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2,400 | Machine learning poses a host of ethical questions. Systems that are trained on datasets collected with biases may exhibit these biases upon use (algorithmic bias), thus digitizing cultural prejudices. For example, in 1988, the UK's Commission for Racial Equality found that St. George's Medical School had been using a computer program trained from data of previous admissions staff and this program had denied nearly 60 candidates who were found to be either women or had non-European sounding names. | Applications of machine learning | 0.834588 |
2,401 | Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction, based on known properties learned from the training data, data mining focuses on the discovery of (previously) unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities (which do often have separate conferences and separate journals, ECML PKDD being a major exception) comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. | Applications of machine learning | 0.834588 |
2,402 | Soil physics is the study of soil's physical properties and processes. It is applied to management and prediction under natural and managed ecosystems. Soil physics deals with the dynamics of physical soil components and their phases as solids, liquids, and gases. It draws on the principles of physics, physical chemistry, engineering, and meteorology. Soil physics applies these principles to address practical problems of agriculture, ecology, and engineering. | Soil physics | 0.83458 |
2,403 | Marine microorganisms, including protists and bacteria and their associated viruses, have been variously estimated as constituting about 70% or about 90% of the total marine biomass. Marine life is studied scientifically in both marine biology and in biological oceanography. The term marine comes from the Latin mare, meaning "sea" or "ocean". | Marine organism | 0.834549 |
2,404 | The Bradford assay is a molecular biology technique which enables the fast, accurate quantitation of protein molecules utilizing the unique properties of a dye called Coomassie Brilliant Blue G-250. Coomassie Blue undergoes a visible color shift from reddish-brown to bright blue upon binding to protein. In its unstable, cationic state, Coomassie Blue has a background wavelength of 465 nm and gives off a reddish-brown color. When Coomassie Blue binds to protein in an acidic solution, the background wavelength shifts to 595 nm and the dye gives off a bright blue color. | Molecular Biologist | 0.834538 |
2,405 | The PRS platform utilizes a neural network to fit data sets to a regression function resulting in a parabolic surface that provides a direct quantitative relationship between drug dose and efficacy. The governing function for the PRS platform is given as the following: E ( C , t ) = x 0 + ∑ i = 1 M x i C i + ∑ i = 1 M y i i C i 2 + ∑ i = 1 M − 1 ∑ j = i + 1 M z i j C i C j {\displaystyle E(C,t)=x_{0}+\sum _{i=1}^{M}x_{i}C_{i}+\sum _{i=1}^{M}y_{ii}C_{i}^{2}+\sum _{i=1}^{M-1}\sum _{j=i+1}^{M}z_{ij}C_{i}C_{j}} where: E is the combination efficacy as a function drug dose and time, given as a biomarker value C is the drug dose t is time x, y, z are PRS coefficients representing drug interaction M is the number of drugsThe parabolic nature of the relationship allows for the minimal required calibration test to utilize the PRS regression in the search area of NM combinations, where N is the number of dosing regimens and M is the number of drugs in the combination. | Phenotypic response surfaces | 0.834531 |
2,406 | Phenotypic response surfaces (PRS) is an artificial intelligence-guided personalized medicine platform that relies on combinatorial optimization principles to quantify drug interactions and efficacies to develop optimized combination therapies to treat a broad spectrum of illnesses. Phenotypic response surfaces fit a parabolic surface to a set of drug doses and biomarker values based on the understanding that the relationship between drugs, their interactions, and their effect on the measure biomarker can be modeled by quadric surface. The resulting surface allows for the omission of both in-vitro and in-silico screening of multi-drug combinations based on a patients unique phenotypic response. This provides a method to utilize small data sets to create time-critical personalized therapies that is independent of the disease or drug mechanism. The adaptable nature of the platform allows it to tackle a wide range of applications from isolating novel combination therapies to predicting daily drug regimen adjustments to support in-patient treatments. | Phenotypic response surfaces | 0.834531 |
2,407 | Combinatory therapy treatments provide significant benefits over monotherapy alternatives including greater efficacies and lower side effects and fatality rates, making them ideal candidates to optimize. In 2011 the PRS methodology was developed by a team led by Dr. Ibrahim Al-Shyoukh and Dr. Chih Ming Ho of the University of California Los Angeles to provide a platform that would allow for a comparatively small number of calibration tests to optimize multi-drug combination therapies based on measurement of cellular biomarkers. Since its inception the PRS platform has been applied to a broad range of disease areas including organ transplants, oncology, and infectiology. The PRS platform has since become the basis for a commercial optimization platform marketed by Singapore based Kyan Therapeutics in partnership with Kite Pharma and the National University of Singapore to provided personalized combination therapies for oncological applications. | Phenotypic response surfaces | 0.834531 |
2,408 | Optimization of combination therapies is of particular importance in oncology. Conventional cancer treatments often rely on the sequential use of chemotherapy drugs, with each new drug starting as soon as the pervious agent loses efficacy. However, this methodology allows for cancerous cells, due to their rapid rate of mutation, to develop resistances to chemotherapy drugs in instances where chemotherapy drugs fail to be effective. | Phenotypic response surfaces | 0.834531 |
2,409 | Some problems are known to be solvable in polynomial time, but no concrete algorithm is known for solving them. For example, the Robertson–Seymour theorem guarantees that there is a finite list of forbidden minors that characterizes (for example) the set of graphs that can be embedded on a torus; moreover, Robertson and Seymour showed that there is an O(n3) algorithm for determining whether a graph has a given graph as a minor. This yields a nonconstructive proof that there is a polynomial-time algorithm for determining if a given graph can be embedded on a torus, despite the fact that no concrete algorithm is known for this problem. | Complexity class P | 0.834517 |
2,410 | This provides a partial converse to Lagrange's theorem giving information about how many subgroups of a given order are contained in G. | Finite group | 0.83451 |
2,411 | Finite groups often occur when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. The theory of Lie groups, which may be viewed as dealing with "continuous symmetry", is strongly influenced by the associated Weyl groups. These are finite groups generated by reflections which act on a finite-dimensional Euclidean space. The properties of finite groups can thus play a role in subjects such as theoretical physics and chemistry. | Finite group | 0.83451 |
2,412 | Burnside's theorem in group theory states that if G is a finite group of order paqb, where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes. | Finite group | 0.83451 |
2,413 | In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century. One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004. | Finite group | 0.83451 |
2,414 | Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G. | Finite group | 0.83451 |
