The Co‐evolution of cooperation and complexity in a multi‐player,local‐interaction prisoners' dilemma

Agents located on a 20 × 20 toroidal lattice play a Prisoners' Dilemma game with their Moore neighbors, adopting policies of cooperation and defection that depend only on their own action and the number of cooperators in the neighborhood in the last round of the game. These policies (“characters”) are encoded in 19‐bit strings, which are subjected to evolution according to a genetic algorithm, with selection based on the cumulative scores of the agents in the neighborhood over 10 rounds of the basic game. Simulations examine the evolution of the population of characters over 1000 generations. Even with selection disabled, the genetic algorithm organizes the population into a small number of surviving characters clustered in spatially homogeneous regions. Selection for fitness rapidly achieves uniform cooperation. The characters evolved cooperate on the initial play, continue to cooperate when five or more of their neighbors cooperate, tend to defect defensively when they have cooperated and most of their neighbors have defected, and switch back to cooperation when five or more neighbors cooperate. When selection operates at the level of the whole society, however, the diversity of the population rapidly collapses, a single character predominates, and the cooperativeness of the dominating character is a matter of chance, so that there is no systematic tendency to evolve cooperation. © 2001 John Wiley & Sons, Inc.     

Agent‐based computational models and generative social science

This article argues that the agent‐based computational model permits a distinctive approach to social science for which the term “generative” is suitable. In defending this terminology, features distinguishing the approach from both “inductive” and “deductive” science are given. Then, the following specific contributions to social science are discussed: The agent‐based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent‐based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent‐based (“bottom up”) models. The agent‐based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent‐based modeling offers powerful new forms of hybrid theoretical‐computational work; these are particularly relevant to the study of non‐equilibrium systems. The agent‐based approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent‐based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. © 1999 John Wiley & Sons, Inc.     

Complexity and T ‐invariant of Abelian and Milnor groups,and complexity of 3‐manifolds

We investigate the notion of complexity for finitely presented groups and the related notion of complexity for three‐dimensional manifolds. We give two‐sided estimates on the complexity of all the Milnor groups (the finite groups with free action on S³), as well as for all finite Abelian groups. The ideas developed in the process also allow to construct two‐sided bounds for the values of the so‐called T ‐invariant (introduced by Delzant) for the above groups, and to estimate from below the value of T ‐invariant for an arbitrary finitely presented group. Using the results of this paper and of previous ones, we then describe an infinite collection of Seifert threemanifolds for which we can asymptotically determine the complexity in an exact fashion up to linear functions. We also provide similar estimates for the complexity of several infinite families of Milnor groups. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Toward scale‐free like behavior under increasing cognitive load

To understand how cognition and response selection processes might emerge from dynamic brain systems, we analyzed reaction times during the performance of both a working memory task and a choice reaction time task at different levels of “cognitive load.” Our findings suggest a continuous transition—tuned by load—from random behavior toward scale‐free like behavior as an expanding connectivity process in a network poised near a critical point. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Signal‐regulated systems and networks

The article presents the use of signal regulatory networks (SRNs), a biologically inspired model based on gene regulatory networks. SRNs are a way of understanding a class of self‐organizing IT systems, signal‐regulated systems (SRSs). This article builds on the theory of SRSs and introduces some formalisms to clarify the discussion. An exemplar SRS that can be evaluated using SRNs is presented. Finally, an implementation of an adaptive and robust solution, built on a theory of SRSs and analyzed as a SRN, is shown to be plausible. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

This paper is devoted to investigate synchronization and antisynchronization of N‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means of the direct design method, the appropriate controllers are designed to transform the fractional‐order error dynamical system into a nonlinear system with antisymmetric structure. Thus, by using the recently established result for the Caputo fractional derivative of a quadratic function and a fractional‐order extension of the Lyapunov direct method, several stability criteria are derived to ensure the occurrence of synchronization and antisynchronization among N‐coupled fractional‐order complex chaotic systems. Moreover, numerical simulations are performed to illustrate the effectiveness of the proposed design.     

Numerical solution of parameter‐dependent linear systems

We are interested in the numerical solution of the complex large linear system, (σ²A+σB+C)x=f(σ), for many, possibly a few hundreds, values of the complex parameter σ in a wide range. We assume that A, B and C are large, sparse, symmetric matrices, as is the case in several application problems. In particular, we focus on the following structured right‐hand side, f(σ)=FΦ(σ), where F is a (tall) rectangular matrix whose entries are independent of σ. We propose to approximate the solution x=x(σ) by means of a projection onto a single vector subspace, and a subsequent solution of the reduced dimension problem, for all values of interest of the parameter σ. Numerical experiments report the effectiveness of our approach on real application problems. Copyright © 2005 John Wiley & Sons, Ltd.     

