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400 | In China, from ancient times counting rods were used to represent numbers, and arithmetic was accomplished with rod calculus and later the suanpan. The Book on Numbers and Computation and the Nine Chapters on the Mathematical Art include exercises that are exemplars of linear algebra.In about 980 Al-Sijzi wrote his Way... | Mathematical exercise | 0.84963 |
401 | In such courses emphasis was on learning by doing, without an attempt to teach specific heuristics: the students worked lots of problems because (according to the implicit instructional model behind such courses) that’s how one gets good at mathematics.Such exercise collections may be proprietary to the instructor and ... | Mathematical exercise | 0.84963 |
402 | ... Supplementary exercises at the end of each chapter expand the other exercise sets and provide cumulative exercises that require skills from earlier chapters.This text includes "Functions and Graphs in Applications" (Ch 0.6) which is fourteen pages of preparation for word problems. Authors of a book on finite fields... | Mathematical exercise | 0.84963 |
403 | These are short stories of adventure and industry with the end omitted and, though betraying a strong family resemblance, are not without a certain element of romance.A distinction between an exercise and a mathematical problem was made by Alan H. Schoenfeld: Students must master the relevant subject matter, and exerci... | Mathematical exercise | 0.84963 |
404 | In primary school students start with single digit arithmetic exercises. Later most exercises involve at least two digits. A common exercise in elementary algebra calls for factorization of polynomials. | Mathematical exercise | 0.84963 |
405 | The connection densities, or neighbourhood densities of memory arrangements help distinguish which elements are a part of, or related to, the target memory. As the density of neural networks increases, the number of retrieval cues (associated nodes) also increases, which may allow for enhanced memory of the event. Howe... | Memory errors | 0.849573 |
406 | A disadvantage is that many of these structures are of proteins of unknown function and do not have corresponding publications. This requires new ways of communicating this structural information to the broader research community. The Bioinformatics core of the Joint center for structural genomics (JCSG) has recently d... | Structural proteomics | 0.849213 |
407 | As opposed to traditional structural biology, the determination of a protein structure through a structural genomics effort often (but not always) comes before anything is known regarding the protein function. This raises new challenges in structural bioinformatics, i.e. determining protein function from its 3D structu... | Structural proteomics | 0.849213 |
408 | In physics, a pair potential is a function that describes the potential energy of two interacting objects solely as a function of the distance between them.Some interactions, like Coulomb's law in electrodynamics or Newton's law of universal gravitation in mechanics naturally have this form for simple spherical objects... | Pair potential | 0.849171 |
409 | Pair potentials are very common in physics and computational chemistry and biology; exceptions are very rare. An example of a potential energy function that is not a pair potential is the three-body Axilrod-Teller potential. Another example is the Stillinger-Weber potential for silicon, which includes the angle in a tr... | Pair potential | 0.84917 |
410 | In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in topics such as the capacita... | Electric displacement field | 0.849134 |
411 | In the fields of bioinformatics and computational biology, Genome survey sequences (GSS) are nucleotide sequences similar to expressed sequence tags (ESTs) that the only difference is that most of them are genomic in origin, rather than mRNA.Genome survey sequences are typically generated and submitted to NCBI by labs ... | Genome survey sequence | 0.849115 |
412 | In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the conven... | Degree (geometry) | 0.8491 |
413 | It is possible to combine dimensional universal physical constants to define fixed quantities of any desired dimension, and this property has been used to construct various systems of natural units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may be convenient t... | Physical constant | 0.848953 |
