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18,400 | The RLDB office in London was located in the main ICRF building at Lincoln's Inn Fields, Holborn and later moved to bigger premises in the adjacent Royal College of Surgeons building. The Lincoln's Inn Fields building was later sold to the London School of Economics and demolished in 2018 to make way for their new Mars... | German Resource Center for Genome Research | 0.812207 |
18,401 | FISH chromosome in-situ hybridization allows the study cytogenetics in pre- and postnatal samples and is also widely used in cytogenetic testing for cancer. While cytogenetics is the study of chromosomes and their structure, cytogenetic testing involves the analysis of cells in the blood, tissue, bone marrow, or fluid ... | Molecular cytogenetics | 0.812207 |
18,402 | One of the current projects involving Molecular Cytogenetics involves genomic research on rare cancers, called the Cancer Genome Characterization Initiative (CGCI). The CGCI is a group interested in describing the genetic abnormalities of some rare cancers, by employing advanced sequencing of genomes, exomes, and trans... | Molecular cytogenetics | 0.812207 |
18,403 | In 1879, Arnold examined sarcoma and carcinoma cells having very large nuclei. Today, the study of molecular cytogenetics can be useful in diagnosing and treating various malignancies such as hematological malignancies, brain tumors, and other precursors of cancer. The field is overall focused on studying the evolution... | Molecular cytogenetics | 0.812207 |
18,404 | Molecular cytogenetics combines two disciplines, molecular biology and cytogenetics, and involves the analysis of chromosome structure to help distinguish normal and cancer-causing cells. Human cytogenetics began in 1956 when it was discovered that normal human cells contain 46 chromosomes. However, the first microscop... | Molecular cytogenetics | 0.812207 |
18,405 | FISH is also used for melanocytic lesions, distinguishing atypical melanocytic or malignant melanoma.Cancer cells often accumulate complex chromosomal structural changes such as loss, duplication, inversion or movement of a segment. When using FISH, any changes to a chromosome will be made visible through discrepancies... | Molecular cytogenetics | 0.812207 |
18,406 | In the area of mathematics known as differential topology, the disc theorem of Palais (1960) states that two embeddings of a closed k-disc into a connected n-manifold are ambient isotopic provided that if k = n the two embeddings are equioriented. The disc theorem implies that the connected sum of smooth oriented manif... | Disc theorem | 0.812206 |
18,407 | The interest in nineteenth century geometry in the Kummer surface came in part from the way a quartic surface represented a quotient of an abelian variety with d = 2, by the group of order 2 of automorphisms generated by x → −x on the abelian variety. | Equations defining abelian varieties | 0.812204 |
18,408 | The Mumford–Kempf theorem states that the fourth power of an ample line bundle is quadratically presented. For a base field of characteristic zero, Giuseppe Pareschi proved a result including these (as the cases p = 0, 1) which had been conjectured by Lazarsfeld: let L be an ample line bundle on an abelian variety A. I... | Equations defining abelian varieties | 0.812204 |
18,409 | The goal of the theory is to prove results on the homogeneous coordinate ring of the embedded abelian variety A, that is, set in a projective space according to a very ample L and its global sections. The graded commutative ring that is formed by the direct sum of the global sections of the L n , {\displaystyle L^{n},\... | Equations defining abelian varieties | 0.812204 |
18,410 | The only 'easy' cases are those for d = 1, for an elliptic curve with linear span the projective plane or projective 3-space. In the plane, every elliptic curve is given by a cubic curve. In P3, an elliptic curve can be obtained as the intersection of two quadrics. In general abelian varieties are not complete intersec... | Equations defining abelian varieties | 0.812204 |
18,411 | Mumford defined a theta group associated to an invertible sheaf L on an abelian variety A. This is a group of self-automorphisms of L, and is a finite analogue of the Heisenberg group. The primary results are on the action of the theta group on the global sections of L. When L is very ample, the linear representation c... | Equations defining abelian varieties | 0.812204 |
18,412 | In mathematics, the concept of abelian variety is the higher-dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of study because every abelian variety is a projective variety. In dimension d ≥ 2, however, it is no longer as straightforward to discuss such equations. T... | Equations defining abelian varieties | 0.812204 |
