On The Parallelization Of Integer Polynomial Multiplication

With the advent of hardware accelerator technologies, multi-core processors and GPUs, much effort for taking advantage of those architectures by designing parallel algorithms has been made. To achieve this goal, one needs to consider both algebraic complexity and parallelism, plus making efficient use of memory traffic, cache, and reducing overheads in the implementations. Polynomial multiplication is at the core of many algorithms in symbolic computation such as real root isolation which will be our main application for now. In this thesis, we first investigate the multiplication of dense univariate polynomials with integer coefficients targeting multi-core processors. Some of the proposed methods are based on well-known serial classical algorithms, whereas a novel algorithm is designed to make efficient use of the targeted hardware. Experimentation confirms our theoretical analysis. Second, we report on the first implementation of subproduct tree techniques on many-core architectures. These techniques are basically another application of polynomial multiplication, but over a prime field. This technique is used in multi-point evaluation and interpolation of polynomials with coefficients over a prime field

Harnessing the power of GPUs for problems in real algebraic geometry

This thesis presents novel parallel algorithms to leverage the power of GPUs (Graphics Processing Units) for exact computations with polynomials having large integer coefficients. The significance of such computations, especially in real algebraic geometry, is hard to undermine. On massively-parallel architectures such as GPU, the degree of datalevel parallelism exposed by an algorithm is the main performance factor. We attain high efficiency through the use of structured matrix theory to assist the realization of relevant operations on polynomials on the graphics hardware. A detailed complexity analysis, assuming the PRAM model, also confirms that our approach achieves a substantially better parallel complexity in comparison to classical algorithms used for symbolic computations. Aside from the theoretical considerations, a large portion of this work is dedicated to the actual algorithm development and optimization techniques where we pay close attention to the specifics of the graphics hardware. As a byproduct of this work, we have developed high-throughput modular arithmetic which we expect to be useful for other GPU applications, in particular, open-key cryptography. We further discuss the algorithms for the solution of a system of polynomial equations, topology computation of algebraic curves and curve visualization which can profit to the full extent from the GPU acceleration. Extensive benchmarking on a real data demonstrates the superiority of our algorithms over several state-of-the-art approaches available to date. This thesis is written in English.Diese Arbeit beschäftigt sich mit neuen parallelen Algorithmen, die das Leistungspotenzial der Grafik-Prozessoren (GPUs) zur exakten Berechnungen mit ganzzahlige Polynomen nutzen. Solche symbolische Berechnungen sind von großer Bedeutung zur Lösung vieler Probleme aus der reellen algebraischen Geometrie. Für die effziente Implementierung eines Algorithmus auf massiv-parallelen Hardwarearchitekturen, wie z.B. GPU, ist vor allem auf eine hohe Datenparallelität zu achten. Unter Verwendung von Ergebnissen aus der strukturierten Matrix-Theorie konnten wir die entsprechenden Operationen mit Polynomen auf der Grafikkarte leicht übertragen. Außerdem zeigt eine Komplexitätanalyse im PRAM-Rechenmodell, dass die von uns entwickelten Verfahren eine deutlich bessere Komplexität aufweisen als dies für die klassischen Verfahren der Fall ist. Neben dem theoretischen Ergebnis liegt ein weiterer Schwerpunkt dieser Arbeit in der praktischen Implementierung der betrachteten Algorithmen, wobei wir auf der Besonderheiten der Grafikhardware achten. Im Rahmen dieser Arbeit haben wir hocheffiziente modulare Arithmetik entwickelt, von der wir erwarten, dass sie sich für andere GPU Anwendungen, insbesondere der Public-Key-Kryptographie, als nützlich erweisen wird. Darüber hinaus betrachten wir Algorithmen für die Lösung eines Systems von Polynomgleichungen, Topologie Berechnung der algebraischen Kurven und deren Visualisierung welche in vollem Umfang von der GPU-Leistung profitieren können. Zahlreiche Experimente belegen dass wir zur Zeit die beste Verfahren zur Verfügung stellen. Diese Dissertation ist in englischer Sprache verfasst

Vers une arithmétique efficace pour le chiffrement homomorphe basé sur le Ring-LWE

