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4,600 | In order to facilitate this process, he constructed what is now known as a polarograph with M. Shikata, which enabled him to record photographically the same curve in a matter of hours. He gave recognition to the importance of potential and its control and also recognized the opportunities of measuring the limiting cur... | Voltammetry | 0.827729 |
4,601 | The beginning of voltammetry was facilitated by the discovery of polarography in 1922 by the Nobel Prize–winning Czech chemist Jaroslav Heyrovský. Early voltammetric techniques had many problems, limiting their viability for everyday use in analytical chemistry. In polarography, these problems included the fact that me... | Voltammetry | 0.827729 |
4,602 | The Applied Probability Trust is a UK-based non-profit foundation for study and research in the mathematical sciences, founded in 1964 and based in the School of Mathematics and Statistics at the University of Sheffield, which it has been affiliated with since 1964. | Applied Probability Trust | 0.827717 |
4,603 | Although no such puzzle could ever be physically constructed, the rules of how they operate are quite rigorously defined mathematically and are analogous to the rules found in three-dimensional geometry. Hence, they can be simulated by software. As with the mechanical sequential move puzzles, there are records for solv... | N-dimensional sequential move puzzle | 0.827714 |
4,604 | In biochemistry, phosphorylation is the attachment of a phosphate group to a molecule or an ion. This process and its inverse, dephosphorylation, are common in biology. Protein phosphorylation often activates (or deactivates) many enzymes. | Phosphorylation | 0.827712 |
4,605 | Protein phosphorylation is the most abundant post-translational modification in eukaryotes. Phosphorylation can occur on serine, threonine and tyrosine side chains (often called 'residues') through phosphoester bond formation, on histidine, lysine and arginine through phosphoramidate bonds, and on aspartic acid and glu... | Phosphorylation | 0.827712 |
4,606 | Ionic transfer is the transfer of ions from one liquid phase to another. This is related to the phase transfer catalysts which are a special type of liquid-liquid extraction which is used in synthetic chemistry. For instance nitrate anions can be transferred between water and nitrobenzene. One way to observe this is to... | Ionic transfer | 0.827708 |
4,607 | RNA Biology is the leading peer-reviewed scientific journal in the field of ribonucleic acid (RNA) research. It is indexed for MEDLINE. The editor-in-chief is Renée Schroeder (University of Vienna). | RNA Biology | 0.827693 |
4,608 | Sonnenschein-Mantel-Debreu theorem (SMD theorem) is a theorem for exchange economy that can be expressed in the following way: for a function that is continuous, homogeneous of degree zero, and in accord with Walras's law,there is an economy with at least as many agents as goods such that, for prices bounded away from ... | Aggregation problem | 0.827692 |
4,609 | William Shakespeare's Falstaff drank Spanish "sherris sack", in contrast to Sir Toby Belch's preference for "canary". Wine references in later centuries branch out to more winegrowing regions.The Microbe is a humorous 1912 poem by Hilaire Belloc, starting with the lines "The microbe is so very small / You cannot make h... | Human interactions with microbes | 0.827686 |
4,610 | Anaerobic microorganisms are important in sewage treatment. In scientific research, yeasts and the bacterium Escherichia coli serve as model organisms especially in genetics and related fields. On the symbolic side, an early poem about brewing is the Sumerian "Hymn to Ninkasi", from 1800 BC. | Human interactions with microbes | 0.827686 |
4,611 | This article describes the roles played by microorganisms in human culture. Since microbes were not known until the Early Modern period, they appear in earlier literature indirectly, through descriptions of baking and brewing. Only with the invention of the microscope, as used by Robert Hooke in his 1665 book Micrograp... | Human interactions with microbes | 0.827686 |
4,612 | Controlled fermentation with microbes in brewing, wine making, baking, pickling and cultured dairy products such as yogurt and cheese, is used to modify ingredients to make foods with desirable properties. The principal microbes involved are yeasts, in the case of beer, wine, and ordinary bread; and bacteria, in the ca... | Human interactions with microbes | 0.827686 |
4,613 | Microorganisms are essential tools in biotechnology, biochemistry, genetics, and molecular biology. The yeasts brewer's yeast (Saccharomyces cerevisiae) and fission yeast (Schizosaccharomyces pombe) are important model organisms in science, since they are simple eukaryotes that can be grown rapidly in large numbers and... | Human interactions with microbes | 0.827686 |
