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4,900 | These two methods had several drawbacks: (1) required substantial input material, (2) low resolution which made pinpointing the actual site with the m6A mark difficult, and (3) cannot directly assess false positives.Especially in MeRIP-Seq, the bioinformatics tools that are currently available are only able to call 1 s... | Epitranscriptomic sequencing | 0.827056 |
4,901 | The m6A levels per site or gene could be quantified by the ERCC-normalized RNA abundances in different pools. Since full-length RNA is used, it is possible to directly compare alternatively spliced isoforms between the m6A+ and m6A- fractions as well as comparing isoform abundance within the m6A+ portion. Despite the a... | Epitranscriptomic sequencing | 0.827056 |
4,902 | In epitranscriptomic sequencing, most methods focus on either (1) enrichment and purification of the modified RNA molecules before running on the RNA sequencer, or (2) improving or modifying bioinformatics analysis pipelines to call the modification peaks. Most methods have been adapted and optimized for mRNA molecules... | Epitranscriptomic sequencing | 0.827056 |
4,903 | Although m6A sites could be profiled at high resolution using UV-based methods, the stoichiometry of m6A sites - the methylation status or the ratio m6A+ to m6A- for each individual site within a type of RNA - is still unknown. SCARLET (2013) and m6A-LAIC-seq (2016) allows for the quantitation of stoichiometry at a spe... | Epitranscriptomic sequencing | 0.827056 |
4,904 | In particular, the Nanopore technology proved to be effective in detecting the presence of two nucleotide analogs in RNA: N6-methyladenosine (m6A) and 5-methylcytosine (5-mC). Using Hidden Markov Models (HMM) or recurrent neural networks (RNN) trained with known sequences, it was possible to demonstrate that the modifi... | Epitranscriptomic sequencing | 0.827056 |
4,905 | Scaffolding is a technique used in bioinformatics. It is defined as follows: Link together a non-contiguous series of genomic sequences into a scaffold, consisting of sequences separated by gaps of known length. The sequences that are linked are typically contiguous sequences corresponding to read overlaps. | Scaffolding (bioinformatics) | 0.827053 |
4,906 | SSPACE is the most commonly cited assembly tool in biology publications, likely due to the fact that it is rated as a significantly more intuitive program to install and run than other assemblers.In recent years, there has been an advent of new kinds of assemblers capable of integrating linkage data from multiple types... | Scaffolding (bioinformatics) | 0.827053 |
4,907 | In materials chemistry, a quaternary phase is a chemical compound containing four elements. Some compounds can be molecular or ionic, examples being chlorodifluoromethane (CHClF2) sodium bicarbonate (NaCO3H). More typically quaternary phase refers to extended solids. A famous example are the yttrium barium copper oxide... | Quaternary phase | 0.827053 |
4,908 | The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. The focus of the center's work was the use of computer graphics and visualization for research and education in pure mathematics... | Geometry Center | 0.827052 |
4,909 | Much of the work done at the center was for the development of Geomview, a three-dimensional interactive geometry program. This focused on mathematical visualization with options to allow hyperbolic space to be visualised. It was originally written for Silicon Graphics workstations, and has been ported to run on Linux ... | Geometry Center | 0.827052 |
4,910 | Richard McGehee, the center's director, has stated that the website was one of the first one hundred websites ever published. Despite the Center being closed, its website is still online at as an archive of a wide range of geometric topics, including: Geometry and the Imagination handouts for a two-week course by John... | Geometry Center | 0.827052 |
4,911 | In practice, this generally requires numerical techniques for some discrete approximation to the exact optimization relationship. Alternatively, the continuous process can be approximated by a discrete system, which leads to a following recurrence relation analog to the Hamilton–Jacobi–Bellman equation: J k ∗ ( x n − k... | Dynamic Programming | 0.82705 |
4,912 | Dynamic programming is widely used in bioinformatics for tasks such as sequence alignment, protein folding, RNA structure prediction and protein-DNA binding. The first dynamic programming algorithms for protein-DNA binding were developed in the 1970s independently by Charles DeLisi in USA and Georgii Gurskii and Alexan... | Dynamic Programming | 0.82705 |
4,913 | Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have optimal substructure. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods... | Dynamic Programming | 0.82705 |
