In other words, find the probability density functions f(·) and g(·) in (2) corresponding to the model (1). (b) Simulate the model (1) to produce T = 100 measurements y1:T . Based on these measurements compute the optimal (in the sense that it minimizes the mean square error) estimate of xt | y1:t for t = 1, . . . , T . Implement a bootstrap particle filter and compare to the optimal estimates....

A “dyadic rectangle” is a set of the form R = [a2−s, (a+1)2−s]×[b2−t, (b+1)2−t], where s and t are non-negative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study n-tilings which consist of 2 nonoverlapping dyadic rectangles, each of area 2−n, whose union is the unit square. We discuss some of the underlying combinatorial structures, provide ...

Let T be a tile made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be tilable by finitely many Qweighted tiles with the same shape as T , and necessary and sufficient conditions for a square to be tilable by finitely many Z-weighted tiles with the sa...

We have reinvestigated the structural and thermodynamic properties of the squarewell and the square-shoulder system using two different theoretical frameworks, i.e., the optimized random-phase approximation and the Rogers–Young integral equation. We discuss the limits of applicability of the respective concepts and compare the results with ‘exact’ Monte Carlo simulation results and with data ob...

UNLABELLED Prostate cancer is one of the most common malignancies in men. The multidrug resistance 1 gene (MDR1) is an important candidate gene for prostate cancer. The aim of this study was to evaluate the association between MDR1 gene polymorphisms and the risk of prostate cancer. MDR1 gene polymorphism and its association with the risk of prostate cancer were investigated in 357 Chinese men....