We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one tra...

If B is an infinite subset of ω and X is a topological group, let CX B be the set of all x ∈ X such that 〈xn : n ∈ B〉 converges to 1. If F is a filter of infinite sets, let DX F = ⋃{CX B : B ∈ F}. The CX B and DX F are subgroups of X when X is abelian. In the circle group T, it is known that CX B always has measure 0. We show that there is a filter F such that DT F has measure 0 but is not cont...

Let f (z)= (t&z) d+(t) be a Markov function, where + is a positive measure with compact support in R. We assume that supp(+)/(&1, 1), and investigate the best rational approximants to f in the Hardy space H 2(V), where V :=[z # C | |z|>1] and H 2(V) is the subset of functions f # H2(V) with f ( )=0. The central topic of the paper is to obtain asymptotic error estimates for these approximants. T...

K e y w o r d s P a r a m e t r i c measure, Nonparametric measure, Csiszg~r's f-divergence, Information measure. 1. I N T R O D U C T I O N There are several types of information divergence measures s tudied in l i te ra ture which compare two probabi l i ty d is t r ibut ions and have appl icat ions in informat ion theory, s tat is t ics and engineering. A convenient classification to differe...

In this paper our aim is to estimate integrals of the form [,"if} = J~... f(ei9)dl-£(8) where 1-£ is, in general a complex measure. We consider quadrature formulas like [n if} = L:7=1 Aj,nf(xj,n) with n distinct nodes Xj,n on the unit circle and so that [,"if} = [n{f} for any f E 'Rn (a certain subspace of Laurent polynomials with dimension n). Under appropriate assumptions on the function f we...

A model function f(x1,. . .,xn) defined in the unit hypercube Hn with Lebesque measure dx= dx1. . .dxn is considered. If the unction is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or roups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, unctional...

We present a logarithmic Sobolev inequality adapted to a log-concave measure. Assume that Φ is a symmetric convex function on R satisfying (1 + ε)Φ(x) 6 xΦ(x) 6 (2 − ε)Φ(x) for x > 0 large enough and with ε ∈]0, 1/2]. We prove that the probability measure on R μΦ(dx) = e /ZΦdx satisfies a modified and adapted logarithmic Sobolev inequality : there exist three constant A,B,D > 0 such that for al...

1. What are these lectures about? Invariant measures, physical measures, and rates of mixing We are interested in discrete-time dynamical systems represented by the iterates f n = f f n?1 (where n 2 Z + represents time) of a transformation f : M ! M which is \chaotic," in the sense that arbitrarily close distinct initial points become \separated" (assuming a metric structure or at least a topol...

BACKGROUND Probabilistic record linkage is a process used to bring together person-based records from within the same dataset (de-duplication) or from disparate datasets using pairwise comparisons and matching probabilities. The linkage strategy and associated match probabilities are often estimated through investigations into data quality and manual inspection. However, as privacy-preserved da...