2,415 | Moreover, as in the case of compact simple Lie groups, the corresponding groups turned out to be almost simple as abstract groups (Tits simplicity theorem). Although it was known since 19th century that other finite simple groups exist (for example, Mathieu groups), gradually a belief formed that nearly all finite simple groups can be accounted for by appropriate extensions of Chevalley's construction, together with cyclic and alternating groups. Moreover, the exceptions, the sporadic groups, share many properties with the finite groups of Lie type, and in particular, can be constructed and characterized based on their geometry in the sense of Tits. The belief has now become a theorem – the classification of finite simple groups. Inspection of the list of finite simple groups shows that groups of Lie type over a finite field include all the finite simple groups other than the cyclic groups, the alternating groups, the Tits group, and the 26 sporadic simple groups. | Finite group | 0.83451 |
2,416 | This theorem generalizes to projective groups of higher dimensions and gives an important infinite family PSL(n, q) of finite simple groups. Other classical groups were studied by Leonard Dickson in the beginning of 20th century. In the 1950s Claude Chevalley realized that after an appropriate reformulation, many theorems about semisimple Lie groups admit analogues for algebraic groups over an arbitrary field k, leading to construction of what are now called Chevalley groups. | Finite group | 0.83451 |
2,417 | A group of Lie type is a group closely related to the group G(k) of rational points of a reductive linear algebraic group G with values in the field k. Finite groups of Lie type give the bulk of nonabelian finite simple groups. Special cases include the classical groups, the Chevalley groups, the Steinberg groups, and the Suzuki–Ree groups. Finite groups of Lie type were among the first groups to be considered in mathematics, after cyclic, symmetric and alternating groups, with the projective special linear groups over prime finite fields, PSL(2, p) being constructed by Évariste Galois in the 1830s. The systematic exploration of finite groups of Lie type started with Camille Jordan's theorem that the projective special linear group PSL(2, q) is simple for q ≠ 2, 3. | Finite group | 0.83451 |
2,418 | The classification of finite simple groups is a theorem stating that every finite simple group belongs to one of the following families: A cyclic group with prime order; An alternating group of degree at least 5; A simple group of Lie type; One of the 26 sporadic simple groups; The Tits group (sometimes considered as a 27th sporadic group).The finite simple groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference with respect to the case of integer factorization is that such "building blocks" do not necessarily determine uniquely a group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution. The proof of the theorem consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. Gorenstein (d.1992), Lyons, and Solomon are gradually publishing a simplified and revised version of the proof. | Finite group | 0.83451 |
2,419 | The Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by Walter Feit and John Griggs Thompson (1962, 1963) | Finite group | 0.83451 |
2,420 | In a June 2016 interview with Forbes, Baszucki stated that the idea for Roblox was inspired by the success of his Interactive Physics and Working Model software applications, especially among young students.Baszucki owns a roughly 13% stake in the Roblox Corporation, the company that owns Roblox, a stake estimated to be worth roughly $470 million as of 2020. He said he would donate any future compensation he earns from Roblox's listing on the New York Stock Exchange for philanthropic purposes. In December 2021, a New York Times investigation alleged that he and his relatives used a tax break intended for small business investors in order to legally avoid tens of millions of dollars in capital gains taxes. According to Business Insider, Baszucki was the seventh-highest-paid CEO in 2021, making $232.8 million. | Interactive Physics | 0.834494 |
2,421 | In 2004, Baszucki, along with Erik Cassel – who worked as Baszucki's VP of Engineering for Interactive Physics – began working on an early prototype of Roblox under the working title DynaBlocks. It was later renamed Roblox, a portmanteau of "robots" and "blocks", in 2005. The website officially launched in 2006. | Interactive Physics | 0.834494 |
2,422 | He later went on to host his own talk radio show for KSCO Radio Santa Cruz from February to July 2003. Baszucki studied engineering and computer science at Stanford University. While there, he did a summer internship at General Motors where he worked in a lab focused on controlling car engines with software. He graduated in 1985 as a General Motors Scholar in electrical engineering. | Interactive Physics | 0.834494 |
2,423 | In the late 1980s, Baszucki, together with his brother Greg Baszucki, founded the company Knowledge Revolution and developed and distributed a simulation called "Interactive Physics", which was designed as an educational supplement that would allow the creation of 2D physics experiments.As a follow-up to Interactive Physics, Knowledge Revolution launched the mechanical design software Working Model in the early 1990s.In December 1998, Knowledge Revolution was acquired by MSC Software, a simulation software company based in Newport Beach, California, for $20 million. Baszucki was named vice president and general manager of MSC Software from 2000 to 2002, but he left to establish Baszucki & Associates, an angel investment firm. Baszucki led Baszucki & Associates from 2003 to 2004. While an investor, he provided seed funding to Friendster, a social networking service. | Interactive Physics | 0.834494 |
2,424 | In 1955 a new department was founded - Physical Electronics. In following years the Telecommunications department was broadened in the areas of electronics, automatics and computer science. The fourth department - Computer science - was formed in 1987. The most recent addition is the department of Software Engineering, which was formed in 2004. Starting with the 2017/2018 school year, 720 students enroll on the first year of the faculty, of which 540 are enrolling at the electrical and computer engineering department and 180 at the software engineering department. | University of Belgrade School of Electrical Engineering | 0.834479 |
2,425 | Due to the lack of lab equipment forming of the fourth department (telecommunications) was postponed until the end of the Second World War. In 1946 the Department of Electrical Engineering was formed. That department grew into the School of Electrical Engineering two years later, with its Power Systems Engineering and Telecommunications departments. | University of Belgrade School of Electrical Engineering | 0.834479 |
2,426 | First diplomas in this area were given in 1922. The education of electrical engineers has been considerably expanded after reorganization of the engineering department in 1935. The mechanical department became Mechanical Electrical Engineering department, within which, in 1937, four new departments were formed- mechanical, aeronautical, power systems engineering and telecommunications. | University of Belgrade School of Electrical Engineering | 0.834479 |
2,427 | The first university level lecture in the area of electrical engineering was held in 1894. Professor Stevan Markovic was the first lecturer and founder of Electrical Engineering Chair with Engineering department of Belgrade Higher School. Only four years later, Professor Markovic also founded electrical engineering laboratory. Since then, this area has been studied at the Higher School, and later at the University of Belgrade which developed from it. | University of Belgrade School of Electrical Engineering | 0.834479 |
