# biologically-inspired computing lecture 12 Informatics luis rocha 2015 INDIANA UNIVERSITY biologically Inspired computing

Save this PDF as:

Size: px
Start display at page:

Download "biologically-inspired computing lecture 12 Informatics luis rocha 2015 INDIANA UNIVERSITY biologically Inspired computing"

## Transcription

1 lecture 12 -inspired

2 Sections I485/H400 course outlook Assignments: 35% Students will complete 4/5 assignments based on algorithms presented in class Lab meets in I1 (West) 109 on Lab Wednesdays Lab 0 : January 14 th (completed) Introduction to Python (No Assignment) Lab 1 : January 28 th Measuring Information (Assignment 1) Graded Lab 2 : February 11 th L-Systems (Assignment 2) Graded Lab 3: March 11 th Cellular Automata and Boolean Networks (Assignment 3)

3 Readings until now Class Book Nunes de Castro, Leandro [2006]. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall. Chapter 2, all sections Chapter 7, sections 7.3 Cellular Automata Chapter 8, sections 8.1, 8.2, Lecture notes Chapter 1: What is Life? Chapter 2: The logical Mechanisms of Life Chapter 3: Formalizing and Modeling the World Chapter 4: Self-Organization and Emergent Complex Behavior posted Optional Flake s [1998], The Computational Beauty of Life. MIT Press. Chapters 10, 11, 14 Dynamics, Attractors and chaos

4 final project schedule ALIFE 15 Projects Due by May 4 th in Oncourse ALIFE 15 (14) Actual conference due date: pages (LNCS proceedings format) D= Preliminary ideas due by April 1 st! Individual or group With very definite tasks assigned per member of group

5 more formally D-dimensional lattice L with a finite automaton in each lattice site (cell) What s a CA? Neighborhood template N State-determined system finite number of states Σ: K= Σ E.g. Σ = {0,1} finite input alphabet α transition function Δ: α Σ uniquely ascribes state s in Σ to input patterns α Example K=8 N=5 α =37,768 D 10 30,000 N α Σ, α = K N D = K Number of possible neighborhood states K N Number of possible transition functions

6 Finding the structure of all possible transition functions Langton s parameter Statistical analysis Identify classes of transition functions with similar behavior Similar dynamics (statistically) Via Higher level statistical observables Like Kauffman The Lambda Parameter (similar to bias in BN) Select a subset of D characterized by λ Arbitrary quiescent state: s q Usually 0 A particular function Δ has n transitions to this state and (K N -n) transitions to other states s of Σ (1-λ) is the probability of having a s q in every position of the rule table λ = N K n K N Range: from most homogeneous to most heterogeneous Langton, C.G. [1990]. Computation at the edge of chaos: phase transitions and emergent computation. Artificial Life II. Addison-Wesley. λ = 0: all transitions lead to s q (n =K N ) λ = 1: no transitions lead to s q (n =0) λ = 1-1/K: equally probable states ( n=1/k. K N )

7 A phase transition? Edge of chaos Transient growth in the vicinity of phase transitions Length of CA lattice only relevant around phase transition (λ=0.5) Conclusion: more complicated behavior found in the phase transition between order and chaos Patterns that move across the lattice

8 Transition region Computation at the edge of chaos? Supports both static and propagating structures λ =0.4+ Propagating waves ( signals?) across the CA lattice Necessary for computation? Signals and storage? Computation Requires storage and transmission of information Any dynamical system supporting computation must exhibit long-range signals in space and time Wolfram s CA classes I: homogeneous state Steady-state II: periodic state Limit cycles III: chaotic IV: complex patterns of localized structures Long transients Capable of universal computation

9 imagine automata as agents quorum sensing or what decision to take? (Density Classification) K N = 2 7 =128

10 density classification task random strategies K N = 2 7 =128 P = 0 Typically chaotic behavior No convergence

11 density classification task local strategy: majority rule K N = 2 7 =128 P = 0 Isolated groups No information transmission

12 density classification task block expansion strategy K N = 2 7 =128 P [ 53%,60% ] blind spreading of local information No information integration Not much better than random choice

13 density classification task emergent computation strategies K N = 2 7 =128 Integration and transmission of information across population

14 for DST best CA rules

15 How to characterize complex behavior? collective (emergent) computation via computational mechanics Crutchfield & Mitchell [1995]. PNAS 92: GA to evolve rules for DCT [1994] Das, Mitchell & Crutchfield [1994]. In: Parallel Problem Solving from Nature-III:

