We study the structure of finite quandles in terms of subquandles. Every finite quandle decomposes in a natural way as a union of disjoint -complemented subquandles; this decomposition coincides with the usual orbit decomposition of . Conversely, the structure of a finite quandle with a given orbit decomposit…
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “Finite Structure”
Study finite singularities in G2 structure flows using Shi-type estimates.
problem Finite time singularities in G2 structure flows.
method Extend Shi-type estimates to G2 structure flows and prove κ-non-collapsing theorem.
result Prove finite time singularities of G2 structure flows.
Researchers find Frobenius manifold structures on orbits spaces of finite groups.
problem Understanding Frobenius manifold structures on orbits spaces of finite groups.
method Applying Dubrovin's method to various orbits spaces of linear representations of finite groups.
result Discoveries of non-trivial Frobenius manifold structures on orbits spaces.
Characterizes monodromies of projective structures on finite-type surfaces.
problem Understanding monodromies of projective structures on finite-type surfaces.
method Geometrical/topological study of local conical projective structures.
result Any representation can be represented as the holonomy of a branched projective structure.
No spin structures found in a hyperbolic 4D space.
problem Finding hyperbolic 4-manifolds without spin structures.
method Constructed a non-compact, orientable, hyperbolic 4-manifold.
result Demonstrated existence of a hyperbolic 4D space without spin structures.
Proves Vaisman solvmanifolds are finite quotients of Kodaira-Thurston manifolds.
problem Characterizing Vaisman solvmanifolds and their properties.
method Analyzing fundamental groups and quotient structures.
result Every Vaisman solvmanifold is a finite quotient of a Kodaira-Thurston manifold.
New corks found with Stein structures and hyperbolic boundaries.
problem Existence of boundary-sum irreducible finite order corks with Stein structures.
method Proved for any positive integer n, constructed corks with Stein structures and verified hyperbolic boundaries.
result Found boundary-sum irreducible -corks with Stein structures and verified hyperbolic boundaries.
The paper bends hyperbolic manifolds into convex structures.
problem Creating convex structures from hyperbolic manifolds.
method Bending totally geodesic hypersurfaces in finite volume hyperbolic manifolds.
result Examples of non-compact, finite volume, properly convex manifolds are found.
Generalizes pseudo-product structures with abnormal extremals.
problem Finiteness of symmetry algebras for non-degenerate pseudo-product structures.
method Modified universal prolongation of graded nilpotent Lie algebras and generalized finiteness criterion.
result Distributions with singularly transitive properties have finite-dimensional symmetries.
Finite groups can be automorphism groups of translation surfaces with poles.
problem Existence of finite automorphism groups on translation surfaces with poles.
method Analyzing translation surfaces with poles and extending results to branched projective structures.
result Finite groups can be automorphism groups of translation surfaces with poles.
This thesis introduces big mapping class groups and their structure.
problem Understanding mapping class groups of infinite-type surfaces.
method Systematic introduction and analysis of structure and topological generation.
result Key differences from finite-type mapping class groups.
Study on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds, proving finiteness or infiniteness of induced distance.
problem Determining the finiteness of the induced distance on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds.
method Analyzing the structural stability of the finiteness/not-finiteness of the induced distance on closed surfaces of genus g≥1.
result Closed surfaces of genus g≥1 can be embedded in such a way that the induced distance is either always finite or always infinite.
Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexitystat.ML
New findings show modern neural networks have finite sample complexity in o-minimal structures.
problem Understanding the learnability of modern neural networks in a broad context.
method Analyzing feedforward neural networks definable in o-minimal structures.
result Modern neural networks, including MLPs, CNNs, GNNs, and transformers, have finite sample complexity in the agnostic PAC setting.
The paper extends Nambu-Poisson structures to infinite dimensions.
problem Extending Nambu-Poisson structures to infinite dimensional settings.
method Adapting finite dimensional Nambu-Poisson structures to a convenient manifold setting.
result Classical results in finite dimensions can be extended to infinite dimensions for partial Nambu structures.
Researchers address the generation of differential invariants for geometric structures.
problem Finite generation of differential algebra of relative differential invariants.
method Investigation of algebraic and differential properties, localization, weight analysis.
result Localization on a finite set of relative invariants makes the differential algebra finitely generated.
