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5,100 | A (population) effect size θ based on means usually considers the standardized mean difference (SMD) between two populations: 78 where μ1 is the mean for one population, μ2 is the mean for the other population, and σ is a standard deviation based on either or both populations. In the practical setting the population va... | Effect size | 0.826549 |
5,101 | In the treatment group, six students pass for every one who fails, so the odds of passing are six to one (or 6/1 = 6). The effect size can be computed by noting that the odds of passing in the treatment group are three times higher than in the control group (because 6 divided by 2 is 3). Therefore, the odds ratio is 3.... | Effect size | 0.826549 |
5,102 | Multiple applications require single-base pair accuracy across populations of closely related sequences. An example is amplicon sequencing to assess the relative contribution of DNA from diverse organisms to a sample. The requirement for single basepair accuracy led to the development of methods which drew on frequency... | Oligotyping (sequencing) | 0.82653 |
5,103 | What optimization-based meta-learning algorithms intend for is to adjust the optimization algorithm so that the model can be good at learning with a few examples. | Meta-learning (computer science) | 0.826524 |
5,104 | There are three common approaches: using (cyclic) networks with external or internal memory (model-based) learning effective distance metrics (metrics-based) explicitly optimizing model parameters for fast learning (optimization-based). | Meta-learning (computer science) | 0.826524 |
5,105 | A Memory-Augmented Neural Network, or MANN for short, is claimed to be able to encode new information quickly and thus to adapt to new tasks after only a few examples. | Meta-learning (computer science) | 0.826524 |
5,106 | The goal of the RL agent is to maximize reward. It learns to accelerate reward intake by continually improving its own learning algorithm which is part of the "self-referential" policy. An extreme type of Meta Reinforcement Learning is embodied by the Gödel machine, a theoretical construct which can inspect and modify ... | Meta-learning (computer science) | 0.826524 |
5,107 | Researchers at Deepmind (Marcin Andrychowicz et al.) extended this approach to optimization in 2017. In the 1990s, Meta Reinforcement Learning or Meta RL was achieved in Schmidhuber's research group through self-modifying policies written in a universal programming language that contains special instructions for changi... | Meta-learning (computer science) | 0.826524 |
5,108 | Some approaches which have been viewed as instances of meta learning: Recurrent neural networks (RNNs) are universal computers. In 1993, Jürgen Schmidhuber showed how "self-referential" RNNs can in principle learn by backpropagation to run their own weight change algorithm, which may be quite different from backpropaga... | Meta-learning (computer science) | 0.826524 |
5,109 | Siamese neural network is composed of two twin networks whose output is jointly trained. There is a function above to learn the relationship between input data sample pairs. The two networks are the same, sharing the same weight and network parameters. | Meta-learning (computer science) | 0.826524 |
5,110 | Reptile is a remarkably simple meta-learning optimization algorithm, given that both of its components rely on meta-optimization through gradient descent and both are model-agnostic. | Meta-learning (computer science) | 0.826524 |
5,111 | This poses strong restrictions on the use of machine learning or data mining techniques, since the relationship between the learning problem (often some kind of database) and the effectiveness of different learning algorithms is not yet understood. By using different kinds of metadata, like properties of the learning p... | Meta-learning (computer science) | 0.826524 |
5,112 | Meta learning is a subfield of machine learning where automatic learning algorithms are applied to metadata about machine learning experiments. As of 2017, the term had not found a standard interpretation, however the main goal is to use such metadata to understand how automatic learning can become flexible in solving ... | Meta-learning (computer science) | 0.826524 |