16 John Horton Conway 2-D the game of life x x i, j = { 0,1} Sum N x i,i = x i,i = ) Any living cell with fewer than two neighbors dies of loneliness. 2) Any living cell with more than three neighbors dies of crowding. 3) Any dead cell with exactly three neighbors comes to life. 4) Any living cell with two or three neighbors lives, unchanged, to the next generation Introduced in Martin Gardner s Scientific American Mathematical Games Column in Conway was interested in a rule that for certain initial conditions would produce patterns that grow without limit, and some others that fade or get stable. Popularized CAs.

17 wide dynamic range game of life Simple Attractors Blinkers block More complicated attractors

18 moving patterns game of life Glider

19 a threshold of complexity? unbounded growth R-pentomino runs 1103 steps before settling down into 6 gliders, 8 blocks, 4 blinkers, 4 beehives, 1 boat, 1 ship, and 1 loaf.

20 Unbounded growth but not complexity the glider gun Fires a glider every 30 iterations.

21 unbounded complexity requires information 1) Patterns that can implement information, descriptions, and construction 2) Gliders, guns, blocks, eaters life and information Very brittle Built, not evolved Not evolving Universal Turing Machine on game of life!!!

22

23 information in attractor patterns Radius 1 Neighborhood =3 Binary 2 3 = 8 input neighborhoods 2 8 = 256 rules Rule 110

24 structures in rule 110 Universal Computation Identification of gliders, spaceships, and other long-range or selfperpetuating patterns On the background domain produced by rule cells repeat every seven iterations: Collisions and combinations of glider patterns are exploited for computation.

25 is self-organization enough? computation and the edge of chaos Many systems biology models operate in the ordered regime Dynamical systems capable of computation exist well before the edge of chaos A much wider transition? A band of chaos. Most important information transmission and computation in Biology an altogether different process than self-organization Turing/Von Neumann Tape

26 readings Next lectures Class Book Nunes de Castro, Leandro [2006]. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall. Chapter 2, 7, 8 Lecture notes Chapter 1: What is Life? Chapter 2: The logical Mechanisms of Life Chapter 3: Formalizing and Modeling the World Chapter 4: Self-Organization and Emergent Complex Behavior posted Papers and other materials Optional Flake s [1998], The Computational Beauty of Life. MIT Press. Chapters 10, 11, 14 Dynamics, Attractors and chaos

### biologically-inspired computing lecture 5 Informatics luis rocha 2015 biologically Inspired computing INDIANA UNIVERSITY

lecture 5 -inspired Sections I485/H400 course outlook Assignments: 35% Students will complete 4/5 assignments based on algorithms presented in class Lab meets in I1 (West) 109 on Lab Wednesdays Lab 0 :

### biologically-inspired computing lecture 6 Informatics luis rocha 2015 INDIANA UNIVERSITY biologically Inspired computing

lecture 6 -inspired Sections I485/H400 course outlook Assignments: 35% Students will complete 4/5 assignments based on algorithms presented in class Lab meets in I1 (West) 109 on Lab Wednesdays Lab 0 :

### Modelling with cellular automata

Modelling with cellular automata Shan He School for Computational Science University of Birmingham Module 06-23836: Computational Modelling with MATLAB Outline Outline of Topics Concepts about cellular

### Motivation. Evolution has rediscovered several times multicellularity as a way to build complex living systems

Cellular Systems 1 Motivation Evolution has rediscovered several times multicellularity as a way to build complex living systems Multicellular systems are composed by many copies of a unique fundamental

### Shannon Information (very briefly!) Lecture 4. Maximum and Minimum Entropy. Entropy. Entropy of Transition Rules. Entropy Examples

Lecture 4 9/4/07 1 Shannon Information (very briefly!) Information varies directly with surprise Information varies inversely with probability Information is additive The information content of a message

### Complexity Classes in the Two-dimensional Life Cellular Automata Subspace

Complexity Classes in the Two-dimensional Life Cellular Automata Subspace Michael Magnier Claude Lattaud Laboratoire d Intelligence Artificielle de Paris V, Université René Descartes, 45 rue des Saints