2,428 | In 1898, Marković also founded the first electrical engineering laboratory in Serbia. The school consists of a number of departments: Software Engineering, which is a separate department students enroll from year one, and the General Course, where from year two the students can select one of the following. Basic Electrical Engineering, Computer Science and Informatics, Telecommunications and Information Technology, Signal Processing and Automation, Power Engineering, Electronics Engineering and Physical Electronics. | University of Belgrade School of Electrical Engineering | 0.834479 |
2,429 | The University of Belgrade School of Electrical Engineering also known as Faculty of Electrical Engineering (Serbian: Електротехнички факултет Универзитета у Београду/Elektrotehnički fakultet Univerziteta u Beogradu) is a constituent body of the University of Belgrade. The word Faculty in Europe stands for an academic institution, the sub-unit inside the university. The first university level lecture in the field of electrical engineering in Serbia was held in 1894. Professor Stevan Marković was the first lecturer and founder of Electrical Engineering Chair within the Engineering department of the Belgrade Higher School. | University of Belgrade School of Electrical Engineering | 0.834479 |
2,430 | The 19th Olympiad was held 27 June - 3 July 2016 and the 20th Olympiad was held 1-7 July 2017, both at Leiden University and organized by the International Computer Game Association, the Leiden Institute of Advanced Computer Science, and the Leiden Centre of Data Science. The 21st Olympiad was held 7-13 July 2018 in Taipei, Taiwan alongside the 10th International Conference on Computers and Games. The World Computer Chess Championships took place from 13-19 July in Stockholm, Sweden. The 22nd Olympiad was held 11-17 August 2019 in Macau, China and the 23rd (2020), 24th (2021), and 25th (2022) Olympiads were held online due to the COVID-19 pandemic. | Computer Olympiad | 0.834477 |
2,431 | The 10th Olympiad was in 2005 in Taipei; the 11th, in 2006 in Turin; the 12th, in 2007 at the Amsterdam Science Park; the 13th, in 2008 at the Beijing Golden Century Golf Club; and the 14th, in 2009 in Pamplona. The 10th Olympiad wasa held at the same time and location as the 11th Advances in Computer Games and its organizing committee was made up of J. W. Hellemons (chair), H. H. L. M. Donkers, M. Greenspan, T-s Hsu, H. J. van den Herik, and M. Tiessen. Hand Talk, which won the gold medal in Computer Go, was originally written in assembly language by a retired chemistry professor of Sun Yat-sen University, China. The 11th Olympiad was held in conjugation with the 14th World Computer Chess Championship and the 5th Computer and Games Conference. | Computer Olympiad | 0.834477 |
2,432 | The 15th Olympiad was held in 2010 in Kanazawa, Japan along with the 18th World Computer Chess Championship (WCCC), and a scientific conference on computer games. The 16th Olympiad was held in 2011 at Tilburg University at the same time as the 19th WCCC. The 17th Olympiad was held in 2013 at Keio University's Collaboration Complex on the Hiyoshi Campus, and was at the same time as the 20th WCCC and a scientific conference on computer games. The 18th Olympiad was in 2015 at Leiden University and was organized by the International Computer Game Association, the Leiden Institute of Advanced Computer Science, and the Leiden Centre of Data Science. | Computer Olympiad | 0.834477 |
2,433 | What is E ∩ F in this case? No living human being is over 1000 years old, so E ∩ F must be the empty set {}. For any set A, the power set P ( A ) {\displaystyle P(A)} is a Boolean algebra under the operations of union and intersection. | Naive Set Theory | 0.834462 |
2,434 | An explicit ruling out of all conceivable inconsistencies (paradoxes) cannot be achieved for an axiomatic set theory anyway, due to Gödel's second incompleteness theorem, so this does not at all hamper the utility of naive set theory as compared to axiomatic set theory in the simple contexts considered below. It merely simplifies the discussion. Consistency is henceforth taken for granted unless explicitly mentioned. | Naive Set Theory | 0.834462 |
2,435 | Complex numbers are sums of a real and an imaginary number: r + s i {\displaystyle r+s\,i} . Here either r {\displaystyle r} or s {\displaystyle s} (or both) can be zero; thus, the set of real numbers and the set of strictly imaginary numbers are subsets of the set of complex numbers, which form an algebraic closure for the set of real numbers, meaning that every polynomial with coefficients in R {\displaystyle \mathbb {R} } has at least one root in this set. A blackboard bold capital C ( C {\displaystyle \mathbb {C} } ) often represents this set. Note that since a number r + s i {\displaystyle r+s\,i} can be identified with a point ( r , s ) {\displaystyle (r,s)} in the plane, C {\displaystyle \mathbb {C} } is basically "the same" as the Cartesian product R × R {\displaystyle \mathbb {R} \times \mathbb {R} } ("the same" meaning that any point in one determines a unique point in the other and for the result of calculations, it doesn't matter which one is used for the calculation, as long as multiplication rule is appropriate for C {\displaystyle \mathbb {C} } ). | Naive Set Theory | 0.834462 |
2,436 | Likewise, an axiomatic set theory is not necessarily consistent: not necessarily free of paradoxes. It follows from Gödel's incompleteness theorems that a sufficiently complicated first order logic system (which includes most common axiomatic set theories) cannot be proved consistent from within the theory itself – even if it actually is consistent. However, the common axiomatic systems are generally believed to be consistent; by their axioms they do exclude some paradoxes, like Russell's paradox. Based on Gödel's theorem, it is just not known – and never can be – if there are no paradoxes at all in these theories or in any first-order set theory. The term naive set theory is still today also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory. | Naïve set theory | 0.834462 |
2,437 | If A and B are sets, then the Cartesian product (or simply product) is defined to be: A × B = {(a,b) | a ∈ A and b ∈ B}.That is, A × B is the set of all ordered pairs whose first coordinate is an element of A and whose second coordinate is an element of B. This definition may be extended to a set A × B × C of ordered triples, and more generally to sets of ordered n-tuples for any positive integer n. It is even possible to define infinite Cartesian products, but this requires a more recondite definition of the product. Cartesian products were first developed by René Descartes in the context of analytic geometry. If R denotes the set of all real numbers, then R2 := R × R represents the Euclidean plane and R3 := R × R × R represents three-dimensional Euclidean space. | Naive Set Theory | 0.834462 |
2,438 | Real numbers represent the "real line" and include all numbers that can be approximated by rationals. These numbers may be rational or algebraic but may also be transcendental numbers, which cannot appear as solutions to polynomial equations with rational coefficients. A blackboard bold capital R ( R {\displaystyle \mathbb {R} } ) often represents this set. | Naive Set Theory | 0.834462 |
2,439 | Algebraic numbers appear as solutions to polynomial equations (with integer coefficients) and may involve radicals (including i = − 1 {\displaystyle i={\sqrt {-1\,}}} ) and certain other irrational numbers. A Q with an overline ( Q ¯ {\displaystyle {\overline {\mathbb {Q} }}} ) often represents this set. The overline denotes the operation of algebraic closure. | Naive Set Theory | 0.834462 |
