Reformulated Markov's conjecture in combinatorial terms.
problem Markov's uniqueness conjecture in integral necklaces.
method Geometric reformulation and combinatorial description.
result Explicitly described set of lengths on modular torus.
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48 results for “Markov spectrum”
RL techniques improve radar spectrum sharing in crowded conditions.
problem Optimizing radar performance in congested spectrum environments.
method Comparison of RL algorithms including policy iteration and Deep RL.
result RL techniques outperform traditional SAA methods in radar spectrum sharing.
Proves simplicity of Lyapunov exponents for specific Anosov flows.
problem Proving all Lyapunov exponents have multiplicity 1 for certain Anosov flows.
method Perturbative results for flows, modification of eigenvalues, Markov partition, and simplicity criterion.
result In a -open and -dense set of Anosov flows, all Lyapunov exponents have multiplicity 1.
We investigate various structures associated with the hyperbolic Markov and homological spectra of a pseudoAnosov map on a surface. Each unstable eigenvalue of the action of on first cohomolgy yields an eigen-cocycle that is transverse and holonomy invariant to the stable foliation of . Each …
Continuous Hausdorff dimension of dynamical spectra under small perturbations.
problem Stability of Hausdorff dimension in dynamical systems.
method Generic perturbations of metrics and functions on surfaces.
result Hausdorff dimension varies continuously and is preserved across Markov spectra.
VAE improves MCMC efficiency by generating diverse prior proposals.
problem Inefficient MCMC methods in Bayesian inverse problems, especially subsurface flow modeling.
method Uses Variational Autoencoder (VAE) to generate broader-spectrum prior proposals.
result VAE achieves comparable accuracy to Karhunen-Loève Expansion (KLE) and outperforms it when correlation length is unknown.
We prove a lower bound for the -th Steklov eigenvalues in terms of an isoperimetric constant called the -th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These lower bounds can be considered as higher order Cheeger type inequalities for the Ste…
New nonlocal neural network learns stable dynamics for deeper nonlocal structures.
problem Capturing long-range dependencies in feature space.
method Spectrum analysis on weight matrices, new nonlocal block formulation.
result Stable dynamics in deeper nonlocal structures.
Paper proposes efficient inference for hidden Markov models with memory decay.
problem Challenges in scalability due to dependencies in hidden Markov model observation data.
method Utilizes memory decay to carry out forward and backward probabilities with subsequences, enabling efficient inference over long sequences.
result Developed an efficient algorithm to numerically estimate the gap of top Lyapunov exponents, which determines the length of subsequences.
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complementing a low-rank appro…
Free Random Projection enhances reinforcement learning by naturally incorporating hierarchical structure.
problem Improving reinforcement learning algorithms for better generalization and adaptability.
method Introduces Free Random Projection, a method that uses free probability theory to create random orthogonal matrices encoding hierarchical structure.
result Empirically shows consistent improvement in generalization over standard methods on multi-environment benchmarks.
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers which identify the distinct covers of the space. We investigat…
New ADMM convergence rates for graph consensus problems identified.
problem Understanding ADMM convergence rates over graph consensus problems.
method Characterization of ADMM convergence using graph topology and random walks.
result ADMM convergence rate is faster than GD by a square root factor for certain graphs.
Study the energy spectrum of metrics on surfaces and its relation to simple length spectrum.
problem Relate the energy spectrum to the simple length spectrum of metrics on surfaces.
method Analyze the energy spectrum of metrics on surfaces and their Teichmüller spaces, considering homotopy conditions.
result The energy spectrum determines the simple length spectrum under certain conditions.
The paper compares two spectrum definitions and finds stability in one modification.
problem Generalizing eigenvalues to arbitrary functionals with stability.
method Comparison of Gromov's homotopy significant spectrum and Krasnoskii spectrum, with a modified definition of the homotopy significant spectrum.
result The modified homotopy significant spectrum is stable, and Cheeger constant corresponds to Krasnoskii eigenvalue.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Study shows spectrum properties for specific Hadamard manifolds.
problem Spectrum properties of Hadamard manifolds.
method Absolute continuity and spectrum determination for two classes of Hadamard manifolds.
result Spectrum properties determined for specific Hadamard manifolds.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.
Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.
problem Understanding transverse link invariants in the annular setting.
method Constructs a stable homotopy type for annular links and defines a map to the Khovanov skein spectrum.
result At extreme gradings, the map from the Khovanov spectrum to the Khovanov skein spectrum recovers the cohomotopy transverse invariant.
Constructs manifolds with specific spectral properties.
problem Spectral properties of Riemannian manifolds.
method Asymptotically hyperbolic manifolds with sharp curvature bounds.
result Embeds singular continuous spectrum into the essential spectrum of the Laplacian.
The spectrum of certain manifolds matches that of hyperbolic space if the bottom spectrum is maximal.
problem Investigating spectral rigidity of manifolds with Ricci bounded below and maximal bottom spectrum.
method Analyzing the spectrum of the Laplacian on manifolds with specific Ricci curvature bounds.
result The spectrum of the manifold coincides with that of hyperbolic space if the bottom spectrum is maximal.
Paper presents a method to train NER models without labelled data using weak supervision.
problem Dealing with NER performance drop in new domains without labelled data.
method Weak supervision through automatic annotation and hidden Markov model integration.
result Improvement of about 7 percentage points in entity-level scores.
Lower bounds for Hodge-Laplacian spectrum on orbifolds.
problem Finding bounds for the essential spectrum of Hodge-Laplacian.
method Deriving lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
result Lower bounds for the essential spectrum of the Hodge-Laplacian.
