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26,000 | Section 14, Geophysics, Astronomy, and Acoustics; Abundance of Elements in the Earth's Crust and in the Sea: R.S. Carmichael (ed. ), CRC Practical Handbook of Physical Properties of Rocks and Minerals, CRC Press, Boca Raton, FL, (1989). | Abundances of the elements (data page) | 0.807364 |
26,001 | From these sources in an online version of David R. Lide (ed. ), CRC Handbook of Chemistry and Physics, 85th Edition. CRC Press. Boca Raton, Florida (2005). | Abundances of the elements (data page) | 0.807364 |
26,002 | A. Earnshaw, N. Greenwood, Chemistry of the Elements, 2nd edition, Butterworth-Heinemann, (1997). ISBN 0-7506-3365-4 Appendix 4, Abundance of Elements in Crustal Rocks. From this source with some modifications and additions of later data: W.S. Fyfe, Geochemistry, Oxford University Press, (1974). | Abundances of the elements (data page) | 0.807364 |
26,003 | Bulk continental crust (C6) from: B.L. Weaver, J. Tamey, Major and trace element composition of the continental lithosphere, in Physics and Chemistry of the Earth, 15, H.N. Pollack, V.R. | Abundances of the elements (data page) | 0.807364 |
26,004 | Acta, 40, 73–83, (1976). Bulk continental crust (C5) from: H. Wänke, G. Dreibus, E. Jagoutz, Mantle chemistry and accretion history of the Earth, in Archean Geochemistry, A. Kröner, G.N. Hanson, A.M. | Abundances of the elements (data page) | 0.807364 |
26,005 | Newsom, Horton E. (1995), "Composition of the Solar System, Planets, Meteorites, and Major Terrestrial Reservoirs", in Ahrens, Thomas J. (ed. ), Global Earth Physics: A Handbook of Physical Constants, AGU Reference Shelf, vol. | Abundances of the elements (data page) | 0.807364 |
26,006 | The traditional Copenhagen interpretation of quantum mechanics rejects counterfactual definiteness as it does not ascribe any value at all to a measurement that was not performed. When measurements are performed, values result, but these are not considered to be revelations of pre-existing values. In the words of Asher... | Counterfactual definiteness | 0.807362 |
26,007 | The subject of counterfactual definiteness receives attention in the study of quantum mechanics because it is argued that, when challenged by the findings of quantum mechanics, classical physics must give up its claim to one of three assumptions: locality (no "spooky action at a distance"), no-conspiracy (called also "... | Counterfactual definiteness | 0.807362 |
26,008 | Experiments have shown that quantum mechanical results predictably exceed those classical limits. Calculating expectations based on Bell's work implies that for quantum physics the assumption of "local realism" must be abandoned. Bell's theorem proves that every type of quantum theory must necessarily violate locality ... | Counterfactual definiteness | 0.807362 |
26,009 | If the person's position has changed by making him or her stand rather than sit, then that person has no lap and neither the statement "the person's lap is empty" nor "there is something on the person's lap" is true. Any statistical calculation based on values where the person is standing at some place in the room and ... | Counterfactual definiteness | 0.807362 |
26,010 | An interpretation of quantum mechanics can be said to involve the use of counterfactual definiteness if it includes in the mathematical modelling outcomes of measurements that are counterfactual; in particular, those that are excluded according to quantum mechanics by the fact that quantum mechanics does not contain a ... | Counterfactual definiteness | 0.807362 |
26,011 | Thus Consistent Histories does not reject counterfactual results per se, it rejects them only when they are being combined with incompatible results. Whereas in the Copenhagen interpretation or the Many Worlds interpretation, the algebraic operations to derive Bell's inequality cannot proceed due to having no value or ... | Counterfactual definiteness | 0.807362 |
26,012 | In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed (i.e., the ability to assume the existence of objects, and properties of objects, even when they have not been measured). The term "counterfactua... | Counterfactual definiteness | 0.807362 |
26,013 | In the mathematical field of topology, a locally finite space is a topological space in which every point has a finite neighborhood, that is, an open neighborhood consisting of finitely many elements. A locally finite space is an Alexandrov space. A T1 space is locally finite if and only if it is discrete. | Locally finite space | 0.80736 |
26,014 | The envelope theorem describes how the value of an optimal solution changes when an underlying parameter changes. The process of computing this change is called comparative statics. The maximum theorem of Claude Berge (1963) describes the continuity of an optimal solution as a function of underlying parameters. | Ordinal optimization | 0.807359 |