18,413 | A Coulomb scattering state in quantum mechanics (a fundamental theory in physics), describes a state of a particle where the particle is subject to Coulomb potential and is not localized to a finite region of space. In general, Coulomb scattering state is a state in Hilbert Space that corresponds to two or more particl... | Coulomb scattering state | 0.812204 |
18,414 | Its 2019 MCQ was 2.29, and its 2019 impact factor was 2.125. The current editors-in-chief are Fabio Toninelli (Technical University of Vienna) and Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics).The journal CiteScore is 3.8 and its SCImago Journal Rank is 3.198, both from 2020. It is curre... | Probability Theory and Related Fields | 0.812204 |
18,415 | Probability Theory and Related Fields is a peer-reviewed mathematics journal published by Springer. Established in 1962, it was originally named Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, with the English replacing the German starting from volume 71 (1986). The journal publishes articles on proba... | Probability Theory and Related Fields | 0.812204 |
18,416 | Molecular Cell is a peer-reviewed scientific journal that covers research on cell biology at the molecular level, with an emphasis on new mechanistic insights. It was established in 1997 and is published two times per month. Its 2021 impact factor is 19.328. Molecular Cell is a Cell Press journal (an imprint of Elsevie... | Molecular Cell | 0.812203 |
18,417 | The next unpaired x can be paired with 2n − 3 different x leaving 2n − 4, and so on. This means that Wick's theorem, uncorrected, says that the expectation value of x2n should be: ⟨ x 2 n ⟩ = ( 2 n − 1 ) ⋅ ( 2 n − 3 ) … ⋅ 5 ⋅ 3 ⋅ 1 ⟨ x 2 ⟩ n {\displaystyle \left\langle x^{2n}\right\rangle =(2n-1)\cdot (2n-3)\ldots \cdo... | Interaction vertex | 0.812201 |
18,418 | There is a subtle point left before Wick's theorem is proved—what if more than two of the ϕ {\displaystyle \phi } s have the same momentum? If it's an odd number, the integral is zero; negative values cancel with the positive values. But if the number is even, the integral is positive. | Interaction vertex | 0.812201 |
18,419 | To clarify and prove the rule, consider a Feynman diagram formed from vertices, terms in the Lagrangian, with Fermion fields. The full term is Bosonic, it is a commuting element of the Grassmann algebra, so the order in which the vertices appear is not important. The Fermi lines are linked into loops, and when traversi... | Interaction vertex | 0.812201 |
18,420 | By using the spatial Fourier transform of the Dirac field as a new basis for the Grassmann algebra, the quadratic part of the Dirac action becomes simple to invert: S = ∫ k ψ ¯ ( i γ μ k μ − m ) ψ . {\displaystyle S=\int _{k}{\bar {\psi }}\left(i\gamma ^{\mu }k_{\mu }-m\right)\psi \,.} The propagator is the inverse of ... | Interaction vertex | 0.812201 |
18,421 | In their presentations of fundamental interactions, written from the particle physics perspective, Gerard 't Hooft and Martinus Veltman gave good arguments for taking the original, non-regularized Feynman diagrams as the most succinct representation of our present knowledge about the physics of quantum scattering of fu... | Interaction vertex | 0.812201 |
18,422 | The matrix that changes coordinates from φ(x) to φ(k) can be read off from the definition of a Fourier transform. A k x = e i k x {\displaystyle A_{kx}=e^{ikx}\,} and the Fourier inversion theorem tells you the inverse: A k x − 1 = e − i k x {\displaystyle A_{kx}^{-1}=e^{-ikx}\,} which is the complex conjugate-transpos... | Interaction vertex | 0.812201 |
18,423 | The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the Sunyaev–Zel'dovich effect. Observations of the Sunyaev–Zel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters. Some synchrotron radiation facilities scatter laser light off the stored elec... | Compton interaction | 0.812199 |
18,424 | Inverse Compton scattering is important in astrophysics. In X-ray astronomy, the accretion disk surrounding a black hole is presumed to produce a thermal spectrum. The lower energy photons produced from this spectrum are scattered to higher energies by relativistic electrons in the surrounding corona. This is surmised ... | Compton interaction | 0.812199 |
18,425 | The concept of a formal theorem is fundamentally syntactic, in contrast to the notion of a true proposition, which introduces semantics. Different deductive systems can yield other interpretations, depending on the presumptions of the derivation rules (i.e. belief, justification or other modalities). The soundness of a... | Theorem | 0.812193 |