2,440 | With the axiom schema of separation as an axiom of the theory, it follows, as a theorem of the theory: Or, more spectacularly (Halmos' phrasing): There is no universe. Proof: Suppose that it exists and call it U. Now apply the axiom schema of separation with X = U and for P(x) use x ∉ x. This leads to Russell's paradox again. Hence U cannot exist in this theory.Related to the above constructions is formation of the set Y = {x | (x ∈ x) → {} ≠ {}},where the statement following the implication certainly is false. | Naive Set Theory | 0.834462 |
2,441 | Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday use of set theory concepts in contemporary mathematics.Sets are of great importance in mathematics; in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory suffices for many purposes, while also serving as a stepping stone towards more formal treatments. | Naïve set theory | 0.834462 |
2,442 | Important algorithms in computational group theory include: the Schreier–Sims algorithm for finding the order of a permutation group the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration the product-replacement algorithm for finding random elements of a groupTwo important computer algebra systems (CAS) used for group theory are GAP and Magma. Historically, other systems such as CAS (for character theory) and Cayley (a predecessor of Magma) were important. Some achievements of the field include: complete enumeration of all finite groups of order less than 2000 computation of representations for all the sporadic groups | Computational group theory | 0.834446 |
2,443 | The Algebra Project is a national U.S. mathematics literacy program aimed at helping low-income students and students of color achieve the mathematical skills in high school that are a prerequisite for a college preparatory mathematics sequence. Founded by Civil Rights activist and Math educator Bob Moses in the 1980s, the Algebra Project provides curricular materials, teacher training, and professional development support and community involvement activities for schools to improve mathematics education.By 2001, the Algebra Project had trained approximately 300 teachers and was reaching 10,000 students in 28 locations in 10 states. | Algebra Project | 0.834443 |
2,444 | Founded in 1996, the Young People's Project (YPP) is a spin-off of the Algebra Project, which recruits and trains high school and college age "Math Literacy Workers" to tutor younger students in mathematics, and is directed by Omowale Moses. YPP has established sites in Jackson, Mississippi, Chicago, and the Greater Boston area of Massachusetts, and is developing programs in Miami, Petersburg, Virginia, Los Angeles, Ann Arbor, and Mansfield, Ohio. Each site employs between 30 and 100 high school and college age students part-time, and serves up to 1,000 elementary and middle-school students through on and off site programs. In 2005, the Algebra Project initiated Quality Education as a Civil Right (QECR), a national organizing effort to establish a federal constitutional guarantee of quality public education for all. Throughout 2005, YPP worked with students from Baltimore, New Orleans, Los Angeles, Oakland, Miami, Jackson, Chicago and Virginia to raise awareness about QECR. The Algebra Project and YPP students from Jackson and New Orleans hosted conferences, organized a Spring Break Community Education Tour to Miami and participated in QECR planning meetings at Howard University, the University of Michigan, and Jackson State University. | Algebra Project | 0.834443 |
2,445 | The Algebra Project was founded in 1982 by Bob Moses in Cambridge, Massachusetts. Moses worked with his daughter's eighth-grade teacher, Mary Lou Mehrling, to provide extra tutoring for several students in her class in algebra. Moses, who had taught secondary school mathematics in New York City and Tanzania, wanted to ensure that those students had sufficient algebra skills to qualify for honors math and science courses in high school. Through his tutorage, students from the Open Program of the Martin Luther King School passed the citywide algebra examination and qualified for ninth grade honors geometry, the first students from the program to do so. The Algebra Project grew out of attempts to recreate this on a wider community level, to provide similar students with a higher level of mathematical literacy. The Algebra Project now focuses on the southern states of the United States, where the Southern Initiative of the Algebra Project is directed by Dave Dennis. | Algebra Project | 0.834443 |
2,446 | Geometric constraint solving is constraint satisfaction in a computational geometry setting, which has primary applications in computer aided design. A problem to be solved consists of a given set of geometric elements and a description of geometric constraints between the elements, which could be non-parametric (tangency, horizontality, coaxiality, etc) or parametric (like distance, angle, radius). The goal is to find the positions of geometric elements in 2D or 3D space that satisfy the given constraints, which is done by dedicated software components called geometric constraint solvers. Geometric constraint solving became an integral part of CAD systems in the 80s, when Pro/Engineer first introduced a novel concept of feature-based parametric modeling concept.There are additional problems of geometric constraint solving that are related to sets of geometric elements and constraints: dynamic moving of given elements keeping all constraints satisfied, detection of over- and under-constrained sets and subsets, auto-constraining of under-constrained problems, etc. | Geometric constraint solving | 0.834399 |
2,447 | Geometric constraint solving has applications in a wide variety of fields, such as computer aided design, mechanical engineering, inverse kinematics and robotics, architecture and construction, molecular chemistry, and geometric theorem proving. The primary application area is computer aided design, where geometric constraint solving is used in both parametric history-based modeling and variational direct modeling. | Geometric constraint solving | 0.834399 |
2,448 | A general scheme of geometric constraint solving consists of modeling a set of geometric elements and constraints by a system of equations, and then solving this system by non-linear algebraic solver. For the sake of performance, a number of decomposition techniques could be used in order to decrease the size of an equation set: decomposition-recombination planning algorithms, tree decomposition, C-tree decomposition, graph reduction, re-parametrization and reduction, computing fundamental circuits, body-and-cad structure, or the witness configuration method.Some other methods and approaches include the degrees of freedom analysis, symbolic computations, rule-based computations, constraint programming and constraint propagation, and genetic algorithms.Non-linear equation systems are mostly solved by iterative methods that resolve the linear problem at each iteration, the Newton-Raphson method being the most popular example. | Geometric constraint solving | 0.834399 |
2,449 | Primary is a term used in organic chemistry to classify various types of compounds (e.g. alcohols, alkyl halides, amines) or reactive intermediates (e.g. alkyl radicals, carbocations). | Primary (chemistry) | 0.834397 |
2,450 | Electron scattering by isolated atoms and molecules occurs in the gas phase. It plays a key role in plasma physics and chemistry and it's important for such applications as semiconductor physics. Electron-molecule/atom scattering is normally treated by means of quantum mechanics. The leading approach to compute the cross sections is using R-matrix method. | Electron scattering experiment | 0.834385 |
