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4,800 | Macromolecular structure validation is the process of evaluating reliability for 3-dimensional atomic models of large biological molecules such as proteins and nucleic acids. These models, which provide 3D coordinates for each atom in the molecule (see example in the image), come from structural biology experiments suc... | Structure validation | 0.827289 |
4,801 | For macromolecular structures, the atomic models are deposited in the Protein Data Bank (PDB), still the single archive of this data. The PDB was established in the 1970s at Brookhaven National Laboratory, moved in 2000 to the RCSB (Research Collaboration for Structural Biology) centered at Rutgers, and expanded in 200... | Structure validation | 0.827289 |
4,802 | Therefore, that one test by itself provides most of the validation needed, but a number of additional consistency and methodology checks are done by automated software as a requirement for small-molecule crystal structure papers submitted to the International Union of Crystallography (IUCr) journals such as Acta Crysta... | Structure validation | 0.827289 |
4,803 | It is difficult to do meaningful validation of an individual, purely computational, macromolecular model in the absence of experimental data for that molecule, because the model with the best geometry and conformational score may not be the one closest to the right answer. Therefore, much of the emphasis in validation ... | Structure validation | 0.827289 |
4,804 | This allows to, for example, knock an enemy down or grab each individual joint and move it around and the physics-based animation would adapt accordingly, which wouldn't be possible with conventional means. This method is called active ragdolls and is often used in combination with inverse kinematics. –× | Game physics | 0.827287 |
4,805 | This is a procedural animation and simulation technique to display the movement of a character when killed. It treats the character's body as a series of rigid bones connected together with hinges at the joints. The simulation models what happens to the body as it collapses to the ground. More sophisticated physics mod... | Game physics | 0.827287 |
4,806 | Common examples in platform games include the ability to start moving horizontally or change direction in mid-air and the double jump ability found in some games. Setting the values of physical parameters, such as the amount of gravity present, is also a part of defining the game physics of a particular game. There are... | Game physics | 0.827287 |
4,807 | Computer animation physics or game physics are laws of physics as they are defined within a simulation or video game, and the programming logic used to implement these laws. Game physics vary greatly in their degree of similarity to real-world physics. Sometimes, the physics of a game may be designed to mimic the physi... | Game physics | 0.827287 |
4,808 | This projectile uses a form of continuous collision detection to make sure that the above-stated problem will not occur (at the cost of inferior performance), since more complex calculations are required to perform such a task. Games such as FIFA 14 require accurate projectile physics for objects such as the soccer bal... | Game physics | 0.827287 |
4,809 | There are two central types of physics simulations: rigid body and soft-body simulators. In a rigid body simulation objects are grouped into categories based on how they should interact and are less performance intensive. Soft-body physics involves simulating individual sections of each object such that it behaves in a... | Game physics | 0.827286 |
4,810 | Depending on the processing power available, the effects of the explosion can be modeled as the split and shattered components propelled by the expanding gas. This is modelled by means of a particle system simulation. A particle system model allows a variety of other physical phenomena to be simulated, including smoke,... | Game physics | 0.827286 |
4,811 | In a computation tree for a decision problem, each output node is labeled Yes or No. If a tree, T, with an input space X, if x ∈ X {\displaystyle x\in X} and the path for x ends in node labeled yes, then the input x is accepted. Else it is rejected.The depth of the computation tree for a given input is the computation ... | Computation tree | 0.82728 |
4,812 | In molecular biology, biosynthesis is a multi-step, enzyme-catalyzed process where substrates are converted into more complex products in living organisms. In biosynthesis, simple compounds are modified, converted into other compounds, or joined to form macromolecules. This process often consists of metabolic pathways. | Biological synthesis | 0.82727 |
