No description available.

A string is a sequence of symbols, usually called letters, drawn from some alphabet. It is one of the most fundamental and important structures in computing, bioinformatics and mathematics. Computer files, contents of a computer memory, network and satellite signals are all instances of strings. The genome of every living thing can be represented by a string drawn from the alphabet {a, c, g, t}. The algorithms processing strings have a wide range of applications such as information retrieval, search engines, data compression, cryptography and bioinformatics. In a DNA sequence the indeterminate symbol {a, c} is used when it is unclear whether a given nucleotide is a or c, We could then say that {a, c} matches another symbol {c, g} which in turn matches {g, t}, but {a, c} certainly does not match {g, t}. The processing of indeterminate strings is much more difficult because of this nontransitivity of matching. Thus a combinatorial understanding of indeterminate strings becomes essential to the development of efficient methods for their processing. With indeterminate strings, as with ordinary ones, the main task is the recognition/computation of patterns called regularities . We are particularly interested in regularities called repeats, whether tandem such as acgacg or nontandem (acgtacg). In this thesis we focus on newly-discovered regularities in strings, especially the enhanced cover array and the Lyndon array, with attention paid to extending the computations to indeterminate strings. Much of this work is necessarily abstract in nature, because the intention is to produce results that are applicable over a wide range of application areas. We will focus on finding algorithms to construct different data structures to represent strings such as cover arrays and Lyndon arrays. The idea of cover comes from strings which are not truly periodic but "almost" periodic in nature. For example abaababa is covered by aba but is not periodic. Similarly the Lyndon array describes the string in another unique way and is used in many fields of string algorithms. These data structures will help us in the field of string processing. As one application of these data structures we will work on "Reverse Engineering"; that is, given data structures derived from of a string, how can we get the string back. Since DNA, RNA and peptide sequences are effectively "strings" with unique properties, we will adapt our algorithms for regular or indeterminate strings to these sequences. Sequence analysis can be used to assign function to genes and proteins by observing the similarities between the compared sequences. Identifying unusual repetitive patterns will aid in the identification of intrinsic features of the sequence such as active sites, gene-structures and regulatory elements. As an application of periodic strings we investigate microsatellites which are short repetitive DNA patterns where repeated substrings are of length 2 to 5. Microsatellites are used in a wide range of studies due to their small size and repetitive nature, and they have played an important role in the identification of numerous important genetic loci. A deeper understanding of the evolutionary and mutational properties of microsatellites is needed, not only to understand how the genome is organized, but also to correctly interpret and use microsatellite data in population genetics studies. / Thesis / Doctor of Philosophy (PhD)

Recent advancements in semiconductor fabrication technology have enabled field-programmable gate arrays (FPGAs) with hundreds of embedded memories. Usually, these embedded memories can be configured to work with different widths of address and data buses, In some FPGAs there is also a variety of different types of embedded memories with different capacities and configuration sets. As a consequence, it is becoming cumbersome to bind the data memory of an algorithm to these embedded memories manually. A computer-aided design tool that automates the process of binding embedded memories can save the engineering time for a design, as well as explore different alternatives to bind the data memory with the use of less embedded memories and less amount of peripheral hardware in terms of logic cells of the FPGA. In this thesis, we first motivate the need for an algorithmic solution to the memory binding problem in FPGAs and explain the design trade-offs. Then we present an exact solution for the problem using a branching method to search the solution space exhaustively. However, due to the large solution space and the plenitude of choices in each step of the algorithm, the runtime of the algorithm is far from being acceptable for realistic problems. To manage the runtime, we have developed a fast heuristic approach. Our experimental results show that the heuristic method can achieve a suboptimal solution, which for the small problem instances is shown to be close to the optimal in acceptable runtime. Moreover, when compared to manual solutions, besides substantially improving the implementation time, the heuristic can often enable a more efficient usage of the FPGA logic resources and embedded memories. / Thesis / Master of Applied Science (MASc)

In this research, we apply modern high performance computing techniques to solve an engineering problem, structural analysis of grid stiffened panels. An existing engineering code, SPANDO, is studied and modified to execute more efficiently on high performance workstations and parallel computers. Two new SPANDO packages, a modified sequential SPANDO and parallel SPANDO, are developed. In developing the new sequential SPANDO, we use two existing high performance numerical packages: LAPACK and ARPACK to solve our linear algebra problems. Also, a new block-oriented algorithm for computing the matrix-vector multiplication w=A⁻¹Bx is developed. The experimental results show that the new sequential SPANDO can save over 70% of memory size, and is at least 10 times faster than the original SPANDO. In parallel SPANDO, ScaLAPACK and BLACS are used. There are many factors that may affect the performance of parallel SPANDO. The parallel performance and the affects of these factors are discussed in this thesis. / Master of Science

Given a geometric graph G = (V,E), where V is the set of vertices and E is the set of edges and a source-target pair {s,t} is a subset of V, a local geometric routing algorithm seeks a route from s to t using only local neighborhood relationships. This thesis proposes a local geometric routing algorithm that uses only a single state bit as message overhead and guarantees delivery of messages in three different classes of edge-augmented planar graphs: convex subdivisions, quasi planar convex subdivisions (allow some augmented edges on a spanning convex subdivision) and 2-augmented triangulations (allow some augmented edges on a spanning triangulation). The proposed algorithm is origin oblivious (does not require the knowledge of the origin vertex s) and predecessor oblivious (does not require the knowledge of the predecessor vertex).