### Cellular Automata. Jason Frank Mathematical Institute

Cellular Automata Jason Frank Mathematical Institute WISM484 Introduction to Complex Systems, Utrecht University, 2015 Cellular Automata Game of Life: Simulator: http://www.bitstorm.org/gameoflife/ Hawking:

### Cellular Automata: Tutorial

Cellular Automata: Tutorial Jarkko Kari Department of Mathematics, University of Turku, Finland TUCS(Turku Centre for Computer Science), Turku, Finland Cellular Automata: examples A Cellular Automaton

### Cellular Automata and Tilings

Cellular Automata and Tilings Jarkko Kari Department of Mathematics, University of Turku, Finland TUCS(Turku Centre for Computer Science), Turku, Finland Outline of the talk (1) Cellular automata (CA)

### Logic Programming for Cellular Automata

Technical Communications of ICLP 2015. Copyright with the Authors. 1 Logic Programming for Cellular Automata Marcus Völker RWTH Aachen University Thomashofstraße 5, 52070 Aachen, Germany (e-mail: marcus.voelker@rwth-aachen.de)

### Computation in Cellular Automata: A Selected Review

Computation in Cellular Automata: A Selected Review Melanie Mitchell Santa Fe Institute 1399 Hyde Park Road Santa Fe, NM 87501 U.S.A. email: mm@santafe.edu In T. Gramss, S. Bornholdt, M. Gross, M. Mitchell,

### Project 1: Edge of Chaos in 1D Cellular Automata

CS 420/527: Biologically-Inspired Computation Project 1: Edge of Chaos in 1D Cellular Automata Due: Friday, Feb. 3, Midnight Introduction In this project you will explore Edge of Chaos phenomena (Wolfram

### Learning Cellular Automaton Dynamics with Neural Networks

Learning Cellular Automaton Dynamics with Neural Networks N H Wulff* and J A Hertz t CONNECT, the Niels Bohr Institute and Nordita Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark Abstract We have trained

### Bio-inspired Models of Computation Seminar. Daniele Sgandurra. 16 October 2009

Bio-inspired Models of Computation Seminar Università di Pisa 16 October 2009 Outline Introduction Motivation History Cellular Systems Wolfram Classes Variants and Extensions Extended Topics Garden of

XX Eesti Arvutiteaduse Talvekool Cellular automata, tilings and (un)computability Jarkko Kari Department of Mathematics and Statistics University of Turku Lecture 1: Tutorial on Cellular automata Introduction

### Simulation of cell-like self-replication phenomenon in a two-dimensional hybrid cellular automata model

Simulation of cell-like self-replication phenomenon in a two-dimensional hybrid cellular automata model Takeshi Ishida Nippon Institute of Technology ishida06@ecoinfo.jp Abstract An understanding of the

### biologically-inspired computing lecture 15 Informatics luis rocha 2015 biologically Inspired computing INDIANA UNIVERSITY

lecture 15 -inspired Sections I485/H400 course outlook Assignments: 35% Students will complete 4/5 assignments based on algorithms presented in class Lab meets in I1 (West) 109 on Lab Wednesdays Lab 0

### Outline 1 Introduction Tiling definitions 2 Conway s Game of Life 3 The Projection Method

A Game of Life on Penrose Tilings Kathryn Lindsey Department of Mathematics Cornell University Olivetti Club, Sept. 1, 2009 Outline 1 Introduction Tiling definitions 2 Conway s Game of Life 3 The Projection

### Controlling chaos in random Boolean networks

EUROPHYSICS LETTERS 20 March 1997 Europhys. Lett., 37 (9), pp. 597-602 (1997) Controlling chaos in random Boolean networks B. Luque and R. V. Solé Complex Systems Research Group, Departament de Fisica

### @igorwhiletrue

Abstrakte Maschinen @igorwhiletrue Programming is hard Why? Link between our universe and computational universe Cellular automata are self-replicating abstract machines Humans are self-replicating biological

### From Glider to Chaos: A Transitive Subsystem Derived From Glider B of CA Rule 110

From Glider to Chaos: A Transitive Subsystem Derived From Glider B of CA Rule 110 Pingping Liu, Fangyue Chen, Lingxiao Si, and Fang Wang School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang,

### Introduction to Cellular automata

Jean-Philippe Rennard Ph.D. 12/2000 Introduction to Cellular automata There is a wealth of literature about cellular automata, as well as many Internet resources (you'll find some of them in the links

### Theory of Rule 6 and it s Application to Round Robin Tournament

Theory of Rule 6 and it s Application to Round Robin Tournament Pabitra Pal Choudhury, Sk. Sarif Hassan Applied Statistics Unit, Indian Statistical Institute, Kolkata, 78, INDIA Email: pabitrapalchoudhury@gmail.com

### Chaotic Subsystem Come From Glider E 3 of CA Rule 110

Chaotic Subsystem Come From Glider E 3 of CA Rule 110 Lingxiao Si, Fangyue Chen, Fang Wang, and Pingping Liu School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, P. R. China Abstract The

### Pascal s Triangle: Cellular Automata and Attractors

Chapter 8 Pascal s Triangle: Cellular Automata and Attractors Mathematics is often defined as the science of space and number [...] It was not until the recent resonance of computers and mathematics that

### Artificial Life. Prof. Dr. Rolf Pfeifer Hanspeter Kunz Marion M. Weber Dale Thomas. Institut für Informatik der Universität Zürich

Artificial Life Prof. Dr. Rolf Pfeifer Hanspeter Kunz Marion M. Weber Dale Thomas Institut für Informatik der Universität Zürich 26. Juni 2001 Contents i Contents Chapter 1: Introduction 1.1 Historical

### Two-Dimensional Automata

Chapter 4 Two-Dimensional Automata The chessboard is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of Nature. Thomas Henry Huxley Two-dimensional

### Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform. Santa Fe Institute Working Paper (Submitted to Complex Systems)

Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations Melanie Mitchell 1, Peter T. Hraber 1, and James P. Crutcheld 2 Santa Fe Institute Working Paper 93-3-14 (Submitted to Complex

### Turing machines Finite automaton no storage Pushdown automaton storage is a stack What if we give the automaton a more flexible storage?

Turing machines Finite automaton no storage Pushdown automaton storage is a stack What if we give the automaton a more flexible storage? What is the most powerful of automata? In this lecture we will introduce

### Evolvability, Complexity and Scalability of Cellular Evolutionary and Developmental Systems

1 Evolvability, Complexity and Scalability of Cellular Evolutionary and Developmental Systems Stefano Nichele February 18, 2015 2 Outline Motivation / Introduction Research Questions Background Results

### Coupled Random Boolean Network Forming an Artificial Tissue

Coupled Random Boolean Network Forming an Artificial Tissue M. Villani, R. Serra, P.Ingrami, and S.A. Kauffman 2 DSSC, University of Modena and Reggio Emilia, via Allegri 9, I-4200 Reggio Emilia villani.marco@unimore.it,

### Computational Mechanics of the Two Dimensional BTW Model

Computational Mechanics of the Two Dimensional BTW Model Rajesh Kommu kommu@physics.ucdavis.edu June 8, 2010 Abstract Some aspects of computational mechanics in two dimensions are investigated in this

### ANDREW WUENSCHE Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico USA,

Classifying Cellular Automata Automatically: Finding Gliders, Filtering, and Relating Space-Time Patterns, Attractor Basins, and the Z Parameter ANDREW WUENSCHE Santa Fe Institute, 1399 Hyde Park Road,

### Properties and Behaviours of Fuzzy Cellular Automata

Properties and Behaviours of Fuzzy Cellular Automata Heather Betel Thesis submitted to the Faculty of Graduate and Postdoctoral Studies in partial fulfilment of the requirements for the PhD degree in Electrical

### Cellular Automata. Introduction

Cellular Automata 1983 Introduction It appears that the basic laws of physics relevant to everyday phenomena are now known. Yet there are many everyday natural systems whose complex structure and behavior

### Introduction to Dynamical Systems Basic Concepts of Dynamics

Introduction to Dynamical Systems Basic Concepts of Dynamics A dynamical system: Has a notion of state, which contains all the information upon which the dynamical system acts. A simple set of deterministic

### Theory of Computation

Theory of Computation Lecture #2 Sarmad Abbasi Virtual University Sarmad Abbasi (Virtual University) Theory of Computation 1 / 1 Lecture 2: Overview Recall some basic definitions from Automata Theory.

