AN INTRODUCTION TO SEQUENTIAL DYNAMICAL SYSTEMS
CONTENTS WHAT IS A SEQUENTIAL DYNAMICAL SYSTEM? SEQUENTIAL DYNAMICAL SYSTEMS: A FIRST LOOK MOTIVATION APPLICATION PARADIGMS TRANSIMS TASK SCHEDULING AND TRANSPORT COMPUTATIONS SDS: CHARACTERISTICS AND RESEARCH QUESTIONS UPDATE ORDER DEPENDENCIES PHASE-SPACE STRUCTURE COMPUTATIONAL AND ALGORITHMIC ASPECTS SUMMARY PROBLEMS ANSWERS TO PROBLEMS A COMPARATIVE STUDY CELLULAR AUTOMATA BACKGROUND STRUCTURE OF CELLULAR AUTOMATA ELEMENTARY CA RULES RANDOM BOOLEAN NETWORKS FINITE-STATE MACHINES (FSMS) GRAPHS, GROUPS, AND DYNAMICAL SYSTEMS GRAPHS SIMPLE GRAPHS AND COMBINATORIAL GRAPHS THE ADJACENCY MATRIX OF A GRAPH ACYCLIC ORIENTATIONS THE UPDATE GRAPH GRAPHS, PERMUTATIONS, AND ACYCLIC ORIENTATIONS GROUP ACTIONS GROUPS ACTING ON GRAPHS GROUPS ACTING ON ACYCLIC ORIENTATIONS DYNAMICAL SYSTEMS CLASSICAL CONTINUOUS DYNAMICAL SYSTEMS CLASSICAL DISCRETE DYNAMICAL SYSTEMS LINEAR AND NONLINEAR SYSTEMS SEQUENTIAL DYNAMICAL SYSTEMS OVER PERMUTATIONS DE?NITIONS AND TERMINOLOGY STATES, VERTEX FUNCTIONS, AND LOCAL MAPS SEQUENTIAL DYNAMICAL SYSTEMS THE PHASE SPACE OF AN SDS SDS ANALYSIS — A NOTE ON APPROACH AND COMMENTS BASIC PROPERTIES DECOMPOSITION OF SDS FIXED POINTS REVERSIBLE DYNAMICS AND INVERTIBILITY INVERTIBLE SDS WITH SYMMETRIC FUNCTIONS OVER FINITE FIELDS EQUIVALENCE FUNCTIONAL EQUIVALENCE OF SDS COMPUTING EQUIVALENCE CLASSES DYNAMICAL EQUIVALENCE ENUMERATION OF DYNAMICALLY NONEQUIVALENT SDS SDS MORPHISMS AND REDUCTIONS COVERING MAPS PROPERTIES OF COVERING MAPS REDUCTION OF SDS DYNAMICAL EQUIVALENCE REVISITED CONSTRUCTION OF COVERING MAPS COVERING MAPS OVER QN ? COVERING MAPS OVER CIRCN PHASE-SPACE STRUCTURE OF SDS AND SPECIAL SYSTEMS FIXED POINTS FOR SDS OVER CIRCN AND CIRCN,R FIXED-POINT COMPUTATIONS FOR GENERAL GRAPHS THRESHOLD SDS SDS OVER SPECIAL GRAPH CLASSES SDS OVER THE COMPLETE GRAPH SDS OVER THE CIRCLE GRAPH SDS OVER THE LINE GRAPH SDS OVER THE STAR GRAPH SDS INDUCED BY SPECIAL FUNCTION CLASSES SDS INDUCED BY (NORK)K AND (NANDK)K SDS INDUCED BY (NORK + NANDK)K GRAPHS, GROUPS, AND SDS SDS WITH ORDER-INDEPENDENT PERIODIC POINTS PRELIMINARIES THE GROUP G(Y, FY ) THE CLASS OF W-INDEPENDENT SDS THE CLASS OF W-INDEPENDENT SDS OVER CIRCN THE GROUPS G(CIRC4, FCIRC4) A PRESENTATION OF S35 COMBINATORICS OF SEQUENTIAL DYNAMICAL SYSTEMS OVER WORDS COMBINATORICS OF SDS OVER WORDS DEPENDENCY GRAPHS AUTOMORPHISMS WORDS THE MAPPING OY A NORMAL FORM RESULT THE BIJECTION COMBINATORICS OF SDS OVER WORDS II GENERALIZED EQUIVALENCES THE BIJECTION (P1) EQUIVALENCE (P2) PHASE-SPACE RELATIONS OUTLOOK STOCHASTIC SDS RANDOM UPDATE ORDER SDS OVER RANDOM GRAPHS GENE-REGULATORY NETWORKS INTRODUCTION THE TRYPTOPHAN-OPERON EVOLUTIONARY OPTIMIZATION OF SDS-SCHEDULES NEUTRAL NETWORKS AND PHENOTYPES OF RNA AND SDS DISTANCES A REPLICATION-DELETION SCHEME EVOLUTION OF SDS-SCHEDULES PSEUDO-CODES DISCRETE DERIVATIVES REAL-VALUED AND CONTINUOUS SDS L-LOCAL SDS ROUTING WEIGHTS PROTOCOLS AS LOCAL MAPS REFERENCES