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11,500 | In natural language processing (NLP), a word embedding is a representation of a word. The embedding is used in text analysis. Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that words that are closer in the vector space are expected to be similar in meaning. Wor... | Word embedding | 0.817902 |
11,501 | A combination of tools is employed: PALMapper (reads alignment), mTiM and mGene (inference of new transcripts). Salmon is a software tool for computing transcript abundance from RNA-seq data using either an alignment-free (based directly on the raw reads) or an alignment-based (based on pre-computed alignments) approac... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,502 | rSeq rSeq is a set of tools for RNA-Seq data analysis. It consists of programs that deal with many aspects of RNA-Seq data analysis, such as read quality assessment, reference sequence generation, sequence mapping, gene and isoform expressions (RPKMs) estimation, etc. RSEM rQuant is a web service (Galaxy (computational... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,503 | ALDEx2 uses compositional data analysis and can be applied to RNAseq, 16S rRNA gene sequencing, metagenomic sequencing, and selective growth experiments. Alexa-Seq is a pipeline that makes possible to perform gene expression analysis, transcript specific expression analysis, exon junction expression and quantitative al... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,504 | IRcall / IRclassifier IRcall is a computational tool for IR event detection from RNA-Seq data. IRclassifier is a supervised machine learning-based approach for IR event detection from RNA-Seq data. | List of RNA-Seq bioinformatics tools | 0.817902 |
11,505 | It includes the possibility to filter data before alignment (remotion of adapters). Pass uses Needleman–Wunsch and Smith–Waterman algorithms, and performs alignment in 3 stages: scanning positions of seed sequences in the genome, testing the contiguous regions and finally refining the alignment. PASSion PASTA QPALMA pr... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,506 | CNVseq detects copy number variations supported on a statistical model derived from array-comparative genomic hybridization. Sequences alignment are performed by BLAT, calculations are executed by R modules and is fully automated using Perl. There are few other bioinformatics tools that can call CNA from RNA-Seq. | List of RNA-Seq bioinformatics tools | 0.817902 |
11,507 | Heat*Seq an interactive web tool for high-throughput sequencing experiment comparison with public data. Ingenuity Systems (commercial) iReport & IPA PathwaySeq Pathway analysis for RNA-Seq data using a score-based approach. petal Co-expression network modelling in R. ToPASeq: an R package for topology-based pathway ana... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,508 | Stage 1 uses linear programming to determine a set of exons for each gene. Stage 2 builds a splice graph representation of a gene, by connecting the exons (vertices) via introns (edges) extracted from spliced read alignments. Stage 3 selects a subset of the candidate transcripts encoded in the graph that can explain al... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,509 | Galaxy: Galaxy is a general purpose workbench platform for computational biology. GENE-Counter is a Perl pipeline for RNA-Seq differential gene expression analyses. Gene-counter performs alignments with CASHX, Bowtie, BWA or other SAM output aligner. | List of RNA-Seq bioinformatics tools | 0.817902 |
11,510 | BioQueue is a web-based queue engine designed preferentially to improve the efficiency and robustness of job execution in bioinformatics research by estimating the system resources required by a certain job. At the same time, BioQueue also aims to promote the accessibility and reproducibility of data analysis in biomed... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,511 | ArrayExpressHTS is a BioConductor package that allows preprocessing, quality assessment and estimation of expression of RNA-Seq datasets. It can be run remotely at the European Bioinformatics Institute cloud or locally. The package makes use of several tools: ShortRead (quality control), Bowtie, TopHat or BWA (alignmen... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,512 | NxTrim Adapter trimming and virtual library creation routine for Illumina Nextera Mate Pair libraries. PRINSEQ generates statistics of your sequence data for sequence length, GC content, quality scores, n-plicates, complexity, tag sequences, poly-A/T tails, odds ratios. Filter the data, reformat and trim sequences. | List of RNA-Seq bioinformatics tools | 0.817902 |
