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25,400 | The first mention of "aerobiology" was made by Fred Campbell Meier in the 1930s. The particles, which can be described as Aeroplankton, generally range in size from nanometers to micrometers which makes them challenging to detect.Aerosolization is the process of a small and light particles becoming suspended in moving ... | Aerobiology | 0.807645 |
25,401 | Deposition is a combination of gravity and inertia. The fall speed for small particles can be calculated by mass and geometry, but the complex shapes of pollen and spores often fall slower than their estimated speed modeled with simple shapes. Spores can also be removed from the air from impact; the inertia of the part... | Aerobiology | 0.807645 |
25,402 | Aerobiology (from Greek ἀήρ, aēr, "air"; βίος, bios, "life"; and -λογία, -logia) is a branch of biology that studies the passive transport of organic particles, such as bacteria, fungal spores, very small insects, pollen grains and viruses. Aerobiologists have traditionally been involved in the measurement and reportin... | Aerobiology | 0.807645 |
25,403 | This implies that if the wheel were not allowed to turn and had to move only in a straight line at all times, it would be a holonomic system.There is one thing that we have not yet considered however, that to find all such modifications for a system, one must perform all eight test equations (four from each constraint ... | Nonholonomic system | 0.807644 |
25,404 | A nonholonomic system in physics and mathematics is a physical system whose state depends on the path taken in order to achieve it. Such a system is described by a set of parameters subject to differential constraints and non-linear constraints, such that when the system evolves along a path in its parameter space (the... | Nonholonomic system | 0.807644 |
25,405 | A substitute for a derivative of f:Rn → X is the metric differential of f at a point z in Rn which is a function on Rn defined by the limit M D ( f , z ) ( x ) = lim r → 0 d X ( f ( z + r x ) , f ( z ) ) r {\displaystyle MD(f,z)(x)=\lim _{r\rightarrow 0}{\frac {d_{X}(f(z+rx),f(z))}{r}}} whenever the limit exists (here ... | Metric differential | 0.807642 |
25,406 | Rademacher's theorem states that a Lipschitz map f: Rn → Rm is differentiable almost everywhere in Rn; in other words, for almost every x, f is approximately linear in any sufficiently small range of x. If f is a function from a Euclidean space Rn that takes values instead in a metric space X, it doesn't immediately ma... | Metric differential | 0.807642 |
25,407 | In mathematical analysis, a metric differential is a generalization of a derivative for a Lipschitz continuous function defined on a Euclidean space and taking values in an arbitrary metric space. With this definition of a derivative, one can generalize Rademacher's theorem to metric space-valued Lipschitz functions. | Metric differential | 0.807642 |
25,408 | Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings, modules, topological spaces, and other 'tangible' mathematical objects. A powerful tool for doing this is provided by spectral sequences. It has played an enormous rol... | Acyclic complex | 0.807642 |
25,409 | Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the ... | Acyclic complex | 0.807642 |
25,410 | A similar definition can be made for certain other algebraic structures. For example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms. More generally, the notion of an exact sequence makes sense in any category with kernels and cokernels. | Acyclic complex | 0.807641 |
25,411 | An associative quasigroup is either empty or is a group, since if there is at least one element, the invertibility of the quasigroup binary operation combined with associativity implies the existence of an identity element, which then implies the existence of inverse elements, thus satisfying all three requirements of ... | Quasigroup | 0.807641 |
25,412 | In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. A quasigroup with an identity element is called a loop. | Quasigroup | 0.807641 |
25,413 | The conception of human reaction to an external stimulus being mediated by a biological interface (such as a nerve) is nearly as old as the philosophical discipline of science itself. Enlightenment thinkers like René Descartes proposed that the reflexive response to pain, for example, is carried by some sort of fiber—w... | Mental chronometry | 0.807637 |
25,414 | Mental chronometry is the scientific study of processing speed or reaction time on cognitive tasks to infer the content, duration, and temporal sequencing of mental operations. Reaction time (RT; sometimes incorrectly referred to as "response time") is measured by the elapsed time between stimulus onset and an individu... | Mental chronometry | 0.807637 |