26,015 | Problems in rigid body dynamics (in particular articulated rigid body dynamics) often require mathematical programming techniques, since you can view rigid body dynamics as attempting to solve an ordinary differential equation on a constraint manifold; the constraints are various nonlinear geometric constraints such as... | Ordinal optimization | 0.807359 |
26,016 | A famous example of governing differential equations within biology is | Governing equation | 0.807359 |
26,017 | Problems with the steady-state model began to emerge in the 1950s and 60s – observations supported the idea that the universe was in fact changing. Bright radio sources (quasars and radio galaxies) were found only at large distances (therefore could have existed only in the distant past due to the effects of the speed ... | Steady-state theories | 0.807358 |
26,018 | Systems engineering processes encompass all creative, manual and technical activities necessary to define the product and which need to be carried out to convert a system definition to a sufficiently detailed system design specification for product manufacture and deployment. Design and development of a system can be d... | Engineering system | 0.807358 |
26,019 | System development often requires contribution from diverse technical disciplines. By providing a systems (holistic) view of the development effort, systems engineering helps mold all the technical contributors into a unified team effort, forming a structured development process that proceeds from concept to production... | Engineering system | 0.807358 |
26,020 | The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory. Reverse mathematics is usually carried out using subsystems of second-order arithmetic, where many of its definitions and methods are inspired by previous work in constru... | Arithmetical transfinite recursion | 0.807357 |
26,021 | Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of deriving theorems from axioms... | Arithmetical transfinite recursion | 0.807357 |
26,022 | It is equivalent to several statements of descriptive set theory whose proofs make use of strongly impredicative arguments; this equivalence shows that these impredicative arguments cannot be removed. The following theorems are equivalent to Π11-CA0 over RCA0: The Cantor–Bendixson theorem (every closed set of reals is ... | Arithmetical transfinite recursion | 0.807357 |
26,023 | HBU (short for "uncountable Heine-Borel") expresses the (open-cover) compactness of the unit interval, involving uncountable covers. The latter aspect of HBU makes it only expressible in the language of third-order arithmetic. Cousin's theorem (1895) implies HBU, and these theorems use the same notion of cover due to C... | Arithmetical transfinite recursion | 0.807357 |
26,024 | Weaker systems than recursive comprehension can be defined. The weak system RCA*0 consists of elementary function arithmetic EFA (the basic axioms plus Δ00 induction in the enriched language with an exponential operation) plus Δ01 comprehension. Over RCA*0, recursive comprehension as defined earlier (that is, with Σ01 ... | Arithmetical transfinite recursion | 0.807357 |
26,025 | Another effect of using second-order arithmetic is the need to restrict general mathematical theorems to forms that can be expressed within arithmetic. For example, second-order arithmetic can express the principle "Every countable vector space has a basis" but it cannot express the principle "Every vector space has a ... | Arithmetical transfinite recursion | 0.807357 |
26,026 | The reason that reverse mathematics is not carried out using set theory as a base system is that the language of set theory is too expressive. Extremely complex sets of natural numbers can be defined by simple formulas in the language of set theory (which can quantify over arbitrary sets). In the context of second-orde... | Arithmetical transfinite recursion | 0.807357 |
26,027 | Most reverse mathematics research focuses on subsystems of second-order arithmetic. The body of research in reverse mathematics has established that weak subsystems of second-order arithmetic suffice to formalize almost all undergraduate-level mathematics. In second-order arithmetic, all objects can be represented as e... | Arithmetical transfinite recursion | 0.807357 |
26,028 | Phenomena that occur differently according to their time direction can ultimately be linked to the Second Law of Thermodynamics, for example ice cubes melt in hot coffee rather than assembling themselves out of the coffee and a block sliding on a rough surface slows down rather than speeds up. The idea that we can reme... | Thermodynamic arrow | 0.807355 |
