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3,300 | ; Hey, A.J.G. (2004). Gauge Theories in Particle Physics: Non-Abelian Gauge Theories: QCD and electroweak theory. | Field equation | 0.831264 |
3,301 | Course of Theoretical Physics. Vol. 4 (2nd ed.). | Field equation | 0.831264 |
3,302 | Not every partial differential equation (PDE) in physics is automatically called a "field equation", even if fields are involved. They are extra equations to provide additional constraints for a given physical system. "Continuity equations" and "diffusion equations" describe transport phenomena, even though they may involve fields which influence the transport processes. | Field equation | 0.831264 |
3,303 | Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables. Whereas the "wave equation", the "diffusion equation", and the "continuity equation" all have standard forms (and various special cases or generalizations), there is no single, special equation referred to as "the field equation". The topic broadly splits into equations of classical field theory and quantum field theory. Classical field equations describe many physical properties like temperature of a substance, velocity of a fluid, stresses in an elastic material, electric and magnetic fields from a current, etc. They also describe the fundamental forces of nature, like electromagnetism and gravity. In quantum field theory, particles or systems of "particles" like electrons and photons are associated with fields, allowing for infinite degrees of freedom (unlike finite degrees of freedom in particle mechanics) and variable particle numbers which can be created or annihilated. | Field equation | 0.831264 |
3,304 | In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. | Field equation | 0.831264 |
3,305 | In quantum field theory, particles are described by quantum fields which satisfy the Schrödinger equation. They are also creation and annihilation operators which satisfy commutation relations and are subject to the spin–statistics theorem. Particular cases of relativistic quantum field equations include the Klein–Gordon equation for spin-0 particles the Dirac equation for spin-1/2 particles the Bargmann–Wigner equations for particles of any spinIn quantum field equations, it is common to use momentum components of the particle instead of position coordinates of the particle's location, the fields are in momentum space and Fourier transforms relate them to the position representation. | Field equation | 0.831264 |
3,306 | G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 978-0-521-57507-2. | Field equation | 0.831264 |
3,307 | Field equations can be classified in many ways: classical or quantum, nonrelativistic or relativistic, according to the spin or mass of the field, and the number of components the field has and how they change under coordinate transformations (e.g. scalar fields, vector fields, tensor fields, spinor fields, twistor fields etc.). They can also inherit the classification of differential equations, as linear or nonlinear, the order of the highest derivative, or even as fractional differential equations. Gauge fields may be classified as in group theory, as abelian or nonabelian. | Field equation | 0.831264 |
3,308 | Sexl, R. U.; Urbantke, H. K. (2001) . Relativity, Groups Particles. Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer. ISBN 978-3211834435. | Field equation | 0.831264 |
3,309 | Microfluidics is the study and design of the control or transport of small volumes of fluid flow through porous material or narrow channels for a variety of applications (e.g. mixing, separations). Capillary pressure is one of many geometry-related characteristics that can be altered in a microfluidic device to optimize a certain process. For instance, as the capillary pressure increases, a wettable surface in a channel will pull the liquid through the conduit. This eliminates the need for a pump in the system, and can make the desired process completely autonomous. | Capillary pressure | 0.831262 |
3,310 | The Sequence Read Archive (SRA, previously known as the Short Read Archive) is a bioinformatics database that provides a public repository for DNA sequencing data, especially the "short reads" generated by high-throughput sequencing, which are typically less than 1,000 base pairs in length. The archive is part of the International Nucleotide Sequence Database Collaboration (INSDC), and run as a collaboration between the NCBI, the European Bioinformatics Institute (EBI), and the DNA Data Bank of Japan (DDBJ). The archive was established by the National Center for Biotechnology Information (NCBI) in 2007 in order to provide a repository for data produced by RNA-Seq and ChIP-Seq studies as well as large-scale studies including the Human Microbiome Project and the 1000 Genomes Project. Originally called the Short Read Archive, the name was changed in anticipation of future sequencing technologies being able to produce longer sequence reads. | Sequence Read Archive | 0.831246 |
3,311 | In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence. | Magnetic charge | 0.831241 |
3,312 | Systematic exploration of chemical space is possible by creating in silico databases of virtual molecules, which can be visualized by projecting multidimensional property space of molecules in lower dimensions. Generation of chemical spaces may involve creating stoichiometric combinations of electrons and atomic nuclei to yield all possible topology isomers for the given construction principles. In Cheminformatics, software programs called Structure Generators are used to generate the set of all chemical structure adhering to given boundary conditions. Constitutional Isomer Generators, for example, can generate all possible constitutional isomers of a given molecular gross formula. | Chemical space | 0.831209 |
3,313 | This number is often misquoted in subsequent publications to be the estimated size of the whole organic chemistry space, which would be much larger if including the halogens and other elements. In addition to the drug-like space and lead-like space that are, in part, defined by the Lipinski's rule of five, the concept of known drug space (KDS), which is defined by the molecular descriptors of marketed drugs, has also been introduced. KDS can be used to help predict the boundaries of chemical spaces for drug development by comparing the structure of the molecules that are undergoing design and synthesis to the molecular descriptor parameters that are defined by the KDS. | Chemical space | 0.831209 |