|T |+‐resplendent models and the Lascar group

In this paper we show that in every |T |⁺‐resplendent model N , for every A ? N such that |A | ≤ |T |, the group Autf(N/A ) of strong automorphisms is the least very normal subgroup of the group Aut(N/A ) and the quotient Aut(N/A )/Autf(N/A ) is the Lascar group over A . Then we generalize this result to every |T |⁺‐saturated and strongly |T |⁺‐homogeneous model. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reliability,signature, and relative quality functions of systems under time‐homogeneous load‐sharing models

For a coherent binary system made of binary components, we consider the assumption that the components' lifetimes are distributed according to a time‐homogeneous, load‐sharing model. Such models are characterized in terms of the so‐called multivariate conditional hazard rate functions. We aim to point out some related properties of the notions of signature, relative quality functions, and reliability functions. On this purpose, we preliminarily collect all the necessary background and review some related literature. This paper concludes with a discussion, also containing some hints for future work.     

An information‐theoretic primer on complexity,self‐organization,and emergence

Complex Systems Science aims to understand concepts like complexity, self‐organization, emergence and adaptation, among others. The inherent fuzziness in complex systems definitions is complicated by the unclear relation among these central processes: does self‐organisation emerge or does it set the preconditions for emergence? Does complexity arise by adaptation or is complexity necessary for adaptation to arise? The inevitable consequence of the current impasse is miscommunication among scientists within and across disciplines. We propose a set of concepts, together with their possible information‐theoretic interpretations, which can be used to facilitate the Complex Systems Science discourse. Our hope is that the suggested information‐theoretic baseline may promote consistent communications among practitioners, and provide new insights into the field. Published 2008 Wiley Periodicals, Inc. Complexity, 2009     

Modulation theory solution for nonlinearly resonant,fifth‐order Korteweg–de Vries,nonclassical, traveling dispersive shock waves

A new class of resonant dispersive shock waves was recently identified as solutions of the Kawahara equation— a Korteweg–de Vries (KdV) type nonlinear wave equation with third‐ and fifth‐order spatial derivatives— in the regime of nonconvex, linear dispersion. Linear resonance resulting from the third‐ and fifth‐order terms in the Kawahara equation was identified as the key ingredient for nonclassical dispersive shock wave solutions. Here, nonlinear wave (Whitham) modulation theory is used to construct approximate nonclassical traveling dispersive shock wave (TDSW) solutions of the fifth‐ order KdV equation without the third derivative term, hence without any linear resonance. A self‐similar, simple wave modulation solution of the fifth order, weakly nonlinear KdV–Whitham equations is obtained that matches a constant to a heteroclinic traveling wave via a partial dispersive shock wave so that the TDSW is interpreted as a nonlinear resonance. The modulation solution is compared with full numerical solutions, exhibiting excellent agreement. The TDSW is shown to be modulationally stable in the presence of sufficiently small third‐order dispersion. The Kawahara–Whitham modulation equations transition from hyperbolic to elliptic type for sufficiently large third‐order dispersion, which provides a possible route for the TDSW to exhibit modulational instability.     

Sturmian morphisms,the braid group <Emphasis Type="Italic">B</Emphasis><Subscript>4</Subscript>, Christoffel words and bases of <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript>

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F ₂) of automorphisms of the rank two free group F ₂ and show that it can be realized as a monoid in the group B ₄ of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F ₂ lifting any given basis of the free abelian group Z ². We further give an algorithm allowing to decide whether two elements of F ₂ form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes. Mathematics Subject Classification (2000) 05E99, 20E05, 20F28, 20F36, 20M05, 37B10, 68R15     

Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

This article investigates the stabilization and control problems for a general active fault‐tolerant control system (AFTCS) in a stochastic framework. The novelty of the research lies in utilizing uncertain nonhomogeneous Markovian structures to take account for the imperfect fault detection and diagnosis (FDD) algorithms of the AFTCS. The underlying AFTCS is supposed to be modeled by two random processes of Markov type; one characterizing the system fault process and the other describing the FDD process. It is assumed that the FDD algorithm is imperfect and provides inaccurate Markovian parameters for the FDD process. Specifically, it provides uncertain transition rates (TRs); the TRs that lie in an interval without any particular structures. This framework is more consistent with real‐world applications to accommodate different types of faults. It is more general than the previously developed AFTCSs because of eliminating the need for an accurate estimation of the fault process. To solve the stabilizability and the controller design problems of this AFTCS, the whole system is viewed as an uncertain nonhomogeneous Markovian jump linear system (NHMJLS) with time‐varying and uncertain specifications. Based on the multiple and stochastic Lyapunov function for the NHMJLS, first a sufficient condition is obtained to analyze the system stabilizability and then, the controller gains are synthesized. Unlike the previous fault‐tolerant controllers, the proposed robust controller only needs to access the FDD process, besides it is easily obtainable through the existing optimization techniques. It is successfully tested on a practical inverted pendulum controlled by a fault‐prone DC motor. © 2016 Wiley Periodicals, Inc. Complexity 21: 318–329, 2016     

