No part of this work may be reproduced by print, photocopy or any other means without the permission in writing from the publisher. Cover page illustration: Front side; Three-dimensional AFM images of LSMO nanowires of different dimensions on STO substrates. Top one is having width 422nm, height 26nm and periodicity 600nm, left one is having width 292nm height 25nm and periodicity 600nm, and ri...

The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary morphism h such that g(α) = h(α). Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of m...

We develop techniques for discovering patterns with periodicity in this work. Patterns with periodicity are those that occur at regular time intervals, and therefore there are two aspects to the problem: finding the pattern, and determining the periodicity. The difficulty of the task lies in the problem of discovering these regular time intervals, i.e., the periodicity. Periodicities in the dat...

Many prokaryotic and eukaryotic genomes feature a characteristic periodic signal in distribution of short runs of A or T (A-tracts) phased with the DNA helical period of ∼10-11 bp. Such periodic spacing of A-tracts has been associated with intrinsic DNA curvature. In eukaryotes, this periodicity is a major component of the nucleosome positioning signal but its physiological role in prokaryotes ...

We discuss different types of almost periodicity of trajectories of cocycles on compact solenoidal groups in relation to various notions of triviality of these cocycles. Introduction Let G be a compact solenoidal group, that is, a compact Abelian group containing, as a dense subgroup, the image of IR by a continuous homomorphism, say a. We shall assume that G is not a circle by requiring a to b...

The concept of periodicity has played over the years a centra1 role in the development of combinatorics on words and has been a highly valuable too1 for the design and analysis of algorithms. Fine and Wilf’s famous periodicity result, which is one of the most used and known results on words, has extensions to partia1 words, or sequences that may have a number of “do not know” symbols. These ext...

The Simple Network Management Protocol (SNMP) is currently widely in use to control, monitor, and configure network elements. Even though SNMP technology is well documented and has been the topic of research a number of times in the past, not much research has yet been done with respect to periodicity in SNMP traffic. This thesis aims at the development of a method through which periodic and ap...

In many application areas (for instance, DNA sequence analysis), it becomes important to compute various kinds of \approximate period" of a given string y. Here we discuss three such approximate periods and the algorithms which compute them: an Abelian generator, a cover, and a seed. Let u be a substring of y. Then u is an Abelian generator of y ii y is a concatenation of substrings which are p...

In 1965, Fine and Wilf proved the following theorem: if (fn)n¿0 and (gn)n¿0 are periodic sequences of real numbers, of period lengths h and k, respectively, and fn = gn for 06 n¡h+ k − gcd(h; k), then fn = gn for all n¿ 0. Furthermore, the constant h + k − gcd(h; k) is best possible. In this paper, we consider some variations on this theorem. In particular, we study the case where fn 6 gn inste...

Let M be a finitely generated module over an Artin algebra. By considering the lengths of each module in the minimal projective resolution of M , we obtain its Betti sequence. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which this holds, using techniques from Hochschild cohomology. We also provide a result which ...