In this paper a regularized stochastic decomposition algorithm with master programs of finite size is described for solving two-stage stochastic linear programming problems with recourse. In a deterministic setting cut dropping schemes in decomposition based algorithms have been used routinely. However, when only estimates of the objective function are available such schemes can only be properl...

This article considers a linear regression model when a set of exact linear restrictions binding the coeecients is available and some observations on the study variable are missing. Estimators for the vectors of regression coeecients are presented and their superiority properties with respect to the criteria of the variance covariance matrix and the risk under balanced loss functions are analyzed.

This paper presents an explicit formula for propagation path loss prediction of microcellular communication in an urban street scene. The formula is derived based on geometrical optics and diffraction theory and it takes into account multiple reflections along main streets, side streets and diffractions around corners. Comparisons between our theoretical results with measurements and ray tracin...

We present a recursive formula for estimating the packet loss rate in IP networks. Specifically, we consider a single link whose capacity is shared dynamically by elastic data flows, each characterized by some peak rate, and derive the formula from the steady-state distribution of the number and peak rates of ongoing flows. The result is particularly useful for dimensioning ISP backhaul network...

We discuss the CreditRisk+ methodology from the perspective of the moment generating function of the credit factors. This representation lends itself to a new recursion formula for the portfolio loss distribution that is more accurate and considerably faster, particularly for large portfolios. We discuss how the model can be extended to incorporate correlations between risk factors and derive t...

The seller of a contingent claim H can always find a self-financing investment strategy that (super)hedges the claim H. When the seller wants to endow an initial capital x less than the one required to get perfect (super)hedging, the shortfall risk minimisation problem arises in a natural way. The aim is to find the strategy that minimises E{`([H(ST )−V x,φ T ])} (shortfall risk), where V x,φ t...

In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies the problem of solving quantified formulas subject to a cost function, and considers the problem in a quantified MaxSAT setting. Two approaches are investigated. One is based on relaxing the soft clauses and performing a l...

The Erlang B formula represents the steady-state blocking probability in the Erlang loss model or M/M/s/s queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we make use of various asymptotic expansions for the incomplete gamma function. A similar inversion problem is invest...

We have investigated the validity of our simulator. The validation item that we have already performed are summarized as follows. 1. Whether the energy loss distribution follows the Landau’s distribution. • thin absorber of Silicon 2. Whether the energy loss along per unit length follows the formula of Bethe-Bloch for protons. • thick absorber of Silicon • thick absorber of Lead 2 Landau’s dist...