相关论文: Bounded Palais-Smale sequences with Morse type inf…

On any surface we give an example of a metric that contains simple closed geodesics with arbitrary high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrary high Morse…

This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…

We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the…

Given a set $S$ of small measure, we discuss existence of sampling sequences for the Paley-Wiener space $PW_S$, which have both densities and sampling bounds close to the optimal ones.

This paper gives performance limits of the segmented compressive sampling (CS) which collects correlated samples. It is shown that the effect of correlation among samples for the segmented CS can be characterized by a penalty term in the…

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper, we announce an explicit formula of the Morse index for the signed area of a cyclic configuration. It depends…

The aim of this note is to present some recent results on the structure of the singular part of measures satisfying a PDE constraint and to describe some applications.

We prove a lower bound on the number of maximally broken trajectories of the negative gradient flow of a Morse-Smale function on a closed aspherical manifold in terms of integral (torsion) homology.

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…

In this paper we survey many of the known results about Morse boundaries and stability.

The main purpose of this paper is to introduce a new sequence space by using de la Vallee-Poussin mean and investigate both the modular structure with some geometric properties and some topological properties with respect to the Luxemburg…

An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This…

In this paper, we prove that discrete Morse functions on digraphs are flat Witten-Morse functions and Witten complexes of transitive digraphs approach to Morse complexes. We construct a chain complex consisting of the formal linear…

In this work we answer an open question asked by Johnson--Scoville. We show that each merge tree is represented by a discrete Morse function on a path. Furthermore, we present explicit constructions for two different but related kinds of…

The main purpose of the present paper is to introduce the notion of squeezing functions of bounded domains and study some properties of them. The relation to geometric and analytic structures of bounded domains will be investigated.…

In this article we prove the strong Morse inequalities for the area functional in codimension one, assuming that the ambient dimension satisfies $3 \leq (n + 1) \leq 7$, in both the closed and the boundary cases.

We show weak lower semi-continuity of functionals assuming the new notion of a "convexly constrained" $\mathcal A$-quasiconvex integrand. We assume $\mathcal A$-quasiconvexity only for functions defined on a set $K$ which is convex.…

In the context of discrete Morse theory, we introduce Morse frames, which are maps that associate a set of critical simplexes to all simplexes. The main example of Morse frames are the Morse references. In particular, these Morse references…