DOCSLIB.ORG

Inductive Pattern Formation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Inductive Pattern Formation INDUCTIVE PATTERN FORMATION A Dissertation by RAYMOND CHARLES MULLICAN Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of the Committee, Gabriela Campagnol Co-Chair of the Committee, Mardelle M. Shepley Committee Members, Jay R. Walton Robert K. Popp Head of Department, Robert Warden December 2017 Major Subject: Architecture Copyright 2017 Raymond Charles Mullican ABSTRACT With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete space- time model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat. ii for kaj editor-in-chief who often gives the impression of thinking this reporter has a good story If not for you The winter would hold no spring Couldn't hear a robin sing I just wouldn't have a clue, if not for you (George Harrison, 1970) thank you iii ACKNOWLEDGEMENTS 2017 College Station, Texas To Gabriela, Mardelle, Jay, and Bob: thank you. I cannot adequately express my gratitude for your kindness, thoughtfulness, encouragement, patience and amazing grace when faced with my often inarticulate meanderings, seemingly lost with only the black maps of my intuition. My ‘big six’ now stands at an even ten. Thank you also to Dean Tom Regan for offering a place to attempt this work. In over forty-five years of intermittent conversation, he always seemed to ask exactly the right question. Which, of course, was one for which I had no answer, prompting the next iteration of investigation. And to Francis Downing. If scripted by Charles Webb, Calder Willingham, and Buck Henry, the synchronicity of our last conversation would have been this single short scene: Dr. Downing: I just want to say one word to you. Just one word. Ray: Yes, ma’am. Dr. Downing: Are you listening? Ray: Yes, I am. Dr. Downing: Situated. Ray: Exactly how do you mean? One could envision a similar scene with Mark Clayton regarding the significance of proof and history. Thank you both. Every day I give thanks for my family and friends: without feeling your support this marathon would not have been possible. And underpinning it all, embedded in the probabilistic adaptive information structures of inductive truth space, thank you to the Deus ex Machina for the synchronicities of Ah-ha! moment local phase transitions that have mapped the 67 year trajectory of this pattern formation process. I’ve done my best, I know it wasn't much I couldn't feel, so I learned to touch I've told the truth, I didn't come here just to fool you And even though it all went wrong I'll stand right here before the Lord of Song With nothing; nothing on my tongue but Hallelujah. (Leonard Cohen, 1984) iv 1998 Blacksburg, Virginia Olivio Ferrari was many things to us, to me. With his memory, the meaning of one word grows ever larger as the years advance: mentor. To us all. The fabric of his weavings often revealed two common threads -- develop, then trust, your intuition, and process is ultimately larger than product. Design, as well as life, seems to be about both. Where are we? Architects were then, as they are now, interested more in the appearance of buildings than in their functioning. Witold Rybczynski “Until we have an understanding of these complicated, changing interactions, our attempts to balance extraction of ecosystem resources against sustainability will remain at best naive, at worst, disastrous. We, as humans, have become so numerous that we perforce extensively modify ecological interactions, with only vague ideas of longer range effects. Yet our wellbeing, even our survival, depends on our ability to use these systems without destroying them.” John Holland As architects we have lost or given up much of our process, as a result we have lost control of our product. We have reduced ourselves to being harbingers of fashion, with little understanding of design consequences to both the human inhabitants and a building’s extended ecosystem. Our cumbersome performance modeling tools are based on the reductionist thinking of linear relationships and are inappropriate for the analysis of architecture’s synergy. Worse, they are of little or no benefit to the creation of architecture. Revolution! Artificial life is the study of man-made systems that exhibit behaviors characteristic of natural living systems. a relatively new field employing a synthetic approach to the study of life-as-it-could be. It views life as a property of the organization of matter, rather than a property of the matter which is so organized. Christopher Langton Artificial life and the related study of complex adaptive systems [CAS] have risen from the power of computers to model the nonlinear relationships common in natural systems. Traditional science has placed emphasis on analyzing and explaining in terms of smallest parts; these are attempts to synthesize behavior and process. Self-organization and order emerge from simple-ruled, bottom-up constructions. v Towards A New Architecture Within fifty to a hundred years, a new class of organisms is likely to emerge. These organisms will be artificial in the sense that they will originally be designed by humans. However, they will reproduce, and will evolve into something other than their initial form; they will be ‘alive’ under any reasonable definition of the word. Doyne Farmer 2050: Scientific foundation of architecture. The tools of cellular automata and genetic algorithms are united with the symmetry operations of mathematical crystallography to evolve architectural morphology in computer time; to generate form in response to environmental forces - physical, social, cultural, economic. 2100: While not derived from carbon based ‘organic’ life as we know it, building assemblies will be alive in every sense -- growing, adapting, reproducing and dying in symbiosis with both inhabitants and environment. Convergence Artificial life, CAS: bottom-up, parallel processing, simple rules, emergent self-organization. Biology, economics, psychology, physics, anthropology, mathematics, art . Architecture. Déjà vu. Intuitively, we have been here before. It was called design studio. To a giant, whose shoulders were broad enough that we may all aspire to stand. Thank you. rcm, 1998 vi CONTRIBUTORS AND FUNDING SOURCES Contributors This work was supported by a dissertation committee consisting of Professors Gabriela Campagnol, advisor, and Mardelle Shepley, co-advisor, of the Department of Architecture, along with Professors Jay Walton of the Department of Mathematics and Robert Popp of the Department of Geology and Geophysics. All work conducted for the dissertation was completed independently by the author. Funding Sources Graduate study was supported by Deus Ex Machina through Federal Student Loans, the generosity of KAJ, and the kindness of strangers. vii TABLE OF CONTENTS Page ABSTRACT ......................................................................................................................................................
