Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

multi objective quadratic fractional programming (moqfp) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the object...

the study of stability problems of functional equations was motivated by a question of s.m. ulam asked in 1940. the first result giving answer to this question is due to d.h. hyers. subsequently, his result was extended and generalized in several ways.we prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=ag(x)+bg(y)on restricted domain. namely, we show, under some weak natural...

Graphical models are fundamental tools for modeling images and other applications. In this paper, we propose the Logistic Random Field (LRF) model for representing a discrete-valued graphical model. The LRF model is based on an underlying quadratic model and a logistic function. The chief advantages of the LRF are its convenience and flexibility. The quadratic model makes inference easy to impl...

1 Quadratic Congruences to Prime Moduli . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Quadratic Congruences to Composite Moduli . . . . . . . . . . . . . . . . . . . . . 5 3 Some Sums of Legendre’s symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 Solutions . . . . . . . . . . . . ...

We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.

We first provide our derivation of the coordinate-ascent method used in the alternating inference, which searches for the best scoring x and v. The overview of our method is given in Algorithm 1 in the main paper. We now show how to rewrite the scoring function S(x,v) as its quadratic form w.r.t. v. Note that γ(v(y)) = (1− δ)v(y) + δ. So we can write the first term (i.e., the global mask term) ...

The paper presents some main aspects regarding multi-parametric quadratic programming (mp-QP) problems. Model Predictive Control (MPC) is considered as a particular mp-QP problem, and this powerful tool is applied for control and simulation through a case study. Since the solutions to mp-QP problems can be expressed as piecewise affine linear functions of the state, a new implementation in term...