11,513 | These commands make possible preprocess the files before mapping with tools like Bowtie. Some of the tasks allowed are: conversion from FASTQ to FASTA format, information about statistics of quality, removing sequencing adapters, filtering and cutting sequences based on quality or conversion DNA/RNA. Flexbar performs r... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,514 | SolexaQA calculates sequence quality statistics and creates visual representations of data quality for second-generation sequencing data. Originally developed for the Illumina system (historically known as “Solexa”), SolexaQA now also supports Ion Torrent and 454 data. Trim galore is a wrapper script to automate qualit... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,515 | However, R scripts can also be used for visualization. SAMStat identifies problems and reports several statistics at different phases of the process. This tool evaluates unmapped, poorly and accurately mapped sequences independently to infer possible causes of poor mapping. | List of RNA-Seq bioinformatics tools | 0.817902 |
11,516 | S4 SequenceSummary objects allow specific tests and functionality to be written around the data collected. RNA-SeQC is a tool with application in experiment design, process optimization and quality control before computational analysis. Essentially, provides three types of quality control: read counts (such as duplicat... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,517 | QC3 a quality control tool designed for DNA sequencing data for raw data, alignment, and variant calling. qrqc Quickly scans reads and gathers statistics on base and quality frequencies, read length, and frequent sequences. Produces graphical output of statistics for use in quality control pipelines, and an optional HT... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,518 | AfterQC - Automatic Filtering, Trimming, Error Removing and Quality Control for fastq data. bam-lorenz-coverage A tool that can generate Lorenz plots and Coverage plots, or export these statistics to text files, directly from BAM file(s). dupRadar An R package which provides functions for plotting and analyzing the dup... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,519 | RNA-Seq is a technique that allows transcriptome studies (see also Transcriptomics technologies) based on next-generation sequencing technologies. This technique is largely dependent on bioinformatics tools developed to support the different steps of the process. Here are listed some of the principal tools commonly emp... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,520 | Quality assessment of raw data is the first step of the bioinformatics pipeline of RNA-Seq. Often, is necessary to filter data, removing low quality sequences or bases (trimming), adapters, contaminations, overrepresented sequences or correcting errors to assure a coherent final result. | List of RNA-Seq bioinformatics tools | 0.817902 |
11,521 | Biopieces are a collection of bioinformatics tools that can be pieced together in a very easy and flexible manner to perform both simple and complex tasks. The Biopieces work on a data stream in such a way that the data stream can be passed through several different Biopieces, each performing one specific task: modifyi... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,522 | AlignerBoost is a generalized software toolkit for boosting Next-Gen sequencing mapping precision using a Bayesian-based mapping quality framework. CADBURE Bioinformatics tool for evaluating aligner performance on your RNA-Seq dataset. QualiMap: Evaluating next generation sequencing alignment data. RNAseqEVAL A collect... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,523 | PRINSEQ is a tool that generates summary statistics of sequence and quality data and that is used to filter, reformat and trim next-generation sequence data. It is particular designed for 454/Roche data, but can also be used for other types of sequence. QC-Chain is a package of quality control tools for next generation... | List of RNA-Seq bioinformatics tools | 0.817902 |
11,524 | Physical or chemical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. The terms "intensive and extensive quantities" were introduced into physics by German writer Georg Helm in 1898... | Intensive variable | 0.8179 |
11,525 | Not all logical systems are truth-valuational in the sense that logical connectives may be interpreted as truth functions. For example, intuitionistic logic lacks a complete set of truth values because its semantics, the Brouwer–Heyting–Kolmogorov interpretation, is specified in terms of provability conditions, and not... | Truth value | 0.817898 |
11,526 | Knowledge management (KM) is the collection of methods relating to creating, sharing, using and managing the knowledge and information of an organization. It refers to a multidisciplinary approach to achieve organizational objectives by making the best use of knowledge.An established discipline since 1991, KM includes ... | Knowledge capture | 0.817898 |