2,451 | Stanford Linear Accelerator Center is located near Stanford University, California. Construction began on the 2 mile long linear accelerator in 1962 and was completed in 1967, and in 1968 the first experimental evidence of quarks was discovered resulting in the 1990 Nobel Prize in Physics, shared by SLAC's Richard Taylor and Jerome I. Friedman and Henry Kendall of MIT. The accelerator came with a 20GeV capacity for the electron acceleration, and while similar to Rutherford's scattering experiment, that experiment operated with alpha particles at only 7MeV. In the SLAC case the incident particle was an electron and the target a proton, and due to the short wavelength of the electron (due to its high energy and momentum) it was able to probe into the proton. | Electron scattering experiment | 0.834385 |
2,452 | The Stanford Positron Electron Asymmetric Ring (SPEAR) addition to the SLAC made further such discoveries possible, leading to the discovery in 1974 of the J/psi particle, which consists of a paired charm quark and anti-charm quark, and another Nobel Prize in Physics in 1976. This was followed up with Martin Perl's announcement of the discovery of the tau lepton, for which he shared the 1995 Nobel Prize in Physics.The SLAC aims to be a premier accelerator laboratory, to pursue strategic programs in particle physics, particle astrophysics and cosmology, as well as the applications in discovering new drugs for healing, new materials for electronics and new ways to produce clean energy and clean up the environment. Under the directorship of Chi-Chang Kao the SLAC's fifth director (as of November 2012), a noted X-ray scientist who came to SLAC in 2010 to serve as associate laboratory director for the Stanford Synchrotron Radiation Lightsource. | Electron scattering experiment | 0.834385 |
2,453 | There are several widely used undergraduate textbooks in electromagnetism, including David Griffiths' Introduction to Electrodynamics as well as Electricity and Magnetism by Edward Mills Purcell and D. J. Morin. The Feynman Lectures on Physics also include a volume on electromagnetism that is available to read online for free, through the California Institute of Technology. In addition, there are popular physics textbooks that include electricity and magnetism among the material they cover, such as David Halliday and Robert Resnick's Fundamentals of Physics. | List of textbooks in electromagnetism | 0.834377 |
2,454 | The study of electromagnetism in higher education, as a fundamental part of both physics and engineering, is typically accompanied by textbooks devoted to the subject. The American Physical Society and the American Association of Physics Teachers recommend a full year of graduate study in electromagnetism for all physics graduate students. A joint task force by those organizations in 2006 found that in 76 of the 80 US physics departments surveyed, a course using John David Jackson's Classical Electrodynamics was required for all first year graduate students. For undergraduates, there are several widely used textbooks, including David Griffiths' Introduction to Electrodynamics and Electricity and Magnetism by Edward Mills Purcell and D. J. Morin. Also at an undergraduate level, Richard Feynman's classic The Feynman Lectures on Physics is available online to read for free. | List of textbooks in electromagnetism | 0.834376 |
2,455 | A 2006 report by a joint taskforce between the American Physical Society and the American Association of Physics Teachers found that 76 of the 80 physics departments surveyed require a first-year graduate course in John David Jackson's Classical Electrodynamics. This made Jackson's book the most popular textbook in any field of graduate-level physics, with Herbert Goldstein's Classical Mechanics as the second most popular with adoption at 48 universities. In a 2015 review of Andrew Zangwill's Modern Electrodynamics in the American Journal of Physics, James S. Russ claims Jackson's textbook has been "he classic electrodynamics text for the past four decades" and that it is "the book from which most current-generation physicists took their first course." | List of textbooks in electromagnetism | 0.834376 |
2,456 | This is a list of geometry topics. | List of geometry topics | 0.834376 |
2,457 | Coordinate-free treatment Chirality Handedness Relative direction Mirror image Erlangen program Four-dimensional space Geometric shape Geometric space Group action, invariant Hadwiger's theorem Infinitesimal transformation Pi Polar sine Symmetry, shape, pattern Crystal system Frieze group Isometry Lattice Point group Point groups in two dimensions Point groups in three dimensions Space group Symmetry group Translational symmetry Wallpaper group Mathematics and fiber arts Van Hiele model - Prevailing theory of how children learn to reason in geometry | List of geometry topics | 0.834376 |
2,458 | Astronomy Computer graphics Image analysis Robot control The Strähle construction is used in the design of some musical instruments. Burmester's theory for the design of mechanical linkages | List of geometry topics | 0.834376 |
2,459 | 3D projection 3D computer graphics Binary space partitioning Ray tracing Graham scan Borromean rings Cavalieri's principle Cross section Crystal Cuisenaire rods Desargues' theorem Right circular cone Hyperboloid Napkin ring problem Pappus's centroid theorem Paraboloid Polyhedron Defect Dihedral angle Prism Prismatoid Honeycomb Pyramid Parallelepiped Tetrahedron Heronian tetrahedron Platonic solid Archimedean solid Kepler-Poinsot polyhedra Johnson solid Uniform polyhedron Polyhedral compound Hilbert's third problem Deltahedron Surface normal 3-sphere, spheroid, ellipsoid Parabolic microphone Parabolic reflector Soddy's hexlet Sphericon Stereographic projection Stereometry | List of geometry topics | 0.834376 |
2,460 | Projective geometry Arc (projective geometry) Desargues' theorem Girard Desargues Desarguesian plane Line at infinity Point at infinity Plane at infinity Hyperplane at infinity Projective line Projective plane Oval (projective plane) Roman surface Projective space Complex projective line Complex projective plane Fundamental theorem of projective geometry Projective transformation Möbius transformation Cross-ratio Duality Homogeneous coordinates Pappus's hexagon theorem Incidence Pascal's theorem Affine geometry Affine space Affine transformation Finite geometry Differential geometry Contact geometry Riemannian geometry Symplectic geometry Non-Euclidean plane geometry Angle excess Hyperbolic geometry Pseudosphere Tractricoid Elliptic geometry Spherical geometry Minkowski space Thurston's conjecture | List of geometry topics | 0.834376 |
2,461 | Another dichotomy theorem for constraint languages is the Hell-Nesetril theorem, which shows a dichotomy for problems on binary constraints with a single fixed symmetric relation. In terms of the homomorphism problem, every such problem is equivalent to the existence of a homomorphism from a relational structure to a given fixed undirected graph (an undirected graph can be regarded as a relational structure with a single binary symmetric relation). The Hell-Nesetril theorem proves that every such problem is either polynomial-time or NP-complete. More precisely, the problem is polynomial-time if the graph is 2-colorable, that is, it is bipartite, and is NP-complete otherwise. | Complexity of constraint satisfaction | 0.834361 |
2,462 | The best known such result is Schaefer's dichotomy theorem, which proves the existence of a dichotomy in the set of constraint languages on a binary domain. More precisely, it proves that a relation restriction on a binary domain is tractable if all its relations belong to one of six classes, and is NP-complete otherwise. Bulatov proved a dichotomy theorem for domains of three elements. | Complexity of constraint satisfaction | 0.834361 |
