The majority of real-world networks are dynamic and extremely large (e.g., Internet Traffic, Twitter, Facebook, ...). To understand the structural behavior of nodes in these large dynamic networks, it may be necessary to model the dynamics of behavioral roles representing the main connectivity patterns over time. In this paper, we propose a dynamic behavioral mixed-membership model (DBMM) that ...

In axiomatic way, in fuzzy setting, we introduce the measure of crispness and the measure of conditional clearness. For these measures we propose a functional form. Then, for the last measure, we give some aggregation operators. Keywords— Aggregation operators, functional equations, fuzzy sets, measures of fuzziness, crispness measures, conditional crispness.

We present a method of producing normal subgroups of the free group on r generators not containing a given word. Special attention is given to the normal subgroups of the free group on two generators. In considering the exponent sum of the generators in a given word, we produce such subgroups and clearly state for what class of words these subgroups are not easily obtainable. We also provide a ...

In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is ...

T he task of designing a systematic program for testing and teaching higher order thinking skills is formidable, yet recent advances in the ory and research provide some basis for defining a core of fundamental skills and for designing exercises that require using such skills Since testing programs at the national, state, and local levels are being used to assess students' reasoning skills, the...

The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primari...

In this paper we shall discuss the numerical simulation of higher order geometric flows by level set methods. Main examples under considerations are surface diffusion and the Willmore flow as well as variants and of them with more complicated surface energies. Such problems find various applications, e.g. in materials science (crystal growth, thin film technology), biophysics (membrane shapes),...

Quasi-Monte Carlo is usually employed to speed up the convergence of Monte Carlo in approximating multivariate integrals. While convergence of the Monte Carlo method is O(N−1/2), that of plain quasi-Monte Carlo can achieve O(N−1). Several methods exist to increase its convergence to O(N−α ), α > 1, if the integrand has enough smoothness. We discuss two methods: lattice rules with periodization ...

This paper presents a method of producing higher order discretization weights for linear differential and integral operators using the Minimum Sobolev Norm idea[1][2] in arbitrary geometry and grid configurations. The weight computation involves solving a severely ill-conditioned weighted least-squares system. A method of solving this system to very high-accuracy is also presented, based on the...