11,527 | Here, electrodynamic fields will be described in terms of differential forms, exterior algebra, and the exterior derivative. Similar to the way that 3-vectors are denoted with an arrow, as in E → , {\textstyle {\vec {E}},} 4-dimensional tensors will be denoted by bold symbols, for example E . | Optical metric | 0.817897 |
11,528 | Using the Gosper-Petkovšek representation one can transform the original recurrence equation into a recurrence equation for a polynomial sequence c ( n ) {\textstyle c(n)} . The other polynomials a ( n ) , b ( n ) {\textstyle a(n),b(n)} can be taken as the monic factors of the first coefficient polynomial p 0 ( n ) {\t... | Petkovšek's algorithm | 0.817883 |
11,529 | Petkovšek's algorithm (also Hyper) is a computer algebra algorithm that computes a basis of hypergeometric terms solution of its input linear recurrence equation with polynomial coefficients. Equivalently, it computes a first order right factor of linear difference operators with polynomial coefficients. This algorithm... | Petkovšek's algorithm | 0.817883 |
11,530 | Thus, for particles with spin S, the maximum number D of particles per Landau level is which for electrons (where Z = 1 and S = 1/2) gives D = 2Φ/Φ0, two available states for each flux quantum that penetrates the system. The above gives only a rough idea of the effects of finite-size geometry. Strictly speaking, using ... | Landau level | 0.817875 |
11,531 | In quantum mechanics, Landau quantization refers to the quantization of the cyclotron orbits of charged particles in a uniform magnetic field. As a result, the charged particles can only occupy orbits with discrete, equidistant energy values, called Landau levels. These levels are degenerate, with the number of electro... | Landau level | 0.817875 |
11,532 | population in this age group).The VSD data-sharing program is now being administered by the National Center for Health Statistics Research Data Center. The data sharing guidelines have been revised to include comments from interested groups as well as recommendations from the Institute of Medicine (IOM). The Vaccine Ad... | Vaccine Safety Datalink | 0.81787 |
11,533 | This is the simplistic DNA → RNA → protein pathway published by James Watson in the first edition of The Molecular Biology of the Gene (1965). Watson's version differs from Crick's because Watson describes a two-step (DNA → RNA and RNA → protein) process as the central dogma. While the dogma as originally stated by Cri... | Central dogma of molecular biology | 0.81787 |
11,534 | He re-stated it in a Nature paper published in 1970: "The central dogma of molecular biology deals with the detailed residue-by-residue transfer of sequential information. It states that such information cannot be transferred back from protein to either protein or nucleic acid." A second version of the central dogma is... | Central dogma of molecular biology | 0.81787 |
11,535 | The central dogma of molecular biology is an explanation of the flow of genetic information within a biological system. It is often stated as "DNA makes RNA, and RNA makes protein", although this is not its original meaning. It was first stated by Francis Crick in 1957, then published in 1958: The Central Dogma. | Central dogma of molecular biology | 0.81787 |
11,536 | These include Eric Mazur's peer instruction, as well as various tutorials in physics. Scientific inquiry is another technique that provides an active engagement opportunity for students and incorporates metacognition and critical thinking. Success with inquiry-based learning activities relies on a deep foundation of fa... | Scientific misconceptions | 0.817869 |
11,537 | Addressing scientific misconceptions is crucial for developing a more accurate understanding of the natural world and improving scientific literacy. In general, scientific misconceptions have their foundations in a few "intuitive knowledge domains, including folkmechanics (object boundaries and movements), folkbiology ... | Scientific misconceptions | 0.817869 |
11,538 | Perhaps the most influential of these concept inventories to date has been the Force Concept Inventory (FCI). Concept inventories can be particularly helpful in identifying difficult ideas that serve as a barrier to effective instruction. Concept inventories in natural selection and basic biology have been developed. | Scientific misconceptions | 0.817869 |
11,539 | "Maximizing f ( ⋅ ) {\displaystyle f(\cdot )} is equivalent to minimizing the L 1 {\displaystyle L_{1}} -distance between the predicted class distribution and the true class distribution (ie: where the p i {\displaystyle p_{i}} induced by A {\displaystyle A} are all equal to 1). A natural alternative is the KL-divergen... | Neighbourhood components analysis | 0.817868 |