25,415 | In the mathematical classification of finite simple groups, the component theorem of Aschbacher (1975, 1976) shows that if G is a simple group of odd type, and various other assumptions are satisfied, then G has a centralizer of an involution with a "standard component" with small centralizer. | Component theorem | 0.807635 |
25,416 | It follows that F ∘ h−1 is a smooth diffeomorphism of the annulus s ≤ |z| ≤ 1 onto the closure of Ω, holomorphic in the interior.Multiply connected domains. For regions with a higher degree of connectivity k + 1, the result is essentially Bers' generalization of the retrosection theorem. There is a smooth diffeomorphis... | Beltrami differential equation | 0.807634 |
25,417 | The method used to prove the smooth Riemann mapping theorem can be generalized to multiply connected planar regions with smooth boundary. The Beltrami coefficient in these cases is smooth on an open set, the complement of which has measure zero. The theory of the Beltrami equation with measurable coefficients is theref... | Beltrami differential equation | 0.807634 |
25,418 | The same method applies equally well on the unit disk and upper half plane and plays a fundamental role in Teichmüller theory and the theory of quasiconformal mappings. Various uniformization theorems can be proved using the equation, including the measurable Riemann mapping theorem and the simultaneous uniformization ... | Beltrami differential equation | 0.807634 |
25,419 | They are therefore equicontinuous on any compact subset of C; they are even holomorphic for |z| > R. So by the Arzelà–Ascoli theorem, passing to a subsequence if necessary, it can be assumed that both fn and gn converge uniformly on compacta to f and g. The limits will satisfy the same Hölder estimates and be holomorph... | Beltrami differential equation | 0.807634 |
25,420 | Furthermore, overhead associated with virtual machine interpretation meant that the efficiency of Lean was not competitive with other proof assistants such as Coq. In 2021, Leonardo de Moura and Sebastian Ullrich released Lean 4: a reimplementation of the Lean theorem prover within itself, with the aim of addressing th... | Lean theorem prover | 0.807634 |
25,421 | Started in 2017, the user-maintained library mathlib contains the largest collection of mathematics that has been formalized in Lean. As of February 2023, mathlib contains over 100,000 theorems and 1,000,000 lines of code.In prior releases of Lean, several core parts of the system's logic were not amenable to being mod... | Lean theorem prover | 0.807634 |
25,422 | It was launched by Leonardo de Moura at Microsoft Research in 2013.Lean has an interface, implemented as a Visual Studio Code extension and Language Server Protocol server, that differentiates it from other interactive theorem provers. It has native support for Unicode symbols, which can be typed using LaTeX-like seque... | Lean theorem prover | 0.807634 |
25,423 | Lean 4 is not backwards-compatible with Lean 3.Lean has gotten attention from mathematicians Thomas Hales and Kevin Buzzard. Hales is using it for his project, Formal Abstracts. Buzzard uses it for the Xena project. One of the Xena Project's goals is to rewrite every theorem and proof in the undergraduate math curricul... | Lean theorem prover | 0.807634 |
25,424 | Lean is a theorem prover and programming language. It is based on the calculus of constructions with inductive types. The Lean project is an open-source project hosted on GitHub. | Lean theorem prover | 0.807634 |
25,425 | Westgard rules are used to define specific performance limits for a particular assay (test) and can be used to detect both random and systematic errors. Westgard rules are programmed into automated analyzers to determine when an analytical run should be rejected. These rules need to be applied carefully so that true er... | Analytical specificity | 0.807632 |
25,426 | In the mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has three hexagonal faces (including the one shown as the external face of the illustration) and twelve pentagonal faces. As a planar graph with only pentagonal and hexagon... | 26-fullerene graph | 0.807631 |
25,427 | One must remove at least five edges from the graph in order to obtain a subgraph that has exactly one perfect matching. This is a unique property of this graph among fullerenes in the sense that, for every other number of vertices of a fullerene, there exists at least one fullerene from which one can remove four edges ... | 26-fullerene graph | 0.807631 |
25,428 | A nested (or hierarchical) metalanguage is similar to an ordered metalanguage in that each level represents a greater degree of abstraction. However, a nested metalanguage differs from an ordered one in that each level includes the one below. The paradigmatic example of a nested metalanguage comes from the Linnean taxo... | Meta language | 0.807629 |