3,314 | In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix. | Homogeneous coordinates | 0.831196 |
3,315 | An autoencoder ANN was used in bioinformatics, to predict gene ontology annotations and gene-function relationships.In medical informatics, deep learning was used to predict sleep quality based on data from wearables and predictions of health complications from electronic health record data. | Deep neural networks | 0.831191 |
3,316 | More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop. | Deep neural networks | 0.831191 |
3,317 | Deep learning has attracted both criticism and comment, in some cases from outside the field of computer science. | Deep neural networks | 0.831191 |
3,318 | A comprehensive list of results on this set is available.Deep learning-based image recognition has become "superhuman", producing more accurate results than human contestants. This first occurred in 2011 in recognition of traffic signs, and in 2014, with recognition of human faces.Deep learning-trained vehicles now interpret 360° camera views. Another example is Facial Dysmorphology Novel Analysis (FDNA) used to analyze cases of human malformation connected to a large database of genetic syndromes. | Deep neural networks | 0.831191 |
3,319 | Some deep learning architectures display problematic behaviors, such as confidently classifying unrecognizable images as belonging to a familiar category of ordinary images (2014) and misclassifying minuscule perturbations of correctly classified images (2013). Goertzel hypothesized that these behaviors are due to limitations in their internal representations and that these limitations would inhibit integration into heterogeneous multi-component artificial general intelligence (AGI) architectures. These issues may possibly be addressed by deep learning architectures that internally form states homologous to image-grammar decompositions of observed entities and events. Learning a grammar (visual or linguistic) from training data would be equivalent to restricting the system to commonsense reasoning that operates on concepts in terms of grammatical production rules and is a basic goal of both human language acquisition and artificial intelligence (AI). | Deep neural networks | 0.831191 |
3,320 | Image reconstruction is the reconstruction of the underlying images from the image-related measurements. Several works showed the better and superior performance of the deep learning methods compared to analytical methods for various applications, e.g., spectral imaging and ultrasound imaging. | Deep neural networks | 0.831191 |
3,321 | Deep TAMER used deep learning to provide a robot the ability to learn new tasks through observation. Using Deep TAMER, a robot learned a task with a human trainer, watching video streams or observing a human perform a task in-person. The robot later practiced the task with the help of some coaching from the trainer, who provided feedback such as "good job" and "bad job". | Deep neural networks | 0.831191 |
3,322 | In 2017, Covariant.ai was launched, which focuses on integrating deep learning into factories.As of 2008, researchers at The University of Texas at Austin (UT) developed a machine learning framework called Training an Agent Manually via Evaluative Reinforcement, or TAMER, which proposed new methods for robots or computer programs to learn how to perform tasks by interacting with a human instructor. First developed as TAMER, a new algorithm called Deep TAMER was later introduced in 2018 during a collaboration between U.S. Army Research Laboratory (ARL) and UT researchers. | Deep neural networks | 0.831191 |
3,323 | Facebook's AI lab performs tasks such as automatically tagging uploaded pictures with the names of the people in them.Google's DeepMind Technologies developed a system capable of learning how to play Atari video games using only pixels as data input. In 2015 they demonstrated their AlphaGo system, which learned the game of Go well enough to beat a professional Go player. Google Translate uses a neural network to translate between more than 100 languages. | Deep neural networks | 0.831191 |
3,324 | Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator. The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. | Deep neural networks | 0.831191 |
3,325 | Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference.The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as Kunihiko Fukushima's rectified linear unit.The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. | Deep neural networks | 0.831191 |
3,326 | One defense is reverse image search, in which a possible fake image is submitted to a site such as TinEye that can then find other instances of it. A refinement is to search using only parts of the image, to identify images from which that piece may have been taken.Another group showed that certain psychedelic spectacles could fool a facial recognition system into thinking ordinary people were celebrities, potentially allowing one person to impersonate another. In 2017 researchers added stickers to stop signs and caused an ANN to misclassify them.ANNs can however be further trained to detect attempts at deception, potentially leading attackers and defenders into an arms race similar to the kind that already defines the malware defense industry. ANNs have been trained to defeat ANN-based anti-malware software by repeatedly attacking a defense with malware that was continually altered by a genetic algorithm until it tricked the anti-malware while retaining its ability to damage the target.In 2016, another group demonstrated that certain sounds could make the Google Now voice command system open a particular web address, and hypothesized that this could "serve as a stepping stone for further attacks (e.g., opening a web page hosting drive-by malware)".In "data poisoning", false data is continually smuggled into a machine learning system's training set to prevent it from achieving mastery. | Deep neural networks | 0.831191 |