26,029 | Some processes that involve high energy particles and are governed by the weak force (such as K-meson decay) defy the symmetry between time directions. However, all known physical processes do preserve a more complicated symmetry (CPT symmetry), and are therefore unrelated to the second law of thermodynamics, or to the... | Thermodynamic arrow | 0.807355 |
26,030 | Many of the automated systems are used to counteract human error as many of the research techniques done by humans counting individual cells have a high chance of error involved. Due to the fact that researchers regularly manually count the cells with the assistance of a transmitted light, this error prone technique ca... | Colony-forming units | 0.807353 |
26,031 | LLVM is a set of compiler and toolchain technologies that can be used to develop a frontend for any programming language and a backend for any instruction set architecture. LLVM is designed around a language-independent intermediate representation (IR) that serves as a portable, high-level assembly language that can be... | LLVM Intermediate Representation | 0.807352 |
26,032 | In discrete geometry, an isosceles set is a set of points with the property that every three of them form an isosceles triangle. More precisely, each three points should determine at most two distances; this also allows degenerate isosceles triangles formed by three equally-spaced points on a line. | Isosceles set | 0.807348 |
26,033 | Kelly's eight-point three-dimensional isosceles set can be decomposed into two sets X {\displaystyle X} (the three points on a line perpendicular to the pentagon) and Y {\displaystyle Y} (the five vertices of the pentagon), with the property that each point in X {\displaystyle X} is equidistant from all points of Y {\d... | Isosceles set | 0.807348 |
26,034 | Let G be a finite, strongly connected, directed graph where all the vertices have the same out-degree k. Let A be the alphabet containing the letters 1, ..., k. A synchronizing coloring (also known as a collapsible coloring) in G is a labeling of the edges in G with letters from A such that (1) each vertex has exactly ... | Road coloring problem | 0.807346 |
26,035 | In chemistry, the calculation of the amount of reactant and products in a chemical reaction, or stoichiometry, is founded on the principle of conservation of mass. The principle implies that during a chemical reaction the total mass of the reactants is equal to the total mass of the products. For example, in the follow... | Conservation of mass | 0.807345 |
26,036 | The conservation of relativistic mass implies the viewpoint of a single observer (or the view from a single inertial frame) since changing inertial frames may result in a change of the total energy (relativistic energy) for systems, and this quantity determines the relativistic mass. The principle that the mass of a sy... | Conservation of mass | 0.807345 |
26,037 | A large error in the initial estimate can contribute to non-convergence of the algorithm. To overcome this problem one can often linearize the function that is being optimized using calculus, logs, differentials, or even using evolutionary algorithms, such as the stochastic tunneling. Good initial estimates lie close t... | Newton iteration | 0.807342 |
26,038 | When medical imaging is coupled with the development of novel radiotracers and contrast agents, theranostics may provide opportunities for precise diagnosis and targeted therapy.Diagnostic-therapeutic approaches are used in theranostics, where the diagnostic method is developed simultaneously with the therapeutic inter... | Theranostics | 0.807342 |
26,039 | Molecular imaging techniques, such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT), enable the visualization and characterization of cancerous lesions, aiding in early detection, staging, and assessment of treatment response. This allows for more accurate and tailored treatm... | Theranostics | 0.807342 |
26,040 | Immunotherapy harnesses the body's immune system to recognize and attack cancer cells or other disease targets. In theranostics, immunotherapeutic approaches can be coupled with diagnostic imaging to assess immune cell infiltration, tumor immunogenicity, and treatment response. Imaging techniques, such as PET and MRI, ... | Theranostics | 0.807342 |
26,041 | Radiotherapy can be integrated with imaging techniques to guide treatment planning, monitor radiation dose distribution, and assess treatment response. Molecular imaging methods, such as PET and SPECT, can be employed to visualize and quantify tumor characteristics, such as hypoxia or receptor expression, aiding in per... | Theranostics | 0.807342 |
26,042 | UIT-VSMEC: is a standard Vietnamese Social Media Emotion Corpus (UIT-VSMEC) with about 6,927 human-annotated sentences with six emotion labels, contributing to emotion recognition research in Vietnamese which is a low-resource language in Natural Language Processing (NLP). BED: provides electroencephalography (EEG) rec... | Emotion recognition | 0.807341 |
