTHER_CIT>, <OTHER_CIT>See also <OTHER_CIT> for the discussion of the core profile and galactic rotation curves within the Bose-Einstein condensate dark matter scenario. in the form of a repulsive, sub-eV, scalar field exhibiting superfluidity in... | 2101.08117__body_000002|2101.08117__body_000003|2101.08117__body_000004 | [SECTION] I. Introduction
[CONTEXT]
An interesting version of self-interacting dark matter was considered in <OTHER_CIT>, <OTHER_CIT>See also <OTHER_CIT> for the discussion of the core profile and galactic rotation curves within the Bose-Einstein condensate dark matter scenario. in the form of a repulsive, sub-eV, sca... | I. Introduction | 85 | 45 | 85 | 45 |
2101.09059__body_000004__cite_0009__start_1097__ref_284dc12f32a840ec28009524294bbba36322ce89 | 2,101.09059 | 2,104.06589 | 2101.09059__body_000004 | 4 | Introduction | 1 | section | {{cite:284dc12f32a840ec28009524294bbba36322ce89}} | 1,097 | 1,146 | 2101.09059__ref__284dc12f32a840ec28009524294bbba36322ce89 | Use of explicit structural solvers in cardiovascular flow problems is mainly related to their flexibility in modeling complex contact configurations. Studies involving coronary stent deployment following endoscopic balloon inflation are proposed, e.g., in {{cite:bcf0731d7b99dc1747a148aa6cc50153002175bf}}, {{cite:c57eb4... | Use of explicit structural solvers in cardiovascular flow problems is mainly related to their flexibility in modeling complex contact configurations. Studies involving coronary stent deployment following endoscopic balloon inflation are proposed, e.g., in <OTHER_CIT>, <OTHER_CIT>, and coupling with an implicit fluid so... | Additionally, Ensemble methods for fluid problems have been recently proposed by <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT> in the context of the Navier-Stokes equations with distinct initial conditions and forcing terms. This is based on the observation that solution of linear systems is responsi... | Use of explicit structural solvers in cardiovascular flow problems is mainly related to their flexibility in modeling complex contact configurations. Studies involving coronary stent deployment following endoscopic balloon inflation are proposed, e.g., in <OTHER_CIT>, <OTHER_CIT>, and coupling with an implicit fluid so... | We motivate the computational advantage of explicit-in-time ensemble solvers through a back-of-the-envelope argument. It is well known how explicit numerical integration schemes are only conditionally stable. For structural problems, the larger stable time step is determined through a CFL condition as {{formula:262689c... | 2101.09059__body_000003|2101.09059__body_000004|2101.09059__body_000005 | [SECTION] Introduction
[CONTEXT]
We motivate the computational advantage of explicit-in-time ensemble solvers through a back-of-the-envelope argument. It is well known how explicit numerical integration schemes are only conditionally stable. For structural problems, the larger stable time step is determined through a ... | Introduction | 60 | 48 | 60 | 48 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.