11,540 | Neighbourhood components analysis was developed by Jacob Goldberger, Sam Roweis, Ruslan Salakhudinov, and Geoff Hinton at the University of Toronto's department of computer science in 2004. | Neighbourhood components analysis | 0.817868 |
11,541 | Note that the inner Kerr geometry is unstable with regard to perturbations in the interior region. This instability means that although the Kerr metric is axis-symmetric, a black hole created through gravitational collapse may not be so. This instability also implies that many of the features of the Kerr geometry descr... | Kerr solution | 0.817864 |
11,542 | There is a pair of principal null congruences (one ingoing and one outgoing). The Weyl tensor is algebraically special, in fact it has Petrov type D. The global structure is known. Topologically, the homotopy type of the Kerr spacetime can be simply characterized as a line with circles attached at each integer point. | Kerr solution | 0.817864 |
11,543 | The Kerr geometry exhibits many noteworthy features: the maximal analytic extension includes a sequence of asymptotically flat exterior regions, each associated with an ergosphere, stationary limit surfaces, event horizons, Cauchy horizons, closed timelike curves, and a ring-shaped curvature singularity. The geodesic e... | Kerr solution | 0.817864 |
11,544 | Features from accelerated segment test (FAST) is a corner detection method, which could be used to extract feature points and later used to track and map objects in many computer vision tasks. The FAST corner detector was originally developed by Edward Rosten and Tom Drummond, and was published in 2006. The most promis... | Features from accelerated segment test | 0.817859 |
11,545 | FAST-ER detector is an improvement of the FAST detector using a metaheuristic algorithm, in this case simulated annealing. So that after the optimization, the structure of the decision tree would be optimized and suitable for points with high repeatability. However, since simulated annealing is a metaheurisic algorithm... | Features from accelerated segment test | 0.817859 |
11,546 | This recursive process ends when the entropy is zero so that either all pixels in that subset are corners or non-corners. This generated decision tree can then be converted into programming code, such as C and C++, which is just a bunch of nested if-else statements. For optimization purpose, profile-guided optimization... | Features from accelerated segment test | 0.817859 |
11,547 | In order to address the first two weakness points of high-speed test, a machine learning approach is introduced to help improve the detecting algorithm. This machine learning approach operates in two stages. Firstly, corner detection with a given N is processed on a set of training images which are preferable from the ... | Features from accelerated segment test | 0.817859 |
11,548 | Nano Letters is a monthly peer-reviewed scientific journal published by the American Chemical Society. It was established in January 2001. The editor-in-chief is Teri W. Odom (Northwestern University). The journal covers all aspects of nanoscience and nanotechnology and their subdisciplines. | Nano Letters | 0.817855 |
11,549 | The properties of ergodicity, weak mixing and strong mixing of a measure-preserving dynamical system can also be characterized by the average of observables. By von Neumann's ergodic theorem, ergodicity of a dynamical system ( X , A , μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} is equivalent to the property that,... | Mixing system | 0.817854 |
11,550 | {\displaystyle f^{n}(A)\cap B\neq \varnothing .} For a continuous-time system, f n {\displaystyle f^{n}} is replaced by the flow φ g {\displaystyle \varphi _{g}} , with g being the continuous parameter, with the requirement that a non-empty intersection hold for all ‖ g ‖ > N {\displaystyle \Vert g\Vert >N} . A weak to... | Mixing system | 0.817854 |
11,551 | A form of mixing may be defined without appeal to a measure, using only the topology of the system. A continuous map f: X → X {\displaystyle f:X\to X} is said to be topologically transitive if, for every pair of non-empty open sets A , B ⊂ X {\displaystyle A,B\subset X} , there exists an integer n such that f n ( A ) ∩... | Mixing system | 0.817854 |
11,552 | Nutritional science as a subject is taught at universities around the world. At the beginning of the programs, the basic subjects of biology, chemistry, mathematics and physics are part of the curriculum. Later, a focus is on inorganic chemistry, functional biology, biochemistry and genetics. At most universities, stud... | Nutrition science | 0.817851 |
11,553 | Sharp calls this WriteView on its scientific calculators and simply Equation Editor on its graphing calculators. HP calls this its Textbook display setting, which can be used in both RPN and Algebraic mode and in both the Stack and in the Equation Writer application. Mathematica calls this Semantic-Faithful Typesetting... | Chain input | 0.81785 |
