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See searches and references containing SEPARABILITY PROBLEM!SEPARABILITY PROBLEM
The separability problem is a concept from the field of social choice theory that describes the situation where two or more issues up for vote on a ballot
Separability_problem
Quantum states that are not entangled
criterion is actually a necessary and sufficient condition for separability. Other separability criteria include (but not limited to) the range criterion,
Separable_state
About polynomials in several variables
false in one dimension, so the separable Jacobian conjecture, also called Adjamagbo's Jacobian conjecture, adds a separability premise to make the conjecture
Jacobian_conjecture
Direct vote on a specific proposal
referendum attack the use of closed questions. A difficulty called the separability problem can plague a referendum on two or more issues. If one issue is in
Referendum
Geometric property of a pair of sets of points in Euclidean geometry
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane)
Linear_separability
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of algebraic field extension
field is separable. It follows that most extensions that are considered in mathematics are separable. Nevertheless, the concept of separability is important
Separable_extension
Algorithm for supervised learning of binary classifiers
(prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired, even with optimal
Perceptron
Legal concept regulating rights of a creative work
A copyright is a type of intellectual property that gives its owner the exclusive legal right to copy, distribute, adapt, display, and perform a creative
Copyright
Partially unsolved problem in mathematics
that acts on a Banach space that is not isomorphic to a separable Hilbert space). The problem seems to have been stated in the mid-20th century after
Invariant_subspace_problem
French mathematician (born 1944)
x_{N})=\sum _{n}f_{n}(x_{n}).} For example, problems of linear optimization are separable. For a separable problem, we consider an optimal solution x min =
Ivar_Ekeland
Physics phenomenon
criterion is merely a necessary one for separability, as the problem becomes NP-hard when generalized. Other separability criteria include (but not limited
Quantum_entanglement
Class of algorithms for solving constrained optimization problems
is separable in x and y. The dual update requires solving a proximity function in x and y at the same time; the ADMM technique allows this problem to
Augmented_Lagrangian_method
Study of optimal transportation and allocation of resources
to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781. In the
Transportation theory (mathematics)
Transportation_theory_(mathematics)
Philosophical question
The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties
Problem_of_universals
Improvement of the coordinate descent algorithm
extend the coordinate descent method (c) to the optimization of non-separable problems (d). The adaptation of an appropriate coordinate system allows adaptive
Adaptive_coordinate_descent
Robotics problem on coordinating two parts of a robot
different methods and solutions developed to solve the problem, broadly defined as either separable, simultaneous solutions. Each type of solution has specific
Hand–eye_calibration_problem
Class of ordinary differential equations
applied mathematics, where Sturm–Liouville problems occur very frequently, particularly when dealing with separable linear partial differential equations.
Sturm–Liouville_theory
Problem in physics and astronomy
In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other
Euler's_three-body_problem
Millennium Prize Problem
existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Ability to make choices voluntarily
"Intricately related to the hard problem of consciousness, the hard problem of free will represents the core problem of conscious free will: Does conscious
Free_will
Technique for solving differential equations
differential equation for the unknown f ( x ) {\displaystyle f(x)} is separable if it can be written in the form d d x f ( x ) = g ( x ) h ( f ( x ) )
Separation_of_variables
Necessary condition for optimality associated with dynamic programming
that if the cost function of the multi-stage optimization problem satisfies a "backward separable" structure, then the appropriate Bellman equation can be
Bellman_equation
time whether a given separable permutation is a pattern in a larger permutation, in contrast to the same problem for non-separable permutations, which
Separable_permutation
Mathematical problem in von Neumann algebra theory
conjecture in C*-algebra theory Tsirelson's problem in quantum information theory The predual of any (separable) von Neumann algebra is finitely representable
Connes_embedding_problem
French applied mathematician
commitment problems"), where nonconvexity appears because of integer constraints: Bertsekas, Dimitri P. (1982). "5.6 Large scale separable integer programming