26,043 | Emotion recognition is used in society for a variety of reasons. Affectiva, which spun out of MIT, provides artificial intelligence software that makes it more efficient to do tasks previously done manually by people, mainly to gather facial expression and vocal expression information related to specific contexts where... | Emotion recognition | 0.807341 |
26,044 | Data is an integral part of the existing approaches in emotion recognition and in most cases it is a challenge to obtain annotated data that is necessary to train machine learning algorithms. For the task of classifying different emotion types from multimodal sources in the form of texts, audio, videos or physiological... | Emotion recognition | 0.807341 |
26,045 | Decades of scientific research have been conducted developing and evaluating methods for automated emotion recognition. There is now an extensive literature proposing and evaluating hundreds of different kinds of methods, leveraging techniques from multiple areas, such as signal processing, machine learning, computer v... | Emotion recognition | 0.807341 |
26,046 | Other uses by Affectiva include helping children with autism, helping people who are blind to read facial expressions, helping robots interact more intelligently with people, and monitoring signs of attention while driving in an effort to enhance driver safety.A patent filed by Snapchat in 2015 describes a method of ex... | Emotion recognition | 0.807341 |
26,047 | Statistical methods commonly involve the use of different supervised machine learning algorithms in which a large set of annotated data is fed into the algorithms for the system to learn and predict the appropriate emotion types. Machine learning algorithms generally provide more reasonable classification accuracy comp... | Emotion recognition | 0.807341 |
26,048 | In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy lost in one radian of the cycle of oscillation. Q factor is alternatively defined a... | Q factor | 0.807341 |
26,049 | This is the inner derivation determined by X {\textstyle X} . : 51: 9 ad X ( ) = + {\displaystyle \operatorname {ad} _{X}()=+} The universal enveloping algebra U ( g ) {\textstyle U({\mathcal {g}})} of Lie algebra g {\textstyle {\mathcal {g}}} is a maximal associative algebra with identity, generated by Lie algebr... | Differential algebra | 0.807337 |
26,050 | A Lie algebra is a finite-dimensional real or complex vector space g {\textstyle {\mathcal {g}}} with a bilinear bracket operator : g × g → g {\textstyle :{\mathcal {g}}\times {\mathcal {g}}\to {\mathcal {g}}} with Skew symmetry and the Jacobi identity property. : 49 Skew symmetry: = − {\displaystyle =-} Jacobi ident... | Differential algebra | 0.807337 |
26,051 | Joseph Ritt developed differential algebra because he viewed attempts to reduce systems of differential equations to various canonical forms as an unsatisfactory approach. However, the success of algebraic elimination methods and algebraic manifold theory motivated Ritt to consider a similar approach for differential e... | Differential algebra | 0.807337 |
26,052 | (Note that running time is measured in terms of the size of the input, which in this case is ~ log n, that being the number of bits needed to represent the number n.) The elliptic curve primality test can be proven to run in O((log n)6), if some conjectures on analytic number theory are true. Similarly, under the gener... | Primality tests | 0.807334 |
26,053 | Near the beginning of the 20th century, it was shown that a corollary of Fermat's little theorem could be used to test for primality. This resulted in the Pocklington primality test. However, as this test requires a partial factorization of n − 1 the running time was still quite slow in the worst case. The first determ... | Primality tests | 0.807334 |
26,054 | The following is a primality test in JavaScript using the same optimization as above. | Primality tests | 0.807334 |
26,055 | The following is a primality test in Haskell using the same optimization as above. | Primality tests | 0.807334 |
26,056 | A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. | Primality tests | 0.807334 |
26,057 | It is the result of a naive understanding or a misapplication of two theorems: Bézout's theorem states that the number of points of intersection of two algebraic curves is equal to the product of their degrees, provided that certain necessary conditions are met. In particular, two curves of degree n {\displaystyle n} g... | Cramer's paradox | 0.807334 |
26,058 | In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensional Euclidean space. The procedure thus appears to be the counterpart of princip... | Multiple correspondence analysis | 0.807333 |