5,113 | MAML, short for Model-Agnostic Meta-Learning, is a fairly general optimization algorithm, compatible with any model that learns through gradient descent. | Meta-learning (computer science) | 0.826524 |
5,114 | LSTM-based meta-learner is to learn the exact optimization algorithm used to train another learner neural network classifier in the few-shot regime. The parametrization allows it to learn appropriate parameter updates specifically for the scenario where a set amount of updates will be made, while also learning a genera... | Meta-learning (computer science) | 0.826524 |
5,115 | The key reason for studentizing is that, in regression analysis of a multivariate distribution, the variances of the residuals at different input variable values may differ, even if the variances of the errors at these different input variable values are equal. The issue is the difference between errors and residuals i... | Studentized residual | 0.826522 |
5,116 | Many programs and statistics packages, such as R, Python, etc., include implementations of Studentized residual. | Studentized residual | 0.826522 |
5,117 | MolecularLab is an Italian website of science, specialized in science, biotechnology, molecular biology, with news, forums, and events. With over 4 million page views in May 2009 it is the most visited Italian science webzine. | MolecularLab | 0.826521 |
5,118 | MolecularLab has several objectives: Providing the latest news and important discoveries in the biotechnology, medical, and molecular fields Developing the building of a community, allowing the encounter and cultural exchange among researchers, teachers, and companies Deepening techniques of molecular biology and cellu... | MolecularLab | 0.826521 |
5,119 | A binary constraint, in mathematical optimization, is a constraint that involves exactly two variables. For example, consider the n-queens problem, where the goal is to place n chess queens on an n-by-n chessboard such that none of the queens can attack each other (horizontally, vertically, or diagonally). The formal s... | Binary constraint | 0.826513 |
5,120 | Molecular Informatics is a peer-reviewed scientific journal published by Wiley VCH. It covers research in cheminformatics, quantitative structure–activity relationships, and combinatorial chemistry. It was established in 1981 as Quantitative Structure-Activity Relationships and renamed to QSAR & Combinatorial Science i... | Molecular Informatics | 0.826501 |
5,121 | {\displaystyle \mathbf {F} =\nabla \phi .\,\!} although this final form holds in any curvilinear coordinate system, not just Cartesian. This expression represents a significant feature of any conservative vector field F, namely F has a corresponding potential ϕ.Using Stokes' theorem, this is equivalently stated as ∇ × ... | Potential gradient | 0.826496 |
5,122 | In biology, a potential gradient is the net difference in electric charge across a cell membrane. | Potential gradient | 0.826495 |
5,123 | In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux. | Potential gradient | 0.826495 |
5,124 | According to the Bohr–Van Leeuwen theorem, a classical system at thermodynamic equilibrium cannot have a magnetic response. The magnetic properties of matter in terms of a microscopic theory are purely quantum mechanical. For an electron gas, the total magnetic response is paramagnetic and its magnetic susceptibility g... | Free electron model | 0.826494 |
5,125 | One open problem in solid-state physics before the arrival of quantum mechanics was to understand the heat capacity of metals. While most solids had a constant volumetric heat capacity given by Dulong–Petit law of about 3 n k B {\displaystyle 3nk_{\rm {B}}} at large temperatures, it did correctly predict its behavior a... | Free electron model | 0.826494 |
5,126 | Main predictions of the free-electron model are derived by the Sommerfeld expansion of the Fermi–Dirac occupancy for energies around the Fermi level.The name of the model comes from the first two assumptions, as each electron can be treated as free particle with a respective quadratic relation between energy and moment... | Free electron model | 0.826494 |
