Earlier designs were driven by the goal of achieving higher performance, but lately, energy efficiency has emerged as an even more important design principle. Strong demand from the consumer electronics drives research in the low power and energy-efficient methodologies. Moreover, with exponential increase in the number of transistors on a chip and with further technology scaling, variability in the design is now of greater concern. Variations can make the design unreliable or the design may suffer from sub-optimal performance. Through the work in this thesis, we present a multi-dimensional investigation into the design of variation aware energy-efficient systems. Our overarching methodology is to use system-level decisions to mitigate undesired effects originating from device-level and circuit-level issues. We first look into the impact of process variation (PV) on energy efficient, scalable throughput many-core DSP systems. In our proposed methodology, we leverage the benefits of aggressive voltage scaling (VS) for obtaining energy efficiency while compensating for the loss in performance by exploiting parallelism present in various DSP designs. We demonstrate this proposed methodology consumes 8% - 77% less power as compared to simple dynamic VS over different workload environments. Later, we show judicious system-level decisions, namely, number of cores, and their operating voltage can greatly mitigate the effects of PV and consequently, improve the energy efficiency of the design. We also present our analysis discussing the impact of aging on the proposed methodology. To validate our proposed system-level approach, design details of a prototype chip fabricated in the 90nm technology node and its findings are also presented. The chip consists of 8 homogeneous FIR cores, which are capable of running from near-threshold to nominal voltages. In the 20-chip population, we observe 7% variation in the speed at nominal voltage (0.9V) and 26% at near threshold voltage (0.55V) among all the cores. We also observe 54% variation in power consumption characteristics of the cores. The chip measurement results show that our proposed methodology of judiciously selecting the cores and their operating voltage can result in 6.27% - 28.15% more energy savings for various workload environments, as compared to globally voltage scaled systems. Furthermore, we present the impact of temperature variations on the energy-efficiency of the above systems. We also study the problem of voltage variations in the integrated circuits. We first present the characteristics of a dynamic voltage noise as measured on a 28nm FPGA. We propose a fully digital on-chip sensor that can detect the fast voltage transients and alert the system of voltage emergency. A traditional approach to mitigate this problem is to use safety guardbands. We demonstrate that our proposed sensor system will be 6% - 27.5% more power efficient than the traditional approach. / Ph. D.

In this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm. / Ph. D. / incomplete_metadata

We study elastic and inelastic (2 cluster) - (2 cluster) scattering amplitudes for N-body quantum systems. For potentials falling off like r⁻^-1-E we prove that below the lowest 3-cluster threshold these amplitudes exist, are continuous and that asymptotic completeness holds. Moreover, if potentials fall off exponentially we prove that these amplitudes can be meromorphically continued in the energy, with square root branch points at the 2 cluster thresholds. / Ph. D.

