Related papers: Perfect discrete Morse functions on Stratifoldds
We establish Morse inequalities for a noncompact manifold with a cocompact and properly discontinuous action of a discrete group, where Morse functions are not necessarily invariant under the group action. The inequalities are given in…
We study two important operations on polynomials defined over complete discrete valuation fields: Euclidean division and factorization. In particular, we design a simple and efficient algorithm for computing slope factorizations, based on…
We give a complete classification of all simple current modular invariants, extending previous results for $(\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this…
We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation…
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.
The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the…
We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain "Relative Morse Inequalities" relating the homology of the…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…
We introduce an algorithm that constructs a discrete gradient field on any simplicial complex. We show that, in all situations, the gradient field is maximal possible and, in a number of cases, optimal. We make a thorough analysis of the…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover,…
Motivated by applications in geomorphology, the aim of this paper is to extend Morse-Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional…
We prove $\ell^2$ estimates for certain discrete maximal operators associated to simplices. These operators are generalizations of the discrete spherical maximal operator.
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
One way to geometrically encode the singularities of a stratified pseudomanifold is to endow its interior with an iterated fibred cusp metric. For such a metric, we develop and study a pseudodifferential calculus generalizing the…
The perfectly matched layers (PMLs), as a boundary termination over an unbounded spatial domain, are widely used in numerical simulations of wave propagation problems. Given a set of discretization parameters, a procedure to select the PML…
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here…