25,429 | An embedded metalanguage is a language formally, naturally and firmly fixed in an object language. This idea is found in Douglas Hofstadter's book, Gödel, Escher, Bach, in a discussion of the relationship between formal languages and number theory: "... it is in the nature of any formalization of number theory that its... | Meta language | 0.807629 |
25,430 | In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive). Although commonly thoug... | Interaction effect | 0.807626 |
25,431 | Continuity and synechism are central in Peirce's philosophy: "I did not at first suppose that it was, as I gradually came to find it, the master-Key of philosophy".From a mathematical point of view, he embraced infinitesimals and worked long on the mathematics of continua. He long held that the real numbers constitute ... | Logic of relatives | 0.807625 |
25,432 | By the later 1890s he was devising existential graphs, a diagrammatic notation for the predicate calculus. Based on them are John F. Sowa's conceptual graphs and Sun-Joo Shin's diagrammatic reasoning. The New Elements of MathematicsPeirce wrote drafts for an introductory textbook, with the working title The New Element... | Logic of relatives | 0.807625 |
25,433 | In 1880–1881 he showed how Boolean algebra could be done via a repeated sufficient single binary operation (logical NOR), anticipating Henry M. Sheffer by 33 years. (See also De Morgan's Laws.) In 1881 he set out the axiomatization of natural number arithmetic, a few years before Richard Dedekind and Giuseppe Peano. | Logic of relatives | 0.807625 |
25,434 | Peirce's most important work in pure mathematics was in logical and foundational areas. He also worked on linear algebra, matrices, various geometries, topology and Listing numbers, Bell numbers, graphs, the four-color problem, and the nature of continuity. He worked on applied mathematics in economics, engineering, an... | Logic of relatives | 0.807625 |
25,435 | Peirce went on to earn a Bachelor of Arts degree and a Master of Arts degree (1862) from Harvard. In 1863 the Lawrence Scientific School awarded him a Bachelor of Science degree, Harvard's first summa cum laude chemistry degree. His academic record was otherwise undistinguished. | Logic of relatives | 0.807625 |
25,436 | Peirce was born at 3 Phillips Place in Cambridge, Massachusetts. He was the son of Sarah Hunt Mills and Benjamin Peirce, himself a professor of mathematics and astronomy at Harvard University. At age 12, Charles read his older brother's copy of Richard Whately's Elements of Logic, then the leading English-language text... | Logic of relatives | 0.807625 |
25,437 | He formulated modern statistics in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). With a repeated measures design, Charles Sanders Peirce and Joseph Jastrow introduced blinded, controlled randomized experiments in 1884 (Hacking 1990:205) (before Ronald A. Fisher). He in... | Logic of relatives | 0.807625 |
25,438 | Peirce held that science achieves statistical probabilities, not certainties, and that spontaneity (absolute chance) is real (see Tychism on his view). Most of his statistical writings promote the frequency interpretation of probability (objective ratios of cases), and many of his writings express skepticism about (and... | Logic of relatives | 0.807625 |
25,439 | His writings bear on a wide array of disciplines, including mathematics, logic, philosophy, statistics, astronomy, metrology, geodesy, experimental psychology, economics, linguistics, and the history and philosophy of science. This work has enjoyed renewed interest and approval, a revival inspired not only by his antic... | Logic of relatives | 0.807625 |
25,440 | Peirce in many writings holds that logic precedes metaphysics (ontological, religious, and physical). Peirce goes on to list four common barriers to inquiry: (1) Assertion of absolute certainty; (2) maintaining that something is absolutely unknowable; (3) maintaining that something is absolutely inexplicable because ab... | Logic of relatives | 0.807624 |
25,441 | He was one of the founders of statistics. As early as 1886, he saw that logical operations could be carried out by electrical switching circuits. The same idea was used decades later to produce digital computers.For metaphysics, Peirce was an "objective idealist" in the tradition of German philosopher Immanuel Kant as ... | Logic of relatives | 0.807624 |
25,442 | In mathematics, it influenced the abstract analysis of E. H. Moore and the lattice theory of Garrett Birkhoff. In computer science, the relational model for databases was developed with Peircean ideas in work of Edgar F. Codd, who was a doctoral student of Arthur W. Burks, a Peirce scholar. In economics, relational log... | Logic of relatives | 0.807624 |
25,443 | Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations pioneered by Augustus De Morgan. Beginning in 1940, Alfred Tarski and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of relation algebra. Relational log... | Logic of relatives | 0.807624 |
