Example 2 (Convexity of a probability vector space) Show that the probability vector space is a convex set. Answer: Consider a random variable X with alphabet X = 1, ..., k. The probability vector space PX = [PX (1) , PX (2) , ..., PX (k)] ∈ R, is the set of all vectors for which PX (i) ≥ 0 ∀i ∈ X , and ∑K i=1 PX (i) = 1. Now consider two probability vectors P (1) X and P (2) X , and the vector

OF THE DISSERTATION Information theory methods in communication complexity by Nikolaos Leonardos Dissertation Director: Michael Saks This dissertation is concerned with the application of notions and methods from the field of information theory to the field of communication complexity. It consists of two main parts. In the first part of the dissertation, we prove lower bounds on the randomized ...

ion and Stepwise Refinement The specifications described above must embody the key concept of Abstraction if they are to be successful. To be abstract, a specification must include the essential requirements that an object must satisfy and omit the unessential. A service specification is abstract primarily in the sense that it a specification must include the essential requirements that an obje...

This paper deals with the new progressive channel coding methods for short message transmission via satellite transponder using predetermined length of frame. The key benefits of this contribution are modification and implementation of a new turbo code and utilization of unique features with applications of methods for bit error rate estimation and algorithm for output message reconstruction. T...

Nowadays, design of embedded systems is confronted with complex signal processing algorithms and amultitude of computational intensive multimedia applications, while time to product launch has been extremely reduced. Especially in the wireless domain, those challenges are stacked with tough requirements on power consumption and chip size. Unfortunately, design productivity did not undergo a sim...

In this paper we make an overview of s-step Conjugate Gradient and develop a novel formulation for s-step BiConjugate Gradient Stabilized iterative method. Also, we show how to add preconditioning to both of these s-step schemes. We explain their relationship to the standard, block and communication-avoiding counterparts. Finally, we explore their advantages, such as the availability of matrix-...

ABSTRACT: Purpose: This article describes the various research methods that are implemented in the field of communication disorders. Research within this field is an expansive and continuously evolving phenomenon and is influenced by a variety of theoretical views from many disciplines, including anthropology, sociology, psychology, medicine, statistics, and philosophy. This review aims to summ...