26,059 | Predictive modelling in archaeology gets its foundations from Gordon Willey's mid-fifties work in the Virú Valley of Peru. Complete, intensive surveys were performed then covariability between cultural remains and natural features such as slope and vegetation were determined. Development of quantitative methods and a g... | Predictive Models | 0.807333 |
26,060 | Work without change of volume is known as isochoric work, for example when an agency, in the surroundings of the system, drives a frictional action on the surface or in the interior of the system. In a process of transfer of energy from or to a thermodynamic system, the change of internal energy of the system is define... | Pressure-volume work | 0.807332 |
26,061 | Isochoric mechanical work for a body in its own state of internal thermodynamic equilibrium is done only by the surroundings on the body, not by the body on the surroundings, so that the sign of isochoric mechanical work with the physics sign convention is always negative. When work, for example pressure–volume work, i... | Pressure-volume work | 0.807332 |
26,062 | This convention has historically been used in chemistry, and has been adopted by most physics textbooks.This equation reflects the fact that the heat transferred and the work done are not properties of the state of the system. Given only the initial state and the final state of the system, one can only say what the tot... | Pressure-volume work | 0.807332 |
26,063 | In the early history of thermodynamics, a positive amount of work done by the system on the surroundings leads to energy being lost from the system. This historical sign convention has been used in many physics textbooks and is used in the present article.According to the first law of thermodynamics for a closed system... | Pressure-volume work | 0.807332 |
26,064 | One might object that A and B are related by the algebraic equation A − B − 2√3 = 0, which does not remain true when A and B are exchanged. However, this relation is not considered here, because it has the coefficient −2√3 which is not rational. We conclude that the Galois group of the polynomial x2 − 4x + 1 consists o... | Solvability by radicals | 0.807328 |
26,065 | For example, the equation A + B = 4 becomes B + A = 4. It is more generally true that this holds for every possible algebraic relation between A and B such that all coefficients are rational; that is, in any such relation, swapping A and B yields another true relation. This results from the theory of symmetric polynomi... | Solvability by radicals | 0.807328 |
26,066 | Consider the quadratic equation x 2 − 4 x + 1 = 0. {\displaystyle x^{2}-4x+1=0.} By using the quadratic formula, we find that the two roots are A = 2 + 3 , B = 2 − 3 . {\displaystyle {\begin{aligned}A&=2+{\sqrt {3}},\\B&=2-{\sqrt {3}}.\end{aligned}}} Examples of algebraic equations satisfied by A and B include A + B = ... | Solvability by radicals | 0.807328 |
26,067 | It allows one to more easily study infinite extensions. Again this is important in algebraic number theory, where for example one often discusses the absolute Galois group of Q, defined to be the Galois group of K/Q where K is an algebraic closure of Q. It allows for consideration of inseparable extensions. This issue ... | Solvability by radicals | 0.807328 |
26,068 | It permits a far simpler statement of the fundamental theorem of Galois theory. The use of base fields other than Q is crucial in many areas of mathematics. For example, in algebraic number theory, one often does Galois theory using number fields, finite fields or local fields as the base field. | Solvability by radicals | 0.807328 |
26,069 | In the modern approach, one starts with a field extension L/K (read "L over K"), and examines the group of automorphisms of L that fix K. See the article on Galois groups for further explanation and examples. The connection between the two approaches is as follows. The coefficients of the polynomial in question should ... | Solvability by radicals | 0.807328 |
26,070 | Outside France, Galois' theory remained more obscure for a longer period. In Britain, Cayley failed to grasp its depth and popular British algebra textbooks did not even mention Galois' theory until well after the turn of the century. In Germany, Kronecker's writings focused more on Abel's result. Dedekind wrote little... | Solvability by radicals | 0.807328 |
26,071 | The UEIT allowed to adjust image geometry and picture settings such as brightness, contrast and colour saturation. Other more technical adjustments were also possible, such as cathode-ray tube focus and raster distortions. The card features the following elements: Grid box - makes up the background of the table. Allows... | Universal Electronic Test Chart | 0.807327 |
26,072 | In mathematics, particularly differential topology, the secondary vector bundle structure refers to the natural vector bundle structure (TE, p∗, TM) on the total space TE of the tangent bundle of a smooth vector bundle (E, p, M), induced by the push-forward p∗: TE → TM of the original projection map p: E → M. This give... | Secondary vector bundle structure | 0.807325 |