3,327 | As deep learning moves from the lab into the world, research and experience show that artificial neural networks are vulnerable to hacks and deception. By identifying patterns that these systems use to function, attackers can modify inputs to ANNs in such a way that the ANN finds a match that human observers would not recognize. For example, an attacker can make subtle changes to an image such that the ANN finds a match even though the image looks to a human nothing like the search target. Such manipulation is termed an "adversarial attack".In 2016 researchers used one ANN to doctor images in trial and error fashion, identify another's focal points and thereby generate images that deceived it. | Deep neural networks | 0.831191 |
3,328 | The United States Department of Defense applied deep learning to train robots in new tasks through observation. | Deep neural networks | 0.831191 |
3,329 | Neural networks have been used for implementing language models since the early 2000s. LSTM helped to improve machine translation and language modeling.Other key techniques in this field are negative sampling and word embedding. Word embedding, such as word2vec, can be thought of as a representational layer in a deep learning architecture that transforms an atomic word into a positional representation of the word relative to other words in the dataset; the position is represented as a point in a vector space. Using word embedding as an RNN input layer allows the network to parse sentences and phrases using an effective compositional vector grammar. | Deep neural networks | 0.831191 |
3,330 | In theoretical computer science, a pointer machine is an atomistic abstract computational machine model akin to the random-access machine. A pointer algorithm could also be an algorithm restricted to the pointer machine model.Depending on the type, a pointer machine may be called a linking automaton, a KU-machine, an SMM, an atomistic LISP machine, a tree-pointer machine, etc. (cf Ben-Amram 1995). At least three major varieties exist in the literature—the Kolmogorov-Uspenskii model (KUM, KU-machine), the Knuth linking automaton, and the Schönhage Storage Modification Machine model (SMM). The SMM seems to be the most common. | Pointer machine | 0.831185 |
3,331 | In mathematics, in the area of abstract algebra known as group theory, a verbal subgroup is a subgroup of a group that is generated by all elements that can be formed by substituting group elements for variables in a given set of words. For example, given the word xy, the corresponding verbal subgroup is generated by the set of all products of two elements in the group, substituting any element for x and any element for y, and hence would be the group itself. On the other hand, the verbal subgroup for the set of words { x 2 , x y 2 x − 1 } {\displaystyle \{x^{2},xy^{2}x^{-1}\}} is generated by the set of squares and their conjugates. | Verbal subgroup | 0.831185 |
3,332 | Lisp and Scheme support anonymous functions using the "lambda" construct, which is a reference to lambda calculus. Clojure supports anonymous functions with the "fn" special form and #() reader syntax. | Function constant | 0.831164 |
3,333 | Decision tree learning uses a decision tree as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels, and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision-making. | Machine learning algorithm | 0.831163 |
3,334 | The difference between optimization and machine learning arises from the goal of generalization: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples. Characterizing the generalization of various learning algorithms is an active topic of current research, especially for deep learning algorithms. | Machine learning algorithm | 0.831163 |
3,335 | Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system: Supervised learning: The computer is presented with example inputs and their desired outputs, given by a "teacher", and the goal is to learn a general rule that maps inputs to outputs. Unsupervised learning: No labels are given to the learning algorithm, leaving it on its own to find structure in its input. Unsupervised learning can be a goal in itself (discovering hidden patterns in data) or a means towards an end (feature learning). | Machine learning algorithm | 0.831163 |
3,336 | In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be.Leo Breiman distinguished two statistical modeling paradigms: data model and algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random Forest. Some statisticians have adopted methods from machine learning, leading to a combined field that they call statistical learning. | Machine learning algorithm | 0.831163 |
3,337 | Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns. According to Michael I. Jordan, the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics. He also suggested the term data science as a placeholder to call the overall field.Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. | Machine learning algorithm | 0.831163 |
3,338 | His website includes his College Basketball Ratings, a tempo based statistics system. Some statisticians have become very famous for having successful prediction systems. | Experimental prediction | 0.831162 |
3,339 | Brian Burke, a former Navy fighter pilot turned sports statistician, has published his results of using regression analysis to predict the outcome of NFL games. Ken Pomeroy is widely accepted as a leading authority on college basketball statistics. | Experimental prediction | 0.831162 |
3,340 | When these and/or related, generalized set of regression or machine learning methods are deployed in commercial usage, the field is known as predictive analytics.In many applications, such as time series analysis, it is possible to estimate the models that generate the observations. If models can be expressed as transfer functions or in terms of state-space parameters then smoothed, filtered and predicted data estimates can be calculated. If the underlying generating models are linear then a minimum-variance Kalman filter and a minimum-variance smoother may be used to recover data of interest from noisy measurements. | Experimental prediction | 0.831162 |
3,341 | In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one possible description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. | Experimental prediction | 0.831162 |
