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.

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

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

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

Estimates bandwidth for CMC initial data sets.

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…

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

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

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

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

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.

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

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

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

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…

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 = \…

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

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

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…

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.

The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger Bands. Next we illustrate the use of Bollinger Bands in pairs trading and prove the e…

New rational band moves simplify knot classification.

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…

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…

We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…

We show that a band-connected sum of knots $K_0$ and $K_1$ along a band $b$ is equal to the connected sum $K_0\# K_1$ if and only if $b$ is a trivial band.

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

Many wireless networks, including 5G NR (New Radio) and future beyond 5G cellular systems, are expected to operate on multiple frequency bands. This paper considers the band assignment (BA) problem in dual-band systems, where the basestation (BS) chooses one of the two available frequency bands (centimeter-wave and mil…

Deep neural networks with convolutional layers usually process the entire spectrogram of an audio signal with the same time-frequency resolutions, number of filters, and dimensionality reduction scale. According to the constant-Q transform, good features can be extracted from audio signals if the low frequency bands ar…

Paper shows that for torus knots, the pinch number equals the unoriented band unknotting number.

New method finds arbitrage opportunities in fluctuating asset bands.

Develops Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.

Every classical knot is band-pass equivalent to the unknot or the trefoil. The band-pass class of a knot is a concordance invariant. Every ribbon knot, for example, is band-pass equivalent to the unknot. Here we introduce the long virtual knot concordance group $\mathscr{VC}$. It is shown that for every concordance cla…

We explicitly classify all $S^1$-invariant free boundary minimal annuli and Möbius bands in $\mathbb{B}^n$. This classification is obtained from an analysis of the spectrum of the Dirichlet-to-Neumann map for $S^1$-invariant metrics on the annulus and Möbius band. First, we determine the supremum of the $k$-th normaliz…

Study surfaces in 4-manifolds using banded unlink diagrams.

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

Study negative band numbers in braids and links.

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…