18,426 | The institute was formed in 2011 as the Institute for Genomics and Multiscale Biology, as part of Mount Sinai's Department of Genetics and Genomic Sciences. Eric Schadt was named as founding director. The institute was renamed in 2012 when philanthropist Carl Icahn pledged $200 million to its parent organization, the I... | Icahn Genomics Institute | 0.812193 |
18,427 | The Icahn Genomics Institute is a biomedical and genomics research institute within the Icahn School of Medicine at Mount Sinai in New York City. Its aim is to establish a new generation of medicines that can better treat diseases afflicting the world, including cancer, heart disease and infectious pathogens. To do thi... | Icahn Genomics Institute | 0.812193 |
18,428 | Scientists from the institute published a paper in Nature Genetics in 2012 demonstrating the ability to derive enough information from non-DNA sources to identify individuals whose supposedly anonymized biological data is stored in large research databases. The authors reported that measuring RNA levels in tissue allow... | Icahn Genomics Institute | 0.812193 |
18,429 | In philosophy of science, strong inference is a model of scientific inquiry that emphasizes the need for alternative hypotheses, rather than a single hypothesis to avoid confirmation bias. The term "strong inference" was coined by John R. Platt, a biophysicist at the University of Chicago. Platt notes that some fields,... | Strong inference | 0.812192 |
18,430 | Like any system of equations, a system of linear differential equations is said to be overdetermined if there are more equations than the unknowns. For an overdetermined system to have a solution, it needs to satisfy the compatibility conditions. For example, consider the system: ∂ u ∂ x i = f i , 1 ≤ i ≤ m . {\display... | Differential system | 0.812192 |
18,431 | A differential system is a means of studying a system of partial differential equations using geometric ideas such as differential forms and vector fields. For example, the compatibility conditions of an overdetermined system of differential equations can be succinctly stated in terms of differential forms (i.e., a for... | Differential system | 0.812192 |
18,432 | Perhaps the most famous example of a non-linear system of differential equations is the Navier–Stokes equations. Unlike the linear case, the existence of a solution of a non-linear system is a difficult problem (cf. Navier–Stokes existence and smoothness.) See also: h-principle. | Differential system | 0.812191 |
18,433 | Several criteria influence the strength of the bonding: the nature of the cation, solvation effects, the nature of the π system, and the geometry of the interaction. | Cation-pi interaction | 0.81219 |
18,434 | Foundations of the Czech chemical nomenclature (official term in Czech: české chemické názvosloví) and terminology were laid during the 1820s and 1830s. These early naming conventions fit the Czech language and, being mostly work of a single person, provided a consistent way to name chemical compounds. Over time, the n... | Czech chemical nomenclature | 0.812187 |
18,435 | A similar attempt, published in "Orbis pictus" (1852), by Karel Slavoj Amerling (1807-1884) to create Czech names for the chemical elements (and to order the elements into a structure, similar to the work of Russian chemist Nikolay Beketov) was not successful.Later work on the nomenclature was performed by Vojtěch Šafa... | Czech chemical nomenclature | 0.812187 |
18,436 | The size effect is gaining in importance as larger and larger structures, of more and more slender forms, are being built. The safety factors, of course, give large safety margins—so large that even for the largest civil engineering structures the classical deterministic analysis based on the mean material properties n... | Size effect on structural strength | 0.812183 |
18,437 | The purpose of the approximation made is: (a) to prevent σ N {\displaystyle \sigma _{N}} from becoming negative for very small D {\displaystyle D} , for which the foregoing argument does not apply; and (b) to satisfy the asymptotic condition that the deterministic size effect must vanish for D / l 0 → ∞ {\displaystyle ... | Size effect on structural strength | 0.812183 |
18,438 | Terran R is a heavy-lift two-stage, partially reusable launch vehicle that is currently under development. Compared to the smaller, expendable Terran 1, it is constructed using the same 3D printing technologies, but is substantially larger, with a maximum payload capacity of 33,500 kg (73,900 lb) to low Earth orbit. Th... | Relativity Space | 0.812182 |
18,439 | Relativity Space was founded in 2015 by CEO Tim Ellis and CTO Jordan Noone on the idea that existing private spaceflight companies were not tapping enough into the potential of additive manufacturing (3D printing). Relativity is aiming to be the first company to successfully launch a fully 3D-printed launch vehicle int... | Relativity Space | 0.812182 |