4,914 | Dynamic programming is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down... | Dynamic Programming | 0.82705 |
4,915 | In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V1, V2, ..., Vn taking y as an argument representing the state of the system at times i from 1 to n.... | Dynamic Programming | 0.82705 |
4,916 | There are two key attributes that a problem must have in order for dynamic programming to be applicable: optimal substructure and overlapping sub-problems. If a problem can be solved by combining optimal solutions to non-overlapping sub-problems, the strategy is called "divide and conquer" instead. This is why merge so... | Dynamic Programming | 0.82705 |
4,917 | This usage is the same as that in the phrases linear programming and mathematical programming, a synonym for mathematical optimization.The above explanation of the origin of the term is lacking. As Russell and Norvig in their book have written, referring to the above story: "This cannot be strictly true, because his fi... | Dynamic Programming | 0.82705 |
4,918 | The term dynamic programming was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions, ... | Dynamic Programming | 0.82705 |
4,919 | In genetics, sequence alignment is an important application where dynamic programming is essential. Typically, the problem consists of transforming one sequence into another using edit operations that replace, insert, or remove an element. Each operation has an associated cost, and the goal is to find the sequence of e... | Dynamic Programming | 0.82705 |
4,920 | Recurrent solutions to lattice models for protein-DNA binding Backward induction as a solution method for finite-horizon discrete-time dynamic optimization problems Method of undetermined coefficients can be used to solve the Bellman equation in infinite-horizon, discrete-time, discounted, time-invariant dynamic optimi... | Dynamic Programming | 0.82705 |
4,921 | Some of the historically important examples of enumerations in algebraic geometry include: 2 The number of lines meeting 4 general lines in space 8 The number of circles tangent to 3 general circles (the problem of Apollonius). 27 The number of lines on a smooth cubic surface (Salmon and Cayley) 2875 The number of line... | Enumerative geometry | 0.827047 |
4,922 | Polynomials are frequently used to encode information about some other object. The characteristic polynomial of a matrix or linear operator contains information about the operator's eigenvalues. The minimal polynomial of an algebraic element records the simplest algebraic relation satisfied by that element. The chromat... | Polynomial notation | 0.827028 |
4,923 | However, this may not be desirable where the programmer wishes to create closed abstractions. A pitfall of structural typing versus nominative typing is that two separately defined types intended for different purposes, but accidentally holding the same properties (e.g. both composed of a pair of integers), could be co... | Structural typing | 0.827022 |
4,924 | The surface of a polyhedron is a topological surface, which is neither a differentiable surface nor an algebraic surface. A hyperbolic paraboloid (the graph of the function z = xy) is a differentiable surface and an algebraic surface. It is also a ruled surface, and, for this reason, is often used in architecture. A tw... | Surface (mathematics) | 0.827011 |
4,925 | A circular cylinder (that is, the locus of a line crossing a circle and parallel to a given direction) is an algebraic surface and a differentiable surface. A circular cone (locus of a line crossing a circle, and passing through a fixed point, the apex, which is outside the plane of the circle) is an algebraic surface ... | Surface (mathematics) | 0.827011 |
4,926 | The graph of a continuous function of two variables, defined over a connected open subset of R2 is a topological surface. If the function is differentiable, the graph is a differentiable surface. A plane is both an algebraic surface and a differentiable surface. It is also a ruled surface and a surface of revolution. | Surface (mathematics) | 0.827011 |
4,927 | Originally, an algebraic surface was a surface which may be defined by an implicit equation f ( x , y , z ) = 0 , {\displaystyle f(x,y,z)=0,} where f is a polynomial in three indeterminates, with real coefficients. The concept has been extended in several directions, by defining surfaces over arbitrary fields, and by c... | Surface (mathematics) | 0.827011 |
4,928 | If there is only one component the n – 2 polynomials define a surface, which is a complete intersection. If there are several components, then one needs further polynomials for selecting a specific component. Most authors consider as an algebraic surface only algebraic varieties of dimension two, but some also consider... | Surface (mathematics) | 0.827011 |