Claude_Lemaréchal
Social choice problem
around. This problem is called non-separability. There are several approaches for eliciting voters' preferences when they are not separable: If there are
Multi-issue_voting
(not necessarily separable) Hilbert space. The problem has been solved in the affirmative for special cases (specifically for separable and Type-I C*-algebras)
Naimark's_problem
Method of analyzing variables in software
locally separable problems. Such problems have generic polynomial-time solutions. In addition to the reaching definitions and live variables problems mentioned
Data-flow_analysis
Sums of sets of vectors are nearly convex
large and separable problems, despite the non-convexities of the summand functions. Ekeland and later authors argued that additive separability produced
Shapley–Folkman_lemma
Conjecture in graph theory
Unsolved problem in mathematics Are graphs uniquely determined by their subgraphs? More unsolved problems in mathematics In graph theory, informally, the
Reconstruction_conjecture
Mathematical model to assist inventory levels
the Morse and Kimball (1951)'s book. The problem was termed the "Christmas tree problem" and "newsboy problem" in the 1960s and 1970s, and beginning in
Newsvendor_model
Mathematical game of resource allocation
The Kolkata Paise Restaurant Problem (KPR Problem) is a mathematical game for competitive resource allocation without any coordination. Its name is drawn
Kolkata Paise Restaurant Problem
Kolkata_Paise_Restaurant_Problem
Class of problems in classical mechanics
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field. A central force is a force
Classical central-force problem
Classical_central-force_problem
should not be confused with the case of a separable ODE, which refers to a somewhat different class of problems that can be broken into a pair of integrals;
Separable partial differential equation
Separable_partial_differential_equation
The SR1 method has computational advantages for sparse or partially separable problems. A twice continuously differentiable function x ↦ f ( x ) {\displaystyle
Symmetric_rank-one
Unique extension of pure states in Hilbert spaces
In mathematics, the Kadison–Singer problem, posed in 1959, was a problem in functional analysis about whether certain extensions of certain linear functionals
Kadison–Singer_problem
Problem in set theory
In mathematics, Suslin's problem is a question about totally ordered sets posed by Mikhail Yakovlevich Suslin (1920) and published posthumously. It has
Suslin's_problem
Hypersurface used by a classification algorithm
maximum margin. If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing
Decision_boundary
mathematics, a logical matrix may be described as d-disjunct and/or d-separable. These concepts play a pivotal role in the mathematical area of non-adaptive
Disjunct_matrix
Class of economic models
the assumption of weak separability, under which groups of goods or inputs can be treated as composite aggregates. Separability allows a high-dimensional
Computable general equilibrium
Computable_general_equilibrium
Term in mathematics
bundle is trivial. This is related to the solution of the second Cousin problem. The standard complex space C n {\displaystyle \mathbb {C} ^{n}} is a Stein
Stein_manifold
Technique in numerical linear algebra
matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the
Low-rank_approximation
Problem on words in group theory
In abstract algebra, the conjugacy problem for a group G with a given presentation is the decision problem of determining, given two words x and y in
Conjugacy_problem
Difficulties arising when analyzing data with many aspects ("dimensions")
One example of the blessing of dimensionality phenomenon is linear separability of a random point from a large finite random set with high probability
Curse_of_dimensionality
School of thought of philosophy of law and jurisprudence
teachings of the empiricists preceded systemization of a positivist method for problems of comprehension and analysis, which was later represented by legal positivism
Legal_positivism
Italian mathematician (1873–1941)
celestial mechanics (notably on the three-body problem), analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and
Tullio_Levi-Civita
Neural network technology
Depthwise separable convolution separates the standard convolution into two steps: depthwise convolution and pointwise convolution. The depthwise separable convolution
Convolutional_layer
Swedish mathematician and concert pianist
operators. The basis problem was posed by Stefan Banach in his book, Theory of Linear Operators. Banach asked whether every separable Banach space has a
Per_Enflo
Type of vector space in math
separable Hilbert spaces are therefore isometrically isomorphic to the square-summable sequence space, ℓ 2 . {\displaystyle \ell ^{2}.} Separability was
Hilbert_space
Thought experiment in quantum mechanics