414 | However, while its value is not known to great precision, the possibility of observing type Ia supernovae which happened in the universe's remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10−10 per year for the gravitational constant ... | Physical constant | 0.848953 |
415 | Some traditional areas include mineral processing, metal production, heat treatment, failure analysis, and the joining of metals (including welding, brazing, and soldering). Emerging areas for metallurgists include nanotechnology, superconductors, composites, biomedical materials, electronic materials (semiconductors) ... | Metal physics | 0.848915 |
416 | Subjects of study in chemical metallurgy include mineral processing, the extraction of metals, thermodynamics, electrochemistry, and chemical degradation (corrosion). In contrast, physical metallurgy focuses on the mechanical properties of metals, the physical properties of metals, and the physical performance of metal... | Metal physics | 0.848915 |
417 | Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the science and the technology of metals; that is, the way in which science is appl... | Metal physics | 0.848915 |
418 | {\displaystyle \rho =(\sigma \otimes \tau )\circ \Delta .} Such a homomorphism Δ is called a comultiplication if it satisfies certain axioms. The resulting structure is called a bialgebra. To be consistent with the definitions of the associative algebra, the coalgebra must be co-associative, and, if the algebra is unit... | Commutative algebra (structure) | 0.848855 |
419 | Consider, for example, two representations σ: A → E n d ( V ) {\displaystyle \sigma :A\rightarrow \mathrm {End} (V)} and τ: A → E n d ( W ) {\displaystyle \tau :A\rightarrow \mathrm {End} (W)} . One might try to form a tensor product representation ρ: x ↦ σ ( x ) ⊗ τ ( x ) {\displaystyle \rho :x\mapsto \sigma (x)\otime... | Commutative algebra (structure) | 0.848855 |
420 | Indeed, this reinterpretation allows one to avoid making an explicit reference to elements of an algebra A. For example, the associativity can be expressed as follows. By the universal property of a tensor product of modules, the multiplication (the R-bilinear map) corresponds to a unique R-linear map m: A ⊗ R A → A {\... | Commutative algebra (structure) | 0.848855 |
421 | The definition is equivalent to saying that a unital associative R-algebra is a monoid object in R-Mod (the monoidal category of R-modules). By definition, a ring is a monoid object in the category of abelian groups; thus, the notion of an associative algebra is obtained by replacing the category of abelian groups with... | Commutative algebra (structure) | 0.848855 |
422 | The Clifford algebras, which are useful in geometry and physics. Incidence algebras of locally finite partially ordered sets are associative algebras considered in combinatorics. The partition algebra and its subalgebras, including the Brauer algebra and the Temperley-Lieb algebra. A differential graded algebra is an a... | Commutative algebra (structure) | 0.848855 |
423 | Let R be a Noetherian integral domain with field of fractions K (for example, they can be Z , Q {\displaystyle \mathbb {Z} ,\mathbb {Q} } ). A lattice L in a finite-dimensional K-vector space V is a finitely generated R-submodule of V that spans V; in other words, L ⊗ R K = V {\displaystyle L\otimes _{R}K=V} . Let A K ... | Commutative algebra (structure) | 0.848855 |
424 | The most basic example is a ring itself; it is an algebra over its center or any subring lying in the center. In particular, any commutative ring is an algebra over any of its subrings. Other examples abound both from algebra and other fields of mathematics. | Commutative algebra (structure) | 0.848855 |
425 | Let A be an algebra over a commutative ring R. Then the algebra A is a right module over A e := A o p ⊗ R A {\displaystyle A^{e}:=A^{op}\otimes _{R}A} with the action x ⋅ ( a ⊗ b ) = a x b {\displaystyle x\cdot (a\otimes b)=axb} . Then, by definition, A is said to separable if the multiplication map A ⊗ R A → A , x ⊗ y... | Commutative algebra (structure) | 0.848855 |
426 | Solexa, now part of Illumina, was founded by Shankar Balasubramanian and David Klenerman in 1998, and developed a sequencing method based on reversible dye-terminators technology, and engineered polymerases. The reversible terminated chemistry concept was invented by Bruno Canard and Simon Sarfati at the Pasteur Instit... | High throughput sequencing | 0.848831 |
427 | The polony sequencing method, developed in the laboratory of George M. Church at Harvard, was among the first high-throughput sequencing systems and was used to sequence a full E. coli genome in 2005. It combined an in vitro paired-tag library with emulsion PCR, an automated microscope, and ligation-based sequencing ch... | High throughput sequencing | 0.848831 |