4,929 | Generally, n – 2 polynomials define an algebraic set of dimension two or higher. If the dimension is two, the algebraic set may have several irreducible components. | Surface (mathematics) | 0.827011 |
4,930 | One cannot define the concept of an algebraic surface in a space of dimension higher than three without a general definition of an algebraic variety and of the dimension of an algebraic variety. In fact, an algebraic surface is an algebraic variety of dimension two. More precisely, an algebraic surface in a space of di... | Surface (mathematics) | 0.827011 |
4,931 | This allows defining surfaces in spaces of dimension higher than three, and even abstract surfaces, which are not contained in any other space. On the other hand, this excludes surfaces that have singularities, such as the vertex of a conical surface or points where a surface crosses itself. In classical geometry, a su... | Surface (mathematics) | 0.827011 |
4,932 | Also, there are surfaces for which there cannot exist a single parametrization that covers the whole surface. Therefore, one often considers surfaces which are parametrized by several parametric equations, whose images cover the surface. This is formalized by the concept of manifold: in the context of manifolds, typica... | Surface (mathematics) | 0.827011 |
4,933 | For example, the unit sphere is an algebraic surface, as it may be defined by the implicit equation x 2 + y 2 + z 2 − 1 = 0. {\displaystyle x^{2}+y^{2}+z^{2}-1=0.} | Surface (mathematics) | 0.827011 |
4,934 | Often, a surface is defined by equations that are satisfied by the coordinates of its points. This is the case of the graph of a continuous function of two variables. The set of the zeros of a function of three variables is a surface, which is called an implicit surface. If the defining three-variate function is a poly... | Surface (mathematics) | 0.827011 |
4,935 | In number theory, an arithmetic number is an integer for which the average of its positive divisors is also an integer. For instance, 6 is an arithmetic number because the average of its divisors is 1 + 2 + 3 + 6 4 = 3 , {\displaystyle {\frac {1+2+3+6}{4}}=3,} which is also an integer. However, 2 is not an arithmetic n... | Arithmetic number | 0.827005 |
4,936 | The number of neurons that "fit" in a given volume is then: If this number is not an integer, then the strides are incorrect and the neurons cannot be tiled to fit across the input volume in a symmetric way. In general, setting zero padding to be P = ( K − 1 ) / 2 {\textstyle P=(K-1)/2} when the stride is S = 1 {\displ... | Convolutional neural networks | 0.826998 |
4,937 | Convolution reduces the number of free parameters, allowing the network to be deeper. For example, using a 5 × 5 tiling region, each with the same shared weights, requires only 25 neurons. Using regularized weights over fewer parameters avoids the vanishing gradients and exploding gradients problems seen during backpro... | Convolutional neural networks | 0.826998 |
4,938 | Each convolutional neuron processes data only for its receptive field. Although fully connected feedforward neural networks can be used to learn features and classify data, this architecture is generally impractical for larger inputs (e.g., high-resolution images), which would require massive numbers of neurons because... | Convolutional neural networks | 0.826998 |
4,939 | For many applications, the training data is less available. Convolutional neural networks usually require a large amount of training data in order to avoid overfitting. A common technique is to train the network on a larger data set from a related domain. Once the network parameters have converged an additional trainin... | Convolutional neural networks | 0.826998 |
4,940 | End-to-end training and prediction are common practice in computer vision. However, human interpretable explanations are required for critical systems such as a self-driving cars. With recent advances in visual salience, spatial attention, and temporal attention, the most critical spatial regions/temporal instants coul... | Convolutional neural networks | 0.826998 |
4,941 | As archaeological findings like clay tablets with cuneiform writing are increasingly acquired using 3D scanners first benchmark datasets are becoming available like HeiCuBeDa providing almost 2.000 normalized 2D- and 3D-datasets prepared with the GigaMesh Software Framework. So curvature-based measures are used in conj... | Convolutional neural networks | 0.826998 |
4,942 | Recurrent neural networks are generally considered the best neural network architectures for time series forecasting (and sequence modeling in general), but recent studies show that convolutional networks can perform comparably or even better. Dilated convolutions might enable one-dimensional convolutional neural netwo... | Convolutional neural networks | 0.826998 |
