arXiv research

New methods estimate point-wise dependency from neural MI models.

A new model for forward curves captures behavior through a single equation.

This paper simplifies conditional Sobol' indices calculation using PCE bases.

A rather complete investigation of anisotropic Bessel potential, Besov, and Hölder spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of the underlying manifold near its 'ends' is determined by a singularity function which leads naturally to the study of weigh…

PACMAN provides bounds for classification tasks considering accuracy vs. negative log-loss mismatch.

Many applications require the ability to judge uncertainty of time-series forecasts. Uncertainty is often specified as point-wise error bars around a mean or median forecast. Due to temporal dependencies, such a method obscures some information. We would ideally have a way to query the posterior probability of the enti…

FreST Loss decorrelates spatio-temporal dependencies in graph signals.

Proves better rigidity theorems for special solitons.

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled surfaces. The finite energy case yields a limit of images, under a suitable topolo…

We establish a point-wise gradient estimate for $all$ positive solutions of the conjugate heat equation. This contrasts to Perelman's point-wise gradient estimate which works mainly for the fundamental solution rather than all solutions. Like Perelman's estimate, the most general form of our gradient estimate does not …

In this paper, we derive a Sobolev inequality along an extended Ricci flow and prove a point-wise Guassian type bound for the fundamental solutions of the conjugate heat equation under the flow.

By using certain idea developed in minimal submanifold theory we study rigidity problem for self-shrinkers in the present paper. We prove rigidity results for squared norm of the second fundamental form of self-shrinkers, either under point-wise conditions or under integral conditions.

Study shows certain spin manifolds can't meet DEC condition.

DiFF-RF detects point-wise and collective anomalies using random partitioning trees.

TimeLAVA learns time series segment values without model dependence.

We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key ingredients are new Bochner-Weitzenböck-Lichnerowicz type formulas for the Weyl tensor,…

We study some basic problems of translating solitons: the volume growth, generalized maximum principle, Gauss maps and certain functions related to the Gauss maps, finally we carry out point-wise estimates and integral estimates for the squared norm of the second fundamental form. Those estimates give rigidity theorems…

We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as backgrou…

Proves rigidity of ancient solutions in mean curvature flow.

In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide rigidity results by the integral inequalities involving the Weyl curvature, the t…

In this paper, we prove some rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals on closed manifolds, characterized by some point-wise inequalities. Moreover, we also provide a few rigidity results that involve the Weyl curvature, the trace-less Ricci cu…

Study shows no large mean curvature fill-ins for nonnegative scalar curvature.

Proposes CCE to assess point-wise reliability of neural network predictions.

New bounds on scalar curvature for metric sequences.

TimeLAVA: A Learning-Agnostic Framework for Valuing Time Series

We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We intr…

Ricci flow controls curvature on manifolds with bounds.

We consider the classical optimal dividends problem under the Cramér-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value functi…

Gaussian processes are conditioned on various types of data.

Preformer improves Transformer for long-term time series forecasting.

Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. As an intermediate result, we develop…

Three geometric analysis results on curve flows and Lie groups.

Study of Pascal algebra matrices and their jet bundle map for vector bundles.

Understanding separation effects on parameter estimation in finite Gaussian mixtures

In this paper, we will show that the projection $\text{Homeo}^+(D^2_n)\to B_n$ does not have a section; i.e. the braid group $B_n$ cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and $n$ marked points in the interior as a set. We also give a new proof of a result o…

This work introduces new ways to compare adversarial robustness of classifiers globally.

Sharp comparison for sub-Gaussian random variables in convex order.

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map from X into C(S) is the restriction of an element of Aut(C(S)), unique up to the (finite) …

Time series forecasting is an important problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. In this paper, we propose to tackle such forecasting problem with Transformer [1]. Although impressed by its performance in our preliminary study, …

Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.

Study of Killing spinor-valued forms and their integrability conditions.

Given $n$ i.i.d. observations of a random vector $(X,Z)$, where $X$ is a high-dimensional vector and $Z$ is a low-dimensional index variable, we study the problem of estimating the conditional inverse covariance matrix $Ω(z) = (E[(X-E[X \mid Z])(X-E[X \mid Z])^T \mid Z=z])^{-1}$ under the assumption that the set of non…

Extends Ricci flow theory to Kato-type curvature bounds, proving manifold properties.

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We a…

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton then it is isometric to a unit sphere S2n+1. Next, we extend this result on a compact k-almost Ricci soli…

Paper proves convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian and robustness to outlier noise.

We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…

Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise to a piecewise linear (PL) approximant. This is extended to isotopic convergenc…