2,463 | Some constraint languages (or non-uniform problems) are known to correspond to problems solvable in polynomial time, and some others are known to express NP-complete problems. However, it is possible that some constraint languages are neither. It is known by Ladner's theorem that if P is not equal to NP, then there exist problems in NP that are neither polynomial-time nor NP-hard. As of 2007, it is not known if such problems can be expressed as constraint satisfaction problems with a fixed constraint language. | Complexity of constraint satisfaction | 0.834361 |
2,464 | Since kinetic energy is entirely a function of an object mass and velocity, the above result may be used with the parallel axis theorem to obtain the kinetic energy associated with simple rolling K rolling = K translation + K rotation {\displaystyle K_{\text{rolling}}=K_{\text{translation}}+K_{\text{rotation}}} | Rolling | 0.834319 |
2,465 | With evidence showing that different memories excite different neurons or system of neurons in the brain the technique of destroying select neurons in the brain to erase specific memories is also being researched. Studies have started to investigate the possibility of using distinct toxins along with biotechnology that allows the researchers to see which areas of the brain are being used during the reward learning process of making a memory to destroy target neurons. In a paper published in 2009, authors showed that neurons in the lateral amygdala that had a higher level of cyclic adenosine monophosphate response element-binding protein (CREB) were activated primarily over other neurons by fear memory expression. This indicated to them that these neurons were directly involved in the making of the memory trace for that fear memory. | Memory erasure | 0.834315 |
2,466 | The neuronal firings look like tiny green fireworks, randomly bursting against a black background, but the scientists have deciphered clear patterns in the chaos. "We can literally figure out where the mouse is in the arena by looking at these lights," said Mark Schnizer, an associate professor of biology and of applied physics. When a mouse is scratching at the wall in a certain area of the arena, a specific neuron will fire and flash green. | Memory erasure | 0.834314 |
2,467 | As early as 2009 researchers were able to trace and destroy neurons involved in supporting the specific type of memory that they were trying to erase. This caused the erasure of the target memory.Aside from the biotechnology approach to studying memory, research in psychiatry on how memories work has also been going on for several years. There have been some studies that show that some behavioral therapy can erase bad memories. There has been some evidence that psychodynamic therapy and other energy techniques can help with forgetting memories among other psychiatric issues there is no proven therapeutic approach for trying to erase bad memories. | Memory erasure | 0.834314 |
2,468 | R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957 Abraham Charnes, William W. Cooper, Management Models and Industrial Applications of Linear Programming, Volumes I and II, New York, John Wiley & Sons, 1961 Abraham Charnes, William W. Cooper, A. Henderson, An Introduction to Linear Programming, New York, John Wiley & Sons, 1953 C. West Churchman, Russell L. Ackoff & E. L. Arnoff, Introduction to Operations Research, New York: J. Wiley and Sons, 1957 George B. Dantzig, Linear Programming and Extensions, Princeton, Princeton University Press, 1963 Lester K. Ford, Jr., D. Ray Fulkerson, Flows in Networks, Princeton, Princeton University Press, 1962 Jay W. Forrester, Industrial Dynamics, Cambridge, MIT Press, 1961 L. V. Kantorovich, "Mathematical Methods of Organizing and Planning Production" Management Science, 4, 1960, 266–422 Ralph Keeney, Howard Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, New York, John Wiley & Sons, 1976 H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, 1–2, 1955, 83–97 H. W. Kuhn, A. W. Tucker, "Nonlinear Programming," pp. 481–492 in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability B. O. Koopman, Search and Screening: General Principles and Historical Applications, New York, Pergamon Press, 1980 Tjalling C. Koopmans, editor, Activity Analysis of Production and Allocation, New York, John Wiley & Sons, 1951 Charles C. Holt, Franco Modigliani, John F. Muth, Herbert A. Simon, Planning Production, Inventories, and Work Force, Englewood Cliffs, NJ, Prentice-Hall, 1960 Philip M. Morse, George E. Kimball, Methods of Operations Research, New York, MIT Press and John Wiley & Sons, 1951 Robert O. Schlaifer, Howard Raiffa, Applied Statistical Decision Theory, Cambridge, Division of Research, Harvard Business School, 1961 | Operations Research | 0.83431 |
2,469 | In 1967 Stafford Beer characterized the field of management science as "the business use of operations research". Like operational research itself, management science (MS) is an interdisciplinary branch of applied mathematics devoted to optimal decision planning, with strong links with economics, business, engineering, and other sciences. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and meaningful management decisions by arriving at optimal or near-optimal solutions to sometimes complex decision problems. Management scientists help businesses to achieve their goals using the scientific methods of operational research. | Operations Research | 0.83431 |
2,470 | Operational research (OR) encompasses the development and the use of a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, ordinal priority approach, neural networks, expert systems, decision analysis, and the analytic hierarchy process. Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science and analytics. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power, or develop a new technique specific to the problem at hand (and, afterwards, to that type of problem). The major sub-disciplines in modern operational research, as identified by the journal Operations Research, are: Computing and information technologies Financial engineering Manufacturing, service sciences, and supply chain management Policy modeling and public sector work Revenue management Simulation Stochastic models Transportation theory (mathematics) Game theory for strategies Linear programming Nonlinear programming Integer programming in NP-complete problem specially for 0-1 integer linear programming for binary Dynamic programming in Aerospace engineering and Economics Information theory used in Cryptography, Quantum computing Quadratic programming for solutions of Quadratic equation and Quadratic function | Operations Research | 0.83431 |
2,471 | The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length l and width w, the formula for the area is: A = lw (rectangle).That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w in the case of a square, the area of a square with side length s is given by the formula: A = s2 (square).The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a definition or axiom. On the other hand, if geometry is developed before arithmetic, this formula can be used to define multiplication of real numbers. | Area (geometry) | 0.834301 |
2,472 | In ancient times, the method of exhaustion was used in a similar way to find the area of the circle, and this method is now recognized as a precursor to integral calculus. Using modern methods, the area of a circle can be computed using a definite integral: A = 2 ∫ − r r r 2 − x 2 d x = π r 2 . {\displaystyle A\;=\;2\int _{-r}^{r}{\sqrt {r^{2}-x^{2}}}\,dx\;=\;\pi r^{2}.} | Area (geometry) | 0.834301 |
2,473 | Thus, the total area of the circle is πr2: A = πr2 (circle).Though the dissection used in this formula is only approximate, the error becomes smaller and smaller as the circle is partitioned into more and more sectors. The limit of the areas of the approximate parallelograms is exactly πr2, which is the area of the circle.This argument is actually a simple application of the ideas of calculus. | Area (geometry) | 0.834301 |