Load more

Recommended publications
  • Self-Organization Principles of Intracellular Pattern Formation
    Self-organization principles of intracellular pattern formation J. Halatek. F. Brauns, and E. Frey∗ Arnold{Sommerfeld{Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universit¨atM¨unchen, Theresienstraße 37, D-80333 M¨unchen,Germany (Dated: February 21, 2018) Abstract Dynamic patterning of specific proteins is essential for the spatiotemporal regulation of many important intracellular processes in procaryotes, eucaryotes, and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article we review quantitative models for intracellular Min protein patterns in E. coli, Cdc42 polarization in S. cerevisiae, and the bipolar PAR protein patterns found in C. elegans. By analyzing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as \activators", \inhibitors", or \substrate-depletion". Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction-diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics. Keywords: self-organization; pattern formation; intracellular patterns; reaction-diffusion; cell polarity; arXiv:1802.07169v1 [physics.bio-ph] 20 Feb 2018 NTPases 1 INTRODUCTION In biological systems self-organization refers to the emergence of spatial and temporal structure.
    [Show full text]
  • Guiding Self-Organized Pattern Formation in Cell Polarity Establishment
    ARTICLES https://doi.org/10.1038/s41567-018-0358-7 Guiding self-organized pattern formation in cell polarity establishment Peter Gross1,2,3,8, K. Vijay Kumar" "3,4,8, Nathan W. Goehring" "5,6, Justin S. Bois" "7, Carsten Hoege2, Frank Jülicher3 and Stephan W. Grill" "1,2,3* Spontaneous pattern formation in Turing systems relies on feedback. But patterns in cells and tissues seldom form spontane- ously—instead they are controlled by regulatory biochemical interactions that provide molecular guiding cues. The relationship between these guiding cues and feedback in controlled biological pattern formation remains unclear. Here, we explore this relationship during cell-polarity establishment in the one-cell-stage Caenorhabditis elegans embryo. We quantify the strength of two feedback systems that operate during polarity establishment: feedback between polarity proteins and the actomyosin cortex, and mutual antagonism among polarity proteins. We characterize how these feedback systems are modulated by guid- ing cues from the centrosome, an organelle regulating cell cycle progression. By coupling a mass-conserved Turing-like reac- tion–diffusion system for polarity proteins to an active-gel description of the actomyosin cortex, we reveal a transition point beyond which feedback ensures self-organized polarization, even when cues are removed. Notably, the system switches from a guide-dominated to a feedback-dominated regime well beyond this transition point, which ensures robustness. Together, these results reveal a general criterion for controlling biological pattern-forming systems: feedback remains subcritical to avoid unstable behaviour, and molecular guiding cues drive the system beyond a transition point for pattern formation. ell polarity establishment in Caenorhabditis elegans zygotes phase where myosin appears to reach a steady state (Supplementary is a prototypical example for cellular pattern formation that Fig.