11,554 | Modern computer algebra systems, as well as many scientific and graphing calculators, allow for "pretty-printing", that is, entry of equations such that fractions, surds and integrals, etc. are displayed in the way they would normally be written. Such calculators are generally similar in appearance to those using infix... | Chain input | 0.81785 |
11,555 | Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules... | Molecular Graphics | 0.81785 |
11,556 | Like earlier seq2seq models, the original transformer model used an encoder/decoder architecture. The encoder consists of encoding layers that process the input tokens iteratively one layer after another, while the decoder consists of decoding layers that iteratively process the encoder's output as well as the decoder ... | Transformer (machine learning) | 0.817843 |
11,557 | The types of symmetry considered in basic geometry include reflectional symmetry, rotation symmetry, translational symmetry and glide reflection symmetry, which are described more fully in the main article Symmetry (geometry). | Mathematical symmetry | 0.817839 |
11,558 | In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL(V). A field automorphism is a bijective ring homomorphism from a ... | Mathematical symmetry | 0.817839 |
11,559 | Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations.Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which prese... | Mathematical symmetry | 0.817839 |
11,560 | Even if a "geometry" does not correspond to an experimental reality, its theorems remain no less "mathematical truths". : 15 A Euclidean model of a non-Euclidean geometry is a choice of some objects existing in Euclidean space and some relations between these objects that satisfy all axioms (and therefore, all theorems... | List of mathematical spaces | 0.817836 |
11,561 | : 24 This discovery forced the abandonment of the pretensions to the absolute truth of Euclidean geometry. It showed that axioms are not "obvious", nor "implications of definitions". | List of mathematical spaces | 0.817836 |
11,562 | A different situation appeared in the 19th century: in some geometries the sum of the three angles of a triangle is well-defined but different from the classical value (180 degrees). Non-Euclidean hyperbolic geometry, introduced by Nikolai Lobachevsky in 1829 and János Bolyai in 1832 (and Carl Friedrich Gauss in 1816, ... | List of mathematical spaces | 0.817836 |
11,563 | At that time, geometric theorems were treated as absolute objective truths knowable through intuition and reason, similar to objects of natural science;: 11 and axioms were treated as obvious implications of definitions. : 15 Two equivalence relations between geometric figures were used: congruence and similarity. Tran... | List of mathematical spaces | 0.817836 |
11,564 | In ancient Greek mathematics, "space" was a geometric abstraction of the three-dimensional reality observed in everyday life. About 300 BC, Euclid gave axioms for the properties of space. Euclid built all of mathematics on these geometric foundations, going so far as to define numbers by comparing the lengths of line s... | List of mathematical spaces | 0.817836 |
11,565 | Standard probability spaces are especially useful. On a standard probability space a conditional expectation may be treated as the integral over the conditional measure (regular conditional probabilities, see also disintegration of measure). Given two standard probability spaces, every homomorphism of their measure alg... | List of mathematical spaces | 0.817836 |
11,566 | Every Borel set in a Euclidean space (and more generally, in a complete separable metric space), endowed with the Borel σ-algebra, is a standard measurable space. All uncountable standard measurable spaces are mutually isomorphic. A measure space is a measurable space endowed with a measure. | List of mathematical spaces | 0.817836 |
11,567 | The topology is not uniquely determined by the Borel σ-algebra; for example, the norm topology and the weak topology on a separable Hilbert space lead to the same Borel σ-algebra. Not every σ-algebra is the Borel σ-algebra of some topology. Actually, a σ-algebra can be generated by a given collection of sets (or functi... | List of mathematical spaces | 0.817836 |
11,568 | In order to turn a topological space into a measurable space one endows it with a σ-algebra. The σ-algebra of Borel sets is the most popular, but not the only choice. (Baire sets, universally measurable sets, etc, are also used sometimes.) | List of mathematical spaces | 0.817836 |