26,073 | It has also been attempted on a larger scale by creating an entire educational computer game on a massive multiplayer scale. This game was first used in the field of biology to go through life cycles of certain animals and also to explain environmental changes to students. It allowed many students to all interact and p... | Meaningful play | 0.807325 |
26,074 | Joint Expert Speciation System (JESS) is a package of computer software and data developed collaboratively at Murdoch University and elsewhere by researchers interested in the chemical thermodynamics of water solutions with important applications in industry, biochemistry, medicine and the environment. Using informatio... | Joint Expert Speciation System | 0.807325 |
26,075 | PubChem is a database of chemical molecules and their activities against biological assays. The system is maintained by the National Center for Biotechnology Information (NCBI), a component of the National Library of Medicine, which is part of the United States National Institutes of Health (NIH). PubChem can be access... | PubChem | 0.807325 |
26,076 | A full range of effective core potentials (ECPs), both relativistic and non-relativistic, with energies, gradients, analytical second derivatives and NMR. Closed-shell MP2 energies and analytical gradients and dual-basis MP2 energies; numerical MP2 second derivatives. Potential scan, including scan + optimization of al... | Parallel Quantum Solutions | 0.807324 |
26,077 | Atoms involved in constraints do not need to be formally bonded and - unlike with a Z matrix - desired constraints do not need to be satisfied in the starting geometry. Expository second subsidiaries for every one of these systems, including the calculation of vibrational frequencies, IR intensities and thermodynamic a... | Parallel Quantum Solutions | 0.807324 |
26,078 | Productive, adaptable geometry optimization for every one of these methods including Eigenvector Following (EF) algorithm for minimization and saddle-point search, Pulay's GDIIS algorithm for minimization, use of Cartesian, Z-matrix and delocalized internal coordinates. Includes new coordinates for efficient optimizati... | Parallel Quantum Solutions | 0.807324 |
26,079 | The basis capabilities in high-level correlated energies for PQS ab initio v. 4.0 include MP3, MP4, CID, CISD, CEPA-0, CEPA-2, QCISD, QCISD(T), CCD, CCSD and CCSD(T) wavefunctions; enforced geometry optimization (used, among other things, to simulate the results of Atomic Force Microscopy (AFM) experiments); full-accur... | Parallel Quantum Solutions | 0.807324 |
26,080 | TEXAS was initially parallelized in 1995–1996 on a cluster of 10 IBM RS6000 workstations.In 1996, Baker joined Pulay and, around the same time, Intel brought out the Pentium Pro, a processor for PC that was competitive with low-end workstations and less costly by around an order of magnitude. Understanding the capabili... | Parallel Quantum Solutions | 0.807324 |
26,081 | Simultaneously, in the 1980s, MOLPRO was extended and mostly rewritten by Hans-Joachim Werner, Peter Knowles and Meyer's coworkers.Meanwhile, in 1976, Pulay was visiting Boggs at the University of Texas, Austin and Schaefer at the University of California. They wrote a new program called TEXAS based on the original MOL... | Parallel Quantum Solutions | 0.807324 |
26,082 | Pulay was interested in implementing gradient geometry optimization, analytical energy derivatives (force), and force constant calculations via the numerical differentiation of analytical forces, while Meyer enthused about the coupled-electron pair approximation (CEPA), spin density calculation, and extremely accurate ... | Parallel Quantum Solutions | 0.807324 |
26,083 | The origin of PQS program was developed by Meyer and Pulay in the late 1960s. They both were at the Max-Planck Institute for Physics and Astrophysics in Munich when they began to write a new ab initio program. The main purpose was to establish new ab initio techniques. Pulay and Meyer had slightly different interests. | Parallel Quantum Solutions | 0.807324 |
26,084 | This extension incorporates generative artificial intelligence into Jupyter notebooks, enabling users to explain and generate code, rectify errors, summarize content, inquire about their local files, and generate complete notebooks based on natural language prompts. JupyterHub is a multi-user server for Jupyter Noteboo... | Project Jupyter | 0.807323 |
26,085 | The DeLano Award for Computational Biosciences is a prize in the field of computational biology. It is awarded annually for "the most accessible and innovative development or application of computer technology to enhance research in the life sciences at the molecular level".The prize was established by the American Soc... | DeLano Award for Computational Biosciences | 0.807323 |
