Related papers: Weak uniform structures on probability distributio…

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…

A class of nets in constructive (in A.A.Markov's sense) topological space for which the convergence is equivalent to convergence of all subsequences, is described. B.A.Kushner's theorem about coincidence of strong and weak constructive…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…

Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…

We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…

We introduce the notion of weak commensurabilty of arithmetic subgroups and relate it to the length equivalence and isospectrality of locally symmetric spaces. We prove many strong consequences of weak commensurabilty and derive from these…

We consider some general classes of random dynamical systems and show that a priori very weak nonuniform hyperbolicity conditions actually imply uniform hyperbolicity.

This paper introduces a conception that any weighted directed network topology is almost decouplable, which can help to transform the topology into a similar form being composed of uncoupled vertices, and thus reduce the complexity of…

We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…

Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several…

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…

Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak…

The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…

We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More…

A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a…

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…