11,569 | Waiving distances and angles while retaining volumes (of geometric bodies) one reaches measure theory. Besides the volume, a measure generalizes the notions of area, length, mass (or charge) distribution, and also probability distribution, according to Andrey Kolmogorov's approach to probability theory. A "geometric bo... | List of mathematical spaces | 0.817836 |
11,570 | : 21 Rather, each mathematical theory describes its objects by some of their properties, precisely those that are put as axioms at the foundations of the theory. : 20 Distances and angles cannot appear in theorems of projective geometry, since these notions are neither mentioned in the axioms of projective geometry nor... | List of mathematical spaces | 0.817836 |
11,571 | For example, all circles are mutually similar, but ellipses are not similar to circles. A third equivalence relation, introduced by Gaspard Monge in 1795, occurs in projective geometry: not only ellipses, but also parabolas and hyperbolas, turn into circles under appropriate projective transformations; they all are pro... | List of mathematical spaces | 0.817836 |
11,572 | More generally, a k-dimensional projective subspace of the projective space corresponds to a (k+1)-dimensional linear subspace of the (n+1)-dimensional linear space, and is isomorphic to the k-dimensional projective space. Defined this way, affine and projective spaces are of algebraic nature; they can be real, complex... | List of mathematical spaces | 0.817836 |
11,573 | The Kleitman–Wang algorithms are two different algorithms in graph theory solving the digraph realization problem, i.e. the question if there exists for a finite list of nonnegative integer pairs a simple directed graph such that its degree sequence is exactly this list. For a positive answer the list of integer pairs ... | Kleitman–Wang algorithms | 0.817831 |
11,574 | If the given list S {\displaystyle S} digraphic then the theorem will be applied at most n {\displaystyle n} times setting in each further step S := S ′ {\displaystyle S:=S'} . This process ends when the whole list S ′ {\displaystyle S'} consists of ( 0 , 0 ) {\displaystyle (0,0)} pairs. In each step of the algorithm o... | Kleitman–Wang algorithms | 0.817831 |
11,575 | The algorithm is based on the following theorem. Let S = ( ( a 1 , b 1 ) , … , ( a n , b n ) ) {\displaystyle S=((a_{1},b_{1}),\dots ,(a_{n},b_{n}))} be a finite list of nonnegative integers that is in nonincreasing lexicographical order and let ( a i , b i ) {\displaystyle (a_{i},b_{i})} be a pair of nonnegative integ... | Kleitman–Wang algorithms | 0.817831 |
11,576 | If the given list S {\displaystyle S} is digraphic, then the theorem will be applied at most n {\displaystyle n} times, setting in each further step S := S ′ {\displaystyle S:=S'} . This process ends when the whole list S ′ {\displaystyle S'} consists of ( 0 , 0 ) {\displaystyle (0,0)} pairs. In each step of the algori... | Kleitman–Wang algorithms | 0.817831 |
11,577 | Nucleofection is an electroporation-based transfection method which enables transfer of nucleic acids such as DNA and RNA into cells by applying a specific voltage and reagents. Nucleofection, also referred to as nucleofector technology, was invented by the biotechnology company Amaxa. "Nucleofector" and "nucleofection... | Nucleofection | 0.817822 |
11,578 | Geometric Constructions is a mathematics textbook on constructible numbers, and more generally on using abstract algebra to model the sets of points that can be created through certain types of geometric construction, and using Galois theory to prove limits on the constructions that can be performed. It was written by ... | Geometric Constructions | 0.817821 |
11,579 | Geometric Constructions has ten chapters. The first two discuss straightedge and compass constructions, including many of the constructions from Euclid's Elements, and their algebraic model, the constructible numbers. They also include impossibility results for the classical Greek problems of straightedge and compass c... | Geometric Constructions | 0.817821 |
11,580 | Martin originally intended his book to be a graduate-level textbook for students planning to become mathematics teachers. However, as well as this use, it can also be read by anyone who is interested in the history of geometry and has an undergraduate-level background in abstract algebra, or used as a reference work on... | Geometric Constructions | 0.817821 |
11,581 | The traditional way of performing hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured... | Grid search | 0.817816 |
11,582 | When hyperparameter optimization is done, the set of hyperparameters are often fitted on a training set and selected based on the generalization performance, or score, of a validation set. However, this procedure is at risk of overfitting the hyperparameters to the validation set. Therefore, the generalization performa... | Grid search | 0.817816 |