25,444 | In his work, fallibilism and pragmatism may seem to work somewhat like skepticism and positivism, respectively, in others' work. However, for Peirce, fallibilism is balanced by an anti-skepticism and is a basis for belief in the reality of absolute chance and of continuity, and pragmatism commits one to anti-nominalist... | Logic of relatives | 0.807624 |
25,445 | "Phenotypic correlations between psychological traits show significant and substantial genetic mediation." "The heritability of intelligence increases throughout development." "Age-to-age stability is mainly due to genetics." | Behavior Genetics | 0.807623 |
25,446 | In response to general concerns about the replicability of psychological research, behavioural geneticists Robert Plomin, John C. DeFries, Valerie Knopik, and Jenae Neiderhiser published a review of the ten most well-replicated findings from behavioural genetics research. The ten findings were: "All psychological trait... | Behavior Genetics | 0.807623 |
25,447 | In ensuring the continued safe operation of the damage tolerant structure, inspection schedules are devised. This schedule is based on many criteria, including: assumed initial damaged condition of the structure stresses in the structure (both fatigue and operational maximum stresses) that cause crack growth from the d... | Damage tolerance | 0.807623 |
25,448 | In engineering, damage tolerance is a property of a structure relating to its ability to sustain defects safely until repair can be effected. The approach to engineering design to account for damage tolerance is based on the assumption that flaws can exist in any structure and such flaws propagate with usage. This appr... | Damage tolerance | 0.807623 |
25,449 | Manufacturers and operators of aircraft, trains, and civil engineering structures like bridges have a financial interest in ensuring that the inspection schedule is as cost-efficient as possible. In the example of aircraft, because these structures are often revenue producing, there is an opportunity cost associated wi... | Damage tolerance | 0.807623 |
25,450 | Let X be a set and let R be a ring. Since addition and multiplication are defined in R, we can construct an algebraic structure known as an algebra out of the functions from X to R by defining addition, multiplication, and scalar multiplication of functions to be done pointwise. If RX denotes the set of functions from ... | Pointwise product | 0.807622 |
25,451 | In a presentation at the "CERN Workshop on Innovations in Scholarly Communications (OAI4)", Murray-Rust said that chemistry actually leads other fields in published data. He estimated that the majority of the data in some scientific fields never reaches publication.Although scientific in nature, the WWMM was part of th... | WorldWide Molecular Matrix | 0.80762 |
25,452 | The WWMM was proposed as a solution to this problem. It would house the results of experiments on over 100,000 molecules in physical chemistry, organic chemistry, biochemistry and medicinal chemistry. In other scientific fields, the need for a similar depository to house inaccessible information could be more acute. | WorldWide Molecular Matrix | 0.80762 |
25,453 | The World Wide Molecular Matrix (WWMM) was a proposed electronic repository for unpublished chemical data. First introduced in 2002 by Peter Murray-Rust and his colleagues in the chemistry department at the University of Cambridge in the United Kingdom, WWMM provided a free, easily searchable database for information a... | WorldWide Molecular Matrix | 0.80762 |
25,454 | Ergodic dynamical systems, that is, systems exhibiting randomness, exhibit flows as well. The most celebrated of these is perhaps the Bernoulli flow. The Ornstein isomorphism theorem states that, for any given entropy H, there exists a flow φ(x, t), called the Bernoulli flow, such that the flow at time t = 1, i.e. φ(x,... | Flow (geometry) | 0.807619 |
25,455 | It is very common in many fields, including engineering, physics and the study of differential equations, to use a notation that makes the flow implicit. Thus, x(t) is written for φ t ( x 0 ) , {\displaystyle \varphi ^{t}(x_{0}),} and one might say that the variable x depends on the time t and the initial condition x =... | Flow (geometry) | 0.807619 |
25,456 | Reports on Mathematical Physics (ISSN 0034-4877) is a peer-reviewed scientific journal, started in 1970, which publishes papers in theoretical physics that present a rigorous mathematical approach to problems of quantum and classical mechanics, field theories, relativity and gravitation, statistical physics, and the ma... | Reports on Mathematical Physics | 0.807617 |
25,457 | However, excluded are examples like two touching circles that share a point to form a figure-8; at the shared point, a satisfactory chart cannot be created. Even with the bending allowed by topology, the vicinity of the shared point looks like a "+", not a line. A "+" is not homeomorphic to a line segment, since deleti... | Manifold with corners | 0.807616 |
