Bayesian nonparametric model for priors on directed graphs.
problem Constructing priors for exchangeable directed graphs.
method Infinite relational digraphon model (di-IRM) for constructing priors.
result Demonstrated inference on synthetic data.
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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 “infinite relational digraphon model”
Intensity Dot Product Graphsstat.ML
IDPGs extend RDPGs with a Poisson process for random latent positions.
problem Modeling randomness in latent positions for graph structure.
method Introduce IDPGs using Poisson point processes on latent Euclidean space.
result Continuous analogues of adjacency matrices link latent structure to observed graphs.
HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.
problem Modeling noisy, sparse, and heterogeneous relational data.
method Hierarchical Chinese restaurant process and Dirichlet process mixture for clustering and modeling relation values.
result HIRM generalizes standard models and discovers relational structure in real-world datasets.
Smooth structures on infinite dimensional Grassmannians and non-commutative cross-ratios.
problem Smooth structures on infinite dimensional Grassmannians and non-commutative cross-ratios.
method Analyzing and expanding the notion of non-commutative cross-ratios, proving their smoothness.
result Smoothness of non-commutative cross-ratios.
The study finds new infinite dilogarithm identities related to number sequences and continued fractions.
problem Finding new infinite dilogarithm identities.
method Demonstrating families of identities associated with specific number sequences and continued fractions.
result New infinite dilogarithm identities related to Fibonacci, Lucas numbers, convergents of even period continued fractions, and recurrence relations.
Dynamic systems linked to infinite permutation matrices.
problem Dynamic equivalence of control systems.
method Association of infinite permutation matrices.
result Relationship between dynamic equivalences and permutation matrices.
Wide CNNs outperform infinite width networks, revealing scaling laws.
problem Understanding the performance difference between finite and infinite width convolutional networks.
method Diagrammatic approach to derive asymptotic width dependence for various quantities.
result The difference in performance between finite and infinite width models vanishes at a definite rate with respect to model width.
Two results on end spaces of infinite type surfaces, answering questions about their topology and equivalence.
problem Topology and equivalence of end spaces of infinite type surfaces.
method Examples and Tsankov's argument to show equivalence relation.
result Examples of infinite type surfaces with end spaces that are not self-similar but have a unique maximal type.
The paper discusses the importance of infinite-mean models in finance and risk management.
problem Classic statistical models assume finite mean or variance, which is not suitable for heavy-tailed data.
method Discussion and recent results on infinite-mean models in economics and finance.
result Classic statistical results for finite-mean models often fail or flip for infinite-mean models.
This paper characterizes projective models in statistical relational learning.
problem Projectivity in statistical relational models is beneficial for inference and learning.
method Representation theorems for infinite exchangeable arrays to characterize projective models.
result A class of directed graphical latent variable models correspond to projective relational models.
The grand arc graph's asymptotic dimension is shown to be infinite.
problem Determining the asymptotic dimension of the grand arc graph.
method Using Gromov-hyperbolic and cocompact arc and curve models, the asymptotic dimension is shown to be infinite for a broad class of surfaces.
result The asymptotic dimension of the grand arc graph is infinite.
Study flip graphs for surfaces of infinite type, finding uncountably many connected components.
problem Understanding relationships between triangulations of infinite type surfaces via flips.
method Associate triangulations to flip graphs and study sequences of simultaneous flips.
result Flip graphs for infinite type surfaces have uncountably many connected components.
Study on Kähler-Ricci flow's infinite-time singularities.
problem Understanding singularities in Kähler-Ricci flow.
method Relates flow's singularity type to fibration's indexes.
result Observation of singularity type's relation to fibration indexes.
We study geodesics on a planar Riemann surface of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these geodesics and relate them to the structure of the boundary of a Dirichlet polygon for…
This paper extends geometric structure theory to infinite type structures.
problem Calculating characteristic class relations in complex Cartan geometries.
method Improves representation theory for infinite type structures.
result Direct calculation of characteristic class relations from structure group representation.