18,440 | Relativity Space is an American aerospace manufacturing company headquartered in Long Beach, California. Relativity Space is developing manufacturing technologies, launch vehicles, and rocket engines for commercial orbital launch services. The company is notable for manufacturing most of their Terran 1 and Terran R roc... | Relativity Space | 0.812182 |
18,441 | Ions are ubiquitous in nature and are responsible for diverse phenomena from the luminescence of the Sun to the existence of the Earth's ionosphere. Atoms in their ionic state may have a different color from neutral atoms, and thus light absorption by metal ions gives the color of gemstones. In both inorganic and organ... | Ion notation | 0.812181 |
18,442 | Mycology is the branch of biology concerned with the systematic study of fungi, including their genetic and biochemical properties, their taxonomy, and their use to humans as a source of medicine, food, and psychotropic substances consumed for religious purposes, as well as their dangers, such as poisoning or infection... | Fungal development | 0.81218 |
18,443 | Several pivotal discoveries in biology were made by researchers using fungi as model organisms, that is, fungi that grow and sexually reproduce rapidly in the laboratory. For example, the one gene-one enzyme hypothesis was formulated by scientists using the bread mold Neurospora crassa to test their biochemical theorie... | Fungal development | 0.81218 |
18,444 | Seed sovereignty can be defined as the right “to breed and exchange diverse open-sourced seeds.” Generally, it comes from the belief that communities should have control over their own seed stock, as a means to increase agricultural biodiversity, resilience, and food security. This idea is closely connected to issues o... | Plant breeders' rights | 0.812178 |
18,445 | In molecular biology, autotransporter proteins are proteins secreted out the Gram-negative bacteria. These beta helixes require a domain which is called the intramolecular autochaperone domain. It shows similarities with other intramolecular chaperone sequences and has a folding-associated function. This increases the ... | Autochaperone | 0.812171 |
18,446 | Operations research (British English: operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. The term management science is occasionally used as a ... | Operations research analyst | 0.812171 |
18,447 | Percy Bridgman brought operational research to bear on problems in physics in the 1920s and would later attempt to extend these to the social sciences.Modern operational research originated at the Bawdsey Research Station in the UK in 1937 as the result of an initiative of the station's superintendent, A. P. Rowe and R... | Operations research analyst | 0.812171 |
18,448 | Visible patterns in nature are governed by physical laws; for example, meanders can be explained using fluid dynamics. In biology, natural selection can cause the development of patterns in living things for several reasons, including camouflage, sexual selection, and different kinds of signalling, including mimicry an... | Da Vinci branching rule | 0.812171 |
18,449 | Living things like orchids, hummingbirds, and the peacock's tail have abstract designs with a beauty of form, pattern and colour that artists struggle to match. The beauty that people perceive in nature has causes at different levels, notably in the mathematics that governs what patterns can physically form, and among ... | Da Vinci branching rule | 0.812171 |
18,450 | In the early twenties Ralph H. Fowler (in collaboration with Charles Galton Darwin) developed a new method in statistical mechanics permitting a systematic calculation of the equilibrium properties of matter. He used this to provide a rigorous derivation of the ionization formula which Saha had obtained, by extending t... | Saha ionization equation | 0.81217 |
18,451 | If the purpose is not to perform strict interpolation but instead more general function approximation or classification the optimization is somewhat more complex because there is no obvious choice for the centers. The training is typically done in two phases first fixing the width and centers and then the weights. This... | Radial basis networks | 0.812168 |
18,452 | The map, in the fully chaotic regime, is given by x ( t + 1 ) = d e f f = 4 x ( t ) {\displaystyle x(t+1)\ {\stackrel {\mathrm {def} }{=}}\ f\left=4x(t)\left} where t is a time index. The value of x at time t+1 is a parabolic function of x at time t. This equation represents the underlying geometry of the chaotic tim... | Radial basis networks | 0.812168 |