Paper detects gradual changes in cluster structure using MC fusion.
problem Detecting gradual changes in cluster structure over time.
method MC fusion for multiple mixture numbers, examining MC transition.
result Accurately captures cluster structure during transitional periods.
We give elementary constructions of manifold with corner structures and associative gluing maps on compactifications of spaces of infinite, half infinite, and finite Morse flow lines.
We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.
AI can identify simple groups and match algebraic tables, even with limited training.
problem Can AI learn algebraic structures?
method Machine learning techniques (SVM, neural classifiers) applied to finite groups and rings.
result AI can correctly identify simple groups and match algebraic tables for small structures.
The paper constructs symplectic forms on frame bundles and proves finite cohomologies.
problem Proving finiteness theorems for basic symplectic cohomologies.
method Construction of invariant 2-forms on the real symplectic group, symplectic form on quotient by a maximal torus, and lifting symplectic structure to frame bundles.
result Valid proof of finiteness theorems for basic symplectic cohomologies.
Finite resources limit false discovery rate control in structured hypothesis spaces.
problem Controlling false discovery rate in hypothesis testing with finite data and structured hypothesis spaces.
method Framework for exact FDR control and adaptive power maximization.
result Exact FDR control and adaptive power maximization.
Study shows fibered knots' quandles have consistent structure.
problem Understanding the structure of fibered knots through their quandles.
method Analyzes the fiber bundle structure of fibered knots and applies it to their quandles.
result Finiteness and equivalence of knot quandles of fibered knots are discussed.
Unified framework for Arnold-type invariants via dual complexes and finite-difference structures.
problem Study of Arnold-type invariants of immersed curves and surfaces.
method Framework on dual complexes, locally normalized maps, finite-difference structures, and Shumakovitch-type identities.
result Unified evaluation of Arnold-type invariants and on dual skeleta.
Finite 2-step nilpotent groups studied by Kim and Manturov.
problem Understanding the structure of groups defined by Kim and Manturov.
method Analyzing the groups for all .
result The groups are finite and 2-step nilpotent.
Let be a finite abelian group. A dynamical system with transformation group is a triple , consisting of a unital locally convex algebra , the finite abelian group and a group homomorphism $α:Λ\rightarrow\Aut(A)$, which induces an action of on . In this paper we present a new, geometricall…
Let V be a closed 3-manifold. In this paper we prove that the homotopy classes of plane fields on V that contain tight contact structures are in finite number and that, if V is atoroidal, the isotopy classes of tight contact structures are also in finite number.
Paper proves existence of Frobenius-like structures using vector bases.
problem Existence of Frobenius-like structures in vector spaces.
method Study of finite sets of vectors in a vector space to find bases.
result Necessary and sufficient condition to find bases in a set of vectors.
The study classifies flat solvmanifolds and finds -structures on them.
problem Classifying and finding -structures on flat solvmanifolds.
method Classification of flat splittable solvmanifolds and search for compatible -structures.
result Examples of compact flat manifolds with specific -structures.
Stochastic Optimization with Variance Reduction for Infinite Datasets with Finite-Sum Structurestat.ML
Paper introduces variance reduction for infinite datasets with finite-sum structure.
problem Optimizing composite and strongly convex objectives with stochastic perturbations.
method Variance reduction approach for stochastic optimization with composite and strongly convex objectives.
result Convergence rate outperforms SGD with a smaller constant factor.
Survey on quadratic differentials in Teichmüller theory.
problem Understanding quadratic differentials in Teichmüller theory.
method Expository survey of quadratic differentials' roles.
result Summarizes results for non-compact surfaces.
Currents on Lie groups form a Hopf algebra structure.
problem Understanding algebraic structure of currents on Lie groups.
method Defined Hopf algebra structure on currents using convolution and wedge product.
result Explicit formulas for Hopf algebra operations on currents are derived.
Extends Dirac structures to infinite dimensions, focusing on convenient Lie algebroids and manifolds.
problem Extending classical geometrical results from finite to infinite dimensions.
method Introduces partial Dirac structures on convenient Lie algebroids and manifolds, explores their properties and limits.
result Classical geometrical results can be extended to infinite dimensional contexts.
