In this paper we demonstrate the use of network analysis to characterise patterns of clustering in spatio-temporal events. Such clustering is of both theoretical and practical importance in the study of crime, and forms the basis for a number of preventative strategies. However, existing analytical methods show only that clustering is present in data, while offering little insight into the natu...

The question of whether the class of decision problems that can be solved by deterministic polynomial-time algorithms (P ) is equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms (NP) has been open since it was first formulated by Cook, Karp, and Levin in 1971. In this paper, we prove that they are not equal by showing that any algorithm that...

Courses covering analytical methods for materials characterization are part of the educational program in many academic faculties, particularly in applied physics and chemistry. Employment of multimedia techniques in the presentation of the subject is increasingly accepted and even demanded by students as the required hardware and software becomes affordable and widely available at reasonable q...

The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-li...

Two implementations of a homology algorithm based on the Forman’s discrete Morse theory combined with the coreduction method are presented. Their efficiency is compared with other implementations of homology algorithms.

A new Bayesian method is proposed for the analysis of discretely sampled diffusion processes. The method, which is termed high frequency augmentation (HFA), is a simple numerical method that is applicable to a wide variety of univariate or multivariate diffusion and jump-diffusion processes. It is furthermore useful when observations are irregularly observed, when one or more elements of the mu...

Interatomic interaction potentials are compared using a molecular dynamics modeling method to choose the simplest, but most effective, model describe of copper nanoparticles and graphene flakes. Three considered: (1) bond-order potential; (2) hybrid embedded-atom-method Morse (3) potential. The is investigated for crumpled filled with determine possibility obtaining composite mechanical propert...

Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and MacPherson [17]. We describe the basics of this theory and prove fundamental theorems relating the topology of a general simplicial complex with the critical simplice...