point of contact. The EPR paper concludes with a claim that this lack of separability meant that quantum mechanics as a theory of reality was incomplete. Schrödinger
Schrödinger's_cat
Book by Marvin Minsky and Seymour Papert
the XOR function, and also the important connectedness predicate. The problem of connectedness is illustrated at the awkwardly colored cover of the book
Perceptrons_(book)
as a series of separable potentials. The Coulomb interaction between two protons is a special problem, in that its expansion in separable potentials does
Faddeev_equations
Basic concept of graph theory
isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience
Connectivity_(graph_theory)
{\displaystyle \displaystyle {f_{x,y}(g)=(T_{g}^{-1}x,T_{g}^{-1}y),}} generate a separable unital C* subalgebra A of the uniformly bounded continuous functions on
Uniformly bounded representation
Uniformly_bounded_representation
Theoretical framework in physics
and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure
Quantum_field_theory
distortion problem is now primarily of interest on the spaces ℓp, all of which are separable and uniform convex, for 1 < p < ∞. In separable and uniform
Distortion_problem
Method of solving differential equations
arbitrary regions and boundary conditions. They do not depend on the separability of the equations or other special properties of the equation. They have
Multigrid_method
Process of producing small rectangular items of fixed dimensions
Madhusudhan Reddy (2020). Byrka, Jaros\law; Meka, Raghu (eds.). "On Guillotine Separability of Squares and Rectangles". Approximation, Randomization, and Combinatorial
Guillotine_cutting
Restriction on topological groups in mathematics
compact, separable metric, locally connected group with no small subgroup is a Lie group. (cf. Hilbert's fifth problem.) Hilbert's fifth problem § No small
No_small_subgroup
Type of feedforward neural network
layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks are trained using backpropagation and are colloquially
Multilayer_perceptron
Process by which a quantum system takes on a definitive state
result in one definite outcome. This difference is called the measurement problem of quantum mechanics. To predict measurement outcomes from quantum solutions
Wave_function_collapse
Process in machine learning and statistics
information; see here. Other available filter metrics include: Class separability Error probability Inter-class distance Probabilistic distance Entropy
Feature_selection
Theory of perception
that animals can learn by "sudden insight" into the "structure" of a problem, over and above the associative and incremental manner of learning that
Gestalt_psychology
Collection of random variables
space. The concept of separability of a stochastic process was introduced by Joseph Doob. The underlying idea of separability is to make a countable
Stochastic_process
The real numbers or their cardinality
y ∈ C such that x < y, then there exists z ∈ S such that x < z < y. (separability axiom) C has no first element and no last element. (Unboundedness axiom)
Continuum_(set_theory)
Concept in topology
In mathematics, a Polish space is a separable, completely metrizable topological space; i.e., a space homeomorphic to a complete metric space that has
Polish_space
of unsolved problems about them. Any open subset of a cosmic space is cosmic since open subsets of separable spaces are separable. Separable metric spaces
Cosmic_space
brief summary of some of the most frequently used methods. Using the separability property of the Gaussian kernel g N ( x 1 , … , x N , t ) = G ( x 1
Scale_space_implementation
Mathematical connection between field theory and group theory
connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to
Galois_theory
Statistics dataset
Fisher in his 1936 paper The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis. It is sometimes called Anderson's
Iris_flower_data_set
Abelian group related to division algebras
of cyclic algebras of degree p {\displaystyle p} . It is a major open problem (raised by Albert) whether every division algebra of prime degree over
Brauer_group
Nonparametric spectral estimation method
separable as N → ∞ {\displaystyle N\rightarrow \infty } . In practice N {\displaystyle N} is fixed and one is interested in approximate separability between
Singular_spectrum_analysis
Galois group of the separable closure
{\displaystyle K} , where K sep {\displaystyle K^{\textrm {sep}}} is a separable closure of K {\displaystyle K} . Alternatively, it is the group of all
Absolute_Galois_group
Type of mathematical functions
meromorphic functions, i.e. the problem of creating a global meromorphic function from zeros and poles, is called the Cousin problem. Also, the interesting phenomena
Function of several complex variables
Function_of_several_complex_variables
2017 United States Supreme Court case
articles" can be restricted by copyright law. The Court created a two-prong "separability" test, granting copyrightability based on separate identification and
Star Athletica, LLC v. Varsity Brands, Inc.