5,127 | The collisions do not depend on the electronic configuration. Pauli exclusion principle: Each quantum state of the system can only be occupied by a single electron. This restriction of available electron states is taken into account by Fermi–Dirac statistics (see also Fermi gas). | Free electron model | 0.826494 |
5,128 | In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drud... | Free electron model | 0.826494 |
5,129 | A phase-fired controller, like a buck-topology switched-mode power supply, is only able to deliver an output voltage not exceeding its input, minus any losses occurring in the control elements themselves. Provided the modulation during each cycle is predictable or repetitive, as it is on the national grid's AC mains, t... | Phase-fired controllers | 0.82648 |
5,130 | In mathematics, dynamic equation can refer to: difference equation in discrete time differential equation in continuous time time scale calculus in combined discrete and continuous time | Dynamic equation | 0.826479 |
5,131 | Kinetic logic, developed by René Thomas, is a Qualitative Modeling approach feasible to model impact, feedback, and the temporal evolution of the variables. It uses symbolic descriptions and avoids continuous descriptions e.g. differential equations.The derivation of the dynamics from the interaction graphs of systems ... | Kinetic logic | 0.826468 |
5,132 | Kinetic logic has been employed to study the factors that influence the selection of specific pathway from many different pathways that the system can follow and the factors that lead the system towards stable states and cyclic behaviors. It has been used to reveal the logic that lie behind the functional organization ... | Kinetic logic | 0.826468 |
5,133 | According to the scale of thresholds of the corresponding variable, the weighted algebraic sum is then discretized, so an n-valued variable is associated with an n-valued function. After discretization the integers of certain weights or sums of weights are called logical parameters. Generalized Kinetic Logic, although ... | Kinetic logic | 0.826468 |
5,134 | Preface, by John F. Nash Jr. and Michael Th. Rassias A Farewell to “A Beautiful Mind and a Beautiful Person”, by Michael Th. Rassias Introduction, John Nash: Theorems and Ideas, by Mikhail Leonidovich Gromov P =? NP, by Scott Aaronson From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, by Owen ... | Open Problems in Mathematics | 0.826466 |
5,135 | The book consists of seventeen expository articles, written by outstanding researchers, on some of the central open problems in the field of mathematics. The book also features an Introduction on John Nash: Theorems and Ideas, by Mikhail Leonidovich Gromov. According to the editors’ Preface, each article is devoted to ... | Open Problems in Mathematics | 0.826466 |
5,136 | PCKeeper Live offers 13 different PC services in 4 categories: Human Assistance (Find & Fix, Geek on Demand, Live Support), Security (Anti-Theft, Data Hider, Shredder, Files Recovery), Cleaning (Disk Cleaner, Disk Explorer, Duplicates Finder, Uninstaller) and Optimization (Context Menu Manager, Startup Manager). | PCKeeper | 0.826452 |
5,137 | PCKeeper is advertised as an optimization services package featuring a set of software utilities for Windows OS owned by Essentware S.A. (company based in Bratislava, Slovakia). It includes 2 separate products for Windows: PCKeeper Live and PCKeeper Antivirus.PCKeeper was originally developed by Zeobit LLC which was fo... | PCKeeper | 0.826452 |
5,138 | PCKeeper Live is rated "Good" (3.5 out of 5) by the PCMag editor, stating "improves PC performance", and "great for novice users" , "The utility won't clean your PC as well as Iolo System Mechanic, but considering its accessibility and wallet friendliness, it's one to check out" and "Kromtech PCKeeper Live's human spec... | PCKeeper | 0.826452 |
5,139 | Rolling circle replication (RCR) is a process of unidirectional nucleic acid replication that can rapidly synthesize multiple copies of circular molecules of DNA or RNA, such as plasmids, the genomes of bacteriophages, and the circular RNA genome of viroids. Some eukaryotic viruses also replicate their DNA or RNA via t... | Rolling circle | 0.826449 |