3,342 | The Numbers Game is a reality television infotainment series premiered on April 22, 2013, on National Geographic Channel that explores the numbers and stats in life's major events- birth, death, marriage, money etc. Hosted by data scientist Jake Porway, the show uses data science to unveil hidden numbers through street experiments and interactive game play to guide us to make smart decisions about our destiny. | The Numbers Game | 0.831148 |
3,343 | The term "open-notebook science" was first used in 2006 in a blog post by Jean-Claude Bradley, an Associate Professor of Chemistry at Drexel University at the time. Bradley described open-notebook science as follows: ... there is a URL to a laboratory notebook that is freely available and indexed on common search engines. It does not necessarily have to look like a paper notebook but it is essential that all of the information available to the researchers to make their conclusions is equally available to the rest of the world | Open Notebook Science | 0.831122 |
3,344 | A public laboratory notebook makes it convenient to cite the exact instances of experiments used to support arguments in articles. For example, in a paper on the optimization of a Ugi reaction, three different batches of product are used in the characterization and each spectrum references the specific experiment where each batch was used: EXP099, EXP203 and EXP206. This work was subsequently published in the Journal of Visualized Experiments, demonstrating that the integrity data provenance can be maintained from lab notebook to final publication in a peer-reviewed journal. | Open Notebook Science | 0.831122 |
3,345 | Junior Physics Lab (307L) at University of New Mexico | Open Notebook Science | 0.831122 |
3,346 | NVIDIA provides an SDK Toolkit for CUDA (Compute Unified Device Architecture) technology that offers both a low and high-level API to the GPU. For their GPUs, AMD offers a similar SDK, called Close to Metal (CTM), which provides a thin hardware interface. PhysX is an example of a physics engine that can use GPGPU based hardware acceleration when it is available. | Physics engine | 0.831116 |
3,347 | Hardware acceleration for physics processing is now usually provided by graphics processing units that support more general computation, a concept known as general-purpose computing on graphics processing units (GPGPU). AMD and NVIDIA provide support for rigid body dynamics computations on their latest graphics cards. NVIDIA's GeForce 8 Series supports a GPU-based Newtonian physics acceleration technology named Quantum Effects Technology. | Physics engine | 0.831116 |
3,348 | This requires more accurate physics so that, for example, the momentum of an object can knock over an obstacle or lift a sinking object. Physically-based character animation in the past only used rigid body dynamics because they are faster and easier to calculate, but modern games and movies are starting to use soft body physics. Soft body physics are also used for particle effects, liquids and cloth. Some form of limited fluid dynamics simulation is sometimes provided to simulate water and other liquids as well as the flow of fire and explosions through the air. | Physics engine | 0.831116 |
3,349 | In most computer games, speed of the processors and gameplay are more important than accuracy of simulation. This leads to designs for physics engines that produce results in real-time but that replicate real world physics only for simple cases and typically with some approximation. More often than not, the simulation is geared towards providing a "perceptually correct" approximation rather than a real simulation. However some game engines, such as Source, use physics in puzzles or in combat situations. | Physics engine | 0.831116 |
3,350 | A physics processing unit (PPU) is a dedicated microprocessor designed to handle the calculations of physics, especially in the physics engine of video games. Examples of calculations involving a PPU might include rigid body dynamics, soft body dynamics, collision detection, fluid dynamics, hair and clothing simulation, finite element analysis, and fracturing of objects. The idea is that specialized processors offload time-consuming tasks from a computer's CPU, much like how a GPU performs graphics operations in the main CPU's place. The term was coined by Ageia's marketing to describe their PhysX chip to consumers. Several other technologies in the CPU-GPU spectrum have some features in common with it, although Ageia's solution was the only complete one designed, marketed, supported, and placed within a system exclusively as a PPU. | Physics engine | 0.831116 |
3,351 | A physics engine is computer software that provides an approximate simulation of certain physical systems, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics, of use in the domains of computer graphics, video games and film (CGI). Their main uses are in video games (typically as middleware), in which case the simulations are in real-time. The term is sometimes used more generally to describe any software system for simulating physical phenomena, such as high-performance scientific simulation. | Physics engine | 0.831116 |
3,352 | Thus, games may put objects to "sleep" by disabling the computation of physics on objects that have not moved a particular distance within a certain amount of time. For example, in the 3D virtual world Second Life, if an object is resting on the floor and the object does not move beyond a minimal distance in about two seconds, then the physics calculations are disabled for the object and it becomes frozen in place. The object remains frozen until physics processing reactivates for the object after collision occurs with some other active physical object. | Physics engine | 0.831116 |
3,353 | In the real world, physics is always active. There is a constant Brownian motion jitter to all particles in our universe as the forces push back and forth against each other. For a game physics engine, such constant active precision is unnecessarily wasting the limited CPU power, which can cause problems such as decreased framerate. | Physics engine | 0.831116 |