4,943 | Furthermore, if a CNN makes use of fully connected layers, translation equivariance does not imply translation invariance, as the fully connected layers are not invariant to shifts of the input. One solution for complete translation invariance is avoiding any down-sampling throughout the network and applying global ave... | Convolutional neural networks | 0.826998 |
4,944 | It is commonly assumed that CNNs are invariant to shifts of the input. Convolution or pooling layers within a CNN that do not have a stride greater than one are indeed equivariant to translations of the input. However, layers with a stride greater than one ignore the Nyquist-Shannon sampling theorem and might lead to a... | Convolutional neural networks | 0.826998 |
4,945 | CNNs have been used in the game of checkers. From 1999 to 2001, Fogel and Chellapilla published papers showing how a convolutional neural network could learn to play checker using co-evolution. The learning process did not use prior human professional games, but rather focused on a minimal set of information contained ... | Convolutional neural networks | 0.826998 |
4,946 | A deep Q-network (DQN) is a type of deep learning model that combines a deep neural network with Q-learning, a form of reinforcement learning. Unlike earlier reinforcement learning agents, DQNs that utilize CNNs can learn directly from high-dimensional sensory inputs via reinforcement learning.Preliminary results were ... | Convolutional neural networks | 0.826998 |
4,947 | However, some incorporate a squirrel cage in the rotor for starting—these are known as line-start or self-starting. These are typically used as higher-efficiency replacements for induction motors (owing to the lack of slip), but must ensure that synchronous speed is reached and that the system can withstand torque ripp... | Synchronous electric motor | 0.826995 |
4,948 | Stokes' theorem relates the surface integral of the curl of a vector field F over a surface Σ in Euclidean three-space to the line integral of the vector field over its boundary ∂Σ: ∬ Σ ∇ × F ⋅ d Σ = ∮ ∂ Σ F ⋅ d r . {\displaystyle \iint _{\Sigma }\nabla \times \mathbf {F} \cdot \mathrm {d} \mathbf {\Sigma } =\oint _{\p... | 3 dimensions | 0.826994 |
4,949 | Many ideas of dimension can be tested with finite geometry. The simplest instance is PG(3,2), which has Fano planes as its 2-dimensional subspaces. It is an instance of Galois geometry, a study of projective geometry using finite fields. Thus, for any Galois field GF(q), there is a projective space PG(3,q) of three dim... | 3 dimensions | 0.826993 |
4,950 | Fine structure genetics encompasses a set of tools used to examine not just the mutations within an entire genome, but can be isolated to either specific pathways or regions of the genome. Ultimately, this more focused lens can lead to a more nuanced and interactive view of the function of a gene. | Fine structure genetics | 0.826989 |
4,951 | Similar to forward genetics, regional mutagenesis seeks to saturate with insertions or point mutations, but instead of for the entire genome, it saturates only a small portion of the genome. By limiting the region in focus, researchers are then able to intensify the number of mutations within any genes or promoters wit... | Fine structure genetics | 0.826989 |
4,952 | Artificial muscles, also known as muscle-like actuators, are materials or devices that mimic natural muscle and can change their stiffness, reversibly contract, expand, or rotate within one component due to an external stimulus (such as voltage, current, pressure or temperature). The three basic actuation responses– co... | Artificial muscles | 0.826968 |
4,953 | Artificial muscle technologies have wide potential applications in biomimetic machines, including robots, industrial actuators and powered exoskeletons. EAP-based artificial muscles offer a combination of light weight, low power requirements, resilience and agility for locomotion and manipulation. Future EAP devices wi... | Artificial muscles | 0.826968 |
4,954 | In summary (provided by Ahn et al.), viable experimental control systems include PID control, adaptive control (Lilly, 2003), nonlinear optimal predictive control (Reynolds et al., 2003), variable structure control (Repperger et al., 1998; Medrano-Cerda et al.,1995), gain scheduling (Repperger et al.,1999), and various... | Artificial muscles | 0.826968 |
4,955 | While kinematical diffraction is adequate to understand the geometry of the diffraction spots, it does not correctly give the intensities and has a number of other limitations. For a more complete approach one has to include multiple scattering of the electrons using methods that date back to the early work of Hans Bet... | Electron diffraction | 0.826967 |
4,956 | Following Kunio Fujiwara and Archibald Howie, the relationship between the total energy of the electrons and the wavevector is written as: with where h {\displaystyle h} is Planck's constant, m ∗ {\displaystyle m^{*}} is a relativistic effective mass used to cancel out the relativistic terms for electrons of energy E {... | Electron diffraction | 0.826967 |
