The paper studies a curvature flow on hypersurfaces in R^(n+1).
problem Analyzing the long-term behavior of a specific type of curvature flow.
method Examining a flow defined by a non-homogeneous anisotropic speed function.
result The flow converges to a sphere for star-shaped and k-convex initial hypersurfaces.
Large GD stepsizes improve margins and speed up training for non-homogeneous networks.
problem Training efficiency and margin improvement in non-homogeneous two-layer networks.
method Investigation of two distinct phases in GD training, showing margin growth and empirical risk decrease.
result Large GD stepsizes lead to faster convergence and improved margins in non-homogeneous networks.
Convex hypersurfaces evolve to spheres under a specific flow.
problem Volume preserving nonhomogeneous mean curvature flow of convex hypersurfaces.
method Monotonicity of isoperimetric ratio, inner and outer radius control, maximum principle arguments.
result Closed convex hypersurfaces converge to round spheres.
Study of non-homogeneous mean curvature flow in hyperbolic space converging to a geodesic sphere.
problem Volume/area preserving curvature flow of convex hypersurfaces in hyperbolic space.
method Generic positive, increasing mean curvature velocity; preserving convexity by horospheres; maximum principle; exponential convergence analysis.
result Exponential convergence to a geodesic sphere.
The paper studies how convex hypersurfaces evolve under a specific speed function of the mean curvature.
problem Evolution of convex hypersurfaces under a non-homogeneous speed function.
method Evolution of a closed convex hypersurface in Rn+1 with a speed function depending only on the mean curvature. result The flow exists on a finite maximal interval, convexity is preserved, and the hypersurfaces shrink to a point.
The study finds conditions for flat isotropic non-homogeneous tori to be Hamiltonian minimal.
problem Finding conditions for Hamiltonian minimality of isotropic non-homogeneous tori.
method Constructing a family of flat isotropic non-homogeneous tori and finding necessary and sufficient conditions.
result Necessary and sufficient conditions for Hamiltonian minimality of isotropic non-homogeneous tori in Hn and CP2n+1. GD iterates for non-homogeneous deep nets increase margin and converge in direction.
problem Understanding implicit bias in non-homogeneous deep networks.
method Characterization of GD iterates' properties starting from small empirical risk.
result GD iterates converge in direction despite diverging norms, satisfying KKT conditions.
Study non-homogeneous operators in 1+0 systems, classifying and analyzing their geometric properties.
problem Classify and analyze geometric properties of non-homogeneous operators in 1+0 systems.
method Complete classification of Casimir functions, tensorial criteria for compatibility, bi-pencils definition.
result Found geometric connections with Nijenhuis geometry, proving compatibility results.
We construct a series of examples of non--flat non--homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
Adaptive sampling improves graph diffusion models by maintaining uniform information speed.
problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.
Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due to by Ferus, Karcher and Munzner.
We obtain the $C^{\a}$ regularity for weak solutions of a class of non-homogeneous ultraparabolic equation, with measurable coefficients. The result generalizes our recent $C^{\a}$ regularity results of homogeneous ultraparabolic equation.
Bayesian NHMMs with non-homogeneous emissions for rainfall modeling.
problem Modeling temporal non-homogeneity in discrete-time hidden Markov models.
method Polya-Gamma data augmentation for Bayesian inference.
result Efficient MCMC sampling for complex NHMMs.
New algorithm optimizes complex model selection for non-homogeneous hidden Markov models.
problem Complex combinatorial optimization problem for model selection in NHHMMs.
method Adaptive simulated annealing EM algorithm (ASA-EM).
result Joint optimization of models and parameters for a criterion of interest.
We classify smooth locally free actions of the real affine group on closed orientable three-dimensional manifolds up to smooth conjugacy. As a corollary, there exists a non-homogeneous action when the manifold is the unit tangent bundle of a closed surface with a hyperbolic metric.
Study how regularization and optimization affect margin in deep models.
problem Understanding margin maximization in deep learning models.
method Analyze the limit of loss minimization with diverging norm constraints and margin paths.
result Discovers lexicographic max-margin solutions for homogeneous models and shows convergence under certain conditions.
In this short note, we study the gradient estimate of positive solutions to Poisson equation and the non-homogeneous heat equation in a compact Riemannian manifold (M^n,g). Our results extend the gradient estimate for positive harmonic functions and positive solutions to heat equations.
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of non homogenous terms vanishing at infinity for which the corresponding capillar…
In this paper we extend the classical theory of combinatorial manifolds to the non-homogeneous setting. NH-manifolds are polyhedra which are locally like Euclidean spaces of varying dimensions. We show that many of the properties of classical manifolds remain valid in this wider context. NH-manifolds appear naturally w…
This study explains how adversarial interaction creates non-homogeneous patterns using a pseudo-Reaction-Diffusion model.
problem Understanding how adversarial interaction leads to non-homogeneous patterns in systems.
method Developed a pseudo-Reaction-Diffusion model to explain the mechanism.
result Turing instability is involved in creating non-homogeneous patterns.
We present examples, both compact and non-compact complete, of lo- cally non-homogeneous proper A-manifolds.
Researchers create non-homogeneous finite-volume ends on quaternionic Kähler manifolds.
problem Constructing non-homogeneous quaternionic Kähler manifolds with finite volume ends.
method Using cohomogeneity one deformation of symmetric spaces, the researchers constructed manifolds with specific fundamental groups.
result The constructed manifolds are aspherical and have finite volume ends, not locally homogeneous.
Classifies and clusters event time data using non-homogeneous Poisson process models.
problem Classifying and clustering event time data from multiple observations.
method Modeling rate functions using spline basis expansion, estimating coefficients using maximum likelihood, and assigning observations to groups based on likelihood.
result The classification and clustering approaches perform well on both synthetic and real-world data.
