Related papers: A note on limit shapes of minimal difference parti…
This paper studies limit profiles for the separation distance. A limit profile records the limiting shape of the distance to stationarity inside the cutoff window, at times of the form $t_n+cw_n$. We start with two famous card shuffles, a…
Let $p_{\textrm{dsd}} (n)$ be the number of partitions of $n$ into distinct squarefree divisors of $n$. In this note, we find a lower bound for $p_{\textrm{dsd}} (n)$, as well as a sequence of $n$ for which $p_{\textrm{dsd}} (n)$ is…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
We discuss the application of variational methods, based on non-smooth critical point theory, to a general class of partial differential inclusions.
The average size of the "smallest gap" of a partition was studied by Grabner and Knopfmacher in 2006. Recently, Andrews and Newman, motivated by the work of Fraenkel and Peled, studied the concept of the "smallest gap" under the name…
We consider a subset of projective space over a finite field and give bounds on the minimal degree of a non-vanishing form with respect to this subset.
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture…
The paper is devoted to the development of a comprehensive calculus for directional limiting normal cones, subdifferentials and coderivatives in finite dimensions. This calculus encompasses the whole range of the standard generalized…
We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity…
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…
We consider the problem of finding an orientation with minimum diameter of a connected bridgeless graph. Fomin et. al. discovered a relation between the minimum oriented diameter an the size of a minimal dominating set. We improve their…
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…
Here we study temporo-spatial differentiation problems with respect to sequences of finite unions of balls. We establish several convergence results, as well as construct pathological temporo-spatial differentiations with prescribed sets of…
Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
We study sheaves of differential forms and their cohomology in the h-topology. This allows to extend standard results from the case of smooth varieties to the general case. As a first application we explain the case of singularities arising…
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $\R^n$ in a way that is completely algebraic.…
A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal partitions coincide with nodal partitions of Courant-sharp…
For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.