This doctoral thesis presents an extensive study on the applications of generalized coherent states (GCS) for the quantum dynamics of many-body systems. The research starts with exploring the fundamental properties of generalized coherent states, which are created by generators of the SU($M$) group acting on an extreme state, and demonstrating their role in representing ideal quantum condensates. A significant feature is the relationship between generalized coherent states and the more standard Glauber coherent states (CS). Similarities in their overcomplete and non-orthogonal nature are shown, alongside crucial differences with respect to $U(1)$ symmetry and entanglement properties, which generalized coherent states solely adhere to. Furthermore, this thesis delves into the nonequilibrium dynamics of GCS as well as Glauber CS under nonlinear interactions. Combining analytical analysis and numerical calculations, it is found that while their two-point correlation functions are equivalent in the thermodynamic limit, their autocorrelation functions exhibit distinctly different characteristics. It is proven analytically that the autocorrelation functions of the evolved GCS relate to the ones of the corresponding Glauber CS through a Fourier series relation, which arises due to the $U(1)$ symmetry of the GCS. A substantial part of this thesis is dedicated to investigating the dynamics of the Bose-Hubbard model, incorporating both nonlinear interaction and tunneling term. This investigation introduces a novel approach which employs an Ansatz for the wave function in terms of a linear combination of GCS, where the differential equations of all the variables are determined by the time-dependent variational principle without truncation. This innovative method is adeptly applied to the nonequilibrium dynamics in various scenarios, from the bosonic Josephson Junction model where some fundamental quantum effects can be revealed by a handful of GCS basis functions, to large system size implementations of the Bose-Hubbard model, where the phenomenon of thermalization can be observed. The proposed variational approach provides an alternative way to study the time-dependent dynamics in many-body quantum systems conserving particle number. The final focus of this thesis is on the boson sampling problem within a linear optical network framework. Again adapting a linear combination of GCS, an exact analytical formula for the output state in standard boson sampling scenarios is derived by means of Kan's formula, showcasing a computational complexity that increases less severely with particle and mode number than the super-exponential scaling of the Fock state Hilbert space. The reduced density matrix of the output state is obtained by tracing out one subsystem. This part of the study extends to examining the properties of the subsystem entanglement creation, and offering novel perspectives on entanglement entropy differences between global and local optical networks. This thesis makes several contributions to the field of quantum many-body systems, particularly highlighting the potential applications of GCS. The presented research offers a new variational method to the nonequilibrium dynamics, and paves the way for future explorations and applications in quantum simulations, quantum computing and beyond.

Parallel architectures, including multi-core processors, many-core processors, and multi-node systems, have become commonplace, as it is no longer feasible to improve single-core performance through increasing its operating clock frequency. Furthermore, to keep up with the exponentially growing desire for more and more computational power, the number of cores/nodes in parallel architectures has continued to dramatically increase. On the other hand, many applications in well-established and emerging fields, such as bioinformatics, social network analysis, and graph processing, exhibit increasing irregularities in memory access, control flow, and communication patterns. While multiple techniques have been introduced into modern parallel architectures to tolerate these irregularities, many irregular applications still execute poorly on current parallel architectures, as their irregularities exceed the capabilities of these techniques. Therefore, it is critical to resolve irregularities in applications for parallel architectures. However, this is a very challenging task, as the irregularities are dynamic, and hence, unknown until runtime. To optimize irregular applications, many approaches have been proposed to improve data locality and reduce irregularities through computational and data transformations. However, there are two major drawbacks in these existing approaches that prevent them from achieving optimal performance. First, these approaches use local optimizations that exploit data locality and regularity locally within a loop or kernel. However, in many applications, there is hidden locality across loops or kernels. Second, these approaches use "one-size-fits-all'' methods that treat all irregular patterns equally and resolve them with a single method. However, many irregular applications have complex irregularities, which are mixtures of different types of irregularities and need differentiated optimizations. To overcome these two drawbacks, we propose a general methodology that includes a taxonomy of irregularities to help us analyze the irregular patterns in an application, and a set of adaptive transformations to reorder data and computation based on the characteristics of the application and architecture. By extending our adaptive data-reordering transformation on a single node, we propose a data-partitioning framework to resolve the load imbalance problem of irregular applications on multi-node systems. Unlike existing frameworks, which use "one-size-fits-all" methods to partition the input data by a single property, our framework provides a set of operations to transform the input data by multiple properties and generates the desired data-partitioning codes by composing these operations into a workflow. / Ph. D. / Irregular applications, which present unpredictable and irregular patterns of data accesses and computation, are increasingly important in well-established and emerging fields, such as biological data analysis, social network analysis, and machine learning, to deal with large datasets. On the other hand, current parallel processors, such as multi-core CPUs (central processing units), GPUs (graphics processing units), and computer clusters (i.e., groups of connected computers), are designed for regular applications and execute irregular applications poorly. Therefore, it is critical to optimize irregular applications for parallel processors. However, it is a very challenging task, as the irregular patterns are dynamic, and hence, unknown until application execution. To overcome this challenge, we propose a general methodology that includes a taxonomy of irregularities to help us analyze the irregular patterns in an application, and a set of adaptive transformations to reorder data and computation for exploring hidden regularities based on the characteristics of the application and processor. We apply our methodology on couples of important and complex irregular applications as case studies to demonstrate that it is effective and efficient.

