This thesis proposes an optimized Co-ordinate Rotation Digital Computer (CORDIC) algorithm in the rotation and extended vectoring mode of the circular co-ordinate system. The CORDIC algorithm computes the values of trigonometric functions and their inverses. The proposed algorithm provides the result with a lower overall latency than existing systems. This is done by using redundant representations and approximations of the required direction and angle of each rotation. The algorithm has been designed to provide the result in a fixed number of iterations $n$ for the rotation mode and $3\lceil n/2 \rceil + \lfloor n/2 \rfloor$ for the extended vectoring mode; where, $n$ is a design parameter. In each iteration, the algorithm performs between 0 and $p/n$ parallel rotations, where, $p$ is the number of precision bits and $n$ is the selected number of iterations. A technique to handle the scaling factor compensation for such an algorithm is proposed. The results of the functional verification for different values of $n$ and an estimation of the overall latency are presented. Based on the results, guidelines to choosing a value of $n$ to meet the required performance have also been presented.

published_or_final_version / abstract / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

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The thesis begins with a general introduction to population genetics in chapter 1. I review the fundamental processes of evolution - mutation, recombination, selection, gene flow and genetic drift - and give an overview of Bayesian inference in statistical population genetics. Later, I introduce the studied species, Alpine ibex (Capra ibex ), and its recent history. This history is intimately linked to the structured population in the Swiss Alps that provides the source of genetic data for this thesis. A particular focus is devoted to approximate Bayesian computation (ABC) in chapter 2, a method of inference that has become important over the last 15 years and is convenient for complex problems of inference. In chapter 3, the biological focus is on estimating the distribution of mutation rates across neutral genetic variation (microsatellites), and on inferring the proportion of male ibex that obtain access to matings each breeding season. The latter is an important determinant of genetic drift. Methodologically, I compare different methods for the choice of summary statistics in ABC. One of the approaches proposed by collaborators and me and based on boosting (a technique developed in machine learning) is found to perform best in this case. Applying that method to microsatellite data from Alpine ibex, I estimate the scaled ancestral mutation rate (THETA anc = 4Neu) to about 1:288, and find that most of the variation across loci of the ancestral mutation rate u is between 7.7*10 -4 and 3.5*10 -3. The proportion of males with access to matings per breeding season is estimated to about 21%. Chapter 4 is devoted to the estimation of migration rates between a large number of pairs of populations. Again, I use ABC for inference. Estimating all rates jointly comes with substantial methodological problems. Therefore, I assess if, by dividing the whole problem into smaller ones and assuming that those are approximately independent, more accuracy may be achieved overall. The net accuracy of the second approach increases with the number of migration rates. Applying that approach to microsatellite data from Alpine ibex, and accounting for the possibility that a model without migration could also explain the data, I find no evidence for substantial gene flow via migration, except for one pair of demes in one direction. While chapters 3 and 4 deal with neutral variation, in chapter 5 I investigate if an allele of the Major Histocompatibility Complex (MHC) has been under selection over the last ten generations. Short- and medium-term methods for detecting signals of selection are combined. For the medium-term analysis, I adapt a matrix iteration approach that allows for joint estimation of the initial allele frequency, the dominance coefficient, and the strength of selection. The focal MHC allele is shared with domestic goat, and an interesting side issue is if this reflects an ancestral polymorphism or is due to recent introgression via hybridization. I find most evidence for asymmetric overdominance (selection coefficient s: 0.974; equilibrium frequency: 0.125) or directional selection against the `goat' allele (s: 0.5) with partial recessivity. Both scenarios suggest a disadvantage of the `goat' homozygote, but differ in the relative fitness of the heterozygotes. Overall, two aspects play a dominating role in this thesis: the biological questions and the process of inference. They are linked, yet while the proximate motivation for the biological component is given by a specific system - the structured population of Alpine ibex in the Swiss Alps - the methods used and advanced here are fairly general and may well be applied in different contexts.

The electropolymerisation of a range of indole derivatives results in the formation of redox active films. These redox films have been observed to be highly luminescent. Earlier studies have investigated electrochemical and photophysical properties, for potential applications such as fast response potentiometric sensors or novel materials for light emitting devices. The work in this thesis extends this approach to electrochemical and computational studies of a range of novel redox-active aromatic systems. This work has exploited the continuing increase of computing power, employing powerful quantum computational models to complement and augment electrochemical methods. Density Functional Theory has been used to show that prediction of oxidation potentials in good agreement with experimental values is achievable for a wide range of aromatic systems. Calculation of the electron spin density of the radical cations has also helped to elucidate the likely coupling locations for the formation of electroactive layers. It is observed that the nature of substituents and additional hetero groups to the aromatic systems can have a profound effect on electron spin density distributions. The redox-active species formed from indole dimers and 5-methylindolocarbazole have also been characterised. The species formed from electropolymerisation of 5- methylindolocarbazole has been found to be a mixture of three isomers of a 5- methylindolocarbazole dimer. Full characterisation of the product of the electropolymerisation of indole dimers was not possible; fluorescence work however suggests this to be a species with a greater degree of conjugation than either indole dimers or trimers. It is thought likely that this product is either a tetramer or longer chain polymer. This work demonstrates the applicability of a combination of computational and electrochemical methods to the characterisation of novel heteroaromatic systems.

Two important trends in computer systems are that applications are moved to the Internet as web applications, and that computer systems are getting an increasing number of cores to increase the performance. It has been shown that JavaScript in web applications has a large potential for parallel execution despite the fact that JavaScript is a sequential language. In this thesis, we show that JavaScript execution in web applications and in benchmarks are fundamentally different and that an effect of this is that Just-in-time compilation does often not improve the execution time, but rather increases the execution time for JavaScript in web applications. Since there is a significant potential for parallel computation in JavaScript for web applications, we show that Thread-Level Speculation can be used to take advantage of this in a manner completely transparent to the programmer. The Thread-Level Speculation technique is very suitable for improving the performance of JavaScript execution in web applications; however we observe that the memory overhead can be substantial. Therefore, we propose several techniques for adaptive speculation as well as for memory reduction. In the last part of this thesis we show that Just-in-time compilation and Thread-Level Speculation are complementary techniques. The execution characteristics of JavaScript in web applications are very suitable for combining Just-in-time compilation and Thread-Level Speculation. Finally, we show that Thread-Level Speculation and Just-in-time compilation can be combined to reduce power usage on embedded devices.

The aggressive scaling of CMOS technology, to reduce device size while also increasing device performance, has reached a point where continuing improvement is becoming increasingly problematic and alternative routes for the development of future memory and processing devices may be necessary; in this thesis the use of phase-change and carbon based materials as one such alternative route is investigated. As pointed out by Ovshinsky [1, 2] some phase-change material should be capable of non-binary arithmetic processing, multi-value logic and biological (neuromorphic) type processing. In this thesis, generic, nanometre-sized, phase-change pseudodevices were fabricated and utilised to perform various types of computational operations for the first time, including addition, subtraction, division, parallel factorization and logic using a novel resistive switching accumulator-type regime in the electrical domain. The same accumulator response is also shown to provide an electronic mimic of an integrate-and-fire type neuron. The accumulator-type regime uses fast electrical pulses to gradually crystallize a phase-change device in a finite number of steps and does not require a multilevel detection scheme. The phase-change materials used in this study were protected by a capping layer of sputtered amorphous carbon. It was found that this amorphous carbon layer also underwent a form of resistive switching when subjected to electrical pulses. In particular, sputtered amorphous carbon layers were found to switch from an initially high resistivity state to a low resistivity state when a voltage pulse was locally applied using a Conductive Atomic Force Microscope (CAFM) tip. Further experiments on amorphous carbon vertical pseudo-devices and lithographically defined planar devices showed that it has potential as a new material for Resistive Random Access Memory (ReRam) applications. The switching mechanism was identified as clustering of the sp2 hybridized carbon sites induced by Joule heating. It was not possible to reset the devices back to their initial high resistivity state presumably due to the highly conductive nature of sputtered amorphous carbon.

This dissertation presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, for triangular meshes, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree. Finally, for rectangular meshes, the test space is reduced, yet the convergence is recovered regardless of parity.

Homomorphic encryption has progressed rapidly in both efficiency and versatility since its emergence in 2009. Meanwhile, a multitude of pressing privacy needs --- ranging from cloud computing to healthcare management to the handling of shared databases such as those containing genomics data --- call for immediate solutions that apply fully homomorpic encryption (FHE) and somewhat homomorphic encryption (SHE) technologies. Recent rapid progress in fully homomorphic encryption has catalyzed renewed efforts to develop efficient privacy preserving protocols. Several works have already appeared in the literature that provide solutions to these problems by employing leveled or somewhat homomorphic encryption techniques. Here, we propose efficient ways of adapting the most fundamental programming problems; boolean algebra, arithmetic in binary and higher radix representation, sorting, and search to the fully homomorphic encryption domain by focusing on the multiplicative depth of the circuits alongside the more traditional metrics. The reduced depth allows much reduced noise growth and thereby makes it possible to select smaller parameter sizes in leveled FHE instantiations resulting in greater efficiency savings. We begin by exploring already existing solutions to these programming problems, and analyze them in terms of homomorphic evaluation and memory costs. Most of these algorithms appear to be not the best candidates for FHE solutions, hence we propose new methods and improvements over the existing algorithms to optimize performance.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 85-92). / This thesis explores various Lagrangian methods for simulating ballistic impact with the ultimate goal of finding a universal, robust and scalable computational framework to assist in the design of armor systems. An overview is provided of existing Lagrangian strategies including particle methods, meshless methods, and the peridynamic approach. We review the continuum formulation of mechanics and its discretization using finite elements. A rigid body contact algorithm for explicit dynamic finite elements is presented and used to model a rigid sphere impacting a confined alumina tile. The constitutive model for the alumina is provided by the Deshpande-Evans ceramic damage model. These simulations were shown to capture experimentally observed radial crack patterns. An adaptive remeshing strategy using finite elements is then explored and applied, with limited success, to the problem of predicting the transition from dwell to penetration for long-rod penetrators impacting confined ceramic targets at high velocities. Motivated by the difficulties of mesh-based Lagrangian approaches for modeling impact, an alternative Lagrangian approach is investigated which uses established constitutive relations within a particle-based computational framework. The resulting algorithm is based on a discretization of the peridynamic formulation of continuum mechanics. A validating benchmark example using a Taylor impact test is shown and compared to previous results from the literature. Further numerical examples involving ballistic impact and the crushing of an aluminum sandwich structures provide further demonstration of the method's potential for armor applications. / by Michael Ronne Tupek. / S.M.