The Gauss-Bonnet formula for classical translation surfaces relates the cone angle of the singularities (geometry) to the genus of the surface (topology). When considering more general translation surfaces, we observe so-called wild singularities for which the notion of cone angle is not applicable any more. We study w…
Infinite rank surface cluster algebras extend traditional concepts to surfaces with accumulation points.
problem Extending surface cluster algebras to infinite surfaces with accumulation points.
method Consider infinite mutation sequences and hyperbolic structures to define cluster variables as lambda lengths of arcs.
result Established transitivity of infinite mutation sequences on triangulations of infinite surfaces and provided expansion formulas for cluster variables.
0-Concordance of 2-knotsmath.GT
The paper shows infinitely many types of 2-knots in 4-space.
problem Understanding the equivalence of 2-knots in 4-dimensional space.
method Using Rochlin's invariant and Heegaard-Floer homology.
result There are infinitely many 0-concordance classes of 2-knots.
We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. W…
Infinite-dimensional universal Cardy-Frobenius algebra is constructed, which unifies all particular algebras of closed and open Hurwitz numbers and is closely related to the algebra of differential operators, familiar from the theory of Generalized Kontsevich Model.
Theory explains neural network scaling with dataset and model size.
problem Neural network scaling laws with dataset and model size.
method Identified variance-limited and resolution-limited scaling behaviors.
result Four scaling regimes explained: infinite data, infinite width, resolution-limited, and large width.
Develops geometric quantum mechanics in infinite dimensions.
problem Quantum dynamics in infinite-dimensional spaces.
method Tulczyjew triple concept for Lagrangian formalism.
result Self-adjoint operators as Lagrangian submanifolds.
Study infinite genus surfaces and Schottky groups for uniformization.
problem Investigate infinite genus surfaces and Schottky groups for uniformization.
method Definitions and proofs for infinite genus surfaces and Schottky groups, showing uniformization by Schottky groups.
result Infinite genus surfaces and handlebodies can be topologically and quasiconformally uniformized by Schottky groups.
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
problem Exploring geometric and analytical structures in infinite-dimensional settings.
method Analyzes numerical schemes, Lie groups, connections, and integration theory.
result Developed new methods for integration and analysis on infinite-dimensional manifolds.
Paper extends Miyazawa's construction to more 4-manifolds, finding exotic involutions and embeddings.
problem Finding exotic involutions and embeddings in 4-manifolds.
method Real Seiberg-Witten theory.
result Many infinite families of exotic involutions and embeddings.
The Infinite Relational Model (IRM) is a probabilistic model for relational data clustering that partitions objects into clusters based on observed relationships. This paper presents Averaged CVB (ACVB) solutions for IRM, convergence-guaranteed and practically useful fast Collapsed Variational Bayes (CVB) inferences. W…
This paper opens the series of articles supplemental to the series (hep-th/9405050,q-alg/9610026,q-alg/9611003,q-alg/9611019,funct-an/9611003), which also lies in lines of general ideology exposed in the review (mp_arc/96-477). The main purpose of the activity, which has its origin and motivation presumably in the auth…
Study surfaces in 4-manifolds with cyclic fundamental group.
problem Characterize surfaces with infinite cyclic knot group.
method Algebraic topological criteria and homeomorphism proofs.
result Ambiently isotopic surfaces with the same genus have a homeomorphism.
New boundary functions yield infinitely many solutions for minimal surfaces.
problem Existence of multiple solutions for minimal surfaces.
method Lawson-Osserman constructions and Dirichlet problem analysis.
result Infinitely many analytic solutions and at least one nonsmooth solution.
We show that the length spectrum metric on Teichmüller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichmüller space with quasiconformal and the Fenchel-Nielsen Teichmüller spaces on such surfaces
We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where is the relator length, going to infinity. (a) $1 + 1/C < \Cdim(…
The study shows that surface groups are the only non-free infinite index subgroups of certain hyperbolic groups.
problem Identifying the only non-free infinite index subgroups of specific hyperbolic and one-relator groups.
method Careful analysis of free and cyclic splittings of cubulated groups.
result Proves that surface groups are the only non-free infinite index subgroups of certain hyperbolic and one-relator groups.