3,354 | Phylogenetic profiling is a bioinformatics technique in which the joint presence or joint absence of two traits across large numbers of species is used to infer a meaningful biological connection, such as involvement of two different proteins in the same biological pathway. Along with examination of conserved synteny, conserved operon structure, or "Rosetta Stone" domain fusions, comparing phylogenetic profiles is a designated "post-homology" technique, in that the computation essential to this method begins after it is determined which proteins are homologous to which. A number of these techniques were developed by David Eisenberg and colleagues; phylogenetic profile comparison was introduced in 1999 by Pellegrini, et al. | Phylogenetic profiling | 0.831116 |
3,355 | Ingestion of saxitoxin, usually through shellfish contaminated by toxic algal blooms, can result in paralytic shellfish poisoning.Saxitoxin has been used in molecular biology to establish the function of the sodium channel. It acts on the voltage-gated sodium channels of nerve cells, preventing normal cellular function and leading to paralysis. The blocking of neuronal sodium channels which occurs in paralytic shellfish poisoning produces a flaccid paralysis that leaves its victim calm and conscious through the progression of symptoms. | Cyanobacterial bloom | 0.831102 |
3,356 | In the 1960s through the 1970s, Paul Boyer, a UCLA Professor, developed the binding change, or flip-flop, mechanism theory, which postulated that ATP synthesis is dependent on a conformational change in ATP synthase generated by rotation of the gamma subunit. The research group of John E. Walker, then at the MRC Laboratory of Molecular Biology in Cambridge, crystallized the F1 catalytic-domain of ATP synthase. The structure, at the time the largest asymmetric protein structure known, indicated that Boyer's rotary-catalysis model was, in essence, correct. For elucidating this, Boyer and Walker shared half of the 1997 Nobel Prize in Chemistry. | ATP synthesis | 0.831088 |
3,357 | More precisely, one should consider algebraic curves C {\displaystyle C} of a given genus g {\displaystyle g} , and their Jacobians Jac ( C ) {\displaystyle \operatorname {Jac} (C)} . There is a moduli space M g {\displaystyle {\mathcal {M}}_{g}} of such curves, and a moduli space of abelian varieties, A g {\displaystyle {\mathcal {A}}_{g}} , of dimension g {\displaystyle g} , which are principally polarized. There is a morphism Jac: M g → A g {\displaystyle \operatorname {Jac} :{\mathcal {M}}_{g}\to {\mathcal {A}}_{g}} which on points (geometric points, to be more accurate) takes isomorphism class {\displaystyle } to {\displaystyle } . The content of Torelli's theorem is that Jac {\displaystyle \operatorname {Jac} } is injective (again, on points). | Schottky problem | 0.831076 |
3,358 | In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties. | Schottky problem | 0.831076 |
3,359 | The Faraday constant can be thought of as the conversion factor between the mole (used in chemistry) and the coulomb (used in physics and in practical electrical measurements), and is therefore of particular use in electrochemistry. Because 1 mole contains exactly 6.02214076×1023 entities, and 1 coulomb contains exactly C/e = 1019/1.602176634 elementary charges, the Faraday constant is given by the quotient of these two quantities: F = NA/1/e = 9.64853321233100184×104 C⋅mol−1.One common use of the Faraday constant is in electrolysis calculations. One can divide the amount of charge (the current integrated over time) by the Faraday constant in order to find the chemical amount of a substance (in moles) that has been electrolyzed. The value of F was first determined by weighing the amount of silver deposited in an electrochemical reaction in which a measured current was passed for a measured time, and using Faraday's law of electrolysis. | Faraday constant | 0.831071 |
3,360 | Modern biotechnology is challenging traditional concepts of organisms and species. Cloning is the process of creating a new multicellular organism, genetically identical to another, with the potential of creating entirely new species of organisms. Cloning is the subject of much ethical debate. | Organism | 0.83107 |
3,361 | Protein A is a 42 kDa surface protein originally found in the cell wall of the bacteria Staphylococcus aureus. It is encoded by the spa gene and its regulation is controlled by DNA topology, cellular osmolarity, and a two-component system called ArlS-ArlR. It has found use in biochemical research because of its ability to bind immunoglobulins. It is composed of five homologous Ig-binding domains that fold into a three-helix bundle. | Protein A | 0.831056 |
3,362 | The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions.The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g, only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. | Sample-complexity bounds | 0.831053 |
3,363 | This trade-off leads to the concept of regularization.It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}}: H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class.This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. | Sample-complexity bounds | 0.831053 |
3,364 | One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large.Thus, in order to make statements about the rate of convergence of the quantity one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. | Sample-complexity bounds | 0.831053 |
3,365 | Under extremely high pressure, as in the cores of dead stars, ordinary matter undergoes a transition to a series of exotic states of matter collectively known as degenerate matter, which are supported mainly by quantum mechanical effects. In physics, "degenerate" refers to two states that have the same energy and are thus interchangeable. Degenerate matter is supported by the Pauli exclusion principle, which prevents two fermionic particles from occupying the same quantum state. Unlike regular plasma, degenerate plasma expands little when heated, because there are simply no momentum states left. | States of matter | 0.831046 |
3,366 | In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates and Fermionic condensates (in extreme cold), neutron-degenerate matter (in extreme density), and quark–gluon plasma (at extremely high energy). | States of matter | 0.831046 |
3,367 | NMR data HypNMR, WINEQNMR2 Archived 2019-07-14 at the Wayback MachineIn biochemistry, formation constants of adducts may be obtained from Isothermal titration calorimetry (ITC) measurements. This technique yields both the stability constant and the standard enthalpy change for the equilibrium. It is mostly limited, by availability of software, to complexes of 1:1 stoichiometry. | Formation constant | 0.831034 |