4,957 | The vector k {\displaystyle \mathbf {k} } is also what is used when drawing ray diagrams. For most cases the electrons are travelling at a respectable fraction of the speed of light, so rigorously need to be considered using relativistic quantum mechanics via the Dirac equation, which as spin does not normally matter c... | Electron diffraction | 0.826967 |
4,958 | What is seen in an electron diffraction pattern depends upon the sample and also the energy of the electrons. The electrons need to be considered as waves, which involves describing the electron via a wavefunction, written in crystallographic notation (see notes and) as: for a position r {\displaystyle \mathbf {r} } . ... | Electron diffraction | 0.826967 |
4,959 | The historical background is divided into several subsections. The first is the general background to electrons in vacuum and the technological developments that led to cathode-ray tubes as well as vacuum tubes that dominated early television and electronics; the second is how these led to the development of electron m... | Electron diffraction | 0.826967 |
4,960 | Gas electron diffraction (GED) can be used to determine the geometry of molecules in gases. A gas carrying the molecules is exposed to the electron beam, which is diffracted by the molecules. Since the molecules are randomly oriented, the resulting diffraction pattern consists of broad concentric rings, see Figure 24. | Electron diffraction | 0.826967 |
4,961 | The first level of more accuracy where it is approximated that the electrons are only scattered once, which is called kinematical diffraction and is also a far-field or Fraunhofer approach. More complete and accurate explanations where multiple scattering is included, what is called dynamical diffraction (e.g. refs). T... | Electron diffraction | 0.826967 |
4,962 | Electron diffraction patterns can further be used to characterize molecules using gas electron diffraction, surfaces using lower energy electrons, a technique called LEED, and by reflecting electrons off surfaces, a technique called RHEED, see later. There are many levels of analysis and explanation of the theoretical ... | Electron diffraction | 0.826967 |
4,963 | Low-energy electron diffraction (LEED) is also surface sensitive, and LEED achieves surface sensitivity through the use of low energy electrons. The main uses of RHEED to date have been during thin film growth, as the geometry is amenable to simultaneous collection of the diffraction data and deposition. It can, for in... | Electron diffraction | 0.826967 |
4,964 | Reflection high energy electron diffraction (RHEED), is a technique used to characterize the surface of crystalline materials by reflecting electrons off a surface as illustrated in Figure 22 and 23. RHEED systems gather information only from the surface layers of the sample, which distinguishes RHEED from other materi... | Electron diffraction | 0.826967 |
4,965 | He was able to explain earlier work such as the quantization of the energy of electrons around atoms in the Bohr model, as well as many other phenomena. Electron waves as hypothesized by de Broglie were automatically part of the solutions to his equation, see also introduction to quantum mechanics and matter waves. Bot... | Electron diffraction | 0.826967 |
4,966 | Independent of the developments for electrons in vacuum, at about the same time the components of quantum mechanics were being assembled. In 1924 Louis de Broglie in his PhD thesis Recherches sur la théorie des quanta introduced his theory of electron waves. He suggested that an electron around a nucleus could be thoug... | Electron diffraction | 0.826967 |
4,967 | Butterworth-Heinemann. ISBN 978-0-7506-8025-7.Wright, T. W. (2002). The Physics and Mathematics of Adiabatic Shear Bands. Cambridge, UK: Cambridge University Press. | Continuum physics | 0.826949 |
4,968 | Apart from the assumption of continuity, two other independent assumptions are often employed in the study of continuum mechanics. These are homogeneity (assumption of identical properties at all locations) and isotropy (assumption of directionally invariant vector properties). If these auxiliary assumptions are not gl... | Continuum physics | 0.826949 |
4,969 | The concept of a continuum underlies the mathematical framework for studying large-scale forces and deformations in materials. Although materials are composed of discrete atoms and molecules, separated by empty space or microscopic cracks and crystallographic defects, physical phenomena can often be modeled by consider... | Continuum physics | 0.826949 |
4,970 | Landscape of Geometry was an educational television show that illustrated the principles and applications of geometry. The series was produced and broadcast by TVOntario in 1982–83 and was hosted by David Stringer. A videotape edition of the show was produced in 1992 by Films for the Humanities. | Landscape of Geometry | 0.826939 |
