<p>Different methods have been designed to solve systems of ordinary differential equations which avoid the restriction on step size imposed by the stability requirements alone and may be severe when the conventional numerical methods are used in solving stiff systems. This area requires further study which will lead to the development of new methods which are suitable for solving stiff equations and at the same time have high order of accuracy.</p> <p>In this investigation, classes of multistep formulas using high derivations are studied and searched for the existence of high order stiffly stable formulas, and of better stability region formulas. Stiffly stable formulas of order as to 14 were found in this search and better stability regions have been obtained by varying the choice of arbitrary coefficients to control the stability characteristics.</p> / Master of Science (MS)

<p>A survey of error detection and error recovery in simple precedence parsers is given, and in particular the error detection of Leinius, and the error recovery of Rhodes are described. An implementation of a system which generates error recovering simple precendence parsers is presented. The system divides into two subsystems, a constructor, and a skeletal parser. The grammar of the simple precedence language (L) for which a parser is required is used as input to the constructor. The constructor processes the grammar, and produces data used to prime the skeletal parser such that it can parse a sentence of L (or, an L program). The skeletal parser includes error detection based on the work of Leinius, and error recovery based on the work of Rhodes.</p> / Master of Engineering (ME)

<p>This report contains a description of the programming language PL/2100, which is a procedure oriented, block structured language with an extensive set of operators, including arithmetic, relational, logical, bit manipulation and shift operators. It is designed for writing PL/2100 programs that conform to the standard of structured programming and for efficiently expressing and implementing algorithms written in it.</p> <p>This report, also, contains a description of the one-pass working compiler (HPCOM) (for PL/2100) written for the HP/2100A minicomputer.</p> / Master of Science (MS)

<p>The global routing problem is becoming more and more important in the design of today's integrated circuits. A small chip may contain up to millions of components and wires. Although global routing can be formulated as an integer linear programming problem, it is hard to solve directly using currently available solvers. We discuss a relaxation of the problem to a linear programming (LP) formulation with a fractional solution. However, the relaxation yields an NP-hard problem. In this thesis, we introduce three relaxations: the primal (<em>Pc</em>), the Lagrange dual (<em>Dc</em>), and the unimodular (<em>PI</em>) formulation. At optimality, all three problems have the same objective value. A new way to tackle the LP problem is introduced: first solve the <em>Dc</em> and try to find Lagrange multipliers in order to build the <em>PI</em> model, from which an integer solution can be obtained directly. An implementation based on the discussed approaches was tested using IBM benchmarks.</p> / Master of Applied Science (MASc)

<p>This thesis considers the Shannon capacity of multiuser multiple input multiple output (MIMO) wireless communication systems. That is, the fundamental limit on the rates at which data can be reliably communicated. The focus is on scenarios in which the channel has long coherence times and perfect channel state information is available to both transmitters and receivers. The thesis considers two important design problems in multiuser MIMO wireless communication systems: the design of the sumrate optimal input distribution for the MIMO multiple access channel (MIMO MAC), and the design of the sum-rate optimal input distribution for the MIMO broadcast channel (MIMO BC).</p> <p>The thesis considers algorithms for solving these design problems that are based on the principle of iterative water-filling. The contributions of the thesis are twofold. First, a correct and rigorous proof of convergence of the family of water-filling algorithms is derived. This proof overcomes weaknesses in the previous attempts of others to prove convergence. Second, an efficient algorithm is presented for the water-filling procedure that lies at the heart of the iterative water-filling algorithm. This algorithm will open the door for further efficient utilization of the iterative water-filling algorithm. This novel algorithm is based on the principle of Fibonacci search, and since the iterative water filling algorithm involves repeated water-filling procedures, the impact of this efficient algorithm is magnified.</p> <p>The outcomes of this research are that the iterative water-filling algorithms are mathematically validated for the above-mentioned design problems in multiuser MIMO wireless communication systems, and that the implementation of these algorithms is made more efficient through the application of the efficient Fibonacci search method for the underlying water-filling procedure.</p> / Master of Applied Science (MASc)

<p>Why sexual reproduction and recombination are prevalent among living organisms is one of the most intriguing questions in biology. It has been studied extensively from a multitude of perspectives ranging from multi-locus population genetics models, in-vivo and more recently in-silico systems. The analysis of complex metabolic networks in living organisms reveals that they can be decomposed into several functionally distinct sub-groups, called modules. This property of modular organization has been accepted as a general organizational feature of biological networks, and has important consequences for the evolution of biologically complex features through different combinations of simpler functions. In this light it has been shown that sexual populations can develop a form of modularity on the genetic level, called mixability, where alleles are selected for their ability to function under a wide variety of genetic contexts, much like a module.</p> <p>However the functional implications of mixability still remain to be seen. We wish to assess whether mixability can develop in a simplified model of populations undergoing evolution for increased biological complexity through the construction of their genomes into simple metabolic chains. We modelled the fitness and growth of complexity in sexual and asexual populations in the presence of recurrent mutations which increase the ability of genes to interact with one another. Our results show that mixability is selected for in sexual populations when genetic diversity is high and under certain conditions gives sexual populations a competitive edge over asexual populations through increased genetic complexity. This provides a starting point for examining the effect of mixability upon growing genetic networks and its role in influencing larger scale modularity, which thus far has not been significantly explored.</p> / Master of Science (MS)