3,368 | In coordination chemistry, a stability constant (also called formation constant or binding constant) is an equilibrium constant for the formation of a complex in solution. It is a measure of the strength of the interaction between the reagents that come together to form the complex. There are two main kinds of complex: compounds formed by the interaction of a metal ion with a ligand and supramolecular complexes, such as host–guest complexes and complexes of anions. The stability constant(s) provide(s) the information required to calculate the concentration(s) of the complex(es) in solution. There are many areas of application in chemistry, biology and medicine. | Formation constant | 0.831034 |
3,369 | Supramolecular complexes are held together by hydrogen bonding, hydrophobic forces, van der Waals forces, π-π interactions, and electrostatic effects, all of which can be described as noncovalent bonding. Applications include molecular recognition, host–guest chemistry and anion sensors. A typical application in molecular recognition involved the determination of formation constants for complexes formed between a tripodal substituted urea molecule and various saccharides. The study was carried out using a non-aqueous solvent and NMR chemical shift measurements. | Formation constant | 0.831034 |
3,370 | Successive stepwise formation constants Kn in a series such as MLn (n = 1, 2, ...) usually decrease as n increases. Exceptions to this rule occur when the geometry of the MLn complexes is not the same for all members of the series. The classic example is the formation of the diamminesilver(I) complex + in aqueous solution. A g + + N H 3 ⇌ + ; K 1 = {\displaystyle \mathrm {Ag^{+}+NH_{3}\rightleftharpoons ^{+};K_{1}={\frac {}{}}} } A g ( N H 3 ) + + N H 3 ⇌ + ; K 2 = {\displaystyle \mathrm {Ag(NH_{3})^{+}+NH_{3}\rightleftharpoons ^{+};K_{2}={\frac {}{}}} } In this case, K2 > K1. | Formation constant | 0.831034 |
3,371 | Tammann temperature was pioneered by German astronomer, solid-state chemistry, and physics professor Gustav Tammann in the first half of the 20th century. : 152 He had considered a lattice motion very important for the reactivity of matter and quantified his theory by calculating a ratio of the given material temperatures at solid-liquid phases at absolute temperatures. The division of a solid's temperature by a melting point would yield a Tammann temperature. The value is usually measured in Kelvins (K):: 152 T Tammann = β × T melting point ( in K ) {\displaystyle T_{\text{Tammann}}={\beta }{\times }T_{\text{melting point}}({\text{in K}})} where β {\displaystyle {\beta }} is a constant dimensionless number. | Tammann and Hüttig temperatures | 0.831026 |
3,372 | Algorithmic Geometry is a textbook on computational geometry. It was originally written in the French language by Jean-Daniel Boissonnat and Mariette Yvinec, and published as Géometrie algorithmique by Edusciences in 1995. It was translated into English by Hervé Brönnimann, with improvements to some proofs and additional exercises, and published by the Cambridge University Press in 1998. | Algorithmic Geometry | 0.831003 |
3,373 | The book covers the theoretical background and analysis of algorithms in computational geometry, their implementation details, and their applications. It is grouped into five sections, the first of which covers background material on the design and analysis of algorithms and data structures, including computational complexity theory, and techniques for designing randomized algorithms. Its subsequent sections each consist of a chapter on the mathematics of a subtopic in this area, presented at the level of detail needed to analyze the algorithms, followed by two or three chapters on algorithms for that subtopic.The topics presented in these sections and chapters include convex hulls and convex hull algorithms, low-dimensional randomized linear programming, point set triangulation for two- and three-dimensional data, arrangements of hyperplanes, of line segments, and of triangles, Voronoi diagrams, and Delaunay triangulations. | Algorithmic Geometry | 0.831003 |
3,374 | The book can be used as a graduate textbook, or as a reference for computational geometry research. Reviewer Peter McMullen calls it "a welcome addition to the shelves of anyone interested in algorithmic geometry". == References == | Algorithmic Geometry | 0.831003 |
3,375 | Structure-Based Assignment (SBA) is a technique to accelerate the resonance assignment which is a key bottleneck of NMR (Nuclear magnetic resonance) structural biology. A homologous (similar) protein is used as a template to the target protein in SBA. This template protein provides prior structural information about the target protein and leads to faster resonance assignment . | Structure-based assignment | 0.830997 |
3,376 | In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permutation pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including Dyck paths and binary trees. | Stack-sortable permutation | 0.830994 |
3,377 | In non-abelian gauge theories, the beta function can be negative, as first found by Frank Wilczek, David Politzer and David Gross. An example of this is the beta function for quantum chromodynamics (QCD), and as a result the QCD coupling decreases at high energies.Furthermore, the coupling decreases logarithmically, a phenomenon known as asymptotic freedom (the discovery of which was awarded with the Nobel Prize in Physics in 2004). The coupling decreases approximately as α s ( k 2 ) = d e f g s 2 ( k 2 ) 4 π ≈ 1 β 0 ln ( k 2 / Λ 2 ) , {\displaystyle \alpha _{\text{s}}(k^{2})\ {\stackrel {\mathrm {def} }{=}}\ {\frac {g_{\text{s}}^{2}(k^{2})}{4\pi }}\approx {\frac {1}{\beta _{0}\ln \left({k^{2}}/{\Lambda ^{2}}\right)}},} where β0 is a constant first computed by Wilczek, Gross and Politzer. Conversely, the coupling increases with decreasing energy. | Strong coupling constant | 0.830972 |
