PATTERN FORMATION AND PHASE TRANSITION OF CONNECTIVITY IN TWO DIMENSIONS

This dissertation is devoted to the study and analysis of different types of emergent behavior in physical systems. Emergence is a phenomenon that has fascinated researchers from various fields of science and engineering. From the emergence of global pandemics to the formation of reaction-diffusion patterns, the main feature that connects all these diverse systems is the appearance of a complex global structure as a result of collective interactions of simple underlying components. This dissertation will focus on two types of emergence in physical systems: emergence of long-range connectivity in networks and emergence and analysis of complex patterns. The most prominent theory which deals with the emergence of long-range connectivity is the percolation theory. This dissertation employs many concepts from the percolation theory to study connectivity transitions in various systems. Ordinary percolation theory is founded upon two main assumptions, namely locality and independence of the underlying components. In Chapters 2 and 3, we relax these assumptions in different manners and show that relaxing these assumptions leads to irregular behaviors such as appearance of different universality classes and, in some instances, violation of universality. Chapter 2 deals with relaxing the assumption of locality of interactions. In this Chapter, we define a hierarchy of various measures of robust connectivity. We study the phase transition of these robustness metrics as a function of site/bond occupation/removal probability on the square lattice. Furthermore, we perform extensive numerical analysis and extract these robustness metrics\u27 critical thresholds and critical behaviors. We show that some of these robustness metrics do not fall under the regular percolation universality class. The extensive numerical results in this work can serve as a foundation for any researcher who aims to design/study various degrees of connectivity in networks. In Chapter 3, we study the non-equilibrium phase transition of long-range connectivity in a multi-particle interacting system on the square lattice. The interactions between different particles translate to relaxing the assumption of independence in the percolation theory. Using extensive numerical simulations, we show that the phase transition observed in this system violates the regular concept of universality. However, it conforms well with the concept of weak-universality recently introduced in the literature. We observe that by varying inter-particle interaction strength in our model, one can control the critical behavior of this phase transition. These observations could be pivotal in studying phase transitions and universality classes. Chapter 4 focuses on the analysis of reaction-diffusion patterns. We utilize a multitude of machine learning algorithms to analyze reaction-diffusion patterns. In particular, we address two main problems using these techniques, namely, pattern regression and pattern classification. Given an observed instance of a pattern with a known generative function, in the pattern regression task, we aim to predict the specific set of reaction-diffusion parameters (i.e. diffusion constant) which can reproduce the observed pattern. We employ supervised learning techniques to successfully solve this problem and show the performance of our model in some real-world instances. We also address the task of pattern classification. In this task, we are interested in grouping different instances of similar patterns together. This task is usually performed visually by the researcher studying certain natural phenomena. However, this method is tedious and can be inconsistent among different researchers. We utilize supervised and unsupervised machine learning algorithms to classify patterns of the Gray-Scott model. We show that our methods show outstanding performance both in supervised and unsupervised settings. The methods introduced in this Chapter could bridge the gaps between researchers studying patterns in different fields of science and engineering

Intensional Cyberforensics

This work focuses on the application of intensional logic to cyberforensic analysis and its benefits and difficulties are compared with the finite-state-automata approach. This work extends the use of the intensional programming paradigm to the modeling and implementation of a cyberforensics investigation process with backtracing of event reconstruction, in which evidence is modeled by multidimensional hierarchical contexts, and proofs or disproofs of claims are undertaken in an eductive manner of evaluation. This approach is a practical, context-aware improvement over the finite state automata (FSA) approach we have seen in previous work. As a base implementation language model, we use in this approach a new dialect of the Lucid programming language, called Forensic Lucid, and we focus on defining hierarchical contexts based on intensional logic for the distributed evaluation of cyberforensic expressions. We also augment the work with credibility factors surrounding digital evidence and witness accounts, which have not been previously modeled. The Forensic Lucid programming language, used for this intensional cyberforensic analysis, formally presented through its syntax and operational semantics. In large part, the language is based on its predecessor and codecessor Lucid dialects, such as GIPL, Indexical Lucid, Lucx, Objective Lucid, and JOOIP bound by the underlying intensional programming paradigm.Comment: 412 pages, 94 figures, 18 tables, 19 algorithms and listings; PhD thesis; v2 corrects some typos and refs; also available on Spectrum at http://spectrum.library.concordia.ca/977460

Large scale dynamic systems

Classes of large scale dynamic systems were discussed in the context of modern control theory. Specific examples discussed were in the technical fields of aeronautics, water resources and electric power