Enabling learners to successfully use their second language (L2) in meaningful ways is a critical goal of instruction. Ultimately, most learners want to meet the L2 demands of the contexts in which they will use the language. To accomplish this, learners must develop linguistic knowledge and apply it in a manner that is contextually appropriate considering the requirements of the task at hand. In other words, learners must develop their L2 across both linguistic and communicative aspects to use it successfully. However, there is a paucity of L2 research in which linguistic and communicative performance have been simultaneously investigated.In this study, I investigated the development of English as a Foreign Language (EFL) learners’ L2 written production across the lexical and communicative dimensions of performance. The study involved 290 Japanese participants recruited from 20 intact EFL classes at four tertiary educational institutions in Japan, representing a wide range of L2 English proficiency levels and instructional contexts. The study used a non-intervention, repeated-measures design, allowing for the general development of participants’ L2 English writing to be examined. Participants’ L2 English written responses were collected using four argumentative writing tasks, which were administered at the beginning and end of the first and second semesters in a counterbalanced manner. Although a total of 952 responses were collected, responses shorter than 50 words were removed, leaving a total of 775 responses written by 250 participants. The 775 responses included in the primary analyses constituted a corpus of 89,122 words. Twenty-four single-word, multi-word, and lexical variation measures were calculated for the responses and subjected to an exploratory factor analysis. Seven latent lexical factors were identified in the data: High-Frequency Trigrams, Lexical Clarity, High-Frequency Bigrams, Lexical Variation, Lexical Breadth, Low-Frequency N-Grams, and Directional Association Strength of N-Grams. In addition, raters scored the responses for functional adequacy (i.e., Content, Comprehensibility, Organization, and Task Completion) and Lexical Appropriateness. The scores were analyzed using many-facet Rasch measurement, which converted the ordinal scores into equal-interval measures that had been adjusted for the influences of task and rater severity. The lexical factor scores and communicative Rasch measures were examined using linear mixed modeling, dominance analysis, and latent growth modeling to investigate (a) if and how lexical development had occurred, (b) if and how communicative development had occurred, (c) the relationships between the lexical and communicative components, and (d) the relationship between lexical and communicative growth. For the lexical factors, the results indicated that Directional Association Strength of N-Grams scores increased in a linear manner. Directional Association Strength of N-Grams comprised ΔP scores, which indicate the degree to which the first word(s) are predictive of the following word(s) in two- and three-word combinations. Thus, the results indicated that participants’ use of multi-word expressions improved. On the other hand, Lexical Clarity, which comprised imageability, concreteness, meaningfulness, and hypernymy scores, showed quadratic change, with scores improving and then regressing. Thus, the findings provide evidence of differing developmental trends for lexical aspects of L2 writing. For the communicative measures, the results indicated that Comprehensibility, Organization, and Lexical Appropriateness changed substantially over time. Improvement of Task Completion was dependent on the university context, and little change was observed for Content. Lexical Appropriateness showed the most improvement, with evidence of both linear and quadratic change. Bias interaction analyses also confirmed the presence of linear and quadratic trends for the communicative measures. Thus, the findings provide evidence of differing developmental trends for communicative aspects of L2 writing. For the relationships between the lexical and communicative components, the results indicated that two lexical factors were of key importance: Lexical Variation and Directional Association Strength of N-Grams. Lexical Variation was found to predict Content, Organization, and Task Completion; and Directional Association Strength of N-Grams was found to predict Comprehensibility and Lexical Appropriateness. The findings suggest that L2 performance assessments should not conflate measurement of lexical variation and use of multi-word expressions because they diverge in terms of the communicative outcomes they predict. The results also indicated a positive relationship between lexical and communicative development. A parallel process latent growth model was constructed that related lexical and communicative growth. The paths tested in the model suggest participants who had lower initial communicative scores were able to increase their lexical scores at faster rates, which in turn leveraged communicative growth. The findings highlight the potential for learners to improve their communicative ability through a targeted focus on multi-word expressions. / Applied Linguistics