3,378 | A fused multiply–add (FMA or fmadd) is a floating-point multiply–add operation performed in one step (fused operation), with a single rounding. That is, where an unfused multiply–add would compute the product b × c, round it to N significant bits, add the result to a, and round back to N significant bits, a fused multiply–add would compute the entire expression a + (b × c) to its full precision before rounding the final result down to N significant bits. A fast FMA can speed up and improve the accuracy of many computations that involve the accumulation of products: Dot product Matrix multiplication Polynomial evaluation (e.g., with Horner's rule) Newton's method for evaluating functions (from the inverse function) Convolutions and artificial neural networks Multiplication in double-double arithmeticFused multiply–add can usually be relied on to give more accurate results. However, William Kahan has pointed out that it can give problems if used unthinkingly. | Multiply add | 0.830969 |
3,379 | Protein Data Bank (PDB): repository for protein sequence and structural information UniProt: provides sequence and functional information Structural Classification of Proteins (SCOP Classifications): hierarchical-based approach Class, Architecture, Topology and Homologous superfamily (CATH): hierarchical-based approach | Structural genomics | 0.830968 |
3,380 | The National Standard Examination in Chemistry or NSEC is an examination in chemistry for higher secondary school students in India, usually conducted in the end of November. The examination is organized by the Indian Association of Chemistry Teachers. Over 30,000 students, mainly from Standard 12, sit for this examination. | National Standard Examination in Chemistry | 0.830958 |
3,381 | The NSEC contains only multiple choice questions. The questions include physical chemistry, organic chemistry, and inorganic chemistry. The stress on biochemistry is more in the NSEC than in the typical school syllabi. | National Standard Examination in Chemistry | 0.830958 |
3,382 | The top 1% students from this examination are selected to sit for the Indian National Chemistry Olympiad. The theory part of the examination is held in the last week of January. The top 30 among all students are selected for the Orientation-Cum-Selection-Camp (OCSC), Chemistry. | National Standard Examination in Chemistry | 0.830958 |
3,383 | In the early twentieth century, these ideas led Kristian Birkeland to build a terrella, or laboratory device which simulates the Earth's magnetic field in a vacuum chamber, and which uses a cathode ray tube to simulate the energetic particles which compose the solar wind. A theory began to be formulated about the interaction between the Earth's magnetic field and the solar wind. Space physics did not begin in earnest, however, until the first in situ measurements in the early 1950s, when a team led by Van Allen launched the first rockets to a height around 110 km. | Solar-terrestrial physics | 0.830936 |
3,384 | Space physics can be traced to the Chinese who discovered the principle of the compass, but did not understand how it worked. During the 16th century, in De Magnete, William Gilbert gave the first description of the Earth's magnetic field, showing that the Earth itself is a great magnet, which explained why a compass needle points north. Deviations of the compass needle magnetic declination were recorded on navigation charts, and a detailed study of the declination near London by watchmaker George Graham resulted in the discovery of irregular magnetic fluctuations that we now call magnetic storms, so named by Alexander Von Humboldt. Gauss and William Weber made very careful measurements of Earth's magnetic field which showed systematic variations and random fluctuations. | Solar-terrestrial physics | 0.830936 |
3,385 | "Nobody can reproduce these conversations verbatim, but I believe that the spirit of what the people said, and how they did, is conserved," the author tries to explain in the preface. Many believe that the golden years of physics around 1925, when "even small people could do big things" are gone. But the people who had been there continue to speak to us through this book. The book was published first in German 1969, in English as Physics and Beyond (1971) and in French in 1972 (La partie et le tout). | Physics and Beyond | 0.830935 |
3,386 | ', 'Yes, I see only whales, but I hope they are only big waves. '", is one of humorous scenes when the author, Bohr and other friends were sailing in a dark night. The book provides a first-hand account about how science is done and how quantum physics, especially the Copenhagen interpretation, emerged. | Physics and Beyond | 0.830935 |
3,387 | With chapters like "The first encounter with the science about atoms", "Quantum mechanics and conversations with Einstein", "Conversation about the relation between biology, physics and chemistry" or "Conversations about language" and "The behavior of an individual during a political disaster", dated 1937–1941, a reader can hear speaking such persons as Erwin Schrödinger, Niels Bohr, Albert Einstein or Max Planck, not only about physics, but also about many other questions related to biology, humans, philosophy, and politics. Not only that, these conversations are often situated in detailed description of the historical atmosphere and a beautiful scenery, as many of them were led in nature during the many journeys they made, backpacking or sailing. "'Do you see whales, Heisenberg? | Physics and Beyond | 0.830935 |
3,388 | Physics and Beyond (German: Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik) is a book by Werner Heisenberg, the German physicist who discovered the uncertainty principle. It tells, from his point of view, the history of exploring atomic science and quantum mechanics in the first half of the 20th century. As the subtitle "Encounters and Conversations" suggests, the core part of this book takes the form of discussions between himself and other scientists. Heisenberg says: "I wanted to show that science is done by people, and the most wonderful ideas come from dialog". | Physics and Beyond | 0.830935 |
3,389 | In Galois theory, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q {\displaystyle \mathbb {Q} } . This problem, first posed in the early 19th century, is unsolved. There are some permutation groups for which generic polynomials are known, which define all algebraic extensions of Q {\displaystyle \mathbb {Q} } having a particular group as Galois group. | Inverse Galois problem | 0.830934 |