4,614 | Melbourne Bioinformatics (formerly the Victorian Life Sciences Computation Initiative, VLSCI) is a centre for computational life science expertise. It provides bioinformatics support for all researchers and students in a wide range of projects and services of local and national significance. Researchers can engage with... | Melbourne Bioinformatics | 0.827684 |
4,615 | Since moving to the nearby offices of IBM Research Australia, Collaboratory staff have continued to work on a range of projects as part of a broader University of Melbourne/IBM partnership under the new name of Melbourne Bioinformatics. Melbourne Bioinformatics's petascale high performance computation facility was acce... | Melbourne Bioinformatics | 0.827684 |
4,616 | The VLSCI was established as part of the Victorian government's plans to support biotechnology, and was listed as a key infrastructure project in the Victorian Biotechnology Action Plan 2011. It was a $100m initiative of the Victorian Government in partnership with The University of Melbourne and the IBM Life Sciences ... | Melbourne Bioinformatics | 0.827684 |
4,617 | Melbourne Bioinformatics together with QFAB Bioinformatics, QCIF and the University of Queensland’s Research Computing Centre jointly built and operate Galaxy Australia which is a major feature of the Genomics Virtual Laboratory. | Melbourne Bioinformatics | 0.827684 |
4,618 | The journal was established as an open-access alternative to the journal Machine Learning. In 2001, forty editorial board members of Machine Learning resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. T... | Journal of Machine Learning Research | 0.827681 |
4,619 | The Journal of Machine Learning Research is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). | Journal of Machine Learning Research | 0.827681 |
4,620 | Thus, the primary structure is better analyzed in traditional branches of bioinformatics. However, the sequence implies restrictions that allow the formation of conserved local conformations of the polypeptide chain, such as alpha-helix, beta-sheets, and loops (secondary structure). Also, weak interactions (such as hyd... | Structural bioinformatics | 0.827677 |
4,621 | The structure of a protein is directly related to its function. The presence of certain chemical groups in specific locations allows proteins to act as enzymes, catalyzing several chemical reactions. In general, protein structures are classified into four levels: primary (sequences), secondary (local conformation of th... | Structural bioinformatics | 0.827677 |
4,622 | Calculating contacts is an important task in structural bioinformatics, being important for the correct prediction of protein structure and folding, thermodynamic stability, protein-protein and protein-ligand interactions, docking and molecular dynamics analyses, and so on.Traditionally, computational methods have used... | Structural bioinformatics | 0.827677 |
4,623 | The classic DNA duplexes structure was initially described by Watson and Crick (and contributions of Rosalind Franklin). The DNA molecule is composed of three substances: a phosphate group, a pentose, and a nitrogen base (adenine, thymine, cytosine, or guanine). The DNA double helix structure is stabilized by hydrogen ... | Structural bioinformatics | 0.827677 |
4,624 | PISCES server for creating non-redundant lists of proteins: Generates PDB list by sequence identity and structural quality criteria. The Structural Biology Knowledgebase: Tools to aid in protein research design. ProtCID: The Protein Common Interface Database Database of similar protein-protein interfaces in crystal str... | Structural bioinformatics | 0.827677 |
4,625 | TOPOFIT-DB: Protein structural alignments based on the TOPOFIT method. Electron Density Server (EDS): Electron-density maps and statistics about the fit of crystal structures and their maps. CASP: Prediction Center Community-wide, worldwide experiment for protein structure prediction CASP. | Structural bioinformatics | 0.827677 |
4,626 | Structural signatures, also called fingerprints, are macromolecule pattern representations that can be used to infer similarities and differences. Comparisons among a large set of proteins using RMSD still is a challenge due to the high computational cost of structural alignments. Structural signatures based on graph d... | Structural bioinformatics | 0.827677 |
4,627 | Structural bioinformatics is the branch of bioinformatics that is related to the analysis and prediction of the three-dimensional structure of biological macromolecules such as proteins, RNA, and DNA. It deals with generalizations about macromolecular 3D structures such as comparisons of overall folds and local motifs,... | Structural bioinformatics | 0.827677 |
4,628 | Protein structure visualization is an important issue for structural bioinformatics. It allows users to observe static or dynamic representations of the molecules, also allowing the detection of interactions that may be used to make inferences about molecular mechanisms. The most common types of visualization are: Cart... | Structural bioinformatics | 0.827677 |
