arXiv research

Generalizes results for Riemannian manifolds with boundary to those without.

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect in superstatistics. Then we confirm that the presented stochastic model is capabl…

The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) o…

We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove…

Study on limits and cut-off phenomena in deep neural networks.

We construct a cut-off version of nonpertubative closed Bosonic string field theory in the light-cone gauge with imaginary string coupling constant. We show that the partition function is a continuous function of the string coupling constant, and conjecture a relation between the formal power series expansion of this p…

Holographic principle matches deformed Liouville theory action.

The paper extends Liouville theorems to sub-Riemannian manifolds.

This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat positi…

We show some characterizations of hyperspheres in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with intrinsic and extrinsic properties such as the $n$-dimensional area of the sections cut off by hyperplanes, the $(n+1)$-dimensional volume of regions between parallel hyperplanes, and the $n$-dimensional surf…

We derive several new applications of the concept of sequences of Laplacian cut-off functions on Riemannian manifolds (which we prove to exist on geodesically complete Riemannian manifolds with nonnegative Ricci curvature): In particular, we prove that this existence implies $\mathsf{L}^q$-estimates of the gradient, a …

Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…

We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.

We study a sequential resource allocation problem between a fixed number of arms. On each iteration the algorithm distributes a resource among the arms in order to maximize the expected success rate. Allocating more of the resource to a given arm increases the probability that it succeeds, yet with a cut-off. We follow…

Deep Neural Networks(DNNs) require huge GPU memory when training on modern image/video databases. Unfortunately, the GPU memory is physically finite, which limits the image resolutions and batch sizes that could be used in training for better DNN performance. Unlike solutions that require physically upgrade GPUs, the G…

Study uses holography to analyze entanglement entropy in deformed CFTs.

New upper bound for Neumann Laplacian eigenvalues on convex domains.

Sharp lower bound for first Neumann eigenvalue found in terms of diameter and width.

Study non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.

Study bounds the measure of zero sets of Neumann Laplace eigenfunctions.

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.

Geodesic disks maximize the first non-trivial Neumann eigenvalue on spheres.

Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely, a distribution derived from the so-called Mittag-Lef…

Algorithm transforms weakly negative plumbing trees to negative definite ones.

Sharp isoperimetric inequalities for Neumann eigenvalues in symmetric spaces.

Neumann's work connects 3-manifold invariants to quantum topology.

Recently, the first named author together with Xinan Ma \cite{ma2015neumann}, have proved the existence of the Neumann problems for Hessian equations. In this paper, we proceed further to study classical Neumann problems for Hessian equations. We prove here the existence of classical Neumann problems under the uniforml…

Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.

Study solves a mathematical problem related to elliptic Schroedinger-to-Neumann maps.

Universal inequalities for Laplacian eigenvalues on convex domains.

Study on biharmonic Steklov problems with Neumann boundary conditions and eigenvalue estimates.

Study uniquely determines Riemannian metric derivatives from boundary data.

Two geodesic balls maximize the third Neumann eigenvalue in hyperbolic space.

New inequalities for planar convex domains' Laplacian eigenvalues.

Background: Many authors have described MELD as a predictor of short-term mortality in the liver transplantation waiting list. However MELD score accuracy to predict long term mortality has not been statistically evaluated. Objective: The aim of this study is to analyze the MELD score as well as other variables as a pr…

Researchers calculate spectral invariants from Dirichlet-to-Neumann map for Witten-Laplacian with potential.

Study Neumann problem for special Lagrangian type equations.

Study relative commutants in von Neumann algebras using contraction notions.

In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher order generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-W…

Neumann eigenmaps improve landmark-based diffusion map embeddings.

Sharp inequality outside ball proved using Neumann method.

Solves Neumann problem on CR manifold boundary.

Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.

We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds for the Neumann eigenvalues which are consistent with Weyl's asymptotics.

Paper derives formulas for static Einstein spaces, linking Neumann data to stability.

In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.

Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.