A machine learning approach for efficient spectrum sharing in distributed DSA networks.
problem Effective spectrum sharing among secondary users (SUs) and primary users (PUs) in a distributed network.
method Deep reinforcement learning (DRL) combined with reservoir computing (RC) for distributed spectrum access decisions.
result The RC-based spectrum access strategy significantly reduces collision chances and outperforms other methods.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
In 2004, Sormani and Wei introduced the covering spectrum: a geometric invariant that isolates part of the length spectrum of a Riemannian manifold. In their paper they observed that certain Sunada isospectral manifolds share the same covering spectrum, thus raising the question of whether the covering spectrum is a sp…
Survey on bottom of spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
problem Bottom of the spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
method Survey on Kähler hyperbolic manifolds and bounded symmetric domains
result Proposed several open problems
The paper extends decay estimates to graphs with positive spectrum.
problem Proving decay estimates for nonnegative functions on graphs.
method Sharp decay estimates for nonnegative generalized subharmonic functions.
result Extends Li and Wang's result to graphs with positive Laplacian spectrum.
Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.
problem Estimating the essential spectrum of minimal submanifolds.
method Using volume growth to bound the bottom of the essential spectrum.
result Improved essential spectrum estimate for minimal submanifolds.
Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.
problem Bounding the volume spectrum of Riemannian manifolds.
method Proves upper bounds that depend on volume, dimension, and a conformal invariant.
result Upper bounds for the volume spectrum are established.
Study on magnetic Dirac operators and their spectrum.
problem Understanding the spectrum of magnetic Dirac operators.
method Analysis of magnetic Dirac operators over complete Riemannian manifolds.
result Find sufficient conditions for maximal or discrete spectrum.
Covering preserves bottom spectrum, implies amenable covering.
problem Spectral preservation in Riemannian coverings.
method Proving spectral properties of Schrödinger operators on coverings.
result Covering preserving bottom spectrum implies amenability.
Notes on continuity of discrete-spectrum Fredholm operators.
problem Continuity properties of discrete-spectrum families of Fredholm operators.
method Relates recent work on discrete-spectrum families to classical continuity properties.
result Establishes connections between new and classical concepts.
Study shows ortho spectrum doesn't fully determine systolic length but limits the number of possible structures.
problem Determining the systolic length of hyperbolic surfaces with boundary.
method Analyzing the ortho spectrum of hyperbolic surfaces with totally geodesic boundary.
result There are only finitely many possibilities for the ortho spectrum and corresponding hyperbolic structures.
The rigidity of marked length spectrum for closed hyperbolic surfaces due to Fricke-Klein [7] has been the motivation of many different rigidity results, specially for manifolds of negative curvature. From the works of Vigneras [18], Sunada [17] and many other authors this result is far from being true for the unmarked…
ManifoldFlow relaxes fixed-spectrum Stiefel layers to learn a positive spectrum.
problem Fixed-spectrum Stiefel layers impose rigid spectral constraints.
method Introduces ManifoldFlow, a relaxation that learns a positive spectrum while keeping the basis on the Stiefel manifold.
result Learnable SPD spectrum improves performance in various settings.
Study essential spectrum of differential operators on geometrically finite orbifolds.
problem Analyzing the essential spectrum of differential operators over specific geometric structures.
method Investigates first order and Laplace type elliptic differential operators on Riemannian vector bundles over geometrically finite orbifolds.
result Discovers properties of essential spectra for these operators.
Study on length spectrum of random hyperbolic 3-manifolds.
problem Understanding the length spectrum of random hyperbolic 3-manifolds.
method Modeling random hyperbolic 3-manifolds using truncated tetrahedra and analyzing their length spectrum as volume tends to infinity.
result The length spectrum converges in distribution to a Poisson point process with a computable intensity λ as volume increases.
Paper proves flat metrics from holomorphic quadratic differentials can be identified by length spectrum.
problem Identifying flat metrics from holomorphic quadratic differentials.
method Proved using length spectrum on closed oriented surfaces.
result Flat metrics from holomorphic quadratic differentials can be distinguished by their length spectrum.
Proves existence of solutions to Poisson equation on manifolds with positive spectrum.
problem Existence of solutions to Poisson equation on manifolds with positive essential spectrum.
method Sharp pointwise decay on source function, unbounded Ricci curvature, general spectrum and curvature bounds.
result Existence of solutions on manifolds with positive essential spectrum and unbounded Ricci curvature.
We study the -spectrum of the Dirac operator on complete manifolds. One of the main questions in this context is whether this spectrum depends on . As a first example where -independence fails we compute explicitly the -spectrum for the hyperbolic space and its product with compact spaces.
Defines half-volume spectrum for manifolds and proves Weyl law holds.
problem Understanding volume distribution in manifolds.
method Introduces half-volume spectrum and uses Weyl law and Allen-Cahn min-max theory.
result Weyl law holds for half-volume spectrum and half-volume constant achieved by specific surfaces.
The study of the spectrum of the Laplacian on forms over manifolds.
problem Analyzing the spectrum of the Laplacian on forms over manifolds with specific curvature properties.
method Generalization of Weyl's criterion, Cheeger-Fukaya-Gromov theory, and continuous perturbations of the operator.
result Significantly stronger results for the spectrum of the Laplacian on forms, including its behavior under metric deformations.
New method proves length spectrum rigidity in various geometric settings.
problem Length spectrum rigidity in geometric settings.
method Combination of dynamical systems and geometric group theory.
result Provides concise proofs and extends classical results.
Paper bounds the lowest spectrum of manifolds with curvature constraints.
problem Estimating the lowest energy level of manifolds with curvature restrictions.
method Used a minimal positive Green's function and its properties.
result Proved an upper bound for the bottom of the spectrum.