    [Show full text]
  • Pattern Formation, Social Forces, and Diffusion Instability in Games
    EPJ manuscript No. (will be inserted by the editor) Pattern Formation, Social Forces, and Diffusion Instability in Games with Success-Driven Motion Dirk Helbing ETH Zurich, UNO D11, Universit¨atstr.41, 8092 Zurich, Switzerland Received: date / Revised version: date Abstract. A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner's dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion. PACS. 02.50.Le Decision theory and game theory { 87.23.Ge Dynamics of social systems { 82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer { 87.23.Cc Population dynamics and ecological pattern formation 1 Introduction tions [17,18], which agree with replicator equations for the fitness-dependent reproduction of individuals in biology Game theory is a well-established theory of individual [19,20,21].
    [Show full text]
  • Using Neural Networks for Pattern Association for the Online Purchase
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by AIS Electronic Library (AISeL) Association for Information Systems AIS Electronic Library (AISeL) All Sprouts Content Sprouts 7-26-2009 Using Neural Networks for Pattern Association for the Online Purchase of Products Arpan Kumar Kar XLRI School of Business & Human Resources, [email protected] Supriyo Kumar De XLRI School of Business & Human Resources, [email protected] Follow this and additional works at: http://aisel.aisnet.org/sprouts_all Recommended Citation Kar, Arpan Kumar and De, Supriyo Kumar, " Using Neural Networks for Pattern Association for the Online Purchase of Products" (2009). All Sprouts Content. 281. http://aisel.aisnet.org/sprouts_all/281 This material is brought to you by the Sprouts at AIS Electronic Library (AISeL). It has been accepted for inclusion in All Sprouts Content by an authorized administrator of AIS Electronic Library (AISeL). For more information, please contact [email protected]. Working Papers on Information Systems ISSN 1535-6078 Using Neural Networks for Pattern Association for the Online Purchase of Products Arpan Kumar Kar XLRI School of Business & Human Resources, India Supriyo Kumar De XLRI School of Business & Human Resources, India Abstract Abstract: Today, a huge percentage of all the business transactions that take place in the domain of e-commerce are dominated by online shopping after the "virtual market" conceptualization of the business. This paper focuses on how pattern association rules may be obtained from the dynamic databases generated during purchases in an e-Store to maximize the profit of the marketer.
    [Show full text]
  • Evolutionary Game Theory: Theoretical Concepts and Applications To
    Physica A 389 (2010) 4265–4298 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Evolutionary game theory: Theoretical concepts and applications to microbial communities Erwin Frey ∗ Ludwig-Maximilians-Universität München, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Theresienstrasse 37, D-80333 Munich, Germany article info a b s t r a c t Article history: Ecological systems are complex assemblies of large numbers of individuals, interacting Received 30 January 2010 competitively under multifaceted environmental conditions. Recent studies using Available online 4 March 2010 microbial laboratory communities have revealed some of the self-organization principles underneath the complexity of these systems. A major role of the inherent stochasticity of its Keywords: dynamics and the spatial segregation of different interacting species into distinct patterns Population dynamics has thereby been established. It ensures the viability of microbial colonies by allowing for Game theory species diversity, cooperative behavior and other kinds of ``social'' behavior. Evolution Stochastic processes A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of Nonlinear dynamics stochastic processes provides the mathematical tools and a conceptual framework for a Pattern formation deeper understanding of these ecological systems. We give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of microbial systems. Intrinsic fluctuations, stemming from the discreteness of individuals, are ubiquitous, and can have an important impact on the stability of ecosystems. In the absence of speciation, extinction of species is unavoidable. It may, however, take very long times. We provide a general concept for defining survival and extinction on ecological time-scales.
    [Show full text]
  • Exploring Reaction-Diffusion and Pattern Formation
    Exploring Reaction-Diffusion and Pattern Formation Ramona Behravan1, Peter J. Bentley1, Robin Carlisle2 1 Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, England 2 Glassworks Ltd., 34 Great Pulteney Street, London W1F 9NP, England Abstract. This article reviews the development of the concept of reaction- diffusion leading to pattern formation in living organisms. The article com- mences with an historical background and then describes biological develop- ment, and ideas of the formation of patterns using dynamic activator inhibitor systems. In addition to this, different models to represent such systems and their computer simulations are discussed. 1 Introduction The first steps toward the sciences arose out of the recognition of patterns and struc- tures. Patterns are all around us in the living and the non-living world. Formation of galaxies, mountains, rivers, crystals, zebra stripes, flower petals and butterfly wings are all examples of ordered structures and regular patterns. While it seems likely that evolution plays the major role in creating, selecting and exploiting features in living organisms, there can be no denying the role of physics in nature. Physical structures can emerge naturally without the selection pressure of natural evolution: sand dunes, snow flakes, clouds and cracks in the ground can all self-organise into ordered and re- petitive forms with clearly defined patterns. The existence of such natural pattern has led many researchers to hypothesise that in some of the features of life, natural evolution has exploited the automatic pattern- formation machinery provided by physics instead of creating her own from scratch. In this article we focus on this class of patterns, namely pattern formation of living or- ganisms.
    [Show full text]
  • Pattern Formation in Reaction-Diffusion System on Membrane with Mechanochemical Feedback
    Pattern Formation in Reaction-Diffusion System on Membrane with Mechanochemical Feedback Naoki Tamemoto and Hiroshi Noguchi* Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan Correspondence and requests for materials should be addressed to H.N. ([email protected] tokyo.ac.jp). 1 ABSTRACT Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non- deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes. 2 INTRODUCTION Membrane deformation is a fundamental biological process involved in many cellular functions such as vesicular transport1, cell division2, and cell motility3. To understand these phenomena, the mechanism of membrane deformation by intracellular proteins has been investigated in detail4–8. Recently, it has been shown that the deformation of biological membranes is not just a passive phenomenon but also plays physiological roles8–15.
    [Show full text]
  • A Review: Pattern Formation and Adaptation in Multi-Robot Systems
    A Review: Pattern Formation and Adaptation in Multi-Robot Systems Erkin Bahc¸eci, Onur Soysal and Erol S¸ahin CMU-RI-TR-03-43 October 2003 Robotics Institute Carnegie Mellon University Pittsburgh, Pennsylvania 15213 c Carnegie Mellon University Abstract Recent advances in robotics have started making it feasible to deploy large numbers of inexpensive robots for tasks such as surveillance and search. However, coordination of multiple robots to accomplish such tasks remains a challenging problem. This report reviews some of the recent literature in multi-robot systems. It consists of two parts. In the first part, we reviewed the studies on the pattern formation problem, that is how can a group of robots be controlled to get into and maintain a formation. The second part reviews the studies that used adaptation strategies in controlling multi- robot systems. Specifically we have investigated (1) how learning (life-long adaptation) is used to make multi-robot systems respond to changes in the environment as well in the capabilities of individual robots, and (2) how evolution is used to generate group behaviors. I Contents 1 Introduction 1 2 Pattern formation in multi-robot systems 1 2.1 Centralized pattern formation . 1 2.2 Decentralized pattern formation . 2 3 Adaptation in multi-robot systems 5 3.1 Individual level adaptation . 5 3.2 Group level adaptation . 7 4 Conclusion 9 5 Acknowledgements 9 III 1 Introduction Recent advances in robotics have started making it feasible to deploy large numbers of inexpensive robots for tasks such as surveillance and search. However, coordination of multiple robots to accomplish such tasks remains a challenging problem.
    [Show full text]
  • Pattern Formation Models and Developmental Constraints GEORGE F
    THE JOURNAL OF EXPERIMENTAL ZOOLOGY 251:186-202 (1989) Pattern Formation Models and Developmental Constraints GEORGE F. OSTER AND JAMES D. MURRAY Departments of Biophysics, Entomology, and Zoology, University of California, Berkeley, California 94720 (G.F.0.); Centre for Mathematical Biology, Mathematical Institute, Oxford, OX1 3LB, England (J.D.M.) ABSTRACT Most schemes for embryonic pattern formation are built around the notion of lateral inhibition. Models of this type arise in many settings, and all share some common character- istics. In this paper we examine a number of pattern formation models and show how the phenome- non of lateral inhibition constrains the possible geometries that can arise. Morphogenetic models have provided embry- how the chemical prepattern is laid down. This ologists with insight into how embryonic patterns can be modeled in one of two ways. 1) Simple may be laid down. In this chapter we shall illus- chemical gradients are established across tissues, trate the basic pattern-forming principles of these assuming that certain cells act as sources or sinks models using as an example the formation of for the chemicals, which diffuse from cell to cell bones in the vertebrate limb. The physics of the via junctions, or through the intercellular space. pattern forming process imposes constraints on 2) A chemical prepattern can arise by means of the possible cartilage patterns the limb may ex- “diffusion-driven instabilities,” a notion first pro- hibit. These constraints are reflected in the gen- posed by Turing (’52), and subsequently elabo- eral similarity one observes amongst all tretrapod rated and applied by numerous authors to a va- limbs.
    [Show full text]
  • Exploring Aesthetic Pattern Formation
    Generative Art 2002 Exploring Aesthetic Pattern Formation Katie A Bentley Computer Science Department, University College London. Email: [email protected] Abstract This paper is an exploration of an interdisciplinary nature. Through studies in fine art, pattern formation in nature, and artificial life, a mechanism for the artistic process is presented. Asynchronous updating schemes implemented in cellular automata and pheromonal agent swarms were evolved to produce aesthetic patterns and compared favourably to non-evolved synchronous production methods. The curious adaptive properties of the resulting patterns were investigated. 1. Introduction “When we stand before great churches, temples, pyramids, and other works of architecture built hundreds, if not thousands of years ago, our minds are filled with awe and admiration. Yet there have been architects millions of years before that. Their work, it is true, owes its existence not to the inspired genius of great artists, but to the unconscious, unremitting activity of the force of life itself.” [1] Pp 2. There remains a great deal of mystery surrounding the processes involved in the generation of aesthetic and functional forms, as they occur in nature and as generated by humans. Many would still like to believe that both human and natural generation of aesthetic form, at some level at least, a conscious creative plan, some central idea, meaning or goal. Artificial life offers an alternative paradigm of thought, and it is the point of this paper to explore how the seemingly disparate domains of pattern formation, social insect communication and artistic processes can be linked. The aim of this paper is to show that the processes involved in the formation and generation of shapes and patterns, aesthetic or functional, are best viewed as evolved adaptive systems.
    [Show full text]
  • Texture Generation with Neural Cellular Automata
    Texture Generation with Neural Cellular Automata Alexander Mordvintsev* Eyvind Niklasson* Ettore Randazzo Google Research fmoralex, eyvind, [email protected] Abstract derlying state manifold. Furthermore, we investigate prop- erties of the learned models that are both useful and in- Neural Cellular Automata (NCA1) have shown a remark- teresting, such as non-stationary dynamics and an inherent able ability to learn the required rules to ”grow” images robustness to damage. Finally, we make qualitative claims [20], classify morphologies [26] and segment images [28], that the behaviour exhibited by the NCA model is a learned, as well as to do general computation such as path-finding distributed, local algorithm to generate a texture, setting [10]. We believe the inductive prior they introduce lends our method apart from existing work on texture generation. arXiv:2105.07299v1 [cs.AI] 15 May 2021 itself to the generation of textures. Textures in the natural We discuss the advantages of such a paradigm. world are often generated by variants of locally interact- ing reaction-diffusion systems. Human-made textures are likewise often generated in a local manner (textile weaving, 1. Introduction for instance) or using rules with local dependencies (reg- Texture synthesis is an actively studied problem of com- ular grids or geometric patterns). We demonstrate learn- puter graphics and image processing. Most of the work in ing a texture generator from a single template image, with this area is focused on creating new images of a texture the generation method being embarrassingly parallel, ex- specified by the provided image pattern [8, 17]. These im- hibiting quick convergence and high fidelity of output, and ages should give the impression, to a human observer, that requiring only some minimal assumptions around the un- they are generated by the same stochastic process that gen- erated the provided sample.
    [Show full text]
  • Evolutionary Game Theory: Theoretical Concepts and Applications to Microbial Communities
    Evolutionary Game Theory: Theoretical Concepts and Applications to Microbial Communities Erwin Frey January 20, 2010 Abstract Ecological systems are complex assemblies of large numbers of indi- viduals, interacting competitively under multifaceted environmental con- ditions. Recent studies using microbial laboratory communities have re- vealed some of the self-organization principles underneath the complexity of these systems. A major role of the inherent stochasticity of its dynam- ics and the spatial segregation of different interacting species into distinct patterns has thereby been established. It ensures viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of \social" behavior. A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the mathematical tools and con- ceptual framework for a deeper understanding of these ecological systems. We give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of micro- bial systems. Intrinsic fluctuations, stemming from the discreteness of individuals, are ubiquitous, and can have important impact on the sta- bility of ecosystems. In the absence of speciation, extinction of species is unavoidable, may, however, take very long times. We provide a gen- eral concept for defining survival and extinction on ecological time-scales. Spatial degrees of freedom come with a certain mobility of individuals. When the latter is sufficiently high, bacterial community structures can be understood through mapping individual-based models, in a contin- uum approach, onto stochastic partial differential equations. These allow progress using methods of nonlinear dynamics such as bifurcation analysis and invariant manifolds. We conclude with a perspective on the current challenges in quantifying bacterial pattern formation, and how this might have an impact on fundamental research in non-equilibrium physics.
    [Show full text]