Two graphs on infinite-type surfaces have finite diameter and related automorphism groups.
problem Characterizing automorphisms and diameter of graphs on infinite-type surfaces.
method Construction of graphs and analysis of automorphisms.
result The graph has finite diameter and the automorphism group of is the extended mapping class group.
We present results connecting crossratios, representations of surface groups in and in an infinite dimensional group related to the group of diffeomorphisms of the circle. More precisely, we show that representations of a surface group in can be interpreted as crossratios satisfying …
Defines an arc metric on Teichmüller spaces of infinite type surfaces with boundary.
problem Defining a metric on Teichmüller spaces of surfaces with infinite type and boundary.
method Using Basmajian identity and geometric conditions, an asymmetric metric (arc metric) is defined.
result An arc metric is constructed on the quasiconformal Teichmüller space of certain infinite type surfaces.
The Akbulut cork cannot transform all exotic 4-manifolds.
problem The Akbulut cork's universality in transforming exotic 4-manifolds.
method Exhibited infinitely many exotic pairs of 4-manifolds not related by any cork.
result The Akbulut cork is not universal.
Study of B-type LG models on open Riemann surfaces.
problem Understanding triangulated structures and D-branes in open Riemann surface models.
method Investigation of B-type topological Landau-Ginzburg models with arbitrary open Riemann surfaces.
result Complete description of the triangulated structure of the category of topological D-branes.
Study index theory for infinite-dimensional manifolds with LT actions.
problem Index theory for infinite-dimensional manifolds with LT actions.
method Introduce LT-equivariant KK-theory and construct three KK-elements: index, Clifford symbol, and Dirac elements.
result Satisfy a relation called the (KK-theoretical) index theorem or KK-theoretical Poincaré duality.
We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to such Frobenius manifolds are found to be certain extensions of the dispersionle…
Develops a Bayesian method for an infinite mixture of inverted Dirichlet distributions.
problem Overcoming the need to pre-determine the number of mixture components in Dirichlet process models.
method Adopted the extended variational inference framework to derive an analytically tractable solution.
result Demonstrates good performance and effectiveness compared to other DP-related methods.
Alexander method extended to infinite-type surfaces.
problem Determining equality of elements in mapping class groups.
method Combinatorial tool extended to infinite-type surfaces.
result Verification of relations and triviality of centers in mapping class groups.
The paper proves infinitely many strong symplectic fillings for cusp singularity links.
problem Proving the existence of infinitely many strong symplectic fillings for specific types of singularity links.
method Analyzing -manifolds and -manifolds with canonical contact structures.
result Links of cusp, unimodal, and hyperbolic Brieskorn singularities admit infinitely many non-diffeomorphic strong symplectic fillings.
The relations between the infinite dimensional geometry of -conformal symmetries at , Berezin quantization of the Lobachevskii plane and Karasev-Maslov asymptotic quantization are explicated. Some aspects of the ``approximate'' representation theory are discussed.
In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the area functional to prove this conjecture in the positive Ricci curvature setting. More precisely, we show that every compact Riemannian manifo…
There are only a few invariants one classically associates with precompact translation surfaces, among them certain numberfields, i.e. fields which are finite extensions of the field Q of rational numbers. These fields are closely related to each other; they are often even equal. We prove by constructing explicit examp…
Let be any dimensional smooth manifold and be the space of all smooth paths, then we showed that is a smooth manifold modelled over a complete normable space. We discussed many geometric structure on Path spaces and its relation to ambient space.
Deep equilibrium models converge globally without explicit computation.
problem Global convergence of deep learning models with implicit layers.
method Analysis of gradient dynamics and proof of convergence rate.
result Deep equilibrium models converge to global optimum at a linear rate.
The study connects ECH capacities to Anosov flows, proving infinite capacities and obstructions.
problem Understanding ECH capacities and their relation to Anosov flows.
method Relating ECH capacities to Anosov flows dynamics, proving infinite capacities and obstructions.
result ECH capacities are infinite for many symplectic 4-manifolds, including cotangent disk bundles over surfaces of genus at least two.