<p>This thesis provides a Fully Polynomial Time Approximation Scheme (FPTAS) for the minimum total weighted tardiness (TWT) problem with a constant number ofdistinct due dates.</p> <p>Given a sequence ofjobs on a single machine, each with a weight, processing time, and a due date, the tardiness of a job is the amount of time that its completion time goes beyond its due date. The TWT problem is to find a schedule of the given jobs such that the total weighted tardiness is minimized. This problem is NP-hard even when the number of distinct due dates is fixed. In this thesis, we present a dynamic programming algorithm for the TWT problem with a constant number of distinct due dates first and then adopt a rounding scheme to obtain an FPTAS.</p> <p>Three major points that we make in this algoritlun are: we observe a series of structural properties of optimal schedules so that we shrink the state space of the DP; we make use of preemption (i.e. allowing the processing of a job to be interrupted and restarted later) for the design of the DP; the rounding scheme that we adopt guarantees that a factor 1+ ℇ of the optimal solution is generated and the algorithm runs within a polynomial time of the problem size.</p> / Master of Applied Science (MASc)

The amount of data that our digital society collects is unprecedented. This represents a valuable opportunity to improve our quality of life by gaining insights about complex problems related to neuroscience, medicine and biology among others. Topological methods, in combination with classical statistical ones, have proven to be a precious resource in understanding and visualizing data. Multidimensional persistence is a method in topological data analysis which allows a multi-parameter analysis of a dataset through an algebraic object called multidimensional persistence module. Multidimensional persistence modules are complicated and contain a lot of information about the input data. This thesis deals with the problem of algorithmically describing multidimensional persistence modules and extracting information that can be used in applications. The information we extract, through invariants, should not only be efficiently computable and informative but also robust to noise. In Paper A we describe in an explicit and algorithmic way multidimensional persistence modules. This is achieved by studying the multifiltration of simplicial complexes defining multidimensional persistence modules. In particular we identify the special structure underlying the modules of n-chains of such multifiltration and exploit it to write multidimensional persistence modules as the homology of a chain complex of free modules. Both the free modules and the homogeneous matrices in such chain complex can be directly read off the multifiltration of simplicial complexes. Paper B deals with identifying stable invariants for multidimensional persistence. We introduce an algebraic notion of noise and use it to compare multidimensional persistence modules. Such definition allows not only to specify the properties of a dataset we want to study but also what should be neglected. By disregarding noise the, so called, persistent features are identified. We also propose a stable discrete invariant which collects properties of persistent features in a multidimensional persistence module. / <p>QC 20150525</p>

No description available.

The thesis comprises of a thorough assessment of turbulent non-premixed combustion modelling techniques, emphasising the fundamental issue of turbulence-chemistry interaction. The combustion models studied are the flame-sheet, equilibrium, eddy breakup and laminar flamelet models. An in-house CFD code is developed and all the combustion models are implemented. Fundamental numerical issues involving the discretisation schemes are addressed by employing three discretisation schemes namely, hybrid, power law and TVD. The combustion models are evaluated for a number of fuels ranging from simple H2/CO and CO/H2/N2 to more complex Cl4/H2 burning in bluff body stabilised burners at different inlet fuel velocities. The bluff body burner with its complex recirculation zone provides a suitable model problem for industrial flows. The initial and boundary conditions are simple and well-defined. The bluff body burner also provides a controlled environment for the study of turbulence-chemistry interaction at the neck zone. The high quality experimental database available from the University of Sydney and other reported measurements are used for the validation and evaluation of combustion models. The present calculations show that all the combustion models provide good predictions for near equilibrium flames for temperature and major species. Although the equilibrium chemistry model is capable of predicting minor species, the predictive accuracy is found to be inadequate when compared to the experimental data. The laminae flamelet model is the only model which has yielded good predictions for the minor species. For flames at higher velocities. the laminar flamelet model again has provided better predictions compared to predictions of other models considered. With different fuels, the laminar flamelet model predictions for CO/H2/N2 fuel are better than those for CH4/H2 fuel. The reasons for this discrepancy are discussed in detail. The effects of differential diffusion are studied in the laminar flamelet modelling strategy. The flamelet with unity Lewis number is found to give a better representation of the transport of species. The laminar flamelet model has yielded reasonably good predictions for NO mass fraction. The predictions of NO mass fraction are found to be very sensitive to differential diffusion effects. This study has also considered the issue of inclusion of radiative heat transfer in the laminar flamelet model. The radiation effects are found to be important only where the temperature is very high. The study undertaken and reported in this thesis shows that the presently available laminar flamelet modelling concepts are capable of predicting species concentrations and temperature fields with an adequate degree of accuracy. The flamelet model is also well suited for the prediction of NO emissions. The inclusion of radiation heat transfer has enhanced the predictive capability of the laminar flamelet model.