4,971 | In statistics, ridit scoring is a statistical method used to analyze ordered qualitative measurements. The tools of ridit analysis were developed and first applied by Bross, who coined the term "ridit" by analogy with other statistical transformations such as probit and logit. A ridit describes how the distribution of ... | Ridit scoring | 0.826935 |
4,972 | Systems of polynomial equations, which are a special case of non linear systems, better solved by specific solvers. Linear and non-linear optimisation problems Systems of ordinary differential equations Systems of differential algebraic equations Boolean satisfiability problems, including SAT solvers Quantified boolean... | Solver | 0.826929 |
4,973 | List of linear programming solvers List of SMT solvers List of solvers for ordinary differential equations == References == | Solver | 0.826929 |
4,974 | As of 2019, IRSA provides access to more than 1 petabyte of data consisting of roughly 1 trillion astronomical measurements, which span wavelengths from 1 micron to 10 millimeters and include all-sky coverage in 24 bands. Approximately 10% of all refereed astronomical journal articles cite data sets curated by IRSA.IRS... | Infrared Science Archive | 0.826925 |
4,975 | The Encyclopedia of Genetics (ISBN 0-12-227080-0) is a print encyclopedia of genetics edited by Sydney Brenner and Jeffrey H. Miller. It has four volumes and 1,700 entries. It is available online at http://www.sciencedirect.com/science/referenceworks/9780122270802. | Encyclopedia of Genetics | 0.826913 |
4,976 | Human Proteinpedia, which is closely associated with Institute of Bioinformatics (IOB), Bangalore and Johns Hopkins University, is a portal for sharing and integration of human proteomic data. It allows research laboratories to contribute and maintain protein annotations. Human Protein Reference Database (HPRD) integra... | Human Proteinpedia | 0.826913 |
4,977 | Protein annotations present in Human Proteinpedia are derived from a number of platforms such as Co-immunoprecipitation and mass spectrometry-based protein–protein interaction Co-immunoprecipitation and Western blotting based protein–protein interaction Fluorescence based experiments Immunohistochemistry Mass spectrome... | Human Proteinpedia | 0.826913 |
4,978 | Mathcounts, stylized as MATHCOUNTS, is a non-profit organization that provides grades 6-8 extracurricular mathematics programs in all U.S. states, plus the District of Columbia, Puerto Rico, Guam and U.S. Virgin Islands. Its mission is to provide engaging math programs for middle school students of all ability levels t... | Mathcounts | 0.826905 |
4,979 | Since mole fraction has no dimension, the quotient of concentrations will, by definition, be a pure number.The procedures, (1) and (2), give identical numerical values for an equilibrium constant. Furthermore, since a concentration c i {\displaystyle c_{i}} is simply proportional to mole fraction x i {\displaystyle x_{... | Acid–base equilibrium | 0.826901 |
4,980 | With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian and Hamiltonian formulations described above. Modern presentations of Newton's laws use the mathematics of vectors, a topic that was not develope... | Newton’s third law | 0.826893 |
4,981 | Euler pioneered the study of rigid bodies and established the basic theory of fluid dynamics. Pierre-Simon Laplace's five-volume Traité de mécanique céleste (1798–1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving questions that the Principia had left open, like a full ... | Newton’s third law | 0.826893 |
4,982 | Newton expressed his second law by saying that the force on a body is proportional to its change of motion, or momentum. By the time he wrote the Principia, he had already developed calculus (which he called "the science of fluxions"), but in the Principia he made no explicit use of it, perhaps because he believed geom... | Newton’s third law | 0.826893 |
4,983 | Taking out the line at infinity L, any oval that stays in the finite part of the affine plane will be contractible, and so represent the identity element of the fundamental group; the other type of oval must therefore intersect L. There is still the question of how the various ovals are nested. This was the topic of Hi... | Real plane curve | 0.826885 |
4,984 | The field of real numbers is not algebraically closed, the geometry of even a plane curve C in the real projective plane. Assuming no singular points, the real points of C form a number of ovals, in other words submanifolds that are topologically circles. The real projective plane has a fundamental group that is a cycl... | Real plane curve | 0.826885 |
4,985 | In mathematics, a real plane curve is usually a real algebraic curve defined in the real projective plane. | Real plane curve | 0.826885 |