Proposes a multi-state model for evaluating life insurance conversion options.
problem Evaluating the value of conversion options in life insurance contracts.
method Age-indexed semi-Markov chains to model duration, time non-homogeneity, and ageing effects.
result Validates the model's ability to accurately evaluate conversion option values.
Model counts interactions in dynamic networks using Poisson processes and clusters.
problem Counting interactions in dynamic networks with unknown cluster structure.
method Developed a model using non-homogeneous Poisson processes and block modeling. Truncated to discrete time for tractability. Used an exact integrated classification likelihood criterion for estimation.
result Estimates cluster memberships and number of clusters simultaneously.
The paper introduces a new insurance pricing model based on driving mileage.
problem Weak link between insurance premiums and mileage, leading to overdriving and accidents.
method Developed a Pay-As-You-Drive insurance pricing model using a counting process and non-homogeneous Poisson distribution.
result The model provides theoretical results for better insurance pricing based on driving behavior.
In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.
The Lagrangian formalism on a arbitrary non-fibrating manifold is considered. The kinematical description of this generic situation is based on the concept of (higher-order) Grassmann manifolds which is the factorization of the regular velocity manifold to the action of the differential group. Here we introduce in this…
Incomplete financial markets are considered, defined by a multi-dimensional non-homogeneous diffusion process, being the direct sum of an Itô process (the price process), and another non-homogeneous diffusion process (the exogenous process, representing exogenous stochastic sources). The drift and the diffusion matrix …
Enhances count process modelling with Markov-modulated non-homogeneous Poisson process.
problem Count data modelling challenges, especially in complex scenarios.
method Introduces a flexible frequency perturbation measure into Markov-modulated Poisson process framework.
result Natural incorporation of observed event arrivals and latent factors.
Extends rigidity results to non-homogeneous manifolds.
problem Measure and topological rigidity in dynamical systems.
method From homogeneous to general manifolds.
result Measure and topological rigidity results extended.
The paper solves a complex control problem with stochastic elements and switching conditions.
problem Non-homogeneous stochastic LQ control with regime switching and random coefficients.
method Explicit optimal control and value obtained through two systems of backward stochastic differential equations (BSDEs). Existence and uniqueness of solutions proved using BMO martingales and contraction mapping method.
result Explicit optimal state feedback control and optimal value derived for the problem.
New manifolds with many hyperbolic planes, not homogeneous.
problem Constructing non-homogeneous manifolds with many hyperbolic planes.
method Constructing manifolds with geodesics in hyperbolic planes.
result Non-homogeneous manifolds with many hyperbolic planes exist.
The paper proposes deep normalization to improve speaker recognition performance.
problem Non-Gaussian and non-homogeneous distributions of deep speaker vectors negatively impact speaker recognition.
method Proposes a deep normalization approach based on a novel discriminative normalization flow (DNF) model.
result DNF-based normalization delivers substantial performance gains and strong generalization capability.
We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of curvature is a second order system of partial differential equations which we sho…
Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.
problem Learning elliptic PDEs with noisy data and non-homogeneous boundary conditions.
method Bayesian approach with a Hölder space prior on neural network weights.
result Posterior contracts at near-minimax rate without prior knowledge of solution smoothness.
Improved decision tree for big data classification.
problem Classification of large datasets.
method Divide and conquer strategy with decision tree segmentation and leaf level classifier.
result Models are interpretable and as accurate as ensemble methods.
It is shown that the non-homogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation admit a regular solution once the H-condition (described in the article) is satisfied. The approach consist in applying the elliptic techniques to the variational setting of the Seiberg-Witten e…
We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we …
We construct a Weil-Petersson geodesic completion of Teichmuller space through the formalism of Coxeter complex with the Teichmuller space as its non-linear non-homogeneous fundamental domain. We show that the metric and geodesic completions both satisfy a finite rank property, demonstrating a similarity with the non-c…
The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given linear ODEs system or a given superior order ODE. The case of a non-homogenous linear…
Study Frobenius pencils and compatible non-homogeneous Poisson structures.
problem Compatibility of multicomponent local Poisson structures.
method Algebraic interpretation via Frobenius algebras and classification of Frobenius pencils.
result Classification of Frobenius pencils under generic conditions.
New algorithm identifies best policy in MDPs faster.
problem Identifying the best policy in Markov Decision Processes.
method Problem-dependent lower bound and first algorithm with instance-specific sample complexity.
result First algorithm with reduced exploration rate for faster convergence.
This study shows how DDPM can be represented by the OU process.
problem Designing optimal noise schedules for DDPM.
method Formal equivalence between DDPM and OU process, heuristic designs based on Fisher Information.
result Fisher-Information-motivated schedule corresponds to cosine noise schedule.
This paper consists of two main results. In the first one we describe all Kaehler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the Wallach set of the domain. In the second one we exhibit an example of complete and non-homogeneous Kaehler-Einstein metric wit…
Paper improves fraud detection in imbalanced financial data.
problem Detecting fraud in imbalanced financial datasets.
method Uses time-varying Poisson processes for fraud prediction.
result Method outperforms baseline in imbalanced data.
We prove that there exist solutions for a non-parametric capillary problem in a wide class of Riemannian manifolds endowed with a Killing vector field. In other terms, we prove the existence of Killing graphs with prescribed mean curvature and prescribed contact angle along its boundary. These results may be useful for…
Paper analyzes robustness of MDPDE under INH setups.
problem Global reliability and breakdown behavior of MDPDE under INH.
method Asymptotic breakdown point analysis of MDPDE.
result Derives a theoretical lower bound for the asymptotic breakdown point.