Many-Body Perturbation Theory is put to test as a method for reliable calculations of the electron-electron interaction in two-dimensional quantum dots. We show that second order correlation gives qualitative agreement with experiments on a level which was not found within the Hartree-Fock description. For weaker confinements, the second order correction is shown to be insufficient and higher order contributions must be taken into account. We demonstrate that all order Many-Body Perturbation Theory in the form of the Coupled Cluster Singles and Doubles method yields very reliable results for confinements close to those estimated from experimental data. The possibility to use very large basis sets is shown to be a major advantage compared to Full Configuration Interaction approaches, especially for more than five confined electrons. Also, the possibility to utilize two-electron correlation in combination with tailor made potentials to achieve useful properties is explored. In the case of a two-dimensional quantum dot molecule we vary the interdot distance, and in the case of a two-dimensional quantum ring we vary the ring radius, in order to alter the spectra. In the latter case we demonstrate that correlation in combination with electromagnetic pulses can be used for the realization of quantum logical gates. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript.

No description available.

Les réseaux-sur-puces (NoCs) utilisés dans les architectures multiprocesseurs-sur-puces posent des défis importants aux approches d'ordonnancement temps réel en ligne (dynamique) et hors-ligne (statique). Un NoC contient un grand nombre de points de contention potentiels, a une capacité de bufferisation limitée et le contrôle réseau fonctionne à l'échelle de petits paquets de données. Par conséquent, l'allocation efficace de ressources nécessite l'utilisation des algorithmes da faible complexité sur des modèles de matériel avec un niveau de détail sans précédent dans l'ordonnancement temps réel. Nous considérons dans cette thèse une approche d'ordonnancement statique sur des architectures massivement parallèles (Massively parallel processor arrays ou MPPAs) caractérisées par un grand nombre (quelques centaines) de c¿urs de calculs. Nous identifions les mécanismes matériels facilitant l'analyse temporelle et l'allocation efficace de ressources dans les MPPAs existants. Nous déterminons que le NoC devrait permettre l'ordonnancement hors-ligne de communications, d'une manière synchronisée avec l'ordonnancement de calculs sur les processeurs. Au niveau logiciel, nous proposons une nouvelle méthode d'allocation et d'ordonnancement capable de synthétiser des ordonnancements globaux de calculs et de communications couvrants toutes les ressources d'exécution, de communication et de la mémoire d'un MPPA. Afin de permettre une utilisation efficace de ressources du matériel, notre méthode prend en compte les spécificités architecturales d'un MPPA et implémente des techniques d'ordonnancement avancées comme la préemption pré-calculée de transmissions de données. Nous avons évalué n / On-chip networks (NoCs) used in multiprocessor systems-on-chips (MPSoCs) pose significant challenges to both on-line (dynamic) and off-line (static) real-time scheduling approaches. They have large numbers of potential contention points, have limited internal buffering capabilities, and network control operates at the scale of small data packets. Therefore, efficient resource allocation requires scalable algorithms working on hardware models with a level of detail that is unprecedented in real-time scheduling. We consider in this thesis a static scheduling approach, and we target massively parallel processor arrays (MPPAs), which are MPSoCs with large numbers (hundreds) of processing cores. We first identify and compare the hardware mechanisms supporting precise timing analysis and efficient resource allocation in existing MPPA platforms. We determine that the NoC should ideally provide the means of enforcing a global communications schedule that is computed off-line (before execution) and which is synchronized with the scheduling of computations on processors. On the software side, we propose a novel allocation and scheduling method capable of synthesizing such global computation and communication schedules covering all the execution, communication, and memory resources in an MPPA. To allow an efficient use of the hardware resources, our method takes into account the specificities of MPPA hardware and implements advanced scheduling techniques such as pre-computed preemption of data transmissions. We evaluate our technique by mapping two signal processing applications, for which we obtain good latency, throughput, and resource use figures.

Thesis (MSc (Physics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities. / AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede.