A rational polytope is the convex hull of a finite set of points in Rd with rational coordinates. Given a rational polytope P ⊆ Rd, Ehrhart proved that, for t ∈ Z>0, the function #(tP ∩ Zd) agrees with a quasi-polynomial LP(t), called the Ehrhart quasi-polynomial. The Ehrhart quasi-polynomial can be regarded as a discrete version of the volume of a polytope. We use that analogy to derive a new ...

Abslrocr -Suppose that a rational function Z ( s ) is defined by a Laurent .series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of Z(s)) to ensure that Re Z ( j w ) > 0 for all red w. The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving ...

Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in analysis of longitudinal data. Both involve estimation of the covariance function. Yet, challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function is proposed by ...

Relative to the rigorous physical model, rational polynomial coefficient (RPC) has been adopted as an alternative common sensor model data for image Geometric correction exploitation. In this paper, based on collected QuickBird imagery in Shanghai region, the iterative least-squares solution with regularization(ILSR) is derived to determine the RPCs by using 50 fair distributed ground control p...

Slope stability is one of the most complex and essential issues for civil and geotechnical engineers, mainly due to life and high economical losses resulting from these failures. In this paper, a new approach is presented for estimating the Safety Factor (SF) for circular failure slope using hybrid support vector regression (SVR) and Ant Colony Optimization (ACO). The ACO is combined with the S...

There is an ongoing debate regarding the efficacy of glycaemic control in critically ill patients. Here we briefly highlight the key function of elevated glucose in critically ill patients, namely, to enable elevation of aerobic glycolysis in rapidly dividing cells. In particular, aerobic glycolysis provides metabolic intermediates necessary for expansion of biomass in immune cells and promotio...

We focus on the implicitization of parametric CAGD entities which are supposed to be of tensor product type. The presented approach is featured by its ability to treat polynomial or rational splines having a great number of control points. For B-splines, we describe a method of exactly obtaining the Fourier coefficients without using quadrature rules. As for NURBS, a preprocessing step is neces...