相关论文: A Kruskal-Katona type result and applications
We present a generalization of a version of the Kruskal-Katona theorem due to Lovasz. A shadow of a d-tuple (S_1,...,S_d) in binom{X}{r}^d consists of d-tuples (S_1',...,S_d') in binom{X}{r-1}^d obtained by removing one element from each of…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
Given a family $S$ of $k$--subsets of $[n]$, its lower shadow $\Delta(S)$ is the family of $(k-1)$--subsets which are contained in at least one set in $S$. The celebrated Kruskal--Katona theorem gives the minimum cardinality of $\Delta(S)$…
We give a short new proof of a version of the Kruskal-Katona theorem due to Lov\'asz. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a…
Building on and extending tools from variational analysis, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas-Plateau problem under simplicial refinement. This convergence is with…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…
We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. We in particular discuss decomposition methods, which reduce the problem to a number of…
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…
We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a…
Compositional minimisation can be an effective technique to reduce the state space explosion problem. This technique considers a parallel composition of several processes. In its simplest form, each sequential process is replaced by an…
We received a solution of the shadow problem in n-dimensional Euclidean space for a family of sets, constructing from any convex domain having nonempty interior with the help of parallel translations and homotheties. We find a number of…
We consider the one-dimensional Perona-Malik functional, that is the energy associated to the celebrated forward-backward equation introduced by P. Perona and J. Malik in the context of image processing, with the addition of a forcing term.…
Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…
The paper is devoted to an approach to the bounded cohomology theory based on the theories of simplicial sets and Postnikov systems. In particular, the main results of the bounded cohomology theory of topological spaces are extended to…
The problem of shadow is solved. It is equivalent to condition for point is in generalized convex hull of a family of compact sets.
We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
Properties of toposes of right $M$-sets are studied, and these toposes are characterised up to equivalence by their canonical points. The solution to the corresponding Morita equivalence problem is presented in the form of an equivalence…