428 | Computer algebra system Cryptography Discrete logarithm Triple DES Caesar cipher Exponentiating by squaring Knapsack problem Shor's algorithm Standard Model Symmetry in physics | List of group theory topics | 0.848667 |
429 | Algebraic geometry Algebraic topology Discrete space Fundamental group Geometry Homology Minkowski's theorem Topological group | List of group theory topics | 0.848667 |
430 | Affine representation Character theory Great orthogonality theorem Maschke's theorem Monstrous moonshine Projective representation Representation theory Schur's lemma | List of group theory topics | 0.848667 |
431 | Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography. | List of group theory topics | 0.848667 |
432 | In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recu... | List of group theory topics | 0.848667 |
433 | A computer science educator stated in Times Higher Education that the examples are clear and accessible. In contrast, The Economist agreed Domingos "does a good job" but complained that he "constantly invents metaphors that grate or confuse". Kirkus Reviews praised the book, stating that "Readers unfamiliar with logic ... | The Master Algorithm | 0.848663 |
434 | The book outlines five approaches of machine learning: inductive reasoning, connectionism, evolutionary computation, Bayes' theorem and analogical modelling. The author explains these tribes to the reader by referring to more understandable processes of logic, connections made in the brain, natural selection, probabili... | The Master Algorithm | 0.848663 |
435 | The general theory of algebraic structures has been formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structures of the same type (homomorphisms). In universal algebra, an algebraic structure is called an algebra; this term m... | Structure (algebraic) | 0.848647 |
436 | In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic str... | Structure (algebraic) | 0.848647 |
437 | Gene sharing is related to, but distinct from, several concepts in genetics, evolution, and molecular biology. Gene sharing entails multiple effects from the same gene, but unlike pleiotropy, it necessarily involves separate functions at the molecular level. A gene could exhibit pleiotropy when single enzyme function a... | Protein moonlighting | 0.848627 |
438 | These expression levels may signify that the protein is performing a different function than previously known.The structure of a protein can also help determine its functions. Protein structure in turn may be elucidated with various techniques including X-ray crystallography or NMR. Dual-polarization interferometry may... | Protein moonlighting | 0.848627 |
439 | For example, the tissue, cellular, or subcellular distribution of a protein may provide hints as to the function. Real-time PCR is used to quantify mRNA and hence infer the presence or absence of a particular protein which is encoded by the mRNA within different cell types. Alternatively immunohistochemistry or mass sp... | Protein moonlighting | 0.848627 |
440 | Gene set enrichment determines if the overlap between two gene sets is statistically significant, in this case the overlap between differentially expressed genes and gene sets from known pathways/databases (e.g., Gene Ontology, KEGG, Human Phenotype Ontology) or from complementary analyses in the same data (like co-exp... | RNA seq | 0.84862 |
441 | Methods: Most tools use regression or non-parametric statistics to identify differentially expressed genes, and are either based on read counts mapped to a reference genome (DESeq2, limma, edgeR) or based on read counts derived from alignment-free quantification (sleuth, Cuffdiff, Ballgown). Following regression, most ... | RNA seq | 0.84862 |
442 | Other covariates (also referred to as factors, features, labels, or parameters) can include batch effects, known artifacts, and any metadata that might confound or mediate gene expression. In addition to known covariates, unknown covariates can also be estimated through unsupervised machine learning approaches includin... | RNA seq | 0.84862 |
443 | RNA-Seq has the potential to identify new disease biology, profile biomarkers for clinical indications, infer druggable pathways, and make genetic diagnoses. These results could be further personalized for subgroups or even individual patients, potentially highlighting more effective prevention, diagnostics, and therap... | RNA seq | 0.84862 |
444 | Fluid Phase Equilibria is a peer-reviewed scientific journal on physical chemistry and thermodynamics that is published by Elsevier. The articles deal with experimental, theoretical and applied research related to properties of pure components and mixtures, especially phase equilibria, caloric and transport properties ... | Fluid Phase Equilibria | 0.848502 |
445 | The current editors are: Clare McCabe - Editor in Chief. Vanderbilt University Department of Chemical and Biomolecular Engineering, Nashville, Tennessee, United States Ioannis Economou - Texas A&M University at Qatar, Education City, PO Box 23874, Doha, Qatar Yoshio Iwai - Kyushu University Faculty of Engineering Gradu... | Fluid Phase Equilibria | 0.848502 |
446 | A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that poin... | Quadrature of the Parabola | 0.848491 |
447 | S. cerevisiae, a model organism in biology has a genome of only around 12 million nucleotide pairs, and was the first unicellular eukaryote to have its whole genome sequenced. The first multicellular eukaryote, and animal, to have its whole genome sequenced was the nematode worm: Caenorhabditis elegans in 1998. Eukaryo... | Whole-genome sequencing | 0.848442 |
448 | Advanced Placement (AP) Physics 2 is a year-long introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a second-semester algebra-based university course in fluid mechanics, thermodynamics, electromagnetism, optics, and modern physics. Along with... | AP Physics 2 | 0.848425 |
449 | AP Physics 2 is an algebra-based, introductory college-level physics course in which students explore fluid statics and dynamics; thermodynamics with kinetic theory; PV diagrams and probability; electrostatics; electrical circuits with capacitors; magnetic fields; electromagnetism; physical and geometric optics; and qu... | AP Physics 2 | 0.848425 |
450 | In February 2014, the official course description and sample curriculum resources were posted to the College Board website, with two practice exams being posted the next month. As of September 2014, face to face workshops are dedicated solely to AP Physics 1 & AP Physics 2. | AP Physics 2 | 0.848425 |
451 | The AP Physics 2 classes began in the fall of 2014, with the first AP exams administered in May 2015. The courses were formed through collaboration between current Advanced Placement teachers and The College Board, with the guidance from the National Research Council and the National Science Foundation. As of August 20... | AP Physics 2 | 0.848425 |
452 | The compression of amino acid sequences is a comparatively challenging task. The existing specialized amino acid sequence compressors are low compared with that of DNA sequence compressors, mainly because of the characteristics of the data. For example, modeling inversions is harder because of the reverse information l... | Protein sequence | 0.848401 |
453 | A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantifie... | Physical quantities | 0.848381 |
454 | Depending on the context, solving an equation may consist to find either any solution (finding a single solution is enough), all solutions, or a solution that satisfies further properties, such as belonging to a given interval. When the task is to find the solution that is the best under some criterion, this is an opti... | Solution (equation) | 0.848351 |
455 | Polynomial equations of degree up to four can be solved exactly using algebraic methods, of which the quadratic formula is the simplest example. Polynomial equations with a degree of five or higher require in general numerical methods (see below) or special functions such as Bring radicals, although some specific cases... | Solution (equation) | 0.848351 |
456 | During the latter half of the 20th century, the fields of genetics and molecular biology matured greatly, significantly increasing understanding of biological heredity. As with other complex and evolving fields of knowledge, the public awareness of these advances has primarily been through the mass media, and a number ... | Common misunderstandings of genetics | 0.848341 |
457 | In the early years of genetics it was suggested that there might be "a gene for" a wide range of particular characteristics. This was partly because the examples studied from Mendel onwards inevitably focused on genes whose effects could be readily identified; partly that it was easier to teach science that way; and pa... | Common misunderstandings of genetics | 0.848341 |