3,390 | Use the scaling (1 − n)x = ny to get y n − { s ( 1 − n n ) n − 1 } y − { s ( 1 − n n ) n } {\displaystyle y^{n}-\left\{s\left({\frac {1-n}{n}}\right)^{n-1}\right\}y-\left\{s\left({\frac {1-n}{n}}\right)^{n}\right\}} and with t = s ( 1 − n ) n − 1 n n , {\displaystyle t={\frac {s(1-n)^{n-1}}{n^{n}}},} we arrive at: g(y, t) = yn − nty + (n − 1)twhich can be arranged to yn − y − (n − 1)(y − 1) + (t − 1)(−ny + n − 1).Then g(y, 1) has 1 as a double zero and its other n − 2 zeros are simple, and a transposition in Gal(f(x, s)/Q(s)) is implied. Any finite doubly transitive permutation group containing a transposition is a full symmetric group. Hilbert's irreducibility theorem then implies that an infinite set of rational numbers give specializations of f(x, t) whose Galois groups are Sn over the rational field Q {\displaystyle \mathbb {Q} } . In fact this set of rational numbers is dense in Q {\displaystyle \mathbb {Q} } . The discriminant of g(y, t) equals ( − 1 ) n ( n − 1 ) 2 n n ( n − 1 ) n − 1 t n − 1 ( 1 − t ) , {\displaystyle (-1)^{\frac {n(n-1)}{2}}n^{n}(n-1)^{n-1}t^{n-1}(1-t),} and this is not in general a perfect square. | Inverse Galois problem | 0.830934 |
3,391 | By taking appropriate sums of conjugates of μ, following the construction of Gaussian periods, one can find an element α of F that generates F over Q {\displaystyle \mathbb {Q} } , and compute its minimal polynomial. This method can be extended to cover all finite abelian groups, since every such group appears in fact as a quotient of the Galois group of some cyclotomic extension of Q {\displaystyle \mathbb {Q} } . (This statement should not though be confused with the Kronecker–Weber theorem, which lies significantly deeper.) | Inverse Galois problem | 0.830934 |
3,392 | It is possible, using classical results, to construct explicitly a polynomial whose Galois group over Q {\displaystyle \mathbb {Q} } is the cyclic group Z/nZ for any positive integer n. To do this, choose a prime p such that p ≡ 1 (mod n); this is possible by Dirichlet's theorem. Let Q(μ) be the cyclotomic extension of Q {\displaystyle \mathbb {Q} } generated by μ, where μ is a primitive p-th root of unity; the Galois group of Q(μ)/Q is cyclic of order p − 1. Since n divides p − 1, the Galois group has a cyclic subgroup H of order (p − 1)/n. The fundamental theorem of Galois theory implies that the corresponding fixed field, F = Q(μ)H, has Galois group Z/nZ over Q {\displaystyle \mathbb {Q} } . | Inverse Galois problem | 0.830934 |
3,393 | Drugs already on the market, such as heparin, erythropoietin and a few anti-flu drugs, have proven effective and highlight the importance of glycans as a new class of drug. Additionally, the search for new anti-cancer drugs is opening up new possibilities in glycobiology. Anti-cancer drugs with new and varied action mechanisms together with anti-inflammatory and anti-infection drugs are today undergoing clinical trials. They may alleviate or complete current therapies. Although these glycans are molecules that are difficult to synthesize in a reproducible way, owing to their complex structure, this new field of research is highly encouraging for the future. | Glycobiology | 0.830931 |
3,394 | Defined in the narrowest sense, glycobiology is the study of the structure, biosynthesis, and biology of saccharides (sugar chains or glycans) that are widely distributed in nature. Sugars or saccharides are essential components of all living things and aspects of the various roles they play in biology are researched in various medical, biochemical and biotechnological fields. | Glycobiology | 0.830931 |
3,395 | "Glycomics, analogous to genomics and proteomics, is the systematic study of all glycan structures of a given cell type or organism" and is a subset of glycobiology. | Glycobiology | 0.830931 |
3,396 | Glycobiology, in which recent developments have been made possible by the latest technological advances, helps provide a more specific and precise understanding of skin aging. It has now been clearly established that glycans are major constituents of the skin and play a decisive role in skin homeostasis. They play a crucial role in the recognition of molecules and cells, they act, most notably, at the surface of cells to deliver biological messages. They are instrumental in the metabolism of cells: synthesis, proliferation and differentiation They have a role to play in the structure and architecture of tissue.Vital to the proper functioning of skin, glycans undergo both qualitative and quantitative changes in the course of aging. The functions of communication and metabolism are impaired and the skin's architecture is degraded. | Glycobiology | 0.830931 |
3,397 | According to Oxford English Dictionary the specific term glycobiology was coined in 1988 by Prof. Raymond Dwek to recognize the coming together of the traditional disciplines of carbohydrate chemistry and biochemistry. This coming together was as a result of a much greater understanding of the cellular and molecular biology of glycans. However, as early as the late nineteenth century pioneering efforts were being made by Emil Fisher to establish the structure of some basic sugar molecules. Each year the Society of Glycobiology awards the Rosalind Kornfeld award for lifetime achievement in the field of glycobiology. | Glycobiology | 0.830931 |
3,398 | Once the ore is mined, the metals must be extracted, usually by chemical or electrolytic reduction. Pyrometallurgy uses high temperatures to convert ore into raw metals, while hydrometallurgy employs aqueous chemistry for the same purpose. The methods used depend on the metal and their contaminants. | Metal ions | 0.83092 |
3,399 | The role of metallic elements in the evolution of cell biochemistry has been reviewed, including a detailed section on the role of calcium in redox enzymes.One or more of the elements iron, cobalt, nickel, copper, and zinc are essential to all higher forms of life. Cobalt is an essential component of vitamin B12. Compounds of all other transition elements and post-transition elements are toxic to a greater or lesser extent, with few exceptions such as certain compounds of antimony and tin. Potential sources of metal poisoning include mining, tailings, industrial wastes, agricultural runoff, occupational exposure, paints, and treated timber. | Metal ions | 0.83092 |
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