2,474 | The area enclosed by a parametric curve u → ( t ) = ( x ( t ) , y ( t ) ) {\displaystyle {\vec {u}}(t)=(x(t),y(t))} with endpoints u → ( t 0 ) = u → ( t 1 ) {\displaystyle {\vec {u}}(t_{0})={\vec {u}}(t_{1})} is given by the line integrals: ∮ t 0 t 1 x y ˙ d t = − ∮ t 0 t 1 y x ˙ d t = 1 2 ∮ t 0 t 1 ( x y ˙ − y x ˙ ) d t {\displaystyle \oint _{t_{0}}^{t_{1}}x{\dot {y}}\,dt=-\oint _{t_{0}}^{t_{1}}y{\dot {x}}\,dt={1 \over 2}\oint _{t_{0}}^{t_{1}}(x{\dot {y}}-y{\dot {x}})\,dt} or the z-component of 1 2 ∮ t 0 t 1 u → × u → ˙ d t . {\displaystyle {1 \over 2}\oint _{t_{0}}^{t_{1}}{\vec {u}}\times {\dot {\vec {u}}}\,dt.} (For details, see Green's theorem § Area calculation.) This is the principle of the planimeter mechanical device. | Area (geometry) | 0.834301 |
2,475 | The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: A = 4πr2 (sphere),where r is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus. | Area (geometry) | 0.834301 |
2,476 | Food microbiology laboratory. CRC Press. p. 121. ISBN 0-8493-1267-1. | Z-value (temperature) | 0.834284 |
2,477 | There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. | Mathematical Physics | 0.834258 |
2,478 | The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry and conserved quantities during the dynamical evolution, as embodied within the most elementary formulation of Noether's theorem. These approaches and ideas have been extended to other areas of physics as statistical mechanics, continuum mechanics, classical field theory and quantum field theory. Moreover, they have provided several examples and ideas in differential geometry (e.g. several notions in symplectic geometry and vector bundle). | Mathematical Physics | 0.834258 |
2,479 | The gravitational field is Minkowski spacetime itself, the 4D topology of Einstein aether modeled on a Lorentzian manifold that "curves" geometrically, according to the Riemann curvature tensor. The concept of Newton's gravity: "two masses attract each other" replaced by the geometrical argument: "mass transform curvatures of spacetime and free falling particles with mass move along a geodesic curve in the spacetime" (Riemannian geometry already existed before the 1850s, by mathematicians Carl Friedrich Gauss and Bernhard Riemann in search for intrinsic geometry and non-Euclidean geometry. ), in the vicinity of either mass or energy. (Under special relativity—a special case of general relativity—even massless energy exerts gravitational effect by its mass equivalence locally "curving" the geometry of the four, unified dimensions of space and time.) | Mathematical Physics | 0.834258 |
2,480 | ), Springer-Verlag, ISBN 978-3-642-07711-1 von Neumann, John (2018), Mathematical Foundations of Quantum Mechanics, Princeton University Press, ISBN 978-0-691-17856-1 Weyl, Hermann (2014), The Theory of Groups and Quantum Mechanics, Martino Fine Books, ISBN 978-1614275800 Ynduráin, Francisco J. (2006), The Theory of Quark and Gluon Interactions (4th ed. ), Springer, ISBN 978-3642069741 Zeidler, Eberhard (2006–2011), Quantum Field Theory: A Bridge Between Mathematicians and Physicists, Vol 1-3, Springer | Mathematical Physics | 0.834258 |
2,481 | ), Springer, doi:10.1007/978-3-319-70706-8, ISBN 978-3-319-70705-1, S2CID 125121522 Robert, Didier; Combescure, Monique (2021), Coherent States and Applications in Mathematical Physics (2nd ed. ), Springer, ISBN 978-3-030-70844-3 Tasaki, Hal (2020), Physics and mathematics of quantum many-body systems, Springer, ISBN 978-3-030-41265-4, OCLC 1154567924 Teschl, Gerald (2009), Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators, American Mathematical Society, ISBN 978-0-8218-4660-5 Thirring, Walter E. (2002), Quantum Mathematical Physics: Atoms, Molecules and Large Systems (2nd ed. | Mathematical Physics | 0.834258 |
2,482 | (2017), Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics, Springer, ISBN 978-3-319-68438-3 Hawking, Stephen W.; Ellis, George F. R. (1973), The Large Scale Structure of Space-Time, Cambridge University Press, ISBN 0-521-20016-4 Jackiw, Roman (1995), Diverse Topics in Theoretical and Mathematical Physics, World Scientific, ISBN 9810216963 Landsman, Klaas (2017), Foundations of Quantum Theory: From Classical Concepts to Operator Algebras, Springer, ISBN 978-3-319-51776-6 Moretti, Valter (2017), Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation, Unitext, vol. 110 (2nd ed. | Mathematical Physics | 0.834258 |
2,483 | ), Springer-Verlag, ISBN 0-387-96477-0 Haag, Rudolf (1996), Local Quantum Physics: Fields, Particles, Algebras (2nd ed. ), Springer-Verlag, ISBN 3-540-61049-9 Hall, Brian C. (2013), Quantum Theory for Mathematicians, Springer, ISBN 978-1-4614-7115-8 Hamilton, Mark J. D. | Mathematical Physics | 0.834258 |
2,484 | Baez, John C.; Muniain, Javier P. (1994), Gauge Fields, Knots, and Gravity, World Scientific, ISBN 981-02-2034-0 Blank, Jiří; Exner, Pavel; Havlíček, Miloslav (2008), Hilbert Space Operators in Quantum Physics (2nd ed. ), Springer, ISBN 978-1-4020-8869-8 Engel, Eberhard; Dreizler, Reiner M. (2011), Density Functional Theory: An Advanced Course, Springer-Verlag, ISBN 978-3-642-14089-1 Glimm, James; Jaffe, Arthur (1987), Quantum Physics: A Functional Integral Point of View (2nd ed. | Mathematical Physics | 0.834258 |
2,485 | Statistical mechanics forms a separate field, which includes the theory of phase transitions. It relies upon the Hamiltonian mechanics (or its quantum version) and it is closely related with the more mathematical ergodic theory and some parts of probability theory. There are increasing interactions between combinatorics and physics, in particular statistical physics. | Mathematical Physics | 0.834258 |
2,486 | Prominent contributors to the 20th century's mathematical physics include (ordered by birth date): William Thomson (Lord Kelvin) Oliver Heaviside Jules Henri Poincaré David Hilbert Arnold Sommerfeld Constantin Carathéodory Albert Einstein Max Born George David Birkhoff Hermann Weyl Satyendra Nath Bose Norbert Wiener John Lighton Synge Mário Schenberg Wolfgang Pauli Paul Dirac Eugene Wigner Andrey Kolmogorov Lars Onsager John von Neumann Sin-Itiro Tomonaga Hideki Yukawa Nikolay Nikolayevich Bogolyubov Subrahmanyan Chandrasekhar Mark Kac Julian Schwinger Richard Phillips Feynman Irving Ezra Segal Ryogo Kubo Arthur Strong Wightman Chen-Ning Yang Rudolf Haag Freeman John Dyson Martin Gutzwiller Abdus Salam Jürgen Moser Michael Francis Atiyah Joel Louis Lebowitz Roger Penrose Elliott Hershel Lieb Yakir Aharonov Sheldon Glashow Steven Weinberg Ludvig Dmitrievich Faddeev David Ruelle Yakov Grigorevich Sinai Vladimir Igorevich Arnold Arthur Michael Jaffe Roman Wladimir Jackiw Leonard Susskind Rodney James Baxter Michael Victor Berry Giovanni Gallavotti Stephen William Hawking Jerrold Eldon Marsden Michael C. Reed John Michael Kosterlitz Israel Michael Sigal Alexander Markovich Polyakov Barry Simon Herbert Spohn John Lawrence Cardy Giorgio Parisi Abhay Ashtekar Edward Witten F. Duncan Haldane Ashoke Sen Juan Martín Maldacena | Mathematical Physics | 0.834258 |
2,487 | Some 3VL modular algebras have been introduced more recently, motivated by circuit problems rather than philosophical issues: Cohn algebra Pradhan algebra Dubrova and Muzio algebra | Three-valued logic | 0.834241 |
2,488 | Matrices, versors (quaternions), and other algebraic things: see the section Linear and Multilinear Algebra Formalism for details.A general rotation in four dimensions has only one fixed point, the centre of rotation, and no axis of rotation; see rotations in 4-dimensional Euclidean space for details. Instead the rotation has two mutually orthogonal planes of rotation, each of which is fixed in the sense that points in each plane stay within the planes. The rotation has two angles of rotation, one for each plane of rotation, through which points in the planes rotate. | Rotation (geometry) | 0.834185 |