Given a geometric graph G = (V,E), where V is the set of vertices and E is the set of edges and a source-target pair {s,t} is a subset of V, a local geometric routing algorithm seeks a route from s to t using only local neighborhood relationships. This thesis proposes a local geometric routing algorithm that uses only a single state bit as message overhead and guarantees delivery of messages in three different classes of edge-augmented planar graphs: convex subdivisions, quasi planar convex subdivisions (allow some augmented edges on a spanning convex subdivision) and 2-augmented triangulations (allow some augmented edges on a spanning triangulation). The proposed algorithm is origin oblivious (does not require the knowledge of the origin vertex s) and predecessor oblivious (does not require the knowledge of the predecessor vertex).

A well-known paradigm for optimisation is the evolutionary algorithm (EA). An EA maintains a population of possible solutions to a problem which converges on a global optimum using biologically-inspired selection and reproduction operators. These algorithms have been shown to perform well on a variety of hard optimisation and search problems. A recent development in evolutionary computation is the Estimation of Distribution Algorithm (EDA) which replaces the traditional genetic reproduction operators (crossover and mutation) with the construction and sampling of a probabilistic model. While this can often represent a significant computational expense, the benefit is that the model contains explicit information about the fitness function. This thesis expands on recent work using a Markov network to model fitness in an EDA, resulting in what we call the Markov Fitness Model (MFM). The work has explored the theoretical foundations of the MFM approach which are grounded in Walsh analysis of fitness functions. This has allowed us to demonstrate a clear relationship between the fitness model and the underlying dynamics of the problem. A key achievement is that we have been able to show how the model can be used to predict fitness and have devised a measure of fitness modelling capability called the fitness prediction correlation (FPC). We have performed a series of experiments which use the FPC to investigate the effect of population size and selection operator on the fitness modelling capability. The results and analysis of these experiments are an important addition to other work on diversity and fitness distribution within populations. With this improved understanding of fitness modelling we have been able to extend the framework Distribution Estimation Using Markov networks (DEUM) to use a multivariate probabilistic model. We have proposed and demonstrated the performance of a number of algorithms based on this framework which lever the MFM for optimisation, which can now be added to the EA toolbox. As part of this we have investigated existing techniques for learning the structure of the MFM; a further contribution which results from this is the introduction of precision and recall as measures of structure quality. We have also proposed a number of possible directions that future work could take.

In this thesis we study a problem that arises in answering boolean queries submitted to a search engine. Usually a search engine stores the set of IDs of documents containing each word in a pre-computed sorted order and to evaluate a query like "computer AND science" the search engine has to evaluate the union of the sets of documents containing the words "computer" and "science". More complex queries will result in more complex set expressions. In this thesis we consider the problem of evaluation of a set expression with union and intersection as operators and ordered sets as operands. We explore properties of comparison-based algorithms for the problem. A <i>proof of a set expression</i> is the set of comparisons that a comparison-based algorithm performs before it can determine the result of the expression. We discuss the properties of the proofs of set expressions and based on how complex the smallest proofs of a set expression <i>E</i> are, we define a measurement for determining how difficult it is for <i>E</i> to be computed. Then, we design an algorithm that is adaptive to the difficulty of the input expression and we show that the running time of the algorithm is roughly proportional to difficulty of the input expression, where the factor is roughly logarithmic in the number of the operands of the input expression.

Nowadays modern electric power systems consist of large-scale and highly complex interconnected transmission systems, thus transmission expansion planning (TEP) is now a significant power system optimisation problem. The TEP problem is a large-scale, complex and nonlinear combinatorial problem of mixed integer nature where the number of candidate solutions to be evaluated increases exponentially with system size. The accurate solution of the TEP problem is essential in order to plan power systems in both an economic and efficient manner. Therefore, applied optimisation methods should be sufficiently efficient when solving such problems. In recent years a number of computational techniques have been proposed to solve this efficiency issue. Such methods include algorithms inspired by observations of natural phenomena for solving complex combinatorial optimisation problems. These algorithms have been successfully applied to a wide variety of electrical power system optimisation problems. In recent years differential evolution algorithm (DEA) procedures have been attracting significant attention from the researchers as such procedures have been found to be extremely effective in solving power system optimisation problems. The aim of this research is to develop and apply a novel DEA procedure directly to a DC power flow based model in order to efficiently solve the TEP problem. In this thesis, the TEP problem has been investigated in both static and dynamic form. In addition, two cases of the static TEP problem, with and without generation resizing, have also been investigated. The proposed method has achieved solutions with good accuracy, stable convergence characteristics, simple implementation and satisfactory computation time. The analyses have been performed within the mathematical programming environment of MATLAB using both DEA and conventional genetic algorithm (CGA) procedures and a detailed comparison has also been presented. Finally, the sensitivity of DEA control parameters has also been investigated.

The main point of this thesis is an introduction to the theory of Grobner bases. The concept of Grobner basis and construction of the Grobner basis by Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we study some nice and useful properties of Grobner bases, such as a uniqueness of reduced Grobner basis and existence of a Grobner basis.In Chapter 3, we explore the Buchberger-Moller algorithm to construct Grobner bases and return a set of polynomials whose residue classes form a basis of a quotient of a polynomial ring. Also, we survey a generalized Buchberger-Moller algorithm to determine directly a Grobner basis for the intersection of a finite number of ideals.In Chapter 4, we conclude this paper with some applications of Grobner bases.