26,086 | The unicellular life cycle of cancer and Entamoeba is uniquely similar, and thus contradicts the molecular phylostratigraphic theory for the origin of cancer. This deep relationship between the two cell systems is supported by the "amoeba model", which provides a greater understanding of the biology of cancer from the ... | Deep homology | 0.807318 |
26,087 | In evolutionary developmental biology, the concept of deep homology is used to describe cases where growth and differentiation processes are governed by genetic mechanisms that are homologous and deeply conserved across a wide range of species. | Deep homology | 0.807318 |
26,088 | In 1822, the French zoologist Étienne Geoffroy Saint-Hilaire dissected a crayfish, discovering that its body is organised like a vertebrate's, but inverted belly to back (dorsoventrally): I just found that all the soft organs, that is to say, the principal organs of life are found in crustaceans, and so in insects, in ... | Deep homology | 0.807318 |
26,089 | In modern day biology, the depth of understanding deep homology has evolved into focusing on the molecular and genetic mechanisms and functions rather than simple morphology. Cancer stem cells (CSCs) are a population of cells within a tumor that have the ability to self-renew and differentiate into different cell types... | Deep homology | 0.807318 |
26,090 | Parameter space contributed to the liberation of geometry from the confines of three-dimensional space. For instance, the parameter space of spheres in three dimensions, has four dimensions—three for the sphere center and another for the radius. According to Dirk Struik, it was the book Neue Geometrie des Raumes (1849)... | Parameter space | 0.80731 |
26,091 | {\displaystyle R^{+}\times R^{+}\times S^{1}.} In complex dynamics, the parameter space is the complex plane C = { z = x + y i: x, y ∈ R }, where i2 = −1.The famous Mandelbrot set is a subset of this parameter space, consisting of the points in the complex plane which give a bounded set of numbers when a particular ite... | Parameter space | 0.80731 |
26,092 | This fertile conception threw new light on both synthetic and algebraic geometry and created new forms of duality. The number of dimensions of a particular form of geometry could now be any positive number, depending on the number of parameters necessary to define the "element". : 165 The requirement for higher dimensi... | Parameter space | 0.80731 |
26,093 | They also form the background for parameter estimation. In the case of extremum estimators for parametric models, a certain objective function is maximized or minimized over the parameter space. Theorems of existence and consistency of such estimators require some assumptions about the topology of the parameter space. ... | Parameter space | 0.80731 |
26,094 | The parameter space is the space of possible parameter values that define a particular mathematical model, often a subset of finite-dimensional Euclidean space. Often the parameters are inputs of a function, in which case the technical term for the parameter space is domain of a function. The ranges of values of the pa... | Parameter space | 0.80731 |
26,095 | Established in 1972, the focus of the research is on cryoinjury, cryosurgery, cryopreservation, lyophilization and hypothermia. Since 1985 the Institute has published the open access peer-reviewed scientific journal Problems of Cryobiology and Cryomedicine. | NASU Institute of Cryobiology and Cryomedicine Issues | 0.80731 |
26,096 | The Institute for Problems of Cryobiology and Cryomedicine in Kharkiv is one of the institutes of the National Academy of Science of Ukraine, and is the largest institute devoted to cryobiology research in the world. | NASU Institute of Cryobiology and Cryomedicine Issues | 0.80731 |
26,097 | The exponential map effects a transformation from the axis-angle representation of rotations to rotation matrices, Essentially, by using a Taylor expansion one derives a closed-form relation between these two representations. Given a unit vector ω ∈ s o ( 3 ) = R 3 {\textstyle {\boldsymbol {\omega }}\in {\mathfrak {so}... | Axis angle | 0.807309 |
26,098 | By Rodrigues' rotation formula, the angle and axis determine a transformation that rotates three-dimensional vectors. The rotation occurs in the sense prescribed by the right-hand rule. The rotation axis is sometimes called the Euler axis. The axis–angle representation is predicated on Euler's rotation theorem, which d... | Axis angle | 0.807309 |
26,099 | In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction (geometry) of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the rotation about the axis. Onl... | Axis angle | 0.807309 |
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