A study is made of a non{smooth matrix optimization problem arising in adaptive{ optics, which involves the optimal real{time control of a very fast{acting deformable mirror designed to compensate for atmospheric turbulence and other image degradation factors, such as wind{induced telescope vibration (windshake). The surface shape of this mirror must change rapidly to correct for time{varying o...

In this section, we derive in detail the closed form solution of problem (12) for binary pairwise factors (Sect. 4.1). Recall that the marginal polytope M(G a) is given by:

Let R be a Krull ring with quotient field K and a1, . . . , an in R. If and only if the ai are pairwise incongruent mod every height 1 prime ideal of infinite index in R does there exist for all values b1, . . . , bn in R an interpolating integer-valued polynomial, i.e., an f ∈ K[x] with f(ai) = bi and f(R) ⊆ R. If S is an infinite subring of a discrete valuation ring Rv with quotient field K a...

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise th...

In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDE), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compu...

This paper studies a multi-relay adaptive turbo-coded cooperative diversity scheme over Nakagami-m fading channels. In the underlying scheme, after receiving a fraction of the codeword determined by a tradeoff parameter denoted by f , all the relays decode, and only the reliable relays forward the rest of the codeword to the destination. We assume binary phase-shift keying modulation and analyz...

Let G = (V,E) be a graph. A k-neighborhood in G is a set of vertices consisting of all the vertices at distance at most k from some vertex of G. The hypergraph on vertex set V which edge set consists of all the k-neighborhoods of G for all k is the neighborhood hypergraph of G. Our goal in this paper is to investigate the complexity of a graph in terms of its neighborhoods. Precisely, we define...

Analytic formulas are developed for various types of power and error rates of some closed testing procedures. The formulas involve non-convex regions that may be integrated with high, pre-specified accuracy using available software. The non-convex regions are represented as a union of hyper-rectangles. These regions are transformed to the unit hypercube, then summed, to create an expression for...

In this paper, an innovative data pre-processing method to improve the classification performance and to determine automatically the vertebral column disorders including disk hernia (DH), spondylolisthesis (SL) and normal (NO) groups has been proposed. In the classification of vertebral column disorders' dataset with three classes, a pairwise fuzzy C-means (FCM) based feature weighting method h...