arXiv research

Paper proves a noncompact version of Gromov's band-width estimate.

Study shows upper limit for torical band width with spectral curvature bounds.

Extends width estimates to family case using index theory.

Estimates bandwidth for CMC initial data sets.

Establish optimal Lipschitz lower bounds for functions on manifolds with negative curvature, revealing interplay between width, boundary area, and topology.

Proves principles and estimates for initial data sets in Einstein equations.

The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.

Study on Gehring link problem and width of bands in curved manifolds.

The paper explores rigidity theorems for spectral curvature bounds in 3-manifolds.

The Rosenberg index vanishes if a manifold admits a wide Riemannian band or cube-like domain.

Inspired by Gromov's work on 'Metric inequalities with scalar curvature' we establish band width inequalities for Riemannian bands of the form $(V=M\times[0,1],g)$, where $M^{n-1}$ is a closed manifold. We introduce a new class of orientable manifolds we call filling enlargeable and prove: If $M$ is filling enlargeable…

The paper constructs optimal confidence bands for kernel gradient flow estimators.

Develops connections between operator K-theory and positive scalar curvature.

The paper proves rigidity for certain product spaces and bounds for band widths.

Extends spectral torus band inequalities for compact manifolds with scalar curvature bounds.

The paper explores index theory for Dirac operators to understand scalar curvature properties.

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.

Develops a robust hedging valuation adjustment measure for dynamic hedging under liquidity-demand stress.

Paper develops a robust HVA measure for dynamic hedging under liquidity stress.

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $σ> 0$, the distance between the boundary components of $V$ is at most $C_n/\sqrtσ$, where $C_n = \…

This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded…

Paper proposes a method to estimate confidence bands for survival random forests.

Develops methods for estimating and providing confidence bands in sparse high-dimensional additive models.

We consider the problem of estimating a large rank-one tensor ${\boldsymbol u}^{\otimes k}\in({\mathbb R}^{n})^{\otimes k}$, $k\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $λ_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown ve…

UTOPIA aggregates multiple prediction intervals efficiently.

In conventional chemisorption model, the d-band center theory (augmented sometimes with the upper edge of d-band for imporved accuarcy) plays a central role in predicting adsorption energies and catalytic activity as a function of d-band center of the solid surfaces, but it requires density functional calculations that…

We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the literature, the kernel regression and the spline method, and is of interest in it…

New calibration bands for various distributions improve testing for auto-calibration.

In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three approximate algorithms are presented: a binary quadratic programming (BQP) algorit…

Confidence bands for tuning curves improve hyperparameter comparison in NLP.

In cellular systems, the user equipment (UE) can request a change in the frequency band when its rate drops below a threshold on the current band. The UE is then instructed by the base station (BS) to measure the quality of candidate bands, which requires a measurement gap in the data transmission, thus lowering the da…

The paper improves nonparametric confidence bands for band-limited functions.

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…

A new pricing controller handles resource constraints to infer target prices effectively.

The study refines known counterexamples in 4D to satisfy certain inequalities.

Study of free boundary minimal Möbius bands in spherical caps.

Generative neural networks improve insurance market risk modeling.

Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…

EGO-MDA identifies optimal spectral-bands for process discrimination.

Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on th…

Study bounds Urysohn width of manifolds under surgeries.

Sharp distance estimates for compact spin manifolds using Dirac operator.

New methods for estimating and inferring nonparametric structural functions and elasticities.

Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current …

Proves a quantitative index theorem for positive scalar curvature metrics.

Satellite knots can be trivialized by a single band move.

Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.