This tutorial treats mixtures of Gaussian probability distribution functions. Gaussian mixtures are combinations of a finite number of Gaussian distributions. They are used to model complex multi-dimensional distributions. When there is a need to learn the parameters of the Gaussian mixture, the EM algorithm is used. In the second part of this tutorial mixtures of Gaussian are used to model the...

This tutorial treats mixtures of Gaussian probability distribution functions. Gaussian mixtures are combinations of a finite number of Gaussian distributions. They are used to model complex multidimensional distributions. When there is a need to learn the parameters of the Gaussian mixture, the EM algorithm is used. In the second part of this tutorial mixtures of Gaussian are used to model the ...

By (extended) Wiener–Ikehara theory, the prime-pair conjectures are equivalent to simple pole-type boundary behavior of corresponding Dirichlet series. Under a weak Riemann-type hypothesis, the boundary behavior of weighted sums of the Dirichlet series can be expressed in terms of the behavior of certain double sums Σ 2k(s). The latter involve the complex zeros of ζ(s) and depend in an essentia...

Optimal Design of Discrete-Time ∆Σ Modulators by Matthew Edward Jackson Dr. Peter A. Stubberud, Examination Committee Chair Professor of Electrical Engineering University of Nevada, Las Vegas In this thesis, optimal signal transfer functions (STFs) and noise transfer functions (NTFs) for discrete time delta sigma (∆Σ) modulators are determined. For a given oversampling rate (OSR), these STFs an...

In this paper, we revisit the Property Matching problem studied by Amir et al. [Property Matching and Weighted Matching, CPM 2006] and present a better indexing scheme for the problem. In particular, the data structure by Amir et al., namely PST, requires O(n log |Σ|+ n log log n) construction time and O(m log |Σ|+ K) query time, where n and m are the length of, respectively, the text and the p...

We consider a generalization of the shortest-path problem: given an alphabet Σ, a graph G whose edges are weighted and Σ-labeled, and a regular language L ⊆ Σ∗, the L-constrained shortest-path problem consists of finding a shortest path p in G such that the concatenated labels along p form a word of L. This definition allows to model, e. g., many traffic-planning problems. We present extensions...

For the interval linear system Ax = b, we consider the linear tolerance problem, requiring inner evaluation of the tolerable solution set Σ∀∃(A,b) = {x∈ R|(∀A∈A)(Ax∈b)} formed by all point vectors x such that the product Ax remains within b for all possible A∈A. We develop solvability theory for the linear tolerance problem that not only settles whether Σ∀∃ is empty or not, but also enables mod...

In section 4.2 of the paper, we compared the distribution modeling of GOG to other distributions. Below, we describe the details of the compared methods. The Mean, Cov and Gauss are global distribution descriptors of pixel features within each region. The Cov-ofCov, Cov-of-Gauss and GOG are hierarchical distribution descriptors. The Cov-of-Cov uses covariance matrix in both patch and region mod...

In this paper, we will examine the backward shift operator Lf = (f − f(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of “pseudocontinuation” of functions across the...