458 | While the central dogma of molecular biology describes how information cannot be passed back to inheritable genetic information, the other causal arrows in this chain can be bidirectional, with complex feedbacks ultimately regulating gene expression. Instead of being a simple, linear mapping, this complex relationship ... | Common misunderstandings of genetics | 0.848341 |
459 | It is widely believed that genes provide a "blueprint" for the body in much the same way that architectural or mechanical engineering blueprints describe buildings or machines. At a superficial level, genes and conventional blueprints share the common property of being low dimensional (genes are organised as a one-dime... | Common misunderstandings of genetics | 0.848341 |
460 | Steroid isolation, depending on context, is the isolation of chemical matter required for chemical structure elucidation, derivitzation or degradation chemistry, biological testing, and other research needs (generally milligrams to grams, but often more or the isolation of "analytical quantities" of the substance of in... | Steroid metabolism | 0.848198 |
461 | In particle physics, charge conservation means that in reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Similarly, when particles are destroyed, equal numbers of positive and negative charges are destroyed. This pro... | Conservation of electric charge | 0.848075 |
462 | In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved. Charge conservation, considered as a physical conservation law... | Conservation of electric charge | 0.848075 |
463 | In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is th... | Solution space | 0.848056 |
464 | Sentences are then built up out of atomic formulas by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. | Sentence (mathematical logic) | 0.847994 |
465 | Massive parallel sequencing or massively parallel sequencing is any of several high-throughput approaches to DNA sequencing using the concept of massively parallel processing; it is also called next-generation sequencing (NGS) or second-generation sequencing. Some of these technologies emerged between 1993 and 1998 and... | Massive parallel sequencing | 0.847978 |
466 | (The adjective genetic, derived from the Greek word genesis—γένεσις, "origin", predates the noun and was first used in a biological sense in 1860.) Bateson both acted as a mentor and was aided significantly by the work of other scientists from Newnham College at Cambridge, specifically the work of Becky Saunders, Nora ... | Genetics | 0.847976 |
467 | He recognized recessive traits and inherent variation by postulating that traits of past generations could reappear later, and organisms could produce progeny with different attributes. These observations represent an important prelude to Mendel's theory of particulate inheritance insofar as it features a transition of... | Genetics | 0.847976 |
468 | The observation that living things inherit traits from their parents has been used since prehistoric times to improve crop plants and animals through selective breeding. The modern science of genetics, seeking to understand this process, began with the work of the Augustinian friar Gregor Mendel in the mid-19th century... | Genetics | 0.847976 |
469 | This messenger RNA molecule then serves to produce a corresponding amino acid sequence through a process called translation. Each group of three nucleotides in the sequence, called a codon, corresponds either to one of the twenty possible amino acids in a protein or an instruction to end the amino acid sequence; this c... | Genetics | 0.847976 |
470 | Population genetics studies the distribution of genetic differences within populations and how these distributions change over time. Changes in the frequency of an allele in a population are mainly influenced by natural selection, where a given allele provides a selective or reproductive advantage to the organism, as w... | Genetics | 0.847976 |
471 | Modern genetics started with Mendel's studies of the nature of inheritance in plants. In his paper "Versuche über Pflanzenhybriden" ("Experiments on Plant Hybridization"), presented in 1865 to the Naturforschender Verein (Society for Research in Nature) in Brünn, Mendel traced the inheritance patterns of certain traits... | Genetics | 0.847976 |
472 | The adjective quadratic comes from the Latin word quadrātum ("square"). A term raised to the second power like x2 is called a square in algebra because it is the area of a square with side x. | Quadratic function | 0.847954 |
473 | Here C is the field of complex numbers and Z is the ring of integer numbers. A theorem of Artin and Schreier asserts that (essentially) these are all the possibilities for finite absolute Galois groups. Artin–Schreier theorem. Let K be a field whose absolute Galois group G is finite. Then either K is separably closed a... | Field Arithmetic | 0.847913 |
474 | Let K be a field and let G = Gal(K) be its absolute Galois group. If K is algebraically closed, then G = 1. If K = R is the real numbers, then G = Gal ( C / R ) = Z / 2 Z . {\displaystyle G=\operatorname {Gal} (\mathbf {C} /\mathbf {R} )=\mathbf {Z} /2\mathbf {Z} .} | Field Arithmetic | 0.847913 |
475 | In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute Galois group. It is an interdisciplinary subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and o... | Field Arithmetic | 0.847913 |
476 | Then K is Hilbertian if and only if K is ω-free. Peter Roquette proved the right-to-left direction of this theorem and conjectured the opposite direction. Michael Fried and Helmut Völklein applied algebraic topology and complex analysis to establish Roquette's conjecture in characteristic zero. Later Pop proved the The... | Field Arithmetic | 0.847913 |
477 | A nice theorem in this spirit connects Hilbertian fields with ω-free fields (K is ω-free if any embedding problem for K is properly solvable). Theorem. Let K be a PAC field. | Field Arithmetic | 0.847913 |
478 | A pseudo algebraically closed field (in short PAC) K is a field satisfying the following geometric property. Each absolutely irreducible algebraic variety V defined over K has a K-rational point. Over PAC fields there is a firm link between arithmetic properties of the field and group theoretic properties of its absolu... | Field Arithmetic | 0.847913 |
479 | Then with probability 1 the absolute Galois group Gal(Ns) is free of countable rank. (This result is due to Moshe Jarden. )In contrast to the above examples, if the fields in question are finitely generated over Q, Florian Pop proves that an isomorphism of the absolute Galois groups yields an isomorphism of the fields:... | Field Arithmetic | 0.847913 |
480 | Let C be an algebraically closed field and x a variable. Then Gal(C(x)) is free of rank equal to the cardinality of C. (This result is due to Adrien Douady for 0 characteristic and has its origins in Riemann's existence theorem. | Field Arithmetic | 0.847913 |
481 | The invariance of charge can be derived as a corollary of Maxwell's equations. The left-hand side of the modified Ampere's law has zero divergence by the div–curl identity. Expanding the divergence of the right-hand side, interchanging derivatives, and applying Gauss's law gives: i.e., By the Gauss divergence theorem, ... | Maxwell's Equations | 0.84789 |
482 | The topological condition is again that the second real cohomology group is 'trivial' (meaning that its form follows from a definition). By the isomorphism with the second de Rham cohomology this condition means that every closed 2-form is exact.Other formalisms include the geometric algebra formulation and a matrix re... | Maxwell's Equations | 0.84789 |
483 | For this reason the relativistic invariant equations are usually called the Maxwell equations as well. Each table below describes one formalism. In the tensor calculus formulation, the electromagnetic tensor Fαβ is an antisymmetric covariant order 2 tensor; the four-potential, Aα, is a covariant vector; the current, Jα... | Maxwell's Equations | 0.84789 |
484 | In fact the Maxwell equations in the space + time formulation are not Galileo invariant and have Lorentz invariance as a hidden symmetry. This was a major source of inspiration for the development of relativity theory. Indeed, even the formulation that treats space and time separately is not a non-relativistic approxim... | Maxwell's Equations | 0.84789 |
485 | A Pappian projective space is a projective space in which Pappus's hexagon theorem holds. The following result, due to Francis Buekenhout, is an astonishing statement for finite projective spaces. Theorem: Let be P n {\displaystyle {\mathfrak {P}}_{n}} a finite projective space of dimension n ≥ 3 {\displaystyle n\geq 3... | Quadratic set | 0.847874 |
486 | ( g {\displaystyle g} is called exterior, tangent and secant line if | g ∩ O | = 0 , | g ∩ O | = 1 {\displaystyle |g\cap {\mathcal {O}}|=0,\ |g\cap {\mathcal {O}}|=1} and | g ∩ O | = 2 {\displaystyle |g\cap {\mathcal {O}}|=2} respectively.) (O2) For any point P ∈ O {\displaystyle P\in {\mathcal {O}}} the union O P {\di... | Quadratic set | 0.847873 |
487 | According to this theorem of Beniamino Segre, for Pappian projective planes of odd order the ovals are just conics: Theorem: Let be P {\displaystyle {\mathfrak {P}}} a Pappian projective plane of odd order. Any oval in P {\displaystyle {\mathfrak {P}}} is an oval conic (non-degenerate quadric). Definition: (ovoid) A no... | Quadratic set | 0.847873 |
488 | For finite planes the following theorem provides a more simple definition. Theorem: (oval in finite plane) Let be P {\displaystyle {\mathfrak {P}}} a projective plane of order n {\displaystyle n} . A set o {\displaystyle {\mathfrak {o}}} of points is an oval if | o | = n + 1 {\displaystyle |{\mathfrak {o}}|=n+1} and if... | Quadratic set | 0.847873 |
489 | The earliest result may be found directly from elementary probability theory. Suppose we model the above process taking L {\displaystyle L} and G {\displaystyle G} as the fragment length and target length, respectively. The probability of "covering" any given location on the target with one particular fragment is then ... | DNA sequencing theory | 0.847829 |
490 | The permanent archive of work is primarily mathematical, although numerical calculations are often conducted for particular problems too. DNA sequencing theory addresses physical processes related to sequencing DNA and should not be confused with theories of analyzing resultant DNA sequences, e.g. sequence alignment. P... | DNA sequencing theory | 0.847829 |
491 | DNA sequencing theory is the broad body of work that attempts to lay analytical foundations for determining the order of specific nucleotides in a sequence of DNA, otherwise known as DNA sequencing. The practical aspects revolve around designing and optimizing sequencing projects (known as "strategic genomics"), predic... | DNA sequencing theory | 0.847829 |
492 | For example, in the so-called "discordant read pairs method", DNA insertions can be inferred if the distance between read pairs is larger than expected. Calculations show that around 50-fold redundancy is needed to avoid false-positive errors at 1% threshold.The advent of next-generation sequencing has also made large-... | DNA sequencing theory | 0.847829 |
493 | Antibodies to particular proteins, or to their modified forms, have been used in biochemistry and cell biology studies. These are among the most common tools used by molecular biologists today. There are several specific techniques and protocols that use antibodies for protein detection. The enzyme-linked immunosorbent... | Protein analysis | 0.847728 |
494 | Now, through bioinformatics, there are computer programs that can in some cases predict and model the structure of proteins. These programs use the chemical properties of amino acids and structural properties of known proteins to predict the 3D model of sample proteins. This also allows scientists to model protein inte... | Protein analysis | 0.847727 |
495 | Although early large-scale shotgun proteomics analyses showed considerable variability between laboratories, presumably due in part to technical and experimental differences between laboratories, reproducibility has been improved in more recent mass spectrometry analysis, particularly on the protein level. Notably, tar... | Protein analysis | 0.847727 |
496 | One example of the use of bioinformatics and the use of computational methods is the study of protein biomarkers. Computational predictive models have shown that extensive and diverse feto-maternal protein trafficking occurs during pregnancy and can be readily detected non-invasively in maternal whole blood. This compu... | Protein analysis | 0.847727 |
497 | Recent advancements in bioorthogonal chemistry have revealed applications in protein analysis. The extension of using organic molecules to observe their reaction with proteins reveals extensive methods to tag them. Unnatural amino acids and various functional groups represent new growing technologies in proteomics. Spe... | Protein analysis | 0.847727 |
498 | Other methods include surface plasmon resonance (SPR), protein microarrays, dual polarisation interferometry, microscale thermophoresis, kinetic exclusion assay, and experimental methods such as phage display and in silico computational methods. Knowledge of protein-protein interactions is especially useful in regard t... | Protein analysis | 0.847727 |
499 | The most useful application here for genetical statistics is the correlation between half-sibs. Recall that the correlation coefficient (r) is the ratio of the covariance to the variance . Therefore, rHS = cov(HS) / s2all HS together = / s2P = ¼ H2 . The correlation between full-sibs is of little utility, being rFS = ... | Quantitative genetics | 0.847725 |
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