On the computation of reducible invariant tori on a parallel computer

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Virtual Runtime Application Partitions for Resource Management in Massively Parallel Architectures

This thesis presents a novel design paradigm, called Virtual Runtime Application Partitions (VRAP), to judiciously utilize the on-chip resources. As the dark silicon era approaches, where the power considerations will allow only a fraction chip to be powered on, judicious resource management will become a key consideration in future designs. Most of the works on resource management treat only the physical components (i.e. computation, communication, and memory blocks) as resources and manipulate the component to application mapping to optimize various parameters (e.g. energy efficiency). To further enhance the optimization potential, in addition to the physical resources we propose to manipulate abstract resources (i.e. voltage/frequency operating point, the fault-tolerance strength, the degree of parallelism, and the configuration architecture). The proposed framework (i.e. VRAP) encapsulates methods, algorithms, and hardware blocks to provide each application with the abstract resources tailored to its needs. To test the efficacy of this concept, we have developed three distinct self adaptive environments: (i) Private Operating Environment (POE), (ii) Private Reliability Environment (PRE), and (iii) Private Configuration Environment (PCE) that collectively ensure that each application meets its deadlines using minimal platform resources. In this work several novel architectural enhancements, algorithms and policies are presented to realize the virtual runtime application partitions efficiently. Considering the future design trends, we have chosen Coarse Grained Reconfigurable Architectures (CGRAs) and Network on Chips (NoCs) to test the feasibility of our approach. Specifically, we have chosen Dynamically Reconfigurable Resource Array (DRRA) and McNoC as the representative CGRA and NoC platforms. The proposed techniques are compared and evaluated using a variety of quantitative experiments. Synthesis and simulation results demonstrate VRAP significantly enhances the energy and power efficiency compared to state of the art.

Efficient Algorithms for Coastal Geographic Problems

The increasing performance of computers has made it possible to solve algorithmically problems for which manual and possibly inaccurate methods have been previously used. Nevertheless, one must still pay attention to the performance of an algorithm if huge datasets are used or if the problem iscomputationally difficult. Two geographic problems are studied in the articles included in this thesis. In the first problem the goal is to determine distances from points, called study points, to shorelines in predefined directions. Together with other in-formation, mainly related to wind, these distances can be used to estimate wave exposure at different areas. In the second problem the input consists of a set of sites where water quality observations have been made and of the results of the measurements at the different sites. The goal is to select a subset of the observational sites in such a manner that water quality is still measured in a sufficient accuracy when monitoring at the other sites is stopped to reduce economic cost. Most of the thesis concentrates on the first problem, known as the fetch length problem. The main challenge is that the two-dimensional map is represented as a set of polygons with millions of vertices in total and the distances may also be computed for millions of study points in several directions. Efficient algorithms are developed for the problem, one of them approximate and the others exact except for rounding errors. The solutions also differ in that three of them are targeted for serial operation or for a small number of CPU cores whereas one, together with its further developments, is suitable also for parallel machines such as GPUs.

Improving Short DNA Sequence Alignment with Parallel Computing

Variations in different types of genomes have been found to be responsible for a large degree of physical diversity such as appearance and susceptibility to disease. Identification of genomic variations is difficult and can be facilitated through computational analysis of DNA sequences. Newly available technologies are able to sequence billions of DNA base pairs relatively quickly. These sequences can be used to identify variations within their specific genome but must be mapped to a reference sequence first. In order to align these sequences to a reference sequence, we require mapping algorithms that make use of approximate string matching and string indexing methods. To date, few mapping algorithms have been tailored to handle the massive amounts of output generated by newly available sequencing technologies. In otrder to handle this large amount of data, we modified the popular mapping software BWA to run in parallel using OpenMPI. Parallel BWA matches the efficiency of multithreaded BWA functions while providing efficient parallelism for BWA functions that do not currently support multithreading. Parallel BWA shows significant wall time speedup in comparison to multithreaded BWA on high-performance computing clusters, and will thus facilitate the analysis of genome sequencing data.

Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes.

Clustering algorithms and shape factor methods to discriminate among small GTPase phenotypes using DIC image analysis.