2,489 | Medivir is listed on the Nasdaq Stockholm Mid Cap List. In February 2020, Medivir announced that the company has signed a licensing agreement for Xerclear with Chinese company Shijiazhuang Yuanmai Biotechnology Co Ltd (SYB). The agreement gives SYB the right to register, manufacture and market the product in China. | Medivir | 0.834174 |
2,490 | Its mathematical formalization is part of the field of topological graph theory which studies the embedding of graphs on surfaces. An important part of the puzzle, but one that is often not stated explicitly in informal wordings of the puzzle, is that the houses, companies, and lines must all be placed on a two-dimensional surface with the topology of a plane, and that the lines are not allowed to pass through other buildings; sometimes this is enforced by showing a drawing of the houses and companies, and asking for the connections to be drawn as lines on the same drawing.In more formal graph-theoretic terms, the problem asks whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} is a planar graph. This graph has six vertices in two subsets of three: one vertex for each house, and one for each utility. It has nine edges, one edge for each of the pairings of a house with a utility, or more abstractly one edge for each pair of a vertex in one subset and a vertex in the other subset. Planar graphs are the graphs that can be drawn without crossings in the plane, and if such a drawing could be found, it would solve the three utilities puzzle. | Three utilities problem | 0.834169 |
2,491 | This puzzle can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with vertices representing the houses and utilities and edges representing their connections, has a graph embedding in the plane. The impossibility of the puzzle corresponds to the fact that K 3 , 3 {\displaystyle K_{3,3}} is not a planar graph. Multiple proofs of this impossibility are known, and form part of the proof of Kuratowski's theorem characterizing planar graphs by two forbidden subgraphs, one of which is K 3 , 3 {\displaystyle K_{3,3}} . | Three utilities problem | 0.834169 |
2,492 | Physical Chemistry Chemical Physics is a weekly peer-reviewed scientific journal publishing research and review articles on any aspect of physical chemistry, chemical physics, and biophysical chemistry. It is published by the Royal Society of Chemistry on behalf of eighteen participating societies. The editor-in-chief is Anouk Rijs, (Vrije Universiteit Amsterdam).The journal was established in 1999 as the results of a merger between Faraday Transactions and a number of other physical chemistry journals published by different societies. | Physical Chemistry Chemical Physics | 0.83416 |
2,493 | Medical biology is a field of biology that has practical applications in medicine, health care and laboratory diagnostics. It includes many biomedical disciplines and areas of specialty that typically contains the "bio-" prefix such as: molecular biology, biochemistry, biophysics, biotechnology, cell biology, embryology, nanobiotechnology, biological engineering, laboratory medical biology, cytogenetics, genetics, gene therapy, bioinformatics, biostatistics, systems biology, microbiology, virology, parasitology, physiology, pathology, toxicology, and many others that generally concern life sciences as applied to medicine.Medical biology is the cornerstone of modern health care and laboratory diagnostics. It concerned a wide range of scientific and technological approaches: from an in vitro diagnostics to the in vitro fertilisation, from the molecular mechanisms of a cystic fibrosis to the population dynamics of the HIV, from the understanding molecular interactions to the study of the carcinogenesis, from a single-nucleotide polymorphism (SNP) to the gene therapy. Medical biology based on molecular biology combines all issues of developing molecular medicine into large-scale structural and functional relationships of the human genome, transcriptome, proteome and metabolome with the particular point of view of devising new technologies for prediction, diagnosis and therapy. | Medical biology | 0.834131 |
2,494 | Greedy algorithms have a long history of study in combinatorial optimization and theoretical computer science. Greedy heuristics are known to produce suboptimal results on many problems, and so natural questions are: For which problems do greedy algorithms perform optimally? For which problems do greedy algorithms guarantee an approximately optimal solution? For which problems are the greedy algorithm guaranteed not to produce an optimal solution?A large body of literature exists answering these questions for general classes of problems, such as matroids, as well as for specific problems, such as set cover. | Exchange algorithm | 0.834122 |
2,495 | A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure. | Exchange algorithm | 0.834122 |
2,496 | Genome skimming is a cost-effective, rapid and reliable method to generate large shallow datasets, since several datasets (plastid, mitochondrial, nuclear) are generated per run. It is very simple to implement, requires less lab work and optimization, and does not require a priori knowledge of the organism nor its genome size. This provides a low-risk avenue for biological inquiry and hypothesis generation without a huge commitment of resources.Genome skimming is an especially advantageous approach regarding cases where the genomic DNA may be old and degraded from chemical treatments, such as specimens from herbarium and museum collections, a largely untapped genomic resource. Genome skimming allows for the molecular characterization of rare or extinct species. | Genome skimming | 0.834106 |
2,497 | Both the wet-lab and the bioinformatics parts of genome skimming have certain challenges with scalability. Although the cost of sequencing in genome skimming is affordable at $80 for 1 Gb in 2016, the library preparation for sequencing is still very expensive, at least ~$200 per sample (as of 2016). Additionally, most library preparation protocols have not been fully automated with robotics yet. On the bioinformatics side, large complex databases and automated workflows need to be designed to handle the large amounts of data resulting from genome skimming. The automation of the following processes need to be implemented: Assembly of the standard barcodes Assembly of organellar DNA (as well as nuclear ribosomal tandem repeats) Annotation of the different assembled fragments Removal of potential contaminant sequences Estimation of sequencing coverage for single-copy genes Extraction of reads corresponding to single-copy genes Identification of unknown specimen from a small shotgun sequencing or any DNA fragment Identification of the different organisms from shotgun sequencing of environmental DNA (metagenomics)Some of these scalability challenges have already been implemented, as shown above in the "Tools and Pipelines" section. | Genome skimming | 0.834106 |
2,498 | In herbaria, even with low yield and low-quality DNA, one study was still able to produce "high-quality complete chloroplast and ribosomal DNA sequences" at a large scale for downstream analyses.In field studies, invertebrates are stored in ethanol which is usually discarded during DNA-based studies. Genome skimming has been shown to detect the low quantity of DNA from this ethanol-fraction and provide information about the biomass of the specimens in a fraction, the microbiota of outer tissue layers and the gut contents (like prey) released by the vomit reflex. Thus, genome skimming can provide an additional method of understanding ecology via low copy DNA. | Genome skimming | 0.834106 |
2,499 | Geneious is a integrative software platform that allows users to perform various steps in bioinformatic analysis such as assembly, alignment, and phylogenetics by incorporating other tools within a GUI based platform. | Genome skimming | 0.834106 |
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