Star_Athletica,_LLC_v._Varsity_Brands,_Inc.
Statistical test for causality
variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation. While Granger causality is best
Convergent_cross_mapping
unified transform, is an algorithmic procedure for analysing boundary value problems for linear partial differential equations and for an important class of
Fokas_method
Differential equation exhibiting high rate of dissipation
In computational mathematics, a stiff equation is an initial value problem u ˙ = f ( u ) , u ( 0 ) = u 0 , t ∈ [ 0 , T ] , {\displaystyle {\dot {u}}=f(u)\
Stiff_equation
Graph whose induced subgraphs preserve distance
discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances in any connected induced subgraph
Distance-hereditary_graph
Special case of the Euler-Lagrange equations
example of an application of the Beltrami identity is the brachistochrone problem, which involves finding the curve y = y ( x ) {\displaystyle y=y(x)} that
Beltrami_identity
American mathematician and educator (1921–2008)
varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in mathematics teaching at
Andrew_M._Gleason
Theory in mathematics
generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician Gennadi
KK-theory
Form of decision making in machine learning
using the concept of piecewise-linear separability of datasets to categorize data. Two datasets are linearly separable if their convex hulls do not intersect
Multi-surface_method
Distance function defined between probability distributions
that needs to be moved times the mean distance it has to be moved. This problem was first formalised by Gaspard Monge in 1781. Because of this analogy
Wasserstein_metric
Mathematical concept
(1973). "P. Enflo solved in the negative Banach's problem on the existence of a basis for every separable Banach space". Fiz.-Mat. Spis. Bulgar. Akad. Nauk
Approximation_property
distinct connected component in the structure (this property is called separability). The find operation is performed by following links from the element
Pointer_algorithm
Topological space that is homeomorphic to a metric space
second-countable. Urysohn's Theorem can be restated as: A topological space is separable and metrizable if and only if it is regular, Hausdorff and second-countable
Metrizable_space
fall' but 'verfallen', 'to decay' or 'to be ruined'. Many verbs have a separable prefix that changes the meaning of the root verb, but that does not always
German_verbs
Ring that is also a vector space or a module
of A, sometimes called the bidimension of A, measures the failure of separability. Let A be a finite-dimensional algebra over a field k. Then A is an Artinian
Associative_algebra
Statement in computational learning theory
complex pattern-classification problem, cast in a high-dimensional space nonlinearly, is more likely to be linearly separable than in a low-dimensional space
Cover's_theorem
Feature of systems that defy description
classes, the separability of the classes, and measures of geometry, topology, and density of manifolds. For non-binary classification problems, instance
Complexity
Description of physical properties at the atomic and subatomic scale
1007/s10701-009-9347-0. S2CID 32755624. Howard, D. (1985). "Einstein on locality and separability". Studies in History and Philosophy of Science Part A. 16 (3): 171–201
Quantum_mechanics
Special state of wave and quantum systems in physics
symmetries of propagating modes in the continuum. Arise when the eigenvalue problem is solved by the Separation of Variables Method, and the wave function
Bound_state_in_the_continuum
State or quality of being bodiless
incorporeal if it is not made out of matter. In the problem of universals, universals are separable from any particular embodiment in one sense, while
Incorporeality
Solving multiple machine learning tasks at the same time
matrices}}\}\subset \mathbb {R} ^{T\times T}} . This factorization property, separability, implies the input feature space representation does not vary by task
Multi-task_learning
Map of history from Big Bang to present
relation to the known. It achieves this novel accomplishment by solving the problem of psychology and giving rise to a truly consilient view of the scientific
Tree_of_knowledge_system
Subpermutation of a longer permutation
{C}}} . This problem is known as C {\displaystyle {\mathcal {C}}} -Pattern PPM and it was shown to be polynomial-time solvable for separable permutations
Permutation_pattern
Mathematical function
approximation and in linear inverse problems, and as apodization tapers or window functions in quadratic problems of spectral density estimation. Slepian
Slepian_function
Numerical integration scheme for Hamiltonian systems
long-term evolution of chaotic Hamiltonian systems ranging from the Kepler problem to the classical and semi-classical simulations in molecular dynamics.
Symplectic_integrator
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