### Evolving Cellular Automata with Genetic Algorithms: A Review of Recent Work

Evolving Cellular Automata with Genetic Algorithms: A Review of Recent Work Melanie Mitchell Santa Fe Institute 1399 Hyde Park Road Santa Fe, NM 8751 mm@santafe.edu James P. Crutchfield 1 Santa Fe Institute

### Chapter 1. Introduction

Chapter 1 Introduction Symbolical artificial intelligence is a field of computer science that is highly related to quantum computation. At first glance, this statement appears to be a contradiction. However,

### Cell-based Model For GIS Generalization

Cell-based Model For GIS Generalization Bo Li, Graeme G. Wilkinson & Souheil Khaddaj School of Computing & Information Systems Kingston University Penrhyn Road, Kingston upon Thames Surrey, KT1 2EE UK

### A Phase Diagram for Elementary Cellular Automata

Complex Systems 7 (1993) 241-247 A Phase Diagram for Elementary Cellular Automata P.-M. Binder IIASA, A-2361 Laxenburg, A ustria Abstract. We construct a phase diagram for the possible dynamics of one-dimensional,

### Quantum Cellular Automata (QCA) Andrew Valesky

Quantum Cellular Automata (QCA) Andrew Valesky Presentation Schedule Quantum Observations (5 min) Cellular Automata (5 min) Quantum Cellular Automata (10 min) Pythagoras of Samos Pythagorean Theorem Pythagoreanism

### A Cellular Automata Approach to Population Modeling

A Cellular Automata Approach to Population Modeling Alexa M. Silverman March 31, 2009 Abstract 1 Introduction 1.1 Cellular automata This project provides an agent-based model of the effects of temperature

### COMPUTER SCIENCE. Computer Science. 15. Turing Machines. Computer Science. An Interdisciplinary Approach. Section 7.4.

COMPUTER SCIENCE S E D G E W I C K / W A Y N E PA R T I I : A L G O R I T H M S, M A C H I N E S, a n d T H E O R Y Computer Science Computer Science An Interdisciplinary Approach Section 7.4 ROBERT SEDGEWICK

### Classification of Random Boolean Networks

in Artificial Life VIII, Standish, Abbass, Bedau (eds)(mit Press) 2002. pp 1 8 1 Classification of Random Boolean Networks Carlos Gershenson, School of Cognitive and Computer Sciences University of Sussex

### Sorting Network Development Using Cellular Automata

Sorting Network Development Using Cellular Automata Michal Bidlo, Zdenek Vasicek, and Karel Slany Brno University of Technology, Faculty of Information Technology Božetěchova 2, 61266 Brno, Czech republic

### Power Spectral Analysis of Elementary Cellular Automata

Power Spectral Analysis o Elementary Cellular Automata Shigeru Ninagawa Division o Inormation and Computer Science, Kanazawa Institute o Technology, 7- Ohgigaoka, Nonoichi, Ishikawa 92-850, Japan Spectral

### Larger than Life: Digital Creatures in a Family of Two-Dimensional Cellular Automata

Discrete Mathematics and Theoretical Computer Science Proceedings AA (DM-CCG), 2001, 177 192 Larger than Life: Digital Creatures in a Family of Two-Dimensional Cellular Automata Kellie Michele Evans California

### TWO-DIMENSIONAL CELLULAR AUTOMATA RECOGNIZER EQUIPPED WITH A PATH VÉRONIQUE TERRIER. GREYC, Campus II, Université de Caen, F Caen Cedex, France

Journées Automates Cellulaires 2008 (Uzès), pp. 174-181 TWO-DIMENSIONAL CELLULAR AUTOMATA RECOGNIZER EQUIPPED WITH A PATH VÉRONIQUE TERRIER GREYC, Campus II, Université de Caen, F-14032 Caen Cedex, France

### Cellular Automata. Dr. Dylan McNamara people.uncw.edu/mcnamarad

Cellular Automata Dr. Dylan McNamara people.uncw.edu/mcnamarad Cellular Automata Cellular automata (CA) A regular grid model made of many automata whose states are finite and discrete ( nonlinearity) Their

### CS.15.A.Turing.Context

P R T I I : L G O R I T H M S, M C H I N E S, a n d T H E O R Y P R T I I : L G O R I T H M S, M C H I N E S, a n d T H E O R Y Computer Science 5. Turing Machines Context 5. Turing Machines Computer Science

### Cellular Automata as Models of Complexity

Cellular Automata as Models of Complexity Stephen Wolfram, Nature 311 (5985): 419 424, 1984 Natural systems from snowflakes to mollusc shells show a great diversity of complex patterns. The origins of