25,458 | Just as there are various types of manifolds, there are various types of maps of manifolds. In addition to continuous functions and smooth functions generally, there are maps with special properties. In geometric topology a basic type are embeddings, of which knot theory is a central example, and generalizations such a... | Manifold with corners | 0.807616 |
25,459 | Frozen tissue cores with 2 mm diameter from the regions of interest are removed from frozen tissue OCT blocks at different freezing temperature since each tissue type has their own temperature preference at frozen stage. Then all the frozen tissue cores are inserted in a recipient OCT frozen block in a precisely spaced... | Frozen tissue array | 0.807613 |
25,460 | Paraffin tissue array was developed during late years in the 1980s; this array can help scientists high throughput analyze gene and protein expressions in multiple tissue samples, especially analyze different protein levels with antibodies by immunohistochemistry. Various paraffin tissue arrays are now commercially ava... | Frozen tissue array | 0.807613 |
25,461 | Neoichnology (Greek néos „new“, íchnos „footprint“, logos „science“) is the science of footprints and traces of extant animals. Thus, it is a counterpart to paleoichnology, which investigates tracks and traces of fossil animals. Neoichnological methods are used in order to study the locomotion and the resulting tracks ... | Neoichnology | 0.807613 |
25,462 | In the field of genomics (and more generally in bioinformatics), the modern usage is to define fold change in terms of ratios, and not by the alternative definition.However, log-ratios are often used for analysis and visualization of fold changes. The logarithm to base 2 is most commonly used, as it is easy to interpre... | Fold change | 0.80761 |
25,463 | A fraction in chemistry is a quantity collected from a batch of a substance in a fractionating separation process. In such a process, a mixture is separated into fractions, which have compositions that vary according to a gradient. A fraction can be defined as a group of chemicals that have similar boiling points. A co... | Fraction (chemistry) | 0.80761 |
25,464 | First as with complex numbers products of bivectors and so the even subalgebra are commutative. This is only true in two dimensions, so properties of the bivector in two dimensions that depend on commutativity do not usually generalise to higher dimensions. | Oriented plane segment | 0.807609 |
25,465 | This multiplies by all vectors to generate the elements of even subalgebra. All the properties of complex numbers can be derived from bivectors, but two are of particular interest. | Oriented plane segment | 0.807609 |
25,466 | With the properties of negative square and unit magnitude, the unit bivector can be identified with the imaginary unit from complex numbers. The bivectors and scalars together form the even subalgebra of the geometric algebra, which is isomorphic to the complex numbers C. The even subalgebra has basis (1, e12), the who... | Oriented plane segment | 0.807609 |
25,467 | The operation "∨" is the meet, which can be defined as above in terms of the join, J = A ∧ B for non-zero A ∧ B. Using these operations projective geometry can be formulated in terms of geometric algebra. For example, given a third (non-zero) bivector C the point p lies on the line given by C if and only if p ∧ C = 0. ... | Oriented plane segment | 0.807609 |
25,468 | Non-zero simple bivectors in ⋀2Rn represent lines in RPn−1, with bivectors differing only by a (positive or negative) scale factor representing the same line. A description of the projective geometry can be constructed in the geometric algebra using basic operations. | Oriented plane segment | 0.807609 |
25,469 | Geometric algebra can be applied to projective geometry in a straightforward way. The geometric algebra used is Cln(R), n ≥ 3, the algebra of the real vector space Rn. This is used to describe objects in the real projective space RPn−1. The non-zero vectors in Cln(R) or Rn are associated with points in the projective s... | Oriented plane segment | 0.807609 |
25,470 | It can also be used to represent physical quantities, like torque and angular momentum. In vector algebra they are usually represented by vectors, perpendicular to the plane of the force, linear momentum or displacement that they are calculated from. But if a bivector is used instead the plane is the plane of the bivec... | Oriented plane segment | 0.807609 |
25,471 | As suggested by their name and that of the algebra, one of the attractions of bivectors is that they have a natural geometric interpretation. This can be described in any dimension but is best done in three where parallels can be drawn with more familiar objects, before being applied to higher dimensions. In two dimens... | Oriented plane segment | 0.807609 |