4,813 | We can relate NL to deterministic space using Savitch's theorem, which tells us that any nondeterministic algorithm can be simulated by a deterministic machine in at most quadratically more space. From Savitch's theorem, we have directly that: N L ⊆ S P A C E ( log 2 n ) equivalently, N L ⊆ L 2 . {\displaystyle {\mat... | NL (complexity class) | 0.827265 |
4,814 | Important results in complexity theory allow us to relate this complexity class with other classes, telling us about the relative power of the resources involved. Results in the field of algorithms, on the other hand, tell us which problems can be solved with this resource. Like much of complexity theory, many importan... | NL (complexity class) | 0.827265 |
4,815 | It only needs to keep a running total of the number of heads in a row it sees, which it can count in log space. Because of the Immerman–Szelepcsényi theorem, according to which NL is closed under complements, the one-sided error in these probabilistic computations can be replaced by zero-sided error. That is, these pro... | NL (complexity class) | 0.827265 |
4,816 | In Papadimitriou 1994, Theorem 16.1, we have: N C 1 ⊆ L ⊆ N L ⊆ N C 2 {\displaystyle {\mathsf {NC_{1}\subseteq L\subseteq NL\subseteq NC_{2}}}} .More precisely, NL is contained in AC1. It is known that NL is equal to ZPL, the class of problems solvable by randomized algorithms in logarithmic space and unbounded time, w... | NL (complexity class) | 0.827265 |
4,817 | It is known that NL is contained in P, since there is a polynomial-time algorithm for 2-satisfiability, but it is not known whether NL = P or whether L = NL. It is known that NL = co-NL, where co-NL is the class of languages whose complements are in NL. This result (the Immerman–Szelepcsényi theorem) was independently ... | NL (complexity class) | 0.827265 |
4,818 | Programmers only need to specify which data a processes depends on. Eden's process model provides direct control over process granularity, data distribution and communication topology. Eden is not a skeleton language in the sense that skeletons are not provided as language constructs. | Algorithmic Skeletons | 0.827258 |
4,819 | The performance model can then be used to decide program transformations which can lead to performance optimizations.A P3L module corresponds to a properly defined skeleton construct with input and output streams, and other sub-modules or sequential C code. Modules can be nested using the two tier model, where the oute... | Algorithmic Skeletons | 0.827258 |
4,820 | Among Marrow's most distinguishable features are a set of skeletons previously unavailable in the GPU context, such as Pipeline and Loop, and the skeleton nesting ability – a feature also new in this context. Moreover, the framework introduces optimizations that overlap communication and computation, hence masking the ... | Algorithmic Skeletons | 0.827258 |
4,821 | Mallba is a library for combinatorial optimizations supporting exact, heuristic and hybrid search strategies. Each strategy is implemented in Mallba as a generic skeleton which can be used by providing the required code. On the exact search algorithms Mallba provides branch-and-bound and dynamic-optimization skeletons.... | Algorithmic Skeletons | 0.827258 |
4,822 | Precocious puberty can be classified into central (gonadotropin-dependent) precocious puberty or peripheral (gonadotropin-independent) puberty. Peripheral precocious puberty has been linked to exposure to exogenous estrogenic compounds. Age of onset of puberty is influenced by many factors such as genetics, nutritional... | Synthetic xenoestrogen | 0.82725 |
4,823 | In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian. It is the equivalent of the term symbol for the atomic ca... | Molecular term symbol | 0.827238 |
4,824 | In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the collection of all open set... | Boldface pointclass | 0.827227 |
4,825 | The National Center for Genome Resources (NCGR) is a not-for-profit research institute that innovates, collaborates, and educates in the field of genomic data science. == References == | National Center for Genome Resources | 0.827225 |
4,826 | {\displaystyle \mathbb {Z} _{2}.} If ( G , ∗ ) {\displaystyle (G,*)} is an infinite cyclic group, then ( G , ∗ ) {\displaystyle (G,*)} is isomorphic to the integers (with the addition operation). From an algebraic point of view, this means that the set of all integers (with the addition operation) is the "only" infinit... | Group isomorphism | 0.827224 |
4,827 | These large-scale adaptive immune receptor repertoire sequencing (AIRR-seq) data require specialized bioinformatics pipelines to be analyzed effectively. Many computational tools are being developed for this purpose, including: The MiXCR is one of the most widely cited platforms for the analysis of high-throughput T ce... | Immune repertoire | 0.827196 |
