# Mathematical Foundations (mathematical + foundation)

Distribution by Scientific Domains

## Selected Abstracts

### On ,-biased generators in NC0

RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2006
Elchanan Mossel
Cryan and Miltersen (Proceedings of the 26th Mathematical Foundations of Computer Science, 2001, pp. 272,284) recently considered the question of whether there can be a pseudorandom generator in NC0, that is, a pseudorandom generator that maps n -bit strings to m -bit strings such that every bit of the output depends on a constant number k of bits of the seed. They show that for k = 3, if m , 4n + 1, there is a distinguisher; in fact, they show that in this case it is possible to break the generator with a linear test, that is, there is a subset of bits of the output whose XOR has a noticeable bias. They leave the question open for k , 4. In fact, they ask whether every NC0 generator can be broken by a statistical test that simply XORs some bits of the input. Equivalently, is it the case that no NC0 generator can sample an ,-biased space with negligible ,? We give a generator for k = 5 that maps n bits into cn bits, so that every bit of the output depends on 5 bits of the seed, and the XOR of every subset of the bits of the output has bias 2. For large values of k, we construct generators that map n bits to bits such that every XOR of outputs has bias . We also present a polynomial-time distinguisher for k = 4,m , 24n having constant distinguishing probability. For large values of k we show that a linear distinguisher with a constant distinguishing probability exists once m , ,(2kn,k/2,). Finally, we consider a variant of the problem where each of the output bits is a degree k polynomial in the inputs. We show there exists a degree k = 2 pseudorandom generator for which the XOR of every subset of the outputs has bias 2,,(n) and which maps n bits to ,(n2) bits. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 [source]

### Integrating the scene length characteristics of MPEG video bitstreams into a direct broadcast satellite network with return channel system

INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING, Issue 2 2004
Fatih Alagöz
Abstract In order to optimize the network resources, we should incorporate all the available information into the network design. However, incorporating irrelevant information may increase the design complexity and/or decrease the performance of the network. In this paper, we investigate the relevance of integrating the scene length characteristics of moving pictures expert group (MPEG) coded video bitstreams into a direct broadcast satellite (DBS) network with return channel system (DVB-RCS). Due to the complexity of the studied system, unless disputable simplifications are made, it is hard to achieve a mathematical foundation for this integration. Our analysis relies on extensive set of simulations. Firstly, we achieve the scene length distributions for MPEG bitstreams based on the proposed scene change models and their subjective observations of the actual video. We show that these models may be used to estimate the scene length of MPEG bitstreams. We then integrate this estimation into a DBS network simulator. Finally, we show that the scene length characteristics may be used to improve the DBS network performance under certain conditions. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Meshless numerical simulation of (full) potential flows in a nozzle by genetic algorithms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2003
G. Winter
Abstract A new procedure to solve some fluid problems formulated in elliptical partial differential equations is presented. A Genetic Algorithm with a dynamical encoding and a partial grid sampling is proposed for it as the advantages of solving the problem without using all grid nodes at the same time, and of adjusting step grid, without increasing the complexity. The designed method has immediate applications some self-contained and some in combination with other traditional methods. Also, it provides a method alternative to the existing ones and uses simpler operations. Theoretical mathematical foundations of the problem are easily incorporated and that as a powerful characteristic of the method. In practice, our focus is to obtain an acceptable approximated solution. The method makes it possible to solveproblems with vague boundary conditions since no algebraic equation system is involved in the process. From the solution reached we have good information available to make an appropriate mesh to solve the problem through a traditional method. Comparative results for both linear and non-linear potential flow problems inside a nozzle are given. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Tutorial on Computational Linguistic Phylogeny

LINGUISTICS & LANGUAGE COMPASS (ELECTRONIC), Issue 5 2008
Johanna Nichols
Over the last 10 or more years, there has been a tremendous increase in the use of computational techniques (many of which come directly from biology) for estimating evolutionary histories (i.e., phylogenies) of languages. This tutorial surveys the different methods and different types of linguistic data that have been used to estimate phylogenies, explains the scientific and mathematical foundations of phylogenetic estimation, and presents methodologies for evaluating a phylogeny estimation method. [source]

### Diffusion-equation method for crystallographic figure of merits

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2010
Anders J. Markvardsen
Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem.93, 3339,3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depending on whether atomic coordinates are fixed or not. The resulting expression is computationally efficient, taking the same order of floating-point operations to evaluate as the starting FOM function measured in terms of the number of atoms in the asymmetric unit. This opens the possibility of implementing diffusion-equation methods for crystallographic global optimization algorithms such as structure determination from powder diffraction data. [source]