4,986 | The MIRAGE Commission consists of three groups which tightly interact with each other. The advisory board consists of leading scientists in glycobiology, who, for example, critically review the outcomes of the working group and promote the reporting guidelines within the community. The working group seeks for external ... | Minimum Information Required About a Glycomics Experiment | 0.82688 |
4,987 | Then given a query in natural language, the embedding for the query can be generated. A top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. This approach is also kn... | Sentence embedding | 0.826868 |
4,988 | In natural language processing, a sentence embedding refers to a numeric representation of a sentence in the form of a vector of real numbers which encodes meaningful semantic information.State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pion... | Sentence embedding | 0.826868 |
4,989 | Studies in Natural Language Processing is the book series of the Association for Computational Linguistics, published by Cambridge University Press. Steven Bird is the series editor. The editorial board has the following members: Chu-Ren Huang, Chair Professor of Applied Chinese Language Studies in the Department of Ch... | Studies in Natural Language Processing | 0.826852 |
4,990 | In computational biology and bioinformatics, analysis of variance – simultaneous component analysis (ASCA or ANOVA–SCA) is a method that partitions variation and enables interpretation of these partitions by SCA, a method that is similar to principal components analysis (PCA). Analysis of variance (ANOVA) is a collecti... | ANOVA–simultaneous component analysis | 0.826848 |
4,991 | Because ASCA models the variation partitions by SCA, the model for effect estimates looks like this: A = T a P a ′ + E a {\displaystyle A=T_{a}P_{a}^{'}+E_{a}\,} B = T b P b ′ + E b {\displaystyle B=T_{b}P_{b}^{'}+E_{b}\,} A B = T a b P a b ′ + E a b {\displaystyle AB=T_{ab}P_{ab}^{'}+E_{ab}\,} E = T e P e ′ + E e {\di... | ANOVA–simultaneous component analysis | 0.826848 |
4,992 | Given a function f {\displaystyle f} , by definition, to each element x {\displaystyle x} of the domain of the function f {\displaystyle f} , there is a unique element associated to it, the value f ( x ) {\displaystyle f(x)} of f {\displaystyle f} at x {\displaystyle x} . There are several ways to specify or describe h... | Function of several variables | 0.826845 |
4,993 | Many functions can be defined as the antiderivative of another function. This is the case of the natural logarithm, which is the antiderivative of 1/x that is 0 for x = 1. Another common example is the error function. More generally, many functions, including most special functions, can be defined as solutions of diffe... | Function of several variables | 0.826845 |
4,994 | This function is called the activation function.The VC dimension of a neural network is bounded as follows:: 234–235 If the activation function is the sign function and the weights are general, then the VC dimension is at most O ( | E | ⋅ log ( | E | ) ) {\displaystyle O(|E|\cdot \log(|E|))} . If the activation funct... | VC Dimension | 0.826845 |
4,995 | A neural network is described by a directed acyclic graph G(V,E), where: V is the set of nodes. Each node is a simple computation cell. E is the set of edges, Each edge has a weight. The input to the network is represented by the sources of the graph – the nodes with no incoming edges. | VC Dimension | 0.826845 |
4,996 | In quantum physics, laser cooling is used to achieve temperatures of near absolute zero (−273.15 °C, −459.67 °F) of atomic and molecular samples to observe unique quantum effects that can only occur at this heat level. Doppler cooling is the most common method of laser cooling. Sympathetic cooling is a process in which... | Thermal transmission | 0.826838 |
4,997 | Certain airspaces are designated as military-use only. Navigating outside commercial airspaces in the country may lead to the risk of the astrayed aircraft.In prior years, airspace has been limited to military and airmail services. The advancement in aerospace engineering brought to fore aircraft designs that lead to t... | Aviation engineering | 0.826811 |
4,998 | Recent designs of airports have been engineered to align with global environmental standards. Advancement in civil engineering and architecture make an interplay of the two disciplines. | Aviation engineering | 0.826811 |
4,999 | Aviation engineering is a branch of engineering which deals with airspace development, airport design, aircraft navigation technologies, and aerodrome planning. It also involves the formulation of public policy, regulations, aviation laws pertaining to airspace, airlines, airports, aerodromes and the conduct of air ser... | Aviation engineering | 0.826811 |
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