Naïvement perçu, le processus d’évolution est une succession d’événements de duplication et de mutations graduelles dans le génome qui mènent à des changements dans les fonctions et les interactions du protéome. La famille des hydrolases de guanosine triphosphate (GTPases) similaire à Ras constitue un bon modèle de travail afin de comprendre ce phénomène fondamental, car cette famille de protéines contient un nombre limité d’éléments qui diffèrent en fonctionnalité et en interactions. Globalement, nous désirons comprendre comment les mutations singulières au niveau des GTPases affectent la morphologie des cellules ainsi que leur degré d’impact sur les populations asynchrones. Mon travail de maîtrise vise à classifier de manière significative différents phénotypes de la levure Saccaromyces cerevisiae via l’analyse de plusieurs critères morphologiques de souches exprimant des GTPases mutées et natives. Notre approche à base de microscopie et d’analyses bioinformatique des images DIC (microscopie d’interférence différentielle de contraste) permet de distinguer les phénotypes propres aux cellules natives et aux mutants. L’emploi de cette méthode a permis une détection automatisée et une caractérisation des phénotypes mutants associés à la sur-expression de GTPases constitutivement actives. Les mutants de GTPases constitutivement actifs Cdc42 Q61L, Rho5 Q91H, Ras1 Q68L et Rsr1 G12V ont été analysés avec succès. En effet, l’implémentation de différents algorithmes de partitionnement, permet d’analyser des données qui combinent les mesures morphologiques de population native et mutantes. Nos résultats démontrent que l’algorithme Fuzzy C-Means performe un partitionnement efficace des cellules natives ou mutantes, où les différents types de cellules sont classifiés en fonction de plusieurs facteurs de formes cellulaires obtenus à partir des images DIC. Cette analyse démontre que les mutations Cdc42 Q61L, Rho5 Q91H, Ras1 Q68L et Rsr1 G12V induisent respectivement des phénotypes amorphe, allongé, rond et large qui sont représentés par des vecteurs de facteurs de forme distincts. Ces distinctions sont observées avec différentes proportions (morphologie mutante / morphologie native) dans les populations de mutants. Le développement de nouvelles méthodes automatisées d’analyse morphologique des cellules natives et mutantes s’avère extrêmement utile pour l’étude de la famille des GTPases ainsi que des résidus spécifiques qui dictent leurs fonctions et réseau d’interaction. Nous pouvons maintenant envisager de produire des mutants de GTPases qui inversent leur fonction en ciblant des résidus divergents. La substitution fonctionnelle est ensuite détectée au niveau morphologique grâce à notre nouvelle stratégie quantitative. Ce type d’analyse peut également être transposé à d’autres familles de protéines et contribuer de manière significative au domaine de la biologie évolutive.

A User-Centric Perspective on Parallel Programming with Focus on OpenMP

The process of developing software that takes advantage of multiple processors is commonly referred to as parallel programming. For various reasons, this process is much harder than the sequential case. For decades, parallel programming has been a problem for a small niche only: engineers working on parallelizing mostly numerical applications in High Performance Computing. This has changed with the advent of multi-core processors in mainstream computer architectures. Parallel programming in our days becomes a problem for a much larger group of developers. The main objective of this thesis was to find ways to make parallel programming easier for them. Different aims were identified in order to reach the objective: research the state of the art of parallel programming today, improve the education of software developers about the topic, and provide programmers with powerful abstractions to make their work easier. To reach these aims, several key steps were taken. To start with, a survey was conducted among parallel programmers to find out about the state of the art. More than 250 people participated, yielding results about the parallel programming systems and languages in use, as well as about common problems with these systems. Furthermore, a study was conducted in university classes on parallel programming. It resulted in a list of frequently made mistakes that were analyzed and used to create a programmers' checklist to avoid them in the future. For programmers' education, an online resource was setup to collect experiences and knowledge in the field of parallel programming - called the Parawiki. Another key step in this direction was the creation of the Thinking Parallel weblog, where more than 50.000 readers to date have read essays on the topic. For the third aim (powerful abstractions), it was decided to concentrate on one parallel programming system: OpenMP. Its ease of use and high level of abstraction were the most important reasons for this decision. Two different research directions were pursued. The first one resulted in a parallel library called AthenaMP. It contains so-called generic components, derived from design patterns for parallel programming. These include functionality to enhance the locks provided by OpenMP, to perform operations on large amounts of data (data-parallel programming), and to enable the implementation of irregular algorithms using task pools. AthenaMP itself serves a triple role: the components are well-documented and can be used directly in programs, it enables developers to study the source code and learn from it, and it is possible for compiler writers to use it as a testing ground for their OpenMP compilers. The second research direction was targeted at changing the OpenMP specification to make the system more powerful. The main contributions here were a proposal to enable thread-cancellation and a proposal to avoid busy waiting. Both were implemented in a research compiler, shown to be useful in example applications, and proposed to the OpenMP Language Committee.