4,629 | Interactions are contacts established between parts of molecules at different levels. They are responsible for stabilizing protein structures and perform a varied range of activities. In biochemistry, interactions are characterized by the proximity of atom groups or molecules regions that present an effect upon one ano... | Structural bioinformatics | 0.827677 |
4,630 | Standard Ball-and-stick model is generated from the electron density map. Analysis of NMR spectroscopy data - Nuclear magnetic resonance spectroscopy experiments produce two (or higher) dimensional data, with each peak corresponding to a chemical group within the sample. Optimization methods are used to convert spectra... | Structural bioinformatics | 0.827677 |
4,631 | This leads to a need for tracking the conditions and results of trials. Furthermore, supervised machine learning algorithms can be used on the stored data to identify conditions that might increase the yield of pure crystals. Analysis of X-Ray crystallographic data - The diffraction pattern obtained as a result of bomb... | Structural bioinformatics | 0.827677 |
4,632 | Informatics approaches used in structural bioinformatics are: Selection of Target - Potential targets are identified by comparing them with databases of known structures and sequence. The importance of a target can be decided on the basis of published literature. Target can also be selected on the basis of its protein ... | Structural bioinformatics | 0.827677 |
4,633 | In structural bioinformatics, de novo modeling, also known as ab initio modeling, refers to approaches for obtaining three-dimensional structures from sequences without the necessity of a homologous known 3D structure. Despite the new algorithms and methods proposed in the last years, de novo protein structure predicti... | Structural bioinformatics | 0.827677 |
4,634 | More generally every finite group is an algebraic group (it can be realised as a finite, hence Zariski-closed, subgroup of some G L n {\displaystyle \mathrm {GL} _{n}} by Cayley's theorem). In addition it is both affine and projective. Thus, in particular for classification purposes, it is natural to restrict statement... | Group variety | 0.827674 |
4,635 | As an algebraic variety G {\displaystyle \mathrm {G} } carries a Zariski topology. It is not in general a group topology, i.e. the group operations may not be continuous for this topology (because Zariski topology on the product is not the product of Zariski topologies on the factors). An algebraic group is said to be ... | Group variety | 0.827674 |
4,636 | An algebraic subgroup is said to be normal if it is stable under every inner automorphism (which are regular maps). If H {\displaystyle \mathrm {H} } is a normal algebraic subgroup of G {\displaystyle \mathrm {G} } then there exists an algebraic group G / H {\displaystyle \mathrm {G} /\mathrm {H} } and a surjective mor... | Group variety | 0.827674 |
4,637 | An algebraic subgroup of an algebraic group G {\displaystyle \mathrm {G} } is a subvariety H {\displaystyle \mathrm {H} } of G {\displaystyle \mathrm {G} } that is also a subgroup of G {\displaystyle \mathrm {G} } (that is, the maps G × G → G {\displaystyle \mathrm {G} \times \mathrm {G} \to \mathrm {G} } and G → G {\d... | Group variety | 0.827674 |
4,638 | Abelian varieties are connected projective algebraic groups, for instance elliptic curves. They are always commutative. They arise naturally in various situations in algebraic geometry and number theory, for example as the Jacobian variety of a curve. | Group variety | 0.827674 |
4,639 | The general linear group G L n {\displaystyle \mathrm {GL} _{n}} of invertible matrices over a field k {\displaystyle k} is an algebraic group. It can be realised as a subvariety in A n 2 + 1 {\displaystyle \mathbb {A} ^{n^{2}+1}} in much the same way as the multiplicative group in the previous example. A non-singular ... | Group variety | 0.827674 |
4,640 | The algebraic group G m {\displaystyle \mathrm {G} _{m}} is called multiplicative group, because its k {\displaystyle k} -points are isomorphic to the multiplicative group of the field k {\displaystyle k} (an isomorphism is given by x ↦ ( x , x − 1 ) {\displaystyle x\mapsto (x,x^{-1})} ; note that the subset of inverti... | Group variety | 0.827674 |
4,641 | The additive group: the affine line A 1 {\displaystyle \mathbb {A} ^{1}} endowed with addition and opposite as group operations is an algebraic group. It is called the additive group (because its k {\displaystyle k} -points are isomorphic as a group to the additive group of k {\displaystyle k} ), and usually denoted by... | Group variety | 0.827674 |
4,642 | An important class of algebraic groups is given by the affine algebraic groups, those whose underlying algebraic variety is an affine variety; they are exactly the algebraic subgroups of the general linear group, and are therefore also called linear algebraic groups. Another class is formed by the abelian varieties, wh... | Group variety | 0.827674 |
4,643 | A more sophisticated definition of an algebraic group over a field k {\displaystyle k} is that it is that of a group scheme over k {\displaystyle k} (group schemes can more generally be defined over commutative rings). Yet another definition of the concept is to say that an algebraic group over k {\displaystyle k} is a... | Group variety | 0.827674 |
4,644 | In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, ort... | Group variety | 0.827674 |
4,645 | For this reason selection sort may be preferable in cases where writing to memory is significantly more expensive than reading, such as with EEPROM or flash memory. While some divide-and-conquer algorithms such as quicksort and mergesort outperform insertion sort for larger arrays, non-recursive sorting algorithms such... | Insertion Sort | 0.827665 |
4,646 | This caveat also applies to UV, even though almost all of it is not ionizing, because UV can damage molecules due to electronic excitation, which is far greater per unit energy than heating effects.Infrared radiation in the spectral distribution of a black body is usually considered a form of heat, since it has an equi... | Electromagnetic signal | 0.827664 |
4,647 | Many authors use the term algebra to mean associative algebra, or unital associative algebra, or in some subjects such as algebraic geometry, unital associative commutative algebra. Replacing the field of scalars by a commutative ring leads to the more general notion of an algebra over a ring. Algebras are not to be co... | Algebra (ring theory) | 0.827663 |
4,648 | An algebra is unital or unitary if it has an identity element with respect to the multiplication. The ring of real square matrices of order n forms a unital algebra since the identity matrix of order n is the identity element with respect to matrix multiplication. It is an example of a unital associative algebra, a (un... | Algebra (ring theory) | 0.827663 |
4,649 | In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms i... | Algebra (ring theory) | 0.827663 |
4,650 | Training method usually requires multiple numerical optimization techniques Similarly by the definition, the discriminative model will need the combination of multiple subtasks for solving a complex real-world problem | Discriminative model | 0.827653 |
4,651 | Discriminative models and generative models also differ in introducing the posterior possibility. To maintain the least expected loss, the minimization of result's misclassification should be acquired. In the discriminative model, the posterior probabilities, P ( y | x ) {\displaystyle P(y|x)} , is inferred from a para... | Discriminative model | 0.827653 |
4,652 | Let's say we are given the m {\displaystyle m} class labels (classification) and n {\displaystyle n} feature variables, Y: { y 1 , y 2 , … , y m } , X: { x 1 , x 2 , … , x n } {\displaystyle Y:\{y_{1},y_{2},\ldots ,y_{m}\},X:\{x_{1},x_{2},\ldots ,x_{n}\}} , as the training samples. A generative model takes the joint pr... | Discriminative model | 0.827653 |
4,653 | Spectral sensitivity is the relative efficiency of detection, of light or other signal, as a function of the frequency or wavelength of the signal. In visual neuroscience, spectral sensitivity is used to describe the different characteristics of the photopigments in the rod cells and cone cells in the retina of the eye... | Spectral sensitivity | 0.827647 |
4,654 | The first phase of the Protein Structure Initiative (PSI-1) lasted from June 2000 until September 2005, and had a budget of $270 million funded primarily by NIGMS with support from the National Institute of Allergy and Infectious Diseases. PSI-1 saw the establishment of nine pilot centers focusing on structural genomic... | Protein Structure Initiative | 0.827646 |
4,655 | The Protein Structure Initiative (PSI) was a USA based project that aimed at accelerating discovery in structural genomics and contribute to understanding biological function. Funded by the U.S. National Institute of General Medical Sciences (NIGMS) between 2000 and 2015, its aim was to reduce the cost and time require... | Protein Structure Initiative | 0.827646 |
4,656 | In October 2008 the NIGMS hosted a meeting concerning the future of structural genomics efforts and invited speakers from the PSI Advisory Committee, members of the NIGMS Advisory Council, and interested scientists who had no previous involvement with the PSI. Representatives of other genomics, proteomics, and structur... | Protein Structure Initiative | 0.827646 |
4,657 | The PSI has received notable criticism from the structural biology community. Among these charges is that the main product of the PSI – PDB files of proteins' atomic coordinates as determined by X-ray crystallography or NMR spectroscopy – are not useful enough to biologists to justify the project's $764 million cost. C... | Protein Structure Initiative | 0.827646 |
4,658 | The third phase of the PSI was called PSI:Biology and was intended to reflect the emphasis on the biological relevance of the work. During this phase, highly organized networks of investigators were applying the new paradigm of high-throughput structure determination, which was successfully developed during the earlier... | Protein Structure Initiative | 0.827646 |
4,659 | The PSI Materials Repository, established in 2006 at the Harvard Institute of Proteomics, stores and ships PSI-generated plasmid clones. Clones are sequence-verified, annotated and stored in the DNASU Plasmid Repository, currently located at the Biodesign Institute at Arizona State University. As of September 2011, the... | Protein Structure Initiative | 0.827646 |
4,660 | Two homology modeling centers, the Joint Center for Molecular Modeling (JCMM) and New Methods for High-Resolution Comparative Modeling (NMHRCM) were also added, as well as two resource centers, the PSI Materials Repository (PSI-MR) and the PSI Structural Biology Knowledgebase (SBKB). The TB Structural Genomics Consorti... | Protein Structure Initiative | 0.827646 |
4,661 | The number of sponsored research centers grew to 14 during PSI-2. Four centers were selected as Large Scale centers, with a mandate to place 15% effort on targets nominated by the broader research community, 15% on targets of biomedical relevance, and 70% on broad structural coverage; these centers were the Joint Cente... | Protein Structure Initiative | 0.827646 |
4,662 | During its term in PSI-1, it deposited structures for over 70 unique proteins from Mycobacterium tuberculosis, which represented more than 35% of total unique M. tuberculosis structures solved through 2007. In following with its biomedical theme to increase coverage of phosphotomes, the NYSGXRC has determined structure... | Protein Structure Initiative | 0.827646 |
4,663 | The project has been organized into three separate phases. The first phase of the Protein Structure Initiative (PSI-1) spanned from 2000 to 2005, and was dedicated to demonstrating the feasibility of high-throughput structure determination, solving unique protein structures, and preparing for a subsequent production ph... | Protein Structure Initiative | 0.827646 |
4,664 | Studies that examine the usefulness of manipulatives have found that outcomes may vary widely depending on physical characteristics of the materials themselves and the ways in which they are used. Emphasis is often placed on the importance of the physicality of the manipulative, but some work on teaching geometry conce... | Mathematical toy | 0.827644 |
4,665 | The original motivation of formal concept analysis was the search for real-world meaning of mathematical order theory. One such possibility of very general nature is that data tables can be transformed into algebraic structures called complete lattices, and that these can be utilized for data visualization and interpre... | Concept lattice | 0.827608 |
4,666 | In information science, formal concept analysis (FCA) is a principled way of deriving a concept hierarchy or formal ontology from a collection of objects and their properties. Each concept in the hierarchy represents the objects sharing some set of properties; and each sub-concept in the hierarchy represents a subset o... | Concept lattice | 0.827608 |
4,667 | The negation of an attribute m is an attribute ¬m, the extent of which is just the complement of the extent of m, i.e., with (¬m)′ = G \ m′. It is in general not assumed that negated attributes are available for concept formation. But pairs of attributes which are negations of each other often naturally occur, for exam... | Concept lattice | 0.827608 |
4,668 | The formal concept analysis can be used as a qualitative method for data analysis. Since the early beginnings of FBA in the early 1980s, the FBA research group at TU Darmstadt has gained experience from more than 200 projects using the FBA (as of 2005). Including the fields of: medicine and cell biology, genetics, ecol... | Concept lattice | 0.827608 |
4,669 | The MNIST database (Modified National Institute of Standards and Technology database) is a large database of handwritten digits that is commonly used for training various image processing systems. The database is also widely used for training and testing in the field of machine learning. It was created by "re-mixing" t... | MNIST database | 0.827605 |
4,670 | Some researchers have achieved "near-human performance" on the MNIST database, using a committee of neural networks; in the same paper, the authors achieve performance double that of humans on other recognition tasks. The highest error rate listed on the original website of the database is 12 percent, which is achieved... | MNIST database | 0.827605 |