### Asynchronous random Boolean network model based on elementary cellular automata

Asynchronous random Boolean networ model based on elementary cellular automata Mihaela T. Matache* Jac Heidel Department of Mathematics University of Nebrasa at Omaha Omaha, NE 6882-243, USA *dmatache@mail.unomaha.edu

Table of Contents General Introduction... xi PART 1. THE STRUCTURE OF THE GEOGRAPHIC SPACE... 1 Part 1. Introduction... 3 Chapter 1. Structure and System Concepts... 5 1.1. The notion of structure... 5

### Cellular automata as emergent systems and models of physical behavior

Cellular automata as emergent systems and models of physical behavior Jason Merritt December 19, 2012 Abstract Cellular automata provide a basic model for complex systems generated by simplistic rulesets.

### Announcements. Problem Set 6 due next Monday, February 25, at 12:50PM. Midterm graded, will be returned at end of lecture.

Turing Machines Hello Hello Condensed Slide Slide Readers! Readers! This This lecture lecture is is almost almost entirely entirely animations that that show show how how each each Turing Turing machine

### cse303 ELEMENTS OF THE THEORY OF COMPUTATION Professor Anita Wasilewska

cse303 ELEMENTS OF THE THEORY OF COMPUTATION Professor Anita Wasilewska LECTURE 13 CHAPTER 4 TURING MACHINES 1. The definition of Turing machine 2. Computing with Turing machines 3. Extensions of Turing

### Stochastic cellular automata model for wildland fire spread dynamics

Journal of Physics: Conference Series Stochastic cellular automata model for wildland fire spread dynamics To cite this article: Rodolfo Maduro Almeida and Elbert E N Macau 2011 J. Phys.: Conf. Ser. 285

### Kolmogorov structure functions for automatic complexity

Kolmogorov structure functions for automatic complexity Bjørn Kjos-Hanssen June 16, 2015 Varieties of Algorithmic Information, University of Heidelberg Internationales Wissenschaftssentrum History 1936:

### Cellular Automata for Modeling Spatial Systems

Chapter 12 Cellular Automata for Modeling Spatial Systems 12.1. The concept of the automaton and its modeling The evolution of computer power in the past few years has facilitated the emergence of simulation

### Variations on Conway s Game of Life and Other Cellular Automata. David Hua and Martin Pelikan

Variations on Conway s Game of Life and Other Cellular Automata David Hua and Martin Pelikan Research Paper Presented to the Students and Teachers as Research Scientists Program at the University of Missouri-St.

### arxiv: v1 [cond-mat.stat-mech] 3 Jul 2014

Conway s game of life is a near-critical metastable state in the multiverse of cellular automata Sandro M. Reia 1 and Osame Kinouchi 1 arxiv:1407.1006v1 [cond-mat.stat-mech] 3 Jul 2014 1 Faculdade de Filosofia,

### Principles of Artificial Intelligence Fall 2005 Handout #7 Perceptrons

Principles of Artificial Intelligence Fall 2005 Handout #7 Perceptrons Vasant Honavar Artificial Intelligence Research Laboratory Department of Computer Science 226 Atanasoff Hall Iowa State University

### CSE 20. Lecture 4: Introduction to Boolean algebra. CSE 20: Lecture4

CSE 20 Lecture 4: Introduction to Boolean algebra Reminder First quiz will be on Friday (17th January) in class. It is a paper quiz. Syllabus is all that has been done till Wednesday. If you want you may

### Elementary cellular automata

Cellular Automata Cellular automata (CA) models epitomize the idea that simple rules can generate complex pa8erns. A CA consists of an array of cells each with an integer state. On each?me step a local

### Complex Systems Theory

Complex Systems Theory 1988 Some approaches to the study of complex systems are outlined. They are encompassed by an emerging field of science concerned with the general analysis of complexity. Throughout

### arxiv: v4 [nlin.cg] 5 Apr 2018

Algorithmic Information Dynamics of Persistent Patterns and Colliding Particles in the Game of Life Hector Zenil 1,2,3,4, Narsis A. Kiani 1,2,3,4, Jesper Tegnér 2,3,5 arxiv:1802.07181v4 [nlin.cg] 5 Apr

### Theory of Computation Lecture 1. Dr. Nahla Belal

Theory of Computation Lecture 1 Dr. Nahla Belal Book The primary textbook is: Introduction to the Theory of Computation by Michael Sipser. Grading 10%: Weekly Homework. 30%: Two quizzes and one exam. 20%:

### Emergence of Glider-like Structures in a Modular Robotic System

Emergence of Glider-like Structures in a Modular Robotic System Joseph T. Lizier 1,2, Mikhail Prokopenko 1, Ivan Tanev 3 and Albert Y. Zomaya 2 1 CSIRO Information and Communications Technology Centre,

### Introduction. Büchi Automata and Model Checking. Outline. Büchi Automata. The simplest computation model for infinite behaviors is the

Introduction Büchi Automata and Model Checking Yih-Kuen Tsay Department of Information Management National Taiwan University FLOLAC 2009 The simplest computation model for finite behaviors is the finite

### Introduction to Random Boolean Networks

Introduction to Random Boolean Networks Carlos Gershenson Centrum Leo Apostel, Vrije Universiteit Brussel. Krijgskundestraat 33 B-1160 Brussel, Belgium cgershen@vub.ac.be http://homepages.vub.ac.be/ cgershen/rbn/tut

### 1 Two-Way Deterministic Finite Automata

1 Two-Way Deterministic Finite Automata 1.1 Introduction Hing Leung 1 In 1943, McCulloch and Pitts [4] published a pioneering work on a model for studying the behavior of the nervous systems. Following

### Introduction to the Theory of Computation. Automata 1VO + 1PS. Lecturer: Dr. Ana Sokolova.

Introduction to the Theory of Computation Automata 1VO + 1PS Lecturer: Dr. Ana Sokolova http://cs.uni-salzburg.at/~anas/ Setup and Dates Lectures Tuesday 10:45 pm - 12:15 pm Instructions Tuesday 12:30

### Complex Systems Theory and Evolution

Complex Systems Theory and Evolution Melanie Mitchell and Mark Newman Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 In Encyclopedia of Evolution (M. Pagel, editor), New York: Oxford University

### Turing machines COMS Ashley Montanaro 21 March Department of Computer Science, University of Bristol Bristol, UK

COMS11700 Turing machines Department of Computer Science, University of Bristol Bristol, UK 21 March 2014 COMS11700: Turing machines Slide 1/15 Introduction We have seen two models of computation: finite

### Lyapunov exponents in random Boolean networks

Physica A 284 (2000) 33 45 www.elsevier.com/locate/physa Lyapunov exponents in random Boolean networks Bartolo Luque a;, Ricard V. Sole b;c a Centro de Astrobiolog a (CAB), Ciencias del Espacio, INTA,

### Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components

Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components John Z. Sun Massachusetts Institute of Technology September 21, 2011 Outline Automata Theory Error in Automata Controlling

### Computing in Spiral Rule Reaction-Diffusion Hexagonal Cellular Automaton

Computing in Spiral Rule Reaction-Diffusion Hexagonal Cellular Automaton Andrew Adamatzky Faculty of Computing, Engineering, and Mathematical Sciences, University of the West of England, Bristol BS16 1QY,

### The Structure of the Elementary Cellular Automata Rule Space

The Structure of the Elementary Cellular Automata Rule Space Wentian Li Santa Fe Institute, 1120 Canyon Road, Santa Fe, NM 87501, USA Norman Packard Center for Complex Systems Research, Physics Department,

### The Power of Extra Analog Neuron. Institute of Computer Science Academy of Sciences of the Czech Republic

The Power of Extra Analog Neuron Jiří Šíma Institute of Computer Science Academy of Sciences of the Czech Republic (Artificial) Neural Networks (NNs) 1. mathematical models of biological neural networks

### Genetic Algorithm for Solving the Economic Load Dispatch

International Journal of Electronic and Electrical Engineering. ISSN 0974-2174, Volume 7, Number 5 (2014), pp. 523-528 International Research Publication House http://www.irphouse.com Genetic Algorithm

### Unbounded hardware is equivalent to deterministic Turing machines

Carnegie Mellon University Research Showcase @ CMU Computer Science Department School of Computer Science 1981 Unbounded hardware is equivalent to deterministic Turing machines Chazelle Carnegie Mellon

### (Feed-Forward) Neural Networks Dr. Hajira Jabeen, Prof. Jens Lehmann

(Feed-Forward) Neural Networks 2016-12-06 Dr. Hajira Jabeen, Prof. Jens Lehmann Outline In the previous lectures we have learned about tensors and factorization methods. RESCAL is a bilinear model for

### LOCAL NAVIGATION. Dynamic adaptation of global plan to local conditions A.K.A. local collision avoidance and pedestrian models

LOCAL NAVIGATION 1 LOCAL NAVIGATION Dynamic adaptation of global plan to local conditions A.K.A. local collision avoidance and pedestrian models 2 LOCAL NAVIGATION Why do it? Could we use global motion

### How to Pop a Deep PDA Matters

How to Pop a Deep PDA Matters Peter Leupold Department of Mathematics, Faculty of Science Kyoto Sangyo University Kyoto 603-8555, Japan email:leupold@cc.kyoto-su.ac.jp Abstract Deep PDA are push-down automata

### Phase Transitions in Possible Dynamics of Cellular and Graph Automata Models of Sparsely Interconnected Multi-Agent Systems

Phase Transitions in Possible Dynamics of Cellular and Graph Automata Models of Sparsely Interconnected Multi-Agent Systems Predrag T. Tošić School of EECS, Washington State University Pullman, Washington,

### From Greek philosophers to circuits: An introduction to boolean logic. COS 116, Spring 2011 Sanjeev Arora

From Greek philosophers to circuits: An introduction to boolean logic. COS 116, Spring 2011 Sanjeev Arora Midterm One week from today in class Mar 10 Covers lectures, labs, homework, readings to date You

### Discovery of the Boolean Functions to the Best Density-Classification Rules Using Gene Expression Programming

Discovery of the Boolean Functions to the Best Density-Classification Rules Using Gene Expression Programming Cândida Ferreira Gepsoft, 37 The Ridings, Bristol BS13 8NU, UK candidaf@gepsoft.com http://www.gepsoft.com

### A Cellular Automata Approach to Population Modeling

A Cellular Automata Approach to Population Modeling Alexa M. Silverman February 24, 2009 Abstract 1 Introduction 1.1 Cellular automata This project provides an agent-based model of the effects of temperature

### A Brief History of Cellular Automata

A Brief History of Cellular Automata PALASH SARKAR Indian Statistical Institute Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention

### Q = Set of states, IE661: Scheduling Theory (Fall 2003) Primer to Complexity Theory Satyaki Ghosh Dastidar

IE661: Scheduling Theory (Fall 2003) Primer to Complexity Theory Satyaki Ghosh Dastidar Turing Machine A Turing machine is an abstract representation of a computing device. It consists of a read/write

### arxiv: v2 [cs.fl] 21 Sep 2016

A A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications Kamalika Bhattacharjee, Indian Institute of Engineering Science and Technology, Shibpur Nazma Naskar, Seacom Engineering

### Introduction to Informatics

Introduction to Informatics Two statisticians were flying from L.A. to New York. About an hour into the flight, the pilot announced, "Unfortunately, we have lost an engine, but don't worry: There are three

### Cellular Automata Evolution for Pattern Recognition

Cellular Automata Evolution for Pattern Recognition Pradipta Maji Center for Soft Computing Research Indian Statistical Institute, Kolkata, 700 108, INDIA Under the supervision of Prof. P Pal Chaudhuri

### PAC-learning, VC Dimension and Margin-based Bounds

More details: General: http://www.learning-with-kernels.org/ Example of more complex bounds: http://www.research.ibm.com/people/t/tzhang/papers/jmlr02_cover.ps.gz PAC-learning, VC Dimension and Margin-based

### FUNDAMENTALS OF NATURAL COMPUTING Basic Concepts, Algorithms, and Applications

FUNDAMENTALS OF NATURAL COMPUTING Basic Concepts, Algorithms, and Applications Leandro Nunes de Castro Catholic University of Santos (UniSantos) Brazil Chapman &. Hall/CRC Taylor &. Francis Croup Boca

### 9. PSPACE 9. PSPACE. PSPACE complexity class quantified satisfiability planning problem PSPACE-complete

Geography game Geography. Alice names capital city c of country she is in. Bob names a capital city c' that starts with the letter on which c ends. Alice and Bob repeat this game until one player is unable

### Lecture 7: Cellular Automata Modelling: Principles of Cell Space Simulation

SCHOOL OF GEOGRAPHY Lecture 7: Cellular Automata Modelling: Principles of Cell Space Simulation Outline Types of Urban Models Again The Cellular Automata Approach: Urban Growth and Complexity Theory The