Evolving Distributed Algorithms with Genetic Programming

Distributed systems are one of the most vital components of the economy. The most prominent example is probably the internet, a constituent element of our knowledge society. During the recent years, the number of novel network types has steadily increased. Amongst others, sensor networks, distributed systems composed of tiny computational devices with scarce resources, have emerged. The further development and heterogeneous connection of such systems imposes new requirements on the software development process. Mobile and wireless networks, for instance, have to organize themselves autonomously and must be able to react to changes in the environment and to failing nodes alike. Researching new approaches for the design of distributed algorithms may lead to methods with which these requirements can be met efficiently. In this thesis, one such method is developed, tested, and discussed in respect of its practical utility. Our new design approach for distributed algorithms is based on Genetic Programming, a member of the family of evolutionary algorithms. Evolutionary algorithms are metaheuristic optimization methods which copy principles from natural evolution. They use a population of solution candidates which they try to refine step by step in order to attain optimal values for predefined objective functions. The synthesis of an algorithm with our approach starts with an analysis step in which the wanted global behavior of the distributed system is specified. From this specification, objective functions are derived which steer a Genetic Programming process where the solution candidates are distributed programs. The objective functions rate how close these programs approximate the goal behavior in multiple randomized network simulations. The evolutionary process step by step selects the most promising solution candidates and modifies and combines them with mutation and crossover operators. This way, a description of the global behavior of a distributed system is translated automatically to programs which, if executed locally on the nodes of the system, exhibit this behavior. In our work, we test six different ways for representing distributed programs, comprising adaptations and extensions of well-known Genetic Programming methods (SGP, eSGP, and LGP), one bio-inspired approach (Fraglets), and two new program representations called Rule-based Genetic Programming (RBGP, eRBGP) designed by us. We breed programs in these representations for three well-known example problems in distributed systems: election algorithms, the distributed mutual exclusion at a critical section, and the distributed computation of the greatest common divisor of a set of numbers. Synthesizing distributed programs the evolutionary way does not necessarily lead to the envisaged results. In a detailed analysis, we discuss the problematic features which make this form of Genetic Programming particularly hard. The two Rule-based Genetic Programming approaches have been developed especially in order to mitigate these difficulties. In our experiments, at least one of them (eRBGP) turned out to be a very efficient approach and in most cases, was superior to the other representations.

On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).

Proposal of a parallel architecture for a motion detection algorithm

This paper proposes a parallel architecture for estimation of the motion of an underwater robot. It is well known that image processing requires a huge amount of computation, mainly at low-level processing where the algorithms are dealing with a great number of data. In a motion estimation algorithm, correspondences between two images have to be solved at the low level. In the underwater imaging, normalised correlation can be a solution in the presence of non-uniform illumination. Due to its regular processing scheme, parallel implementation of the correspondence problem can be an adequate approach to reduce the computation time. Taking into consideration the complexity of the normalised correlation criteria, a new approach using parallel organisation of every processor from the architecture is proposed

A parallel genetic algorithm for the Steiner Problem in Networks

This paper presents a parallel genetic algorithm to the Steiner Problem in Networks. Several previous papers have proposed the adoption of GAs and others metaheuristics to solve the SPN demonstrating the validity of their approaches. This work differs from them for two main reasons: the dimension and the characteristics of the networks adopted in the experiments and the aim from which it has been originated. The reason that aimed this work was namely to build a comparison term for validating deterministic and computationally inexpensive algorithms which can be used in practical engineering applications, such as the multicast transmission in the Internet. On the other hand, the large dimensions of our sample networks require the adoption of a parallel implementation of the Steiner GA, which is able to deal with such large problem instances.

Implementing a generic systolic array for genetic algorithms

We have designed a highly parallel design for a simple genetic algorithm using a pipeline of systolic arrays. The systolic design provides high throughput and unidirectional pipelining by exploiting the implicit parallelism in the genetic operators. The design is significant because, unlike other hardware genetic algorithms, it is independent of both the fitness function and the particular chromosome length used in a problem. We have designed and simulated a version of the mutation array using Xilinix FPGA tools to investigate the feasibility of hardware implementation. A simple 5-chromosome mutation array occupies 195 CLBs and is capable of performing more than one million mutations per second. I. Introduction Genetic algorithms (GAs) are established search and optimization techniques which have been applied to a range of engineering and applied problems with considerable success [1]. They operate by maintaining a population of trial solutions encoded, using a suitable encoding scheme.

Systolic random number generation for genetic algorithms

A parallel hardware random number generator for use with a VLSI genetic algorithm processing device is proposed. The design uses an systolic array of mixed congruential random number generators. The generators are constantly reseeded with the outputs of the proceeding generators to avoid significant biasing of the randomness of the array which would result in longer times for the algorithm to converge to a solution. 1 Introduction In recent years there has been a growing interest in developing hardware genetic algorithm devices [1, 2, 3]. A genetic algorithm (GA) is a stochastic search and optimization technique which attempts to capture the power of natural selection by evolving a population of candidate solutions by a process of selection and reproduction [4]. In keeping with the evolutionary analogy, the solutions are called chromosomes with each chromosome containing a number of genes. Chromosomes are commonly simple binary strings, the bits being the genes.