18,453 | Robot Cache, S.L. is a video game company established to allow for digital buying and selling of video games. It was founded in January 2018 by Brian Fargo, and reached open beta in May 2020. Robot Cache is a game distribution platform, which claims to be an alternative shop to Steam Unlike Steam, it enables customers ... | Robot Cache | 0.812167 |
18,454 | The RG Chromaticity space is used in computer vision applications. It shows the color of light (red, yellow, green etc.), but not its intensity (dark, bright). The TSL color space (Tint, Saturation and Luminance) is used in face detection. | Color spaces | 0.812165 |
18,455 | Bounding Theorems of Plastic-Limit Load Analysis: Plastic limit theorems provide a way to calculate limit loads without having to solve the boundary value problem in continuum mechanics. Finite element analysis provides an alternative way to estimate limit loads. They are: The Upper Bound Plastic Collapse Theorem The L... | Limit load (physics) | 0.812164 |
18,456 | Beside the serious mathematics and number theory, Wells occasionally makes humorous or playful comments on the numbers he is discussing. For example, his entry for the number 39 largely consists of a joke involving the interesting number paradox: 39This appears to be the first uninteresting number, which of course make... | The Penguin Dictionary of Curious and Interesting Numbers | 0.81216 |
18,457 | The Penguin Dictionary of Curious and Interesting Numbers is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (ISBN 0-14-026149-4). | The Penguin Dictionary of Curious and Interesting Numbers | 0.81216 |
18,458 | There are two ternary operations involving dot product and cross product. The scalar triple product of three vectors is defined as Its value is the determinant of the matrix whose columns are the Cartesian coordinates of the three vectors. It is the signed volume of the parallelepiped defined by the three vectors, and ... | Dot product | 0.812155 |
18,459 | In physics, vector magnitude is a scalar in the physical sense (i.e., a physical quantity independent of the coordinate system), expressed as the product of a numerical value and a physical unit, not just a number. The dot product is also a scalar in this sense, given by the formula, independent of the coordinate syste... | Dot product | 0.812155 |
18,460 | The projective line is a fundamental example of an algebraic curve. From the point of view of algebraic geometry, P1(K) is a non-singular curve of genus 0. If K is algebraically closed, it is the unique such curve over K, up to rational equivalence. In general a (non-singular) curve of genus 0 is rationally equivalent ... | Projective line | 0.812155 |
18,461 | Any function field K(V) of an algebraic variety V over K, other than a single point, has a subfield isomorphic with K(T). From the point of view of birational geometry, this means that there will be a rational map from V to P1(K), that is not constant. The image will omit only finitely many points of P1(K), and the inv... | Projective line | 0.812155 |
18,462 | Adding a point at infinity to the complex plane results in a space that is topologically a sphere. Hence the complex projective line is also known as the Riemann sphere (or sometimes the Gauss sphere). It is in constant use in complex analysis, algebraic geometry and complex manifold theory, as the simplest example of ... | Projective line | 0.812155 |
18,463 | This is the beginning of methods in algebraic geometry that are inductive on dimension. The rational maps play a role analogous to the meromorphic functions of complex analysis, and indeed in the case of compact Riemann surfaces the two concepts coincide. If V is now taken to be of dimension 1, we get a picture of a ty... | Projective line | 0.812155 |
18,464 | In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity. The statement and the proof of many theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exa... | Projective line | 0.812155 |
18,465 | It follows from the error analysis of the trapezoidal rule for quadrature that the local truncation error τ n {\displaystyle \tau _{n}} of the trapezoidal rule for solving differential equations can be bounded as: Thus, the trapezoidal rule is a second-order method. This result can be used to show that the global error... | Trapezoidal rule (differential equations) | 0.812154 |
18,466 | Integrating the differential equation from t n {\displaystyle t_{n}} to t n + 1 {\displaystyle t_{n+1}} , we find that The trapezoidal rule states that the integral on the right-hand side can be approximated as Now combine both formulas and use that y n ≈ y ( t n ) {\displaystyle y_{n}\approx y(t_{n})} and y n + 1 ≈ y ... | Trapezoidal rule (differential equations) | 0.812154 |
18,467 | In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals. The trapezoidal rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multis... | Trapezoidal rule (differential equations) | 0.812154 |
18,468 | In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators. The adjective "central" refers to the center of the symmetry group—the subgroup of elements that commute with all other elements of the original group—often embedded within a Lie algebra. In some cases, such a... | Central charge | 0.812154 |
18,469 | More precisely, the central charge is the charge that corresponds, by Noether's theorem, to the center of the central extension of the symmetry group. In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all... | Central charge | 0.812154 |
18,470 | Computer program Hello world (a common form of example program for learning programmers) Application software Software suite Database management system Programming software Programming tool Text editor Source code editor Integrated development environment (IDE) Assembler Compiler Interpreter Linker Debugger System soft... | Outline of computer programming | 0.81215 |
18,471 | Software engineering – Implementation Execution Software architecture Software reliability Software quality Software testing Software maintenance Software optimization Software brittleness | Outline of computer programming | 0.81215 |
18,472 | Programmer Source code Parsing Compilation Preprocessing Translation Assembly Linking Compiler optimization Compilation error | Outline of computer programming | 0.81215 |
18,473 | History of computer science History of computing hardware History of computing hardware (1960s–present) History of programming languages Timeline of programming languages Computer programming in the punched card era Operating systems timeline | Outline of computer programming | 0.81215 |
18,474 | In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently unintere... | Theoretical physicist | 0.812149 |
18,475 | Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally de... | Theoretical physicist | 0.812149 |
18,476 | "Thought" experiments are situations created in one's mind, asking a question akin to "suppose you are in this situation, assuming such is true, what would follow?". They are usually created to investigate phenomena that are not readily experienced in every-day situations. Famous examples of such thought experiments ar... | Theoretical physicist | 0.812149 |
18,477 | There have been numerous developments within the past decade in convex optimization techniques which have influenced the application of proximal gradient methods in statistical learning theory. Here we survey a few important topics which can greatly improve practical algorithmic performance of these methods. | Proximal gradient methods for learning | 0.812149 |
18,478 | Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is ℓ 1 {\displaystyle \el... | Proximal gradient methods for learning | 0.812149 |
18,479 | The curve has genus two, and so by Faltings theorem there are only a finite number of rational points on it. These rational points were proven by Nils Bruin using the computer program Kash to be the only ones on C168, and they give only four distinct trinomial polynomials with Galois group PSL(2,7): x7-7x+3 (the Trinks... | Elkies trinomial curves | 0.812143 |
18,480 | In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups. One curve, C168, gives Galois group PSL(2,7) from a polynomial of deg... | Elkies trinomial curves | 0.812143 |
18,481 | Proving the NLTS conjecture is an obstacle for resolving the qPCP conjecture, an even harder theorem to prove. The qPCP conjecture is a quantum analogue of the classical PCP theorem. The classical PCP theorem states that satisfiability problems like 3SAT are NP-hard when estimating the maximal number of clauses that ca... | NLTS conjecture | 0.812141 |
18,482 | NLTS and qPCP conjectures posit the near-infinite complexity involved in predicting the outcome of quantum systems with many interacting states. These calculations of complexity would have implications for quantum computing such as the stability of entangled states at higher temperatures, and the occurrence of entangle... | NLTS conjecture | 0.812141 |
18,483 | In quantum information theory, the no low-energy trivial state (NLTS) conjecture is a precursor to a quantum PCP theorem (qPCP) and posits the existence of families of Hamiltonians with all low-energy states of non-trivial complexity. An NLTS proof would be a consequence of one aspect of qPCP problems – the inability t... | NLTS conjecture | 0.812141 |
18,484 | In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). In the context of NLTS, Kliesch states: "a family of local gapped Hamiltonians is called topologically ordered if any ground states cannot be prepared from a product state by a constant-depth circuit... | NLTS conjecture | 0.812141 |