11,583 | The same kind of machine learning model can require different constraints, weights or learning rates to generalize different data patterns. These measures are called hyperparameters, and have to be tuned so that the model can optimally solve the machine learning problem. Hyperparameter optimization finds a tuple of hyp... | Grid search | 0.817816 |
11,584 | In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process. By contrast, the values of other parameters (typically node weights) are learned. | Grid search | 0.817816 |
11,585 | Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a c... | Grid search | 0.817816 |
11,586 | A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best res... | Grid search | 0.817816 |
11,587 | For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector m... | Grid search | 0.817816 |
11,588 | A class of early stopping-based hyperparameter optimization algorithms is purpose built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focus... | Grid search | 0.817816 |
11,589 | In the late 1990s, the Decision Support Group at the University of Fribourg developed a model for decision support software. This described the interface between data and models on one hand, and graphical interfaces for exploring them and making decisions on the other, as a knowledge engine. They also developed a mathe... | Knowledge engine | 0.817816 |
11,590 | The foundation hosts servers for mailing lists, websites, and code repositories for a number of bioinformatics-related open source projects, including: BioJava – Java toolkit BioMOBY – Data and application execution through web services BioPerl – Perl toolkit BioPython – Python toolkit BioRuby – Ruby toolkit BioPHP EMB... | Open Bioinformatics Foundation | 0.817813 |
11,591 | The Open Bioinformatics Foundation is a non-profit, volunteer-run organization focused on supporting open source programming in bioinformatics. The mission of the foundation is to support the development of open source toolkits for bioinformatics, organise developer-centric hackathon events and generally assist in the ... | Open Bioinformatics Foundation | 0.817813 |
11,592 | Here # ( θ ) _ {\displaystyle {\underline {\#(\theta )}}} is the numeral of the canonical Gödel number of the sentence θ. Post's theorem is a sharper version of the undefinability theorem that shows a relationship between the definability of Th( N {\displaystyle {\mathcal {N}}} ) and the Turing degrees, using the arith... | True arithmetic | 0.81781 |
11,593 | The central result on true arithmetic is the undefinability theorem of Alfred Tarski (1936). It states that the set Th( N {\displaystyle {\mathcal {N}}} ) is not arithmetically definable. This means that there is no formula φ ( x ) {\displaystyle \varphi (x)} in the language of first-order arithmetic such that, for eve... | True arithmetic | 0.81781 |
11,594 | As discussed above, Th( N {\displaystyle {\mathcal {N}}} ) is not arithmetically definable, by Tarski's theorem. A corollary of Post's theorem establishes that the Turing degree of Th( N {\displaystyle {\mathcal {N}}} ) is 0(ω), and so Th( N {\displaystyle {\mathcal {N}}} ) is not decidable nor recursively enumerable. ... | True arithmetic | 0.81781 |
11,595 | The true theory of second-order arithmetic consists of all the sentences in the language of second-order arithmetic that are satisfied by the standard model of second-order arithmetic, whose first-order part is the structure N {\displaystyle {\mathcal {N}}} and whose second-order part consists of every subset of N {\di... | True arithmetic | 0.817809 |
11,596 | In physics, Planck's law (also Planck radiation law: 1305 ) describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.At the end of the 19th century, physicists w... | Planck law | 0.817806 |
11,597 | Then d p ( x , y ) = | x − y | p {\displaystyle d_{p}(x,y)=|x-y|_{p}} defines a metric on Q . {\displaystyle \mathbb {Q} .} The metric space ( Q , d p ) {\displaystyle (\mathbb {Q} ,d_{p})} is not complete, and its completion is the p-adic number field Q p . {\displaystyle \mathbb {Q} _{p}.} Ostrowski's theorem states ... | Field of rationals | 0.817805 |
11,598 | {\displaystyle (p_{1},q_{1})\sim (p_{2},q_{2})\iff p_{1}q_{2}=p_{2}q_{1}.} The fraction p q {\displaystyle {\tfrac {p}{q}}} then denotes the equivalence class of (p, q).Rational numbers together with addition and multiplication form a field which contains the integers, and is contained in any field containing the integ... | Field of rationals | 0.817805 |
11,599 | {\displaystyle \mathbb {Z} .} The algebraic closure of Q , {\displaystyle \mathbb {Q} ,} i.e. the field of roots of rational polynomials, is the field of algebraic numbers. The rationals are a densely ordered set: between any two rationals, there sits another one, and, therefore, infinitely many other ones. | Field of rationals | 0.817805 |
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