Evaluating an hepatic enzyme induction mechanism through coarse‐ and fine‐grained measurements of an in silico liver

Results from simulation experiments falsified the hypothesis that a uniform distribution of simulated drug passing through an in silico liver (ISL) will produce a uniform extent of enzyme induction (EI). Wet‐lab EI experiments, as formulated, are infeasible. The simulated EI is intended to have a hepatic counterpart. The ISL is synthetic, physiologically based, fine‐grained, and multi‐agent. It has been validated against in situ drug disposition data. We discuss methodological considerations regarding the phenomenal manifold, multi‐level observation, and manipulation of synthetic models and their referents. Interestingly, a lower probability of metabolism caused higher EI and, counter‐intuitively, more extraction. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

Positive computational modelling of the dynamics of active and inert biomass with extracellular polymeric substances

Departing from a complex system of nonlinear partial differential equations that models the growth dynamics of biological films, we provide a finite-difference model to approximate its solutions. The variables of interest are measured in absolute scales, whence the need of preserving the positivity of the solutions is a mathematical constraint that must be observed. In this work, we provide a numerical discretization of our mathematical model which is capable of preserving the non-negative character of approximations under suitable conditions on the model and computational parameters. As opposed to the nonlinear model which motivates this report, our numerical technique is a linear method which, under suitable circumstances, may be represented by an M-matrix. The fact that our method is a positivity-preserving scheme is established using the inverse-positive properties of these matrices. Computer simulations corroborate the validity of the theoretical findings.     

Groups,group actions and fields definable in first‐order topological structures

Given a group (G, ·), G?M^m, definable in a first‐order structure $\mathcal {M}=(M,\ldots )Given a group (G, ·), G?M^m, definable in a first‐order structure $\mathcal {M}=(M,\ldots )$ equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V?G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from M^m. Likewise we topologize transitive group actions and fields definable in $\mathcal {M}$. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest.     

Group theory and p‐adic valued models of swarm behaviour

The swarm behaviour can be controlled by different localizations of attractants (food pieces) and repellents (dangerous places), which, respectively, attract and repel the swarm propagation. If we assume that at each time step, the swarm can find out not more than p ?1 attractants ( ), then the swarm behaviour can be coded by p ‐adic integers, ie, by the numbers of the ring Z _p . Each swarm propagation has the following 2 stages: (1) the discover of localizations of neighbour attractants and repellents and (2) the logistical optimization of the road system connecting all the reachable attractants and avoiding all the neighbour repellents. In the meanwhile, at the discovering stage, the swarm builds some direct roads and, at the logistical stage, the transporting network of the swarm gets loops (circles) and it permanently changes. So, at the first stage, the behaviour can be expressed by some linear p ‐adic valued strings. At the second stage, it is expressed by non‐linear modifications of p ‐adic valued strings. The second stage cannot be described by conventional algebraic tools; therefore, I have introduced the so‐called non‐linear group theory for describing both stages in the swarm propagation.     

Merging bottom‐up and top‐down approaches to study prostate cancer biology

The sequencing of the human genome has opened new areas of possibility for understanding diseases such as cancers. Sequencing has given us the necessary building blocks for identifying the components of important signaling networks, whereas new tools such as automated gene sequencing, cDNA microassays, and tissue arrays are beginning to produce a torrent of data about these components. As we determine the components of these signaling networks, we can learn how the components are altered by transformations in the cell DNA. However, this torrent of information has also imposed a barrier: It is often unclear how to organize and use the data in ways that tell us more about the signaling networks. As with building blocks in a box, many of the components are still to be assembled into coherent structures. © 2002 Wiley Periodicals, Inc.     

The existence of disjoint (hooked) near‐Rosa sequences and applications

We show that the necessary conditions are sufficient for the existence of two disjoint near (hooked) Rosa sequences, with all admissible orders $n\ge 6$ and all possible defects. Further, we apply this result for the existence of new types of cyclic and simple GDDs.     

Alternating groups and flag‐transitive 2‐(v,k, 4) symmetric designs

In this article, we study the classification of flag‐transitive, point‐primitive 2‐ (v, k, 4) symmetric designs. We prove that if the socle of the automorphism group G of a flag‐transitive, point‐primitive nontrivial 2‐ (v, k, 4) symmetric design ?? is an alternating group A_n for n≥5, then (v, k) = (15, 8) and ?? is one of the following: (i) The points of ?? are those of the projective space PG(3, 2) and the blocks are the complements of the planes of PG(3, 2), G = A₇ or A₈, and the stabilizer G_x of a point x of ?? is L₃(2) or AGL₃(2), respectively. (ii) The points of ?? are the edges of the complete graph K₆ and the blocks are the complete bipartite subgraphs K_{2, 4} of K₆, G = A₆ or S₆, and G_x = S₄ or S₄ × Z₂, respectively. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:475‐483, 2011