25,472 | As noted in the previous section the magnitude of a simple bivector, that is one that is the exterior product of two vectors a and b, is |a| |b| sin θ, where θ is the angle between the vectors. It is written |B|, where B is the bivector. For general bivectors the magnitude can be calculated by taking the norm of the bi... | Oriented plane segment | 0.807609 |
25,473 | While bivectors are isomorphic to vectors (via the dual) in three dimensions they can be represented by skew-symmetric matrices in any dimension. This is useful for relating bivectors to problems described by matrices, so they can be re-cast in terms of bivectors, given a geometric interpretation, then often solved mor... | Oriented plane segment | 0.807609 |
25,474 | As has been suggested in earlier sections much of geometric algebra generalises well into higher dimensions. The geometric algebra for the real space Rn is Cln(R), and the subspace of bivectors is ⋀2Rn. The number of simple bivectors needed to form a general bivector rises with the dimension, so for n odd it is (n − 1)... | Oriented plane segment | 0.807609 |
25,475 | The bivector Ωθ generates a rotation through the exponential map. The even elements generated rotate a general vector in three dimensions in the same way as quaternions: As in two dimensions, the quantity e-Ωθ/2 is called a rotor and written R. The quantity eΩθ/2 is then R−1, and they generate rotations as This is iden... | Oriented plane segment | 0.807609 |
25,476 | Gibbs used vectors to fill the role of bivectors in three dimensions, and used bivector in Hamilton's sense, a use that has sometimes been copied. Today the bivector is largely studied as a topic in geometric algebra, a Clifford algebra over real or complex vector spaces with a quadratic form. Its resurgence was led by... | Oriented plane segment | 0.807609 |
25,477 | Henry Forder used the term bivector to develop exterior algebra in 1941.In the 1890s Josiah Willard Gibbs and Oliver Heaviside developed vector calculus, which included separate cross product and dot products that were derived from quaternion multiplication. The success of vector calculus, and of the book Vector Analys... | Oriented plane segment | 0.807609 |
25,478 | The bivector was first defined in 1844 by German mathematician Hermann Grassmann in exterior algebra as the result of the exterior product of two vectors. Just the previous year, in Ireland, William Rowan Hamilton had discovered quaternions. Hamilton coined both vector and bivector, the latter in his Lectures on Quater... | Oriented plane segment | 0.807609 |
25,479 | The rotation vector is an example of an axial vector. Axial vectors, or pseudovectors, are vectors with the special feature that their coordinates undergo a sign change relative to the usual vectors (also called "polar vectors") under inversion through the origin, reflection in a plane, or other orientation-reversing l... | Oriented plane segment | 0.807609 |
25,480 | Introgression, also known as introgressive hybridization, in genetics is the transfer of genetic material from one species into the gene pool of another by the repeated backcrossing of an interspecific hybrid with one of its parent species. Introgression is a long-term process, even when artificial; it may take many hy... | Introgression line | 0.807606 |
25,481 | The Needleman–Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences. It was one of the first applications of dynamic programming to compare biological sequences. The algorithm was developed by Saul B. Needleman and Christian D. Wunsch and published in 1970. The algorithm essen... | Needleman-Wunsch algorithm | 0.807599 |
25,482 | The AI Memos are a series of influential memorandums and technical reports published by the MIT AI Lab, Massachusetts Institute of Technology, United States. They cover Artificial Intelligence, a field of computer science. Noteworthy memos in the series include: AI Memo 39, "The New Compiler", describing the first impl... | AI Memo | 0.807595 |
25,483 | Other ways of modelling concurrent computation have been proposed, including vector addition systems, communicating finite-state machines, Kahn process networks, process algebra, the actor model, and trace theory. Different models provide tradeoffs of concepts such as compositionality, modularity, and locality. An appr... | Petri Net | 0.807594 |
25,484 | Radiation hazards may also come from man-made sources, for example, medical investigations, radio-isotopic power generators or from small experiments as on Earth. Lunar and Martian missions may include either nuclear reactors for power or related nuclear propulsion systems. Astronautical hygienists will need to assess ... | Astronautical hygiene | 0.807593 |
25,485 | Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph G, and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly ... | Maximum-cardinality matching | 0.807588 |
25,486 | Such bottom-up approaches should be capable of producing devices in parallel and be much cheaper than top-down methods, but could potentially be overwhelmed as the size and complexity of the desired assembly increases. Most useful structures require complex and thermodynamically unlikely arrangements of atoms. Neverthe... | Nanoscale machines | 0.807587 |
25,487 | Nitrogen-15 (15N) tracing is a technique to study the nitrogen cycle using the heavier, stable nitrogen isotope 15N. Despite the different weights, 15N is involved in the same chemical reactions as the more abundant 14N and is therefore used to trace and quantify conversions of one nitrogen compound to another. 15N tra... | Nitrogen-15 tracing | 0.807587 |
25,488 | Mihail Roco, one of the architects of the USA's National Nanotechnology Initiative, has proposed four states of nanotechnology that seem to parallel the technical progress of the Industrial Revolution, progressing from passive nanostructures to active nanodevices to complex nanomachines and ultimately to productive nan... | Nanoscale machines | 0.807587 |
25,489 | This is more theoretical than the other subfields, and many of its proposed techniques are beyond current capabilities. Nanorobotics centers on self-sufficient machines of some functionality operating at the nanoscale. There are hopes for applying nanorobots in medicine. | Nanoscale machines | 0.807587 |
25,490 | These subfields seek to anticipate what inventions nanotechnology might yield, or attempt to propose an agenda along which inquiry might progress. These often take a big-picture view of nanotechnology, with more emphasis on its societal implications than the details of how such inventions could actually be created. Mol... | Nanoscale machines | 0.807587 |
25,491 | This led to an exchange of letters in the ACS publication Chemical & Engineering News in 2003. Though biology clearly demonstrates that molecular machine systems are possible, non-biological molecular machines are today only in their infancy. | Nanoscale machines | 0.807587 |
25,492 | The physics and engineering performance of exemplar designs were analyzed in Drexler's book Nanosystems: Molecular Machinery, Manufacturing, and Computation.In general it is very difficult to assemble devices on the atomic scale, as one has to position atoms on other atoms of comparable size and stickiness. Another vie... | Nanoscale machines | 0.807587 |
25,493 | The premise was that molecular-scale biological analogies of traditional machine components demonstrated molecular machines were possible: by the countless examples found in biology, it is known that sophisticated, stochastically optimized biological machines can be produced. It is hoped that developments in nanotechno... | Nanoscale machines | 0.807587 |
25,494 | Molecular nanotechnology, sometimes called molecular manufacturing, describes engineered nanosystems (nanoscale machines) operating on the molecular scale. Molecular nanotechnology is especially associated with the molecular assembler, a machine that can produce a desired structure or device atom-by-atom using the prin... | Nanoscale machines | 0.807587 |
25,495 | Modern synthetic chemistry has reached the point where it is possible to prepare small molecules to almost any structure. These methods are used today to manufacture a wide variety of useful chemicals such as pharmaceuticals or commercial polymers. This ability raises the question of extending this kind of control to t... | Nanoscale machines | 0.807587 |
25,496 | {\displaystyle e^{-\tanh ^{-1}(\beta ){\frac {\boldsymbol {\beta }}{\beta }}\cdot \mathbf {K} }=e^{-{\tanh ^{-1}\beta \over c\beta }\mathbf {u} \cdot \mathbf {K} }\equiv B(\mathbf {u} )~.} The set of velocities satisfying 0 ≤ u < c is an open ball in ℝ3 and is called the space of admissible velocities in the literature... | Thomas rotation | 0.807584 |
25,497 | The passage from a velocity to a boost is obtained as follows. An arbitrary boost is given by e − ζ ⋅ K , {\displaystyle e^{-{\boldsymbol {\zeta }}\cdot \mathbf {K} },} where ζ is a triple of real numbers serving as coordinates on the boost subspace of the Lie algebra so(3, 1) spanned by the matrices ( K 1 , K 2 , K 3 ... | Thomas rotation | 0.807584 |
25,498 | In theoretical physics, the composition of two non-collinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation. This rotation is called Thomas rotation, Thomas–Wigner rotation or Wigner rotation. If a sequence of non-collinear boosts returns an ... | Thomas rotation | 0.807583 |
25,499 | In organic chemistry, amine value is a measure of the nitrogen content of an organic molecule. Specifically, it is usually used to measure the amine content of amine functional compounds. It may be defined as the number of milligrams of potassium hydroxide (KOH) equivalent to one gram of epoxy hardener resin. The units... | Amine value | 0.807583 |
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