5,140 | Artificial neural networks (ANN) is a subfield of the research area machine learning. Work on ANNs has been somewhat inspired by knowledge of neural computation. == References == | Neural Computation | 0.826447 |
5,141 | These sorts of operations are characterized by systems of differential equations.Neural computation can be studied for example by building models of neural computation. There is a scientific journal dedicated to this subject, Neural Computation. | Neural Computation | 0.826447 |
5,142 | However, the two branches greatly disagree upon which sorts of experimental data should be used to construct explanatory models of cognitive phenomena. Connectionists rely upon behavioral evidence to construct models to explain cognitive phenomena, whereas computational neuroscience leverages neuroanatomical and neurop... | Neural Computation | 0.826447 |
5,143 | All three branches agree that cognition is computation, however, they disagree on what sorts of computations constitute cognition. The classicism tradition believes that computation in the brain is digital, analogous to digital computing. Both connectionism and computational neuroscience do not require that the computa... | Neural Computation | 0.826447 |
5,144 | Neural computation is the information processing performed by networks of neurons. Neural computation is affiliated with the philosophical tradition known as Computational theory of mind, also referred to as computationalism, which advances the thesis that neural computation explains cognition. The first persons to pro... | Neural Computation | 0.826447 |
5,145 | Other closely related fields to medical physics include fields which deal with medical data, information technology and computer science for medicine. Information and communication in medicine Medical informatics Image processing, display and visualization Computer-aided diagnosis Picture archiving and communication sy... | Medical biophysics | 0.826427 |
5,146 | Radiation therapeutic physics is also known as radiotherapy physics or radiation oncologist physics. The majority of medical physicists currently working in the US, Canada, and some western countries are of this group. A radiation therapy physicist typically deals with linear accelerator (Linac) systems and kilovoltage... | Medical biophysics | 0.826427 |
5,147 | Medical physics departments may be found in institutions such as universities, hospitals, and laboratories. University departments are of two types. The first type are mainly concerned with preparing students for a career as a hospital Medical Physicist and research focuses on improving the practice of the profession. ... | Medical biophysics | 0.826427 |
5,148 | Medical physics of diagnostic and interventional radiology involves medical imaging techniques such as magnetic resonance imaging, ultrasound, computed tomography and x-ray. Nuclear medicine will include positron emission tomography and radionuclide therapy. However one can find Medical Physicists in many other areas s... | Medical biophysics | 0.826427 |
5,149 | Medical physics deals with the application of the concepts and methods of physics to the prevention, diagnosis and treatment of human diseases with a specific goal of improving human health and well-being. Since 2008, medical physics has been included as a health profession according to International Standard Classific... | Medical biophysics | 0.826427 |
5,150 | The parameters for molecular simulations of biological macromolecules such as proteins, DNA, and RNA were often derived from observations for small organic molecules, which are more accessible for experimental studies and quantum calculations. Thereby, multiple issues arise, such as (1) unreliable atomic charges from q... | Universal force field | 0.826421 |
5,151 | The workflow may involve (1) retrieving an x-ray crystal structure or chemical formula, (2) defining atom types, (3) obtaining atomic charges, (4) assigning initial Lennard-Jones and bonded parameters, (5) computational tests of density and geometry relative to experimental reference data, (6) computational tests of en... | Universal force field | 0.826421 |