Fully homomorphic encryption is a kind of encryption offering the ability to manipulate encrypted data directly through their ciphertexts. In this way it is possible to process sensitive data without having to decrypt them beforehand, ensuring therefore the datas' confidentiality. At the numeric and cloud computing era this kind of encryption has the potential to considerably enhance privacy protection. However, because of its recent discovery by Gentry in 2009, we do not have enough hindsight about it yet. Therefore several uncertainties remain, in particular concerning its security and efficiency in practice, and should be clarified before an eventual widespread use. This thesis deals with this issue and focus on performance enhancement of this kind of encryption in practice. In this perspective we have been interested in the optimization of the arithmetic used by these schemes, either the arithmetic underlying the Ring Learning With Errors problem on which the security of these schemes is based on, or the arithmetic specific to the computations required by the procedures of some of these schemes. We have also considered the optimization of the computations required by some specific applications of homomorphic encryption, and in particular for the classification of private data, and we propose methods and innovative technics in order to perform these computations efficiently. We illustrate the efficiency of our different methods through different software implementations and comparisons to the related art.Le chiffrement totalement homomorphe est un type de chiffrement qui permet de manipuler directement des données chiffrées. De cette manière, il est possible de traiter des données sensibles sans avoir à les déchiffrer au préalable, permettant ainsi de préserver la confidentialité des données traitées. À l'époque du numérique à outrance et du "cloud computing" ce genre de chiffrement a le potentiel pour impacter considérablement la protection de la vie privée. Cependant, du fait de sa découverte récente par Gentry en 2009, nous manquons encore de recul à son propos. C'est pourquoi de nombreuses incertitudes demeurent, notamment concernant sa sécurité et son efficacité en pratique, et devront être éclaircies avant une éventuelle utilisation à large échelle.Cette thèse s'inscrit dans cette problématique et se concentre sur l'amélioration des performances de ce genre de chiffrement en pratique. Pour cela nous nous sommes intéressés à l'optimisation de l'arithmétique utilisée par ces schémas, qu'elle soit sous-jacente au problème du "Ring-Learning With Errors" sur lequel la sécurité des schémas considérés est basée, ou bien spécifique aux procédures de calculs requises par certains de ces schémas. Nous considérons également l'optimisation des calculs nécessaires à certaines applications possibles du chiffrement homomorphe, et en particulier la classification de données privées, de sorte à proposer des techniques de calculs innovantes ainsi que des méthodes pour effectuer ces calculs de manière efficace. L'efficacité de nos différentes méthodes est illustrée à travers des implémentations logicielles et des comparaisons aux techniques de l'état de l'art

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Proceedings, MSVSCC 2014

Proceedings of the 8th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 17, 2014 at VMASC in Suffolk, Virginia

Deep Model for Improved Operator Function State Assessment

A deep learning framework is presented for engagement assessment using EEG signals. Deep learning is a recently developed machine learning technique and has been applied to many applications. In this paper, we proposed a deep learning strategy for operator function state (OFS) assessment. Fifteen pilots participated in a flight simulation from Seattle to Chicago. During the four-hour simulation, EEG signals were recorded for each pilot. We labeled 20- minute data as engaged and disengaged to fine-tune the deep network and utilized the remaining vast amount of unlabeled data to initialize the network. The trained deep network was then used to assess if a pilot was engaged during the four-hour simulation

A Field Guide to Genetic Programming

xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction -- Representation, initialisation and operators in Tree-based GP -- Getting ready to run genetic programming -- Example genetic programming run -- Alternative initialisations and operators in Tree-based GP -- Modular, grammatical and developmental Tree-based GP -- Linear and graph genetic programming -- Probalistic genetic programming -- Multi-objective genetic programming -- Fast and distributed genetic programming -- GP theory and its applications -- Applications -- Troubleshooting GP -- Conclusions.Contents xi 1 Introduction 1.1 Genetic Programming in a Nutshell 1.2 Getting Started 1.3 Prerequisites 1.4 Overview of this Field Guide I Basics 2 Representation, Initialisation and GP 2.1 Representation 2.2 Initialising the Population 2.3 Selection 2.4 Recombination and Mutation Operators in Tree-based 3 Getting Ready to Run Genetic Programming 19 3.1 Step 1: Terminal Set 19 3.2 Step 2: Function Set 20 3.2.1 Closure 21 3.2.2 Sufficiency 23 3.2.3 Evolving Structures other than Programs 23 3.3 Step 3: Fitness Function 24 3.4 Step 4: GP Parameters 26 3.5 Step 5: Termination and solution designation 27 4 Example Genetic Programming Run 4.1 Preparatory Steps 29 4.2 Step-by-Step Sample Run 31 4.2.1 Initialisation 31 4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming 5 Alternative Initialisations and Operators in 5.1 Constructing the Initial Population 5.1.1 Uniform Initialisation 5.1.2 Initialisation may Affect Bloat 5.1.3 Seeding 5.2 GP Mutation 5.2.1 Is Mutation Necessary? 5.2.2 Mutation Cookbook 5.3 GP Crossover 5.4 Other Techniques 32 5.5 Tree-based GP 39 6 Modular, Grammatical and Developmental Tree-based GP 47 6.1 Evolving Modular and Hierarchical Structures 47 6.1.1 Automatically Defined Functions 48 6.1.2 Program Architecture and Architecture-Altering 50 6.2 Constraining Structures 51 6.2.1 Enforcing Particular Structures 52 6.2.2 Strongly Typed GP 52 6.2.3 Grammar-based Constraints 53 6.2.4 Constraints and Bias 55 6.3 Developmental Genetic Programming 57 6.4 Strongly Typed Autoconstructive GP with PushGP 59 7 Linear and Graph Genetic Programming 61 7.1 Linear Genetic Programming 61 7.1.1 Motivations 61 7.1.2 Linear GP Representations 62 7.1.3 Linear GP Operators 64 7.2 Graph-Based Genetic Programming 65 7.2.1 Parallel Distributed GP (PDGP) 65 7.2.2 PADO 67 7.2.3 Cartesian GP 67 7.2.4 Evolving Parallel Programs using Indirect Encodings 68 8 Probabilistic Genetic Programming 8.1 Estimation of Distribution Algorithms 69 8.2 Pure EDA GP 71 8.3 Mixing Grammars and Probabilities 74 9 Multi-objective Genetic Programming 75 9.1 Combining Multiple Objectives into a Scalar Fitness Function 75 9.2 Keeping the Objectives Separate 76 9.2.1 Multi-objective Bloat and Complexity Control 77 9.2.2 Other Objectives 78 9.2.3 Non-Pareto Criteria 80 9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80 9.4 Multi-objective Optimisation via Operator Bias 81 10 Fast and Distributed Genetic Programming 83 10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83 10.2 Reducing Cost of Fitness with Caches 86 10.3 Parallel and Distributed GP are Not Equivalent 88 10.4 Running GP on Parallel Hardware 89 10.4.1 Master–slave GP 89 10.4.2 GP Running on GPUs 90 10.4.3 GP on FPGAs 92 10.4.4 Sub-machine-code GP 93 10.5 Geographically Distributed GP 93 11 GP Theory and its Applications 97 11.1 Mathematical Models 98 11.2 Search Spaces 99 11.3 Bloat 101 11.3.1 Bloat in Theory 101 11.3.2 Bloat Control in Practice 104 III Practical Genetic Programming 12 Applications 12.1 Where GP has Done Well 12.2 Curve Fitting, Data Modelling and Symbolic Regression 12.3 Human Competitive Results – the Humies 12.4 Image and Signal Processing 12.5 Financial Trading, Time Series, and Economic Modelling 12.6 Industrial Process Control 12.7 Medicine, Biology and Bioinformatics 12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii 12.9 Entertainment and Computer Games 127 12.10The Arts 127 12.11Compression 128 13 Troubleshooting GP 13.1 Is there a Bug in the Code? 13.2 Can you Trust your Results? 13.3 There are No Silver Bullets 13.4 Small Changes can have Big Effects 13.5 Big Changes can have No Effect 13.6 Study your Populations 13.7 Encourage Diversity 13.8 Embrace Approximation 13.9 Control Bloat 13.10 Checkpoint Results 13.11 Report Well 13.12 Convince your Customers 14 Conclusions Tricks of the Trade A Resources A.1 Key Books A.2 Key Journals A.3 Key International Meetings A.4 GP Implementations A.5 On-Line Resources 145 B TinyGP 151 B.1 Overview of TinyGP 151 B.2 Input Data Files for TinyGP 153 B.3 Source Code 154 B.4 Compiling and Running TinyGP 162 Bibliography 167 Inde