Finite-time Lyapunov exponents of deep neural networkscond-mat.dis-nn
Study of deep neural networks using finite-time Lyapunov exponents.
problem Understanding the geometric structures in input space formed by deep neural networks.
method Analogy with dynamical systems, computing finite-time Lyapunov exponents.
result Ridges of large positive exponents divide input space into regions associated with different classes.
The paper examines conditions for commuting conjugates of finite-order mapping classes.
problem Conditions for commuting conjugates of finite-order mapping classes.
method Derived necessary and sufficient conditions for commuting conjugates.
result Conditions for the primitivity of finite-order mapping classes.
The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.
problem Analyzing finite-time singularities in Spin(7)-structure flows.
method Proves Shi-type derivative estimates and shows that Λ(x,t) must blow up at finite-time singularities.
result Establishes a general analytic framework for studying Spin(7)-structure flows.
Finite automorphisms group for certain CR manifolds.
problem Locally homogeneous CR manifolds and their automorphisms.
method Condition on underlying contact structure, finite dimensional Lie group.
result CR automorphisms form a finite dimensional Lie group.
Unified algebraic framework for virtual braid structures with strong structural consequences.
problem Unified algebraic framework for virtual braid structures with various types of crossings.
method Introducing the universal virtual braid group and proving its properties.
result Strong structural consequences including residual finiteness, linearity, and solvability of conjugacy problems.
We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between …
On symplectic quandlesmath.QA
We study the structure of symplectic quandles, quandles which are also R-modules equipped with an antisymmetric bilinear form. We show that every finite dimensional symplectic quandle over a finite field F or arbitrary field F of characteristic other than 2 is a disjoint union of a trivial quandle and a connected quand…
Defines invariants for reflection groups and connects them to Frobenius structures.
problem Understanding invariants for reflection groups and their relation to Frobenius structures.
method Defines good basic invariants and shows their connection to Frobenius structures.
result Good basic invariants for reflection groups lead to Frobenius structure constants.
Singularity structures and impacts on parameter estimation in finite mixtures of distributionsmath.ST
Study singularity structures in finite mixtures affecting parameter estimation rates.
problem Understanding how singularity structures impact parameter estimation in finite mixtures.
method Developed a general framework to identify singularity structures in finite mixtures and studied their effects on convergence rates and minimax lower bounds.
result Established convergence rates for finite mixtures of skew-normal distributions, revealing complex asymptotic behaviors.
Self-shrinkers in 3D have simple ends.
problem Understanding the structure of self-shrinkers.
method Analyzing asymptotic behavior of noncompact self-shrinkers.
result Each end of a self-shrinker is asymptotic to a cone or cylinder.
Study on numerical analysis for corporate bonds using a unified 2 factor model.
problem Develop a numerical method to solve a unified 2 factor model for corporate bonds with fixed discrete coupons.
method Used explicit finite difference scheme to analyze stability and compute bond prices.
result Found conditions for the explicit finite difference scheme to be stable and computed bond prices, credit spread, and duration.
The paper studies a heat flow for almost complex structures and proves convergence under certain conditions.
problem The study of harmonic heat flow for almost complex structures compatible with a Riemannian metric.
method Definition and analysis of the harmonic heat flow, proving existence and convergence under small energy conditions.
result The flow converges to a Kähler structure if the initial energy is small, but there are finite time singularities for small enough initial energy.
Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of…
Defines pre-Kähler structures and their properties.
problem Geometry of Levi degenerate CR hypersurfaces.
method Introduces pre-Kähler structures, holomorphic degeneration, and finite-nondegeneracy.
result Symmetry algebra is finite-dimensional if and only if structure is finitely nondegenerate.
New property for pseudo-Anosov maps and their mapping tori.
problem Understanding pseudo-Anosov maps and their mapping tori.
method Analyzing finite covers and spectral radii of homology actions.
result Monodromy properties of pseudo-Anosov maps' covers.
Survey on deformations of convex structures on manifolds and orbifolds.
problem Understanding the deformation spaces of convex real projective structures.
method Study of representations into Lie groups, focusing on character varieties and geometric structures.
result Survey of basics of character varieties, geometric structures on orbifolds, and Hilbert geometry.