18,485 | A k-local Hamiltonian (quantum mechanics) H {\displaystyle H} is a Hermitian matrix acting on n qubits which can be represented as the sum of m {\displaystyle m} Hamiltonian terms acting upon at most k {\displaystyle k} qubits each: H = ∑ i = 1 m H i . {\displaystyle H=\sum _{i=1}^{m}H_{i}.} The general k-local Hamilto... | NLTS conjecture | 0.812141 |
18,486 | NLTS on its own is difficult to prove, though a simpler no low-error trivial states (NLETS) theorem has been proven, and that proof is a precursor for NLTS.NLETS is defined as: Let k > 1 be some integer, and {Hn}n ∈ N be a family of k-local Hamiltonians. {Hn}n ∈ N is NLETS if there exists a constant ε > 0 such that any... | NLTS conjecture | 0.812141 |
18,487 | In mathematics (particularly linear algebra), a shear matrix or transvection is an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity matrix and replacing one of the zero elements with a non-zero value. The name shear reflect... | Shear matrix | 0.812139 |
18,488 | This journal is indexed by the following services: Current Contents / Physics, Chemical, & Earth Sciences Web of Science Mathematical Reviews INSPEC Zentralblatt MATH Scopus | Journal of Geometry and Physics | 0.812138 |
18,489 | The Journal of Geometry and Physics is a scientific journal in mathematical physics. Its scope is to stimulate the interaction between geometry and physics by publishing primary research and review articles which are of common interest to practitioners in both fields. The journal is published by Elsevier since 1984. Th... | Journal of Geometry and Physics | 0.812138 |
18,490 | Ultan McDermott heads the McDermott Group. The group utilizes next-generation sequencing technologies, genetic screens, and bioinformatics to increase the knowledge of the effect that cancer genomes have on drug sensitivity and resistance in relation to patients. The different types of genetic screens being used includ... | Cancer Genome Project | 0.812138 |
18,491 | Research goes beyond just sequencing to include therapeutic biomarker discoveries made utilizing bioinformatics programs. Among these discoveries are drug sensitivity biomarkers and inhibitor biomarkers. These discoveries paired with the evolution of DNA sequencing technologies to next-generation sequencing techniques,... | Cancer Genome Project | 0.812138 |
18,492 | Pentao Liu leads the Liu group, which utilizes genetics, genomics, and cell biology in mice to study the role of gene functions in the development of normal cells and tissues as well as the development of various diseased cells and tissue, including cancer. The group invests a large interest in lineage choice, stem cel... | Cancer Genome Project | 0.812138 |
18,493 | In type theory, constructive mathematics and their applications to computer science, constructing analogues of subsets is often problematic—in these contexts PERs are therefore more commonly used, particularly to define setoids, sometimes called partial setoids. Forming a partial setoid from a type and a PER is analogo... | Partial equivalence relation | 0.812137 |
18,494 | Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model. It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far le... | Tuple relational calculus | 0.812135 |
18,495 | DES – An educational tool for working with Tuple Relational Calculus and other formal languages WinRDBI – An educational tool for working with Tuple Relational Calculus and other formal languages | Tuple relational calculus | 0.812135 |
18,496 | Since the calculus is a query language for relational databases we first have to define a relational database. The basic relational building block is the domain (somewhat similar, but not equal to, a data type). A tuple is a finite sequence of attributes, which are ordered pairs of domains and values. A relation is a s... | Tuple relational calculus | 0.812135 |
18,497 | To solve these problems we will restrict our attention to those queries that are domain independent, i.e., the queries that return the same result for a database under all of its schemas. An interesting property of these queries is that if we assume that the tuple variables range over tuples over the so-called active d... | Tuple relational calculus | 0.812134 |
18,498 | Tangles have been shown to be useful in studying DNA topology. The action of a given enzyme can be analysed with the help of tangle theory. | Algebraic tangle | 0.812133 |
18,499 | In mathematics, a tangle is generally one of two related concepts: In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary. In link theory, a tangle is an embedding of n arc... | Algebraic tangle | 0.812133 |
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