Contextual Social Networking

The thesis centers around the multi-faceted research question of how contexts may be detected and derived that can be used for new context aware Social Networking services and for improving the usefulness of existing Social Networking services, giving rise to the notion of Contextual Social Networking. In a first foundational part, we characterize the closely related fields of Contextual-, Mobile-, and Decentralized Social Networking using different methods and focusing on different detailed aspects. A second part focuses on the question of how short-term and long-term social contexts as especially interesting forms of context for Social Networking may be derived. We focus on NLP based methods for the characterization of social relations as a typical form of long-term social contexts and on Mobile Social Signal Processing methods for deriving short-term social contexts on the basis of geometry of interaction and audio. We furthermore investigate, how personal social agents may combine such social context elements on various levels of abstraction. The third part discusses new and improved context aware Social Networking service concepts. We investigate special forms of awareness services, new forms of social information retrieval, social recommender systems, context aware privacy concepts and services and platforms supporting Open Innovation and creative processes. This version of the thesis does not contain the included publications because of copyrights of the journals etc. Contact in terms of the version with all included publications: Georg Groh, [email protected] zentrale Gegenstand der vorliegenden Arbeit ist die vielschichtige Frage, wie Kontexte detektiert und abgeleitet werden können, die dazu dienen können, neuartige kontextbewusste Social Networking Dienste zu schaffen und bestehende Dienste in ihrem Nutzwert zu verbessern. Die (noch nicht abgeschlossene) erfolgreiche Umsetzung dieses Programmes führt auf ein Konzept, das man als Contextual Social Networking bezeichnen kann. In einem grundlegenden ersten Teil werden die eng zusammenhängenden Gebiete Contextual Social Networking, Mobile Social Networking und Decentralized Social Networking mit verschiedenen Methoden und unter Fokussierung auf verschiedene Detail-Aspekte näher beleuchtet und in Zusammenhang gesetzt. Ein zweiter Teil behandelt die Frage, wie soziale Kurzzeit- und Langzeit-Kontexte als für das Social Networking besonders interessante Formen von Kontext gemessen und abgeleitet werden können. Ein Fokus liegt hierbei auf NLP Methoden zur Charakterisierung sozialer Beziehungen als einer typischen Form von sozialem Langzeit-Kontext. Ein weiterer Schwerpunkt liegt auf Methoden aus dem Mobile Social Signal Processing zur Ableitung sinnvoller sozialer Kurzzeit-Kontexte auf der Basis von Interaktionsgeometrien und Audio-Daten. Es wird ferner untersucht, wie persönliche soziale Agenten Kontext-Elemente verschiedener Abstraktionsgrade miteinander kombinieren können. Der dritte Teil behandelt neuartige und verbesserte Konzepte für kontextbewusste Social Networking Dienste. Es werden spezielle Formen von Awareness Diensten, neue Formen von sozialem Information Retrieval, Konzepte für kontextbewusstes Privacy Management und Dienste und Plattformen zur Unterstützung von Open Innovation und Kreativität untersucht und vorgestellt. Diese Version der Habilitationsschrift enthält die inkludierten Publikationen zurVermeidung von Copyright-Verletzungen auf Seiten der Journals u.a. nicht. Kontakt in Bezug auf die Version mit allen inkludierten Publikationen: Georg Groh, [email protected]

IST Austria Thesis

This dissertation focuses on algorithmic aspects of program verification, and presents modeling and complexity advances on several problems related to the static analysis of programs, the stateless model checking of concurrent programs, and the competitive analysis of real-time scheduling algorithms. Our contributions can be broadly grouped into five categories. Our first contribution is a set of new algorithms and data structures for the quantitative and data-flow analysis of programs, based on the graph-theoretic notion of treewidth. It has been observed that the control-flow graphs of typical programs have special structure, and are characterized as graphs of small treewidth. We utilize this structural property to provide faster algorithms for the quantitative and data-flow analysis of recursive and concurrent programs. In most cases we make an algebraic treatment of the considered problem, where several interesting analyses, such as the reachability, shortest path, and certain kind of data-flow analysis problems follow as special cases. We exploit the constant-treewidth property to obtain algorithmic improvements for on-demand versions of the problems, and provide data structures with various tradeoffs between the resources spent in the preprocessing and querying phase. We also improve on the algorithmic complexity of quantitative problems outside the algebraic path framework, namely of the minimum mean-payoff, minimum ratio, and minimum initial credit for energy problems. Our second contribution is a set of algorithms for Dyck reachability with applications to data-dependence analysis and alias analysis. In particular, we develop an optimal algorithm for Dyck reachability on bidirected graphs, which are ubiquitous in context-insensitive, field-sensitive points-to analysis. Additionally, we develop an efficient algorithm for context-sensitive data-dependence analysis via Dyck reachability, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is (i)~linear in the number of call sites and (ii)~only logarithmic in the size of the whole library, as opposed to linear in the size of the whole library. Finally, we prove that Dyck reachability is Boolean Matrix Multiplication-hard in general, and the hardness also holds for graphs of constant treewidth. This hardness result strongly indicates that there exist no combinatorial algorithms for Dyck reachability with truly subcubic complexity. Our third contribution is the formalization and algorithmic treatment of the Quantitative Interprocedural Analysis framework. In this framework, the transitions of a recursive program are annotated as good, bad or neutral, and receive a weight which measures the magnitude of their respective effect. The Quantitative Interprocedural Analysis problem asks to determine whether there exists an infinite run of the program where the long-run ratio of the bad weights over the good weights is above a given threshold. We illustrate how several quantitative problems related to static analysis of recursive programs can be instantiated in this framework, and present some case studies to this direction. Our fourth contribution is a new dynamic partial-order reduction for the stateless model checking of concurrent programs. Traditional approaches rely on the standard Mazurkiewicz equivalence between traces, by means of partitioning the trace space into equivalence classes, and attempting to explore a few representatives from each class. We present a new dynamic partial-order reduction method called the Data-centric Partial Order Reduction (DC-DPOR). Our algorithm is based on a new equivalence between traces, called the observation equivalence. DC-DPOR explores a coarser partitioning of the trace space than any exploration method based on the standard Mazurkiewicz equivalence. Depending on the program, the new partitioning can be even exponentially coarser. Additionally, DC-DPOR spends only polynomial time in each explored class. Our fifth contribution is the use of automata and game-theoretic verification techniques in the competitive analysis and synthesis of real-time scheduling algorithms for firm-deadline tasks. On the analysis side, we leverage automata on infinite words to compute the competitive ratio of real-time schedulers subject to various environmental constraints. On the synthesis side, we introduce a new instance of two-player mean-payoff partial-information games, and show how the synthesis of an optimal real-time scheduler can be reduced to computing winning strategies in this new type of games