4,828 | An important example in the theory of Lie groups arises when G {\displaystyle G} is taken to be G L ( n ; C ) {\displaystyle \mathrm {GL} (n;\mathbb {C} )} , the group of invertible n × n {\displaystyle n\times n} matrices with complex entries. In that case, a basic result is the following: Theorem: Suppose φ: R → G L ... | One-parameter subgroup | 0.827196 |
4,829 | See Stone's theorem on one-parameter unitary groups. In his 1957 monograph Lie Groups, P. M. Cohn gives the following theorem on page 58: Any connected 1-dimensional Lie group is analytically isomorphic either to the additive group of real numbers R {\displaystyle {\mathfrak {R}}} , or to T {\displaystyle {\mathfrak {T... | One-parameter subgroup | 0.827196 |
4,830 | Such one-parameter groups are of basic importance in the theory of Lie groups, for which every element of the associated Lie algebra defines such a homomorphism, the exponential map. In the case of matrix groups it is given by the matrix exponential. Another important case is seen in functional analysis, with G {\displ... | One-parameter subgroup | 0.827196 |
4,831 | Using the parametrization of the hyperbola with hyperbolic angle, the theory of special relativity provided a calculus of relative motion with the one-parameter group indexed by rapidity. The rapidity replaces the velocity in kinematics and dynamics of relativity theory. Since rapidity is unbounded, the one-parameter g... | One-parameter subgroup | 0.827196 |
4,832 | In physics, one-parameter groups describe dynamical systems. Furthermore, whenever a system of physical laws admits a one-parameter group of differentiable symmetries, then there is a conserved quantity, by Noether's theorem. In the study of spacetime the use of the unit hyperbola to calibrate spatio-temporal measureme... | One-parameter subgroup | 0.827196 |
4,833 | At its core the CCL still is a mailing list, a quaint survivor from early Internet time, in which discussions take place about general principles, practical interpretations of theory, and computational methods. The membership of the list has evolved but continues to hold a mix of theoreticians, computationalists, and e... | Computational Chemistry List | 0.827192 |
4,834 | The Computational Chemistry List (CCL) was established on January 11, 1991, as an independent electronic forum for chemistry researchers and educators from around the world. According to the forum's web site, it is estimated that more than 3000 members in more than 50 countries are reading CCL messages regularly, and t... | Computational Chemistry List | 0.827192 |
4,835 | However, they have not “caught” enough to displace the CCL, in part because some of the most valued members of the CCL have not migrated to those platforms, either for professional purposes only, or at all. The most valuable resource that keeps the CCL together, in this view, is its own community.It is a general trend ... | Computational Chemistry List | 0.827192 |
4,836 | The list also hosts many resources on computational chemistry. For example, it hosted a pre-publication version of Computational Chemistry by David Young.Online social media not only comes to mind as an analogy for what the CCL achieves in its combination of mailing list, online forum, and portal, but also as a threat ... | Computational Chemistry List | 0.827192 |
4,837 | The CCL is a mailing list, portal, and community which brings together people interested in computational chemistry. It was formed in 1991 by initiative of Jan Labanowski, at the time a computational chemistry specialist in the Ohio Supercomputing Center, as a mailing list for the hundred persons who had participated i... | Computational Chemistry List | 0.827192 |
4,838 | The CCL as a tool for the community is thus not only a way to “educate and get educated” (in Labanowski's words), but also an arena where a vast diversity of topics can be debated.The “threaded conversation” structure (where the header of a first post defines the topic of a series of answers thus constituting a thread)... | Computational Chemistry List | 0.827192 |
4,839 | Leibniz gave another response to the paradox in §6 of Discourse on Metaphysics: "That God does nothing which is not orderly, and that it is not even possible to conceive of events which are not regular." Thus, even a miracle, the Event by excellence, does not break the regular order of things. What is seen as irregular... | Problem of future contingents | 0.82718 |
4,840 | For functional group manipulations, the distinction between LSF and functional-group-tolerant reactions is more subtle. For example, peptide bioconjugation reactions make use of the native functionality in amino acid side chains, and thus classify as LSF. In contrast, bioorthogonal 1,3-dipolar cycloadditions (see also ... | Late-stage functionalization | 0.82717 |
4,841 | Late-stage functionalization (LSF) is a desired, chemical or biochemical, chemoselective transformation on a complex molecule to provide at least one analog in sufficient quantity and purity for a given purpose without needing the addition of a functional group that exclusively serves to enable said transformation.Mole... | Late-stage functionalization | 0.82717 |
4,842 | The Critical Assessment of Genome Interpretation (CAGI) is an annual bioinformatics competition focused on interpretation of genome variation. == References == | Critical Assessment of Genome Interpretation | 0.827158 |
4,843 | A common compiler optimization is to recognize the existence of induction variables and replace them with simpler computations; for example, the code above could be rewritten by the compiler as follows, on the assumption that the addition of a constant will be cheaper than a multiplication. This optimization is a speci... | Induction variable | 0.827149 |
4,844 | 3D object recognition and reconstruction Biologically inspired object recognition Artificial neural networks and Deep Learning especially convolutional neural networks Context Explicit and implicit 3D object models Fast indexing Global scene representations Gradient histograms Stochastic grammars Intraclass transfer le... | Object Recognition | 0.827144 |
4,845 | The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A t... | Non-Euclidean Geometry | 0.827143 |
4,846 | Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast, there are infinitely many lines through A paral... | Non-Euclidean Geometry | 0.827143 |
4,847 | The start of integrated human biology started in the 1920's, caused by Charles Darwin's theories, such as evolution, were re-conceptualized by many scientists. Human attributes, such as child growth and genetics, were put into question and thus human biology was created. | Human biology | 0.827138 |
4,848 | The key aspects of human biology are those ways in which humans are substantially different from other mammals.Humans have a very large brain in a head that is very large for the size of the animal. This large brain has enabled a range of unique attributes including the development of complex languages and the ability ... | Human biology | 0.827138 |
4,849 | Human biology tries to understand and promotes research on humans as living beings as a scientific discipline. It makes use of various scientific methods, such as experiments and observations, to detail the biochemical and biophysical foundations of human life describe and formulate the underlying processes using model... | Human biology | 0.827138 |
4,850 | Human biology is an interdisciplinary area of academic study that examines humans through the influences and interplay of many diverse fields such as genetics, evolution, physiology, anatomy, epidemiology, anthropology, ecology, nutrition, population genetics, and sociocultural influences. It is closely related to the ... | Human biology | 0.827138 |
4,851 | Human biology also encompasses all those organisms that live on or in the human body. Such organisms range from parasitic insects such as fleas and ticks, parasitic helminths such as liver flukes through to bacterial and viral pathogens. Many of the organisms associated with human biology are the specialised biome in t... | Human biology | 0.827138 |
4,852 | The capabilities of the human brain and the human dexterity in making and using tools, has enabled humans to understand their own biology through scientific experiment, including dissection, autopsy, prophylactic medicine which has, in turn, enable humans to extend their life-span by understanding and mitigating the ef... | Human biology | 0.827138 |
4,853 | In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number ζ ( 3 ) = ∑ n = 1 ∞ 1 n 3 = lim n → ∞ ( 1 1 3 + 1 2 3 + ⋯ + 1 n 3 ) , {\displaystyle {\begin{aligned}\zeta (3)&=\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}\\&=\lim _{n\to \infty }\left({\frac {1}{1^{3}... | Apéry's constant | 0.827137 |
4,854 | Mathspace is an online mathematics program designed for students in primary/elementary, secondary, and higher education. It is designed for students aged between 7 and 18, and is used by schools in Australia, New Zealand, the United States, Canada, the United Kingdom, Hong Kong and India.Mathspace uses an adaptive lear... | Mathspace | 0.827124 |
4,855 | There are so many different ways a teacher can implement small group discussion in to the class, such as making a game out of it, a competition, or an assignment. Statistics show that small group discussions is more beneficial to students than large group discussions when it comes to participation, expressing thoughts,... | Active learning | 0.827119 |
4,856 | One study described in the report found that students in traditional lecture courses were twice as likely to leave engineering and three times as likely to drop out of college entirely compared with students taught using active learning techniques. In another cited study, students in a physics class that used active le... | Active learning | 0.827119 |
4,857 | Numerous studies have shown evidence to support active learning, given adequate prior instruction. A meta-analysis of 225 studies comparing traditional lecture to active learning in university math, science, and engineering courses found that active learning reduces failure rates from 32% to 21%, and increases student ... | Active learning | 0.827119 |
4,858 | The difference polynomial ring K { y } = K { y 1 , … , y n } {\displaystyle K\{y\}=K\{y_{1},\ldots ,y_{n}\}} over a difference field K {\displaystyle K} in the (difference) variables y 1 , … , y n {\displaystyle y_{1},\ldots ,y_{n}} is the polynomial ring over K {\displaystyle K} in the infinitely many variables σ i ( ... | Difference algebra | 0.827111 |
4,859 | In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter. It is in this essay that the term 'potential function' first occurs. Herein also his remarkable theorem in pure mathematics, since universally k... | An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism | 0.827111 |
4,860 | An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism is a fundamental publication by George Green in 1828, where he extends previous work of Siméon Denis Poisson on electricity and magnetism. The work in mathematical analysis, notably including what is now universally known ... | An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism | 0.827111 |
4,861 | We need only mention, as an example of the power of his method, the following: — Suppose that there is a hollow conducting shell, bounded by two closed surfaces, and that a number of electrified bodies are placed, some within and some without it; and let the inner surface and interior bodies be called the interior syst... | An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism | 0.827111 |
4,862 | Not only do they afford a natural and complete explanation of the beautiful quantitative experiments which has been so interesting at all times to practical electricians, but they suggest to the mathematician the simplest and most powerful methods of dealing with problems which, if attacked by the mere force of the old... | An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism | 0.827111 |
4,863 | Green's 1828 essay was neglected by mathematicians till 1846, and before that time most of its important theorems had been rediscovered by Gauss, Chasles, Sturm, and Thomson J. It did influence the work of Lord Kelvin and James Clerk Maxwell. The self-taught mathematician's essay was one of the greatest advances that w... | An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism | 0.827111 |
4,864 | Difference algebra is related to many other mathematical areas, such as discrete dynamical systems, combinatorics, number theory, or model theory. While some real life problems, such as population dynamics, can be modeled by algebraic difference equations, difference algebra also has applications in pure mathematics. F... | Difference algebra | 0.827111 |
4,865 | Difference algebra is a branch of mathematics concerned with the study of difference (or functional) equations from the algebraic point of view. Difference algebra is analogous to differential algebra but concerned with difference equations rather than differential equations. As an independent subject it was initiated ... | Difference algebra | 0.827111 |
4,866 | The role of difference rings in difference algebra is similar to the role of commutative rings in commutative algebra and algebraic geometry. A morphism of difference rings is a morphism of rings that commutes with σ {\displaystyle \sigma } . A difference algebra over a difference field K {\displaystyle K} is a differe... | Difference algebra | 0.827111 |
4,867 | There is a one-to-one correspondence between the difference varieties defined by algebraic difference equations in the variables y 1 , … , y n {\displaystyle y_{1},\ldots ,y_{n}} and certain ideals in K { y } {\displaystyle K\{y\}} , namely the perfect difference ideals of K { y } {\displaystyle K\{y\}} . One of the ba... | Difference algebra | 0.827111 |
4,868 | Intuitively, a difference variety over a difference field K {\displaystyle K} is the set of solutions of a system of algebraic difference equations over K {\displaystyle K} . This definition has to be made more precise by specifying where one is looking for the solutions. Usually one is looking for solutions in the so-... | Difference algebra | 0.827111 |
4,869 | In the field of bioinformatics and computational biology, many statistical methods have been proposed and used to analyze codon usage bias. Methods such as the 'frequency of optimal codons' (Fop), the relative codon adaptation (RCA) or the codon adaptation index (CAI) are used to predict gene expression levels, while m... | Codon optimization | 0.827106 |
4,870 | There is a way to compute the semi-direct product of groups using the topology of fibrations and properties of Eilenberg-Maclane spaces. Recall that for a semi-direct product of groups G = N ⋊ H {\displaystyle G=N\rtimes H} there is an associated short exact sequence of groups 1 → N → N ⋊ H → H → 1 {\displaystyle 1\to ... | Crossed homomorphism | 0.827093 |
4,871 | Given a topological group G, i.e., a group equipped with a topology such that product and inverse are continuous maps, it is natural to consider continuous G-modules, i.e., requiring that the action G × M → M {\displaystyle G\times M\to M} is a continuous map. For such modules, one can again consider the derived functo... | Crossed homomorphism | 0.827093 |
4,872 | Apply the covariant functor ⋅ ⊗ Z M {\displaystyle \cdot \otimes _{\mathbb {Z} }M} to F termwise to get a chain complex F ⊗ Z M {\displaystyle F\otimes _{\mathbb {Z} }M}: ⋯ → F n ⊗ Z M → F n − 1 ⊗ Z M → ⋯ → F 0 ⊗ Z M → Z ⊗ Z M . {\displaystyle \cdots \to F_{n}\otimes _{\mathbb {Z} }M\to F_{n-1}\otimes _{\mathbb {... | Crossed homomorphism | 0.827093 |
4,873 | Algebraic K-theory is closely related to group cohomology: in Quillen's +-construction of K-theory, K-theory of a ring R is defined as the homotopy groups of a space B G L ( R ) + . {\displaystyle \mathrm {BGL} (R)^{+}.} Here G L ( R ) = ∪ n ≥ 1 G L n ( R ) {\displaystyle \mathrm {GL} (R)=\cup _{n\geq 1}\mathrm {GL} _{... | Crossed homomorphism | 0.827093 |
4,874 | We might expect U ( g 1 ) U ( g 2 ) = U ( g 1 g 2 ) , {\displaystyle U(g_{1})U(g_{2})=U(g_{1}g_{2}),} but the rules of quantum mechanics only require U ( g 1 ) U ( g 2 ) = exp { 2 π i ω ( g 1 , g 2 ) } U ( g 1 g 2 ) , {\displaystyle U(g_{1})U(g_{2})=\exp\{2\pi i\omega (g_{1},g_{2})\}U(g_{1}g_{2}),} where exp { 2 π ... | Crossed homomorphism | 0.827093 |
4,875 | In quantum mechanics we often have systems with a symmetry group G . {\displaystyle G.} We expect an action of G {\displaystyle G} on the Hilbert space H {\displaystyle {\mathcal {H}}} by unitary matrices U ( g ) . {\displaystyle U(g).} | Crossed homomorphism | 0.827093 |
4,876 | If, M = k is a field, then H*(G; k) is a graded k-algebra and the cohomology of a product of groups is related to the ones of the individual groups by a Künneth formula: H ∗ ( G 1 × G 2 ; k ) ≅ H ∗ ( G 1 ; k ) ⊗ H ∗ ( G 2 ; k ) . {\displaystyle H^{*}(G_{1}\times G_{2};k)\cong H^{*}(G_{1};k)\otimes H^{*}(G_{2};k).} For ... | Crossed homomorphism | 0.827093 |
4,877 | The Annals of Probability is a leading peer-reviewed probability journal published by the Institute of Mathematical Statistics, which is the main international society for researchers in the areas probability and statistics. The journal was started in 1973 as a continuation in part of the Annals of Mathematical Statist... | Annals of Probability | 0.827088 |
4,878 | Sulfuric acid is known to be abundant in the clouds of Venus, in the form of aerosol droplets. In a biochemistry that used sulfuric acid as a solvent, the alkene group (C=C), with two carbon atoms joined by a double bond, could function analogously to the carbonyl group (C=O) in water-based biochemistry.A proposal has ... | Ammonia-based life | 0.827087 |
4,879 | Membrane biophysics is the study of biological membrane structure and function using physical, computational, mathematical, and biophysical methods. A combination of these methods can be used to create phase diagrams of different types of membranes, which yields information on thermodynamic behavior of a membrane and i... | Membrane biology | 0.827087 |
4,880 | Membrane biology is the study of the biological and physiochemical characteristics of membranes, with applications in the study of cellular physiology.Membrane bioelectrical impulses are described by the Hodgkin cycle. | Membrane biology | 0.827087 |
4,881 | In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models... | Nearest neighbour function | 0.827086 |
4,882 | The fact that the spherical distribution function Hs(r) and nearest neighbor function Do(r) are identical for the Poisson point process can be used to statistically test if point process data appears to be that of a Poisson point process. For example, in spatial statistics the J-function is defined for all r ≥ 0 as: J ... | Nearest neighbour function | 0.827086 |
4,883 | In general, the spherical contact distribution function and the corresponding nearest neighbor function are not equal. However, these two functions are identical for Poisson point processes. In fact, this characteristic is due to a unique property of Poisson processes and their Palm distributions, which forms part of t... | Nearest neighbour function | 0.827086 |
4,884 | Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been observed in the Mi... | Special Relativity | 0.827082 |
4,885 | But general relativity incorporates non-Euclidean geometry to represent gravitational effects as the geometric curvature of spacetime. Special relativity is restricted to the flat spacetime known as Minkowski space. As long as the universe can be modeled as a pseudo-Riemannian manifold, a Lorentz-invariant frame that a... | Special Relativity | 0.827082 |
4,886 | Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = m c 2 {\displaystyle E=mc^{2}} , where c {\displaystyle c} is the speed of light in vacuum. It also explains how the phenomena of electricity ... | Special Relativity | 0.827082 |
4,887 | In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 treatment, the theory is presented as being based on just two postulates: The laws of physics are invariant (identical) in all inertial frames of re... | Special Relativity | 0.827082 |
4,888 | In words, Gauss's law states: The net electric flux through any hypothetical closed surface is equal to 1/ε0 times the net electric charge enclosed within that closed surface. The closed surface is also referred to as Gaussian surface.Gauss's law has a close mathematical similarity with a number of laws in other areas ... | Gauss' law for electricity | 0.827069 |
4,889 | In mathematics, 2E6 is the name of a family of Steinberg or twisted Chevalley groups. It is a quasi-split form of E6, depending on a quadratic extension of fields K⊂L. Unfortunately the notation for the group is not standardized, as some authors write it as 2E6(K) (thinking of 2E6 as an algebraic group taking values in... | 2E6 (mathematics) | 0.827068 |
4,890 | 10x Genomics, Inc. is an American biotechnology company that designs and manufactures gene sequencing technology used in scientific research. It was founded in 2012 by Serge Saxonov, Ben Hindson, and Kevin Ness. | 10x Genomics | 0.827061 |
4,891 | Four months later, 10x Genomics acquired Spatial Transcriptomics, a biotechnology company working in the field of spatial genomics. In November 2018, 10x Genomics announced expansion plans including opening a manufacturing facility in Pleasanton, California in early 2019.10x Genomics announced its initial public offeri... | 10x Genomics | 0.827061 |
4,892 | 10x Genomics was founded in 2012 by Serge Saxonov, Ben Hindson and Kevin Ness to create advanced testing equipment for use in cellular biology. Prior to starting the company, Saxonov was the founding architect, and director of research and development at 23andMe. Ness left 10x Genomics in December 2016 and in 2018, Jus... | 10x Genomics | 0.827061 |
4,893 | If G {\displaystyle G} is a reductive algebraic group over an algebraically closed field K {\displaystyle K} with a split maximal torus T {\displaystyle T} then its root datum is a quadruple ( X ∗ , Φ , X ∗ , Φ ∨ ) {\displaystyle (X^{*},\Phi ,X_{*},\Phi ^{\vee })} ,where X ∗ {\displaystyle X^{*}} is the lattice of char... | Root data | 0.827059 |
4,894 | In mathematical group theory, the root datum of a connected split reductive algebraic group over a field is a generalization of a root system that determines the group up to isomorphism. They were introduced by Michel Demazure in SGA III, published in 1970. | Root data | 0.827059 |
4,895 | When choosing primary standards in analytical chemistry, compounds with higher equivalent weights are generally more desirable because weighing errors are reduced. An example is the volumetric standardisation of a solution of sodium hydroxide which has been prepared to approximately 0.1 mol dm−3. It is necessary to cal... | Equivalent mass | 0.827058 |
4,896 | In polymer chemistry, the equivalent weight of a reactive polymer is the mass of polymer which has one equivalent of reactivity (often, the mass of polymer which corresponds to one mole of reactive side-chain groups). It is widely used to indicate the reactivity of polyol, isocyanate, or epoxy thermoset resins which wo... | Equivalent mass | 0.827058 |
4,897 | In chemistry, equivalent weight (also known as gram equivalent or equivalent mass) is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is the mass which combines with or displaces 1.008 gram o... | Equivalent mass | 0.827058 |
4,898 | The use of equivalent weights in general chemistry has largely been superseded by the use of molar masses. Equivalent weights may be calculated from molar masses if the chemistry of the substance is well known: sulfuric acid has a molar mass of 98.078(5) g mol−1, and supplies two moles of hydrogen ions per mole of sulf... | Equivalent mass | 0.827058 |
4,899 | Short proteins can also be synthesized chemically by a family of methods known as peptide synthesis, which rely on organic synthesis techniques such as chemical ligation to produce peptides in high yield. Chemical synthesis allows for the introduction of non-natural amino acids into polypeptide chains, such as attachme... | Cellular protein | 0.827056 |
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