4,671 | This is a table of some of the machine learning methods used on the dataset and their error rates, by type of classifier: | MNIST database | 0.827605 |
4,672 | Also, the Parallel Computing Center (Khmelnytskyi, Ukraine) obtained an ensemble of only 5 convolutional neural networks which performs on MNIST at 0.21 percent error rate. Some images in the testing dataset are barely readable and may prevent reaching test error rates of 0%. In 2018, researchers from Department of Sys... | MNIST database | 0.827605 |
4,673 | In 2013, an approach based on regularization of neural networks using DropConnect has been claimed to achieve a 0.21 percent error rate. In 2016, the single convolutional neural network best performance was 0.25 percent error rate. As of August 2018, the best performance of a single convolutional neural network trained... | MNIST database | 0.827605 |
4,674 | The fundamental idea in the development of the theory is given by replacing topological spaces by condensed sets, defined below. The category of condensed sets, as well as related categories such as that of condensed abelian groups, are much better behaved than the category of topological spaces. In particular, unlike ... | Condensed mathematics | 0.827588 |
4,675 | In 2013, Bhargav Bhatt and Peter Scholze introduced a general notion of pro-étale site associated to an arbitrary scheme. In 2018, together with Dustin Clausen they arrived at the conclusion that already the pro-étale site of a single point, which is isomorphic to the site of profinite sets introduced above, has rich e... | Condensed mathematics | 0.827588 |
4,676 | Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which aims to unify various mathematical subfields, including topology, complex geometry, and algebraic geometry. | Condensed mathematics | 0.827588 |
4,677 | A condensed set is a sheaf of sets on the site of profinite sets, with the Grothendieck topology given by finite, jointly surjective collections of maps. Similarly, a condensed group, condensed ring, etc. is defined as a sheaf of groups, rings etc. on this site. To any topological space X {\displaystyle X} one can asso... | Condensed mathematics | 0.827588 |
4,678 | The fact that finding a square root of a number modulo a large composite n is equivalent to factoring (which is widely believed to be a hard problem) has been used for constructing cryptographic schemes such as the Rabin cryptosystem and the oblivious transfer. The quadratic residuosity problem is the basis for the Gol... | Quadratic residue | 0.827583 |
4,679 | That is, given a number a and a modulus n, how hard is it to tell whether an x solving x2 ≡ a (mod n) exists assuming one does exist, to calculate it?An important difference between prime and composite moduli shows up here. Modulo a prime p, a quadratic residue a has 1 + (a|p) roots (i.e. zero if a N p, one if a ≡ 0 (m... | Quadratic residue | 0.827583 |
4,680 | It is possible to find a corresponding computational branch for every major field in physics: Computational mechanics consists of computational fluid dynamics (CFD), computational solid mechanics and computational contact mechanics.Computational electrodynamics is the process of modeling the interaction of electromagne... | Computational biophysics | 0.827563 |
4,681 | Due to the broad class of problems computational physics deals, it is an essential component of modern research in different areas of physics, namely: accelerator physics, astrophysics, general theory of relativity (through numerical relativity), fluid mechanics (computational fluid dynamics), lattice field theory/latt... | Computational biophysics | 0.827563 |
4,682 | Computational physics problems are in general very difficult to solve exactly. This is due to several (mathematical) reasons: lack of algebraic and/or analytic solvability, complexity, and chaos. For example, - even apparently simple problems, such as calculating the wavefunction of an electron orbiting an atom in a st... | Computational biophysics | 0.827563 |
4,683 | In physics, different theories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution doe... | Computational biophysics | 0.827563 |
4,684 | Each module is able to vote for or against each smaller action in a set of actions, and the arbiter selects the action with the most votes, meaning that it benefits the most behavior modules. This can be seen as violating the general rule against creating representations of the world in behavior-based AI, established b... | Winner-take-all in action selection | 0.827563 |
4,685 | Feldman's architecture functioned on the simple rule that in a network of interconnected action modules, each module will set its own output to zero if it reads a higher input than its own in any other module. In 1986, Rodney Brooks introduced behavior-based artificial intelligence. Winner-take-all architectures for ac... | Winner-take-all in action selection | 0.827563 |
