Thesis (M. Sc.)--University of Alberta, 2009. / Title from PDF file main screen (viewed on Nov. 27, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science, Department of Computing Science, University of Alberta." Includes bibliographical references.

Pseudo-random sequences are a crucial component of cryptography, particularly in stream cipher design. In this thesis we will investigate several measures of randomness for certain classes of finitely generated sequences. We will present a heuristic algorithm for calculating the k-error linear complexity of a general sequence, of either finite or infinite length, and results on the closeness of the approximation generated. We will present an linear time algorithm for determining the linear complexity of a sequence whose characteristic polynomial is a power of an irreducible element, again presenting variations for both finite and infinite sequences. This algorithm allows the linear complexity of such sequences to be determined faster than was previously possible. Finally we investigate the stability of m-sequences, in terms of both k-error linear complexity and k-error period. We show that such sequences are inherently stable, but show that some are more stable than others.

No description available.

This thesis investigates the possibility to analyse a mobile network with sequences of UERC switches specific to each user equipment. An UERC is essentially a channel that carries information and a user equipment connects to different UERCs depending on whether they want to talk and/or send data with different qualities. As a major player in the mobile technology industry, Ericsson strives to optimise the use of the UERCs and are looking for an automated way to detect changes. The first task was to identify and retrieve the required events from the network log files in order to create the UERC sequences. As a way to test the thesis assumption, and give a proof of concept, two different data sets were analysed were changes had been made to the network settings that should have affected the UERC sequences. With the use of n-grams, Markov chains and Bayesian Estimation testing, the changes could be identified and the thesis assumption could be confirmed - UERC sequences provides a possible way of analysing a mobile network.

No description available.

This thesis deals with the behaviour modulo n of linear recurring sequences of integers with characteristic polynomial ƒ ( x ) where n is a positive integer and ƒ ( x ) is a monic polynomial of degree k. Let α [subscript 1], α [subscript 2],...,α [subscript k] be the zeros of ƒ ( x ) and D ( ƒ ) ≠ 0 its discriminant. We focus on the v-sequence ( v [subscript j] ), defined by v [subscript j] = α[superscript j] over [subscript 1] + α [superscript j] over [subscript 2] + ... + α [superscript j] over [subscript k] for j ≥ 0. Our main interest is in algebraic congruences modulo n which hold when n is a prime and which involve only terms of the sequence and rational integers. For k = 1,2 such results have been used extensively in primality testing and have led to the study of various types of pseudoprimes. For k = 3, such results have been studied by Adams and Shanks ( 1 ) under the further assumption ƒ ( 0 ) = - 1. For general k, quite different approaches have been taken by Gurak ( 2 ) and Szekeres ( 3 ). The infinite test matrix modulo n is the infinite matrix M with rows and columns numbered 0,1,2 ... whose ( i, j ) entry is m [subscript ij], the least residue modulo n of v [subscript in + j] - v [subscript i + j] for i ≥ 0 and j ≥ 0. We study the congruence properties of M and especially of the k x k submatrix M ( [superscript k] ) determined by rows and columns 0 to k - 1. Chapters 1 and 2 introduce the thesis and summarise auxiliary results. Chapter 3 presents background on linear recurring sequences with an emphasis on the matrix approach, including the v - sequence and the k " u - sequences " ( whose initial vectors are the rows of Ik ). Chapter 4 comprises theoretical study of the properties of M for a general k, both when n is a prime and for general n, together with investigation of the condition of Gurak ( 2 ). For ( n, k!D ( ƒ ) ) = 1, we show that the condition of Szekeres is equivalent to the condition that m [subscript i0] = 0 for 1 ≤ i ≤ k and also to certain permutation conditions. Gurak ' s condition is then described using these conditions. Chapter 5 assumes k = 3. For this case we study congruences modulo n satisfied by the m [subscript ij] when n is a prime, and hence develop a combination of tests on M ( [superscript 3] ) which are passed by all primes. We report on extensive computer investigation of composites passing these tests. Such composites are found to be rare. Investigation of the relevant work of Adams and Shanks and colleagues, together with use of the permutation condition of Chapter 4, leads to a modification of the earlier tests on M ( [superscript 3] ). Under suitable assumptions we show that the new modified condition is equivalent to the basic condition of Adams and Shanks and also to that of Gurak but has significant advantages over both. References ( 1 ) Adams, W. and Shanks, D. Strong primality tests that are not sufficient, Math. Comp., 39, 1982, 255-300. ( 2 ) Gurak, S. Pseudoprimes for higher - order linear recurrence sequences, Math. Comp., 55, 1990, 783-813. ( 3 ) Szekeres, G., Higher order pseudoprimes in primality testing, pp 451-458, in Combinatorics, Paul Erdos is eighty, Vol. 2 ( Jesztgektm 1993 ), Bolyai Soc. Math. Stud., 2, Jnos Bolyai Math. Soc. Budapest, 1996. / Thesis (M.Sc.)--School of Mathematical Sciences, 2006.

Thesis (M.S.)--Ohio University, August, 2000. / Title from PDF t.p.

Thesis (M.S.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains iii, 33 p. Includes abstract. Includes bibliographical references (p. 33).

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.

This thesis adopts a geoarchaeological approach to palaeoenvironmental research in the Konya basin of South-Central Turkey. It involves the analysis of sediment sequencesth rough cultural and alluvial depositsa crossa broad alluvial fan which has developed on the southern edge of the basin since the beginning of the Holocene. Sediments have been analysed by mineral magnetics, particle size, carbonate and organic matter content, and grouping into lithological units has been aided by statistical techniques including principal components analysis and discriminant analysis. Resultso f the analysis have shown a complex sequenceo f deposition across the alluvial fan throughout the Holocene, and within the sequences a number of archaeological sites ranging in date from the Early Neolithic to the Byzantine periods have been identified as being established on various land surfaces. During the early to mid Holocene, the predominant alluvial deposit across the fan was a fine-grained, heavy backswamp clay, deposition of which was time transgressive, i. e. area of deposition changed over this period as the course of the depositing river migrated laterally, and up/down fan. Evidence from the largest and earliest site studied, I; atalh6yiik, where archaeological excavation has recently recommenced, shows that the site was established during the Early Neolithic in an actively flooding alluvial environment. This has implications, not only for the populations inhabiting the site, but also for the wider reasoning behind the establishment of early agricultural settlements in the Near East. Other sites in the area up to the Early Bronze Age have also been seen to have been established in actively depositing alluvial settings. Shortly before c. 4000 BP there was a permanent change in the nature of alluvial deposition, with the heavy backswamp clay being replaced by a less fine-grained deposit of different origin. This initial change was concurrent with an apparent depopulation of the alluvial fan and a relationship between the two phenomena is possible. More importantly, there appear to have been major population changes and increased human influence on the environment of both the fan catchment and the wider region subsequent to these phenomena. Such changes appear to have had a long-term effect on the fan environment as the nature of the alluvial deposition remained relatively unaltered between these events and intensive irrigation schemes which restricted alluvial deposition in the early twentieth century.