5,152 | SAFT - A top-down coarse-grained model developed in the Molecular Systems Engineering group at Imperial College London fitted to liquid phase densities and vapor pressures of pure compounds by using the SAFT equation of state. SIRAH – a coarse-grained force field developed by Pantano and coworkers of the Biomolecular S... | Universal force field | 0.826421 |
5,153 | DPD (Dissipative particle dynamics) - This is a method commonly applied in chemical engineering. It is typically used for studying the hydrodynamics of various simple and complex fluids which require consideration of time and length scales larger than those accessible to classical Molecular dynamics. The potential was ... | Universal force field | 0.826421 |
5,154 | PHAST - polarizable potential developed by Chris Cioce and coworkers. ORIENT – procedure developed by Anthony J. Stone (Cambridge University) and coworkers. Gaussian Electrostatic Model (GEM) – a polarizable force field based on Density Fitting developed by Thomas A. Darden and G. Andrés Cisneros at NIEHS; and Jean-Phi... | Universal force field | 0.826421 |
5,155 | AMBER – polarizable force field developed by Jim Caldwell and coworkers. AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) – force field developed by Pengyu Ren (University of Texas at Austin) and Jay W. Ponder (Washington University). AMOEBA force field is gradually moving to more physics-ri... | Universal force field | 0.826421 |
5,156 | OPLS (Optimized Potential for Liquid Simulations) (variants include OPLS-AA, OPLS-UA, OPLS-2001, OPLS-2005, OPLS3e, OPLS4) – developed by William L. Jorgensen at the Yale University Department of Chemistry. QCFF/PI – A general force fields for conjugated molecules. UFF (Universal Force Field) – A general force field wi... | Universal force field | 0.826421 |
5,157 | MM2 was developed by Norman Allinger mainly for conformational analysis of hydrocarbons and other small organic molecules. It is designed to reproduce the equilibrium covalent geometry of molecules as precisely as possible. It implements a large set of parameters that is continuously refined and updated for many differ... | Universal force field | 0.826421 |
5,158 | AMBER (Assisted Model Building and Energy Refinement) – widely used for proteins and DNA. CFF (Consistent Force Field) – a family of force fields adapted to a broad variety of organic compounds, includes force fields for polymers, metals, etc. CFF was developed by Arieh Warshel, Lifson, and coworkers as a general metho... | Universal force field | 0.826421 |
5,159 | In the context of chemistry and molecular modelling, a force field is a computational method that is used to estimate the forces between atoms within molecules and also between molecules. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system ... | Universal force field | 0.826421 |
5,160 | The spherical Bernstein's problem, a generalization of Bernstein's problem Carathéodory conjecture: any convex, closed, and twice-differentiable surface in three-dimensional Euclidean space admits at least two umbilical points. Cartan–Hadamard conjecture: can the classical isoperimetric inequality for subsets of Euclid... | Open problem in mathematics | 0.826415 |
5,161 | Hanna Neumann conjecture (Joel Friedman, 2011, Igor Mineyev, 2011) Density theorem (Hossein Namazi, Juan Souto, 2010) Full classification of finite simple groups (Koichiro Harada, Ronald Solomon, 2008) | Open problem in mathematics | 0.826415 |
5,162 | Duffin-Schaeffer conjecture (Dimitris Koukoulopoulos, James Maynard, 2019) Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian Demeter, Larry Guth, 2015) Goldbach's weak conjecture (Harald Helfgott, 2013) Existence of bounded gaps between primes (Yitang Zhang, Polymath8, James Maynard, 2013) Sido... | Open problem in mathematics | 0.826415 |
5,163 | Kummer–Vandiver conjecture: primes p {\displaystyle p} do not divide the class number of the maximal real subfield of the p {\displaystyle p} -th cyclotomic field. Lang and Trotter's conjecture on supersingular primes that the number of supersingular primes less than a constant X {\displaystyle X} is within a constant ... | Open problem in mathematics | 0.826415 |
5,164 | Class number problem: are there infinitely many real quadratic number fields with unique factorization? Fontaine–Mazur conjecture: actually numerous conjectures, all proposed by Jean-Marc Fontaine and Barry Mazur. Gan–Gross–Prasad conjecture: a restriction problem in representation theory of real or p-adic Lie groups. ... | Open problem in mathematics | 0.826415 |
5,165 | Zariski–Lipman conjecture: for a complex algebraic variety V {\displaystyle V} with coordinate ring R {\displaystyle R} , if the derivations of R {\displaystyle R} are a free module over R {\displaystyle R} , then V {\displaystyle V} is smooth. Zauner's conjecture: do SIC-POVMs exist in all dimensions? Zilber–Pink conj... | Open problem in mathematics | 0.826415 |
5,166 | Serre's conjecture II: if G {\displaystyle G} is a simply connected semisimple algebraic group over a perfect field of cohomological dimension at most 2 {\displaystyle 2} , then the Galois cohomology set H 1 ( F , G ) {\displaystyle H^{1}(F,G)} is zero. Serre's multiplicity conjectures Uniform boundedness conjecture fo... | Open problem in mathematics | 0.826415 |
5,167 | Hilbert's sixteenth problem: what are the possible configurations of the connected components of M-curves? Homological conjectures in commutative algebra Jacobson's conjecture: the intersection of all powers of the Jacobson radical of a left-and-right Noetherian ring is precisely 0. Kaplansky's conjectures Köthe conjec... | Open problem in mathematics | 0.826415 |
5,168 | Williamson conjecture: the problem of finding Williamson matrices, which can be used to construct Hadamard matrices. Hadamard's maximal determinant problem: what is the largest determinant of a matrix with entries all equal to 1 or –1? Hilbert's fifteenth problem: put Schubert calculus on a rigorous foundation. | Open problem in mathematics | 0.826415 |
5,169 | Green's conjecture: the Clifford index of a non-hyperelliptic curve is determined by the extent to which it, as a canonical curve, has linear syzygies. Grothendieck–Katz p-curvature conjecture: a conjectured local–global principle for linear ordinary differential equations. Hadamard conjecture: for every positive integ... | Open problem in mathematics | 0.826415 |
5,170 | Bost conjecture: a specific case of the Farrell–Jones conjecture Finite lattice representation problem: is every finite lattice isomorphic to the congruence lattice of some finite algebra? Goncharov conjecture on the cohomology of certain motivic complexes. | Open problem in mathematics | 0.826415 |
5,171 | Birch–Tate conjecture on the relation between the order of the center of the Steinberg group of the ring of integers of a number field to the field's Dedekind zeta function. Bombieri–Lang conjectures on densities of rational points of algebraic surfaces and algebraic varieties defined on number fields and their field e... | Open problem in mathematics | 0.826415 |
5,172 | Minimum overlap problem of estimating the minimum possible maximum number of times a number appears in the termwise difference of two equally large sets partitioning the set { 1 , … , 2 n } {\displaystyle \{1,\ldots ,2n\}} Pollock's conjectures Does every nonnegative integer appear in Recamán's sequence? Skolem problem... | Open problem in mathematics | 0.826415 |
5,173 | Volume conjecture relating quantum invariants of knots to the hyperbolic geometry of their knot complements. Whitehead conjecture: every connected subcomplex of a two-dimensional aspherical CW complex is aspherical. Zeeman conjecture: given a finite contractible two-dimensional CW complex K {\displaystyle K} , is the s... | Open problem in mathematics | 0.826415 |
5,174 | Arthur's conjectures Dade's conjecture relating the numbers of characters of blocks of a finite group to the numbers of characters of blocks of local subgroups. Demazure conjecture on representations of algebraic groups over the integers. Kazhdan–Lusztig conjectures relating the values of the Kazhdan–Lusztig polynomial... | Open problem in mathematics | 0.826415 |
5,175 | Arnold–Givental conjecture and Arnold conjecture – relating symplectic geometry to Morse theory. Berry–Tabor conjecture in quantum chaos Banach's problem – is there an ergodic system with simple Lebesgue spectrum? Birkhoff conjecture – if a billiard table is strictly convex and integrable, is its boundary necessarily a... | Open problem in mathematics | 0.826415 |
5,176 | Singmaster's conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle? The uniqueness conjecture for Markov numbers that every Markov number is the largest number in exactly one normalized solution to the Markov Diophantine equation. Vojta's conjecture on height... | Open problem in mathematics | 0.826415 |
5,177 | Leopoldt's conjecture: a p-adic analogue of the regulator of an algebraic number field does not vanish. Lindelöf hypothesis that for all ϵ > 0 {\displaystyle \epsilon >0} , ζ ( 1 / 2 + i t ) = o ( t ϵ ) {\displaystyle \zeta (1/2+it)=o(t^{\epsilon })} The density hypothesis for zeroes of the Riemann zeta function Little... | Open problem in mathematics | 0.826415 |
5,178 | Hilbert's ninth problem: find the most general reciprocity law for the norm residues of k {\displaystyle k} -th order in a general algebraic number field, where k {\displaystyle k} is a power of a prime. Hilbert's twelfth problem: extend the Kronecker–Weber theorem on Abelian extensions of Q {\displaystyle \mathbb {Q} ... | Open problem in mathematics | 0.826415 |
5,179 | Hall's conjecture: for any ϵ > 0 {\displaystyle \epsilon >0} , there is some constant c ( ϵ ) {\displaystyle c(\epsilon )} such that either y 2 = x 3 {\displaystyle y^{2}=x^{3}} or | y 2 − x 3 | > c ( ϵ ) x 1 / 2 − ϵ {\displaystyle |y^{2}-x^{3}|>c(\epsilon )x^{1/2-\epsilon }} . Hardy–Littlewood zeta-function conjecture... | Open problem in mathematics | 0.826415 |
5,180 | Catalan–Dickson conjecture on aliquot sequences: no aliquot sequences are infinite but non-repeating. Congruent number problem (a corollary to Birch and Swinnerton-Dyer conjecture, per Tunnell's theorem): determine precisely what rational numbers are congruent numbers. Erdős–Moser problem: is 1 1 + 2 1 = 3 1 {\displays... | Open problem in mathematics | 0.826415 |
5,181 | Twin prime conjecture: there are infinitely many twin primes. Does the converse of Wolstenholme's theorem hold for all natural numbers?Are all Euclid numbers square-free? Are all Fermat numbers square-free? | Open problem in mathematics | 0.826415 |
5,182 | Gillies' conjecture on the distribution of prime divisors of Mersenne numbers. Goldbach conjecture: all even natural numbers greater than 2 {\displaystyle 2} are the sum of two prime numbers. Landau's problems Problems associated to Linnik's theorem New Mersenne conjecture: for any odd natural number p {\displaystyle p... | Open problem in mathematics | 0.826415 |
5,183 | Standard conjectures on algebraic cycles Tate conjecture on the connection between algebraic cycles on algebraic varieties and Galois representations on étale cohomology groups. Virasoro conjecture: a certain generating function encoding the Gromov–Witten invariants of a smooth projective variety is fixed by an action ... | Open problem in mathematics | 0.826415 |
5,184 | Nakai conjecture: if a complex algebraic variety has a ring of differential operators generated by its contained derivations, then it must be smooth. Parshin's conjecture: the higher algebraic K-groups of any smooth projective variety defined over a finite field must vanish up to torsion. Section conjecture on splittin... | Open problem in mathematics | 0.826415 |
5,185 | Hartshorne's conjectures Jacobian conjecture: if a polynomial mapping over a characteristic-0 field has a constant nonzero Jacobian determinant, then it has a regular (i.e. with polynomial components) inverse function. Manin conjecture on the distribution of rational points of bounded height in certain subsets of Fano ... | Open problem in mathematics | 0.826415 |
5,186 | Dixmier conjecture: any endomorphism of a Weyl algebra is an automorphism. Fröberg conjecture on the Hilbert functions of a set of forms. Fujita conjecture regarding the line bundle K M ⊗ L ⊗ m {\displaystyle K_{M}\otimes L^{\otimes m}} constructed from a positive holomorphic line bundle L {\displaystyle L} on a compac... | Open problem in mathematics | 0.826415 |
5,187 | Abundance conjecture: if the canonical bundle of a projective variety with Kawamata log terminal singularities is nef, then it is semiample. Bass conjecture on the finite generation of certain algebraic K-groups. Bass–Quillen conjecture relating vector bundles over a regular Noetherian ring and over the polynomial ring... | Open problem in mathematics | 0.826415 |
5,188 | The Kourovka Notebook (Russian: Коуровская тетрадь) is a collection of unsolved problems in group theory, first published in 1965 and updated many times since. The Sverdlovsk Notebook (Russian: Свердловская тетрадь) is a collection of unsolved problems in semigroup theory, first published in 1969 and updated many times... | Open problem in mathematics | 0.826415 |
5,189 | Is every infinite, minimal field of characteristic zero algebraically closed? (Here, "minimal" means that every definable subset of the structure is finite or co-finite.) Is the Borel monadic theory of the real order (BMTO) decidable? | Open problem in mathematics | 0.826415 |
5,190 | The Cherlin–Zilber conjecture: A simple group whose first-order theory is stable in ℵ 0 {\displaystyle \aleph _{0}} is a simple algebraic group over an algebraically closed field. Generalized star height problem: can all regular languages be expressed using generalized regular expressions with limited nesting depths of... | Open problem in mathematics | 0.826415 |
5,191 | The Brennan conjecture: estimating the integral of powers of the moduli of the derivative of conformal maps into the open unit disk, on certain subsets of C {\displaystyle \mathbb {C} } The four exponentials conjecture: the transcendence of at least one of four exponentials of combinations of irrationals Fuglede's conj... | Open problem in mathematics | 0.826415 |
5,192 | Sudoku: How many puzzles have exactly one solution? How many puzzles with exactly one solution are minimal? What is the maximum number of givens for a minimal puzzle? Tic-tac-toe variants: Given a width of tic-tac-toe board, what is the smallest dimension such that X is guaranteed a winning strategy? (See also: Hales-J... | Open problem in mathematics | 0.826415 |
5,193 | Woodin's Ω-conjecture: if there is a proper class of Woodin cardinals, then Ω-logic satisfies an analogue of Gödel's completeness theorem.Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal? Does there exist a Jónsson algebra on ℵω? Is OCA (the ... | Open problem in mathematics | 0.826415 |
5,194 | Maximal rank conjecture (Eric Larson, 2018) Weibel's conjecture (Moritz Kerz, Florian Strunk, and Georg Tamme, 2018) Yau's conjecture (Antoine Song, 2018) Pentagonal tiling (Michaël Rao, 2017) Willmore conjecture (Fernando Codá Marques and André Neves, 2012) Erdős distinct distances problem (Larry Guth, Nets Hawk Katz,... | Open problem in mathematics | 0.826415 |
5,195 | Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set th... | Open problem in mathematics | 0.826415 |
5,196 | Lafforgue's theorem (Laurent Lafforgue, 1998) Fermat's Last Theorem (Andrew Wiles and Richard Taylor, 1995) | Open problem in mathematics | 0.826415 |
5,197 | Kauffman–Harary conjecture (Thomas Mattman, Pablo Solis, 2009) Surface subgroup conjecture (Jeremy Kahn, Vladimir Markovic, 2009) Normal scalar curvature conjecture and the Böttcher–Wenzel conjecture (Zhiqin Lu, 2007) Nirenberg–Treves conjecture (Nils Dencker, 2005) Lax conjecture (Adrian Lewis, Pablo Parrilo, Motakuri... | Open problem in mathematics | 0.826415 |
5,198 | Kahn–Kalai conjecture (Jinyoung Park and Huy Tuan Pham, 2022) Blankenship–Oporowski conjecture on the book thickness of subdivisions (Vida Dujmović, David Eppstein, Robert Hickingbotham, Pat Morin, and David Wood, 2021) Ringel's conjecture on graceful labeling of trees (Richard Montgomery, Benny Sudakov, Alexey Pokrovs... | Open problem in mathematics | 0.826415 |
5,199 | It is important to understand the terms "heterozygous", "homozygous", "double heterozygote" (or homozygote), "dominant allele" and "recessive allele" when using the Punnett square method. For multiple traits, using the "forked-line method" is typically much easier than the Punnett square. Phenotypes may be predicted wi... | Allele chart | 0.826415 |
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