4,686 | Winner-take-all is a computer science concept that has been widely applied in behavior-based robotics as a method of action selection for intelligent agents. Winner-take-all systems work by connecting modules (task-designated areas) in such a way that when one action is performed it stops all other actions from being p... | Winner-take-all in action selection | 0.827563 |
4,687 | Elementary calculus is the calculus of real-valued functions of one real variable, and the principal ideas of differentiation and integration of such functions can be extended to functions of more than one real variable; this extension is multivariable calculus. | Multi-variable function | 0.82754 |
4,688 | Multivariable functions of real variables arise inevitably in engineering and physics, because observable physical quantities are real numbers (with associated units and dimensions), and any one physical quantity will generally depend on a number of other quantities. | Multi-variable function | 0.82754 |
4,689 | Very similar to the least-squares approach is the probabilistic approach: If we know the statistics of the noise that contaminates the data, we can think of seeking the most likely model m, which is the model that matches the maximum likelihood criterion. If the noise is Gaussian, the maximum likelihood criterion appea... | Forward problem | 0.827538 |
4,690 | As mentioned above, noise may be such that our measurements are not the image of any model, so that we cannot look for a model that produces the data but rather look for the best (or optimal) model: that is, the one that best matches the data. This leads us to minimize an objective function, namely a functional that qu... | Forward problem | 0.827538 |
4,691 | This approach met a lot of success. Nowadays inverse problems are also investigated in fields outside physics, such as chemistry, economics, and computer science. Eventually, as numerical models become prevalent in many parts of society, we may expect an inverse problem associated with each of these numerical models. | Forward problem | 0.827538 |
4,692 | Describing this situation after many decades, Ambartsumian said, "If an astronomer publishes an article with a mathematical content in a physics journal, then the most likely thing that will happen to it is oblivion." Nonetheless, toward the end of the Second World War, this article, written by the 20-year-old Ambartsu... | Forward problem | 0.827538 |
4,693 | He then asked: given a family of eigenvalues, is it possible to find the form of the equations whose eigenvalues they are? Essentially Ambartsumian was examining the inverse Sturm–Liouville problem, which dealt with determining the equations of a vibrating string. This paper was published in 1929 in the German physics ... | Forward problem | 0.827538 |
4,694 | Today known as Weyl's law, it is perhaps most easily understood as an answer to the question of whether it is possible to hear the shape of a drum. Weyl conjectured that the eigenfrequencies of a drum would be related to the area and perimeter of the drum by a particular equation, a result improved upon by later mathem... | Forward problem | 0.827538 |
4,695 | : ch13 The field is defined by the Lorentz force law and is, at each instant, perpendicular to both the motion of the charge and the force it experiences. There are two different, but closely related vector fields which are both sometimes called the "magnetic field" written B and H. While both the best names for these ... | Magnetic Field | 0.827534 |
4,696 | In modern physics, the electromagnetic field is understood to be not a classical field, but rather a quantum field; it is represented not as a vector of three numbers at each point, but as a vector of three quantum operators at each point. The most accurate modern description of the electromagnetic interaction (and muc... | Magnetic Field | 0.827534 |
4,697 | The term "Bayesian", which displaced "inverse probability", was introduced by Ronald Fisher in 1950. Inverse probability, variously interpreted, was the dominant approach to statistics until the development of frequentism in the early 20th century by Ronald Fisher, Jerzy Neyman and Egon Pearson. Following the developme... | Inverse probability | 0.827533 |
4,698 | In probability theory, inverse probability is an obsolete term for the probability distribution of an unobserved variable. Today, the problem of determining an unobserved variable (by whatever method) is called inferential statistics, the method of inverse probability (assigning a probability distribution to an unobser... | Inverse probability | 0.827533 |
4,699 | A simple example would be the problem of estimating the position of a star in the sky (at a certain time on a certain date) for purposes of navigation. Given the data, one must estimate the true position (probably by averaging). This problem would now be considered one of inferential statistics. The terms "direct proba... | Inverse probability | 0.827533 |
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