Decision Making

The following sections are included:

• PREFACE

• Workshop Speakers

• CONTENTS

This program brings together researchers from disparate disciplines to work on a complex research problem that defies confinement within any single discipline. Consequently, not only are new and rewarding solutions sought and obtained for a problem of importance to society and the Army, that is, the human dimension of complex networks, but, in addition, collaborations are established that would not otherwise have formed given the traditional disciplinary compartmentalization of research. This program develops the basic research foundation of a science of networks supporting the linkage between the physical and human (cognitive and social) domains as they relate to human decision making. The strategy is to extend the recent methods of non-equilibrium statistical physics to non-stationary, renewal stochastic processes that appear to be characteristic of the interactions among nodes in complex networks. We also pursue understanding of the phenomenon of synchronization, whose mathematical formulation has recently provided insight into how complex networks reach accommodation and cooperation. The theoretical analyses of complex networks, although mathematically rigorous, often elude analytic solutions and require computer simulation and computation to analyze the underlying dynamic process.

In the course of the past 60 years, the brain — and in lockstep with it, Cognition — became liberated from confinement to the skull: the liberation I am referring to consists of the transition from being a distinct physical entity in indirect, mediated contact with the rest of the physical world to being an integral component of it, in a manner envisioned by the Extended Mind Hypothesis of Clark & Chalmers: in current terminology, merging brain, body and world into ONE complex system. As background, I briefly review the progression of steps that culminated in the Extended Mind Hypothesis, and allude to the controversies it raised. Assuming the validity of this hypothesis, I will explore the issues that arise from viewing brain, body and world as ONE complex dynamical system. This will lead me to suggest that interrelations between complex system and fractal dynamics enable the seamless integration of human capabilities and the material world.

To perceive, and more particularly to sense, is conditional upon the state of uncertainty of the perceiving system. This idea is developed from its philosophical base, to the equations that encode it, and through to the experimental data that provide its support. Much of the paper constitutes a review of research conducted over past years, but viewed now with some perspective. This uncertainty concept represents a kind of thermodynamic principle, which tells us how various sensory phenomena will occur, but does not provide a physiological mechanism. Hence, for example, the mathematical structure of the Weber-Fechner law will emerge, but it remains for mechanisms such as, perhaps, neural networks, to define exactly how the law will be implemented physiologically. The latter part of the paper deals with the attempt to link sensation, for one special case, to the physical entropy of the received signal.

The unique dynamical features of the critical state can endow the brain with properties which are fundamental for adaptive behavior. This proposal, put forward with Per Bak several years ago, is now supported by a wide body of empirical evidence at different scales demonstrating that the spatiotemporal brain dynamics exhibits key signatures of critical dynamics previously recognized in other complex systems. The rationale behind this program is discussed in these notes, followed by an account of the most recent results, together with a discussion of the physiological significance of these ideas.

The Bak–Sneppen model demonstrates that extremal selection of poorly adapted variables, which are interconnected in a system, can lead to a highly correlated state that is both, well-adapted and responsive. We have developed a solvable version of the model that provides detailed insights in how memory is acquired in the system. We have employed the Bak–Sneppen dynamics to design a highly efficient optimization heuristic, called "Extremal Optimization" (EO), to find low-energy or low-cost configurations for many combinatorial problems in physics and computer science. Analysis of the local search dynamics induced by EO reveals that the configuration space is traversed most efficiently at the "edge of ergodicity" which effectively exploits the long-range memory encapsulated in the strongly correlated state of the variables. There, the dynamics of local search possesses a generic critical point under the variation of its sole parameter, separating phases of too greedy (non-ergodic, jammed) and too random (ergodic, diffusive) exploration. Analytic comparison with other local search methods, such as a fixed temperature Metropolis algorithm, within this model suggests that the existence of the critical point is the essential distinction leading to the optimal performance of the extremal optimization heuristic.

We study random walks on networks, either regular or complex, and we show that the observation of a single walker is not quite adequate to properly determine the network efficiency, which is expected to increase with the network topological complexity. In fact, the time complexity of a single walker is compatible with the two opposite conditions, of regular topology, with minimum efficiency, and of scale-free topology, with rich nodes that are linked to all the other nodes of the network, thereby generating the condition of maximum efficiency. The observation of the motion of a large number of walkers leads to unambiguous results, with the former limiting condition yielding equilibrium with a time scale proportional to the number of nodes, N, and the latter limiting condition corresponding to an almost instantaneous transition to equilibrium, more precisely with a time scale proportional to log N.

We study a model of cooperating units, each of which is a stochastic clock, and we show that when the cooperation strength is critical the model yields coherence and complexity at the same time. We conjecture concerning the relevance of this model to understanding brain dynamics.

In this Chapter we study a set of cooperating neurons generating quakes with the same size distribution as the neuronal avalanches in mature cultured networks, recently revealed by the experimental observation. We prove that in addition to this form of complexity this model yields a form of phase transition generating also temporal complexity. This means that the distance from two consecutive quakes fits the prescription of a Mittag-Leffler (ML) function renewal theory. There exists a critical value of the cooperation parameter at which this description applies to the whole time regime. By increasing the cooperation parameter the ML theory breaks down and the sequence of quakes tend to become periodic and the quakes have the same intensity. We make the conjecture that the recently discovered principle of complexity matching may be conveniently applied to the neuro-physiological processes that are properly described by this model.

We describe herein a multidisciplinary research, as it developes and applies concepts of the theory of complexity, in turn stemming from recent advancements of statistical physics, onto cognitive neuroscience. We discuss (define) complexity, and how the human brain is a paradigm of it. We discuss how the hypothesis of brain activity dynamically behaving as a critical system is taking momentum in literature, then we focus on a feature of critical systems (hence of the brain), which is the intermittent passage between metastable states, marked by events, locally resetting the memory, but giving rise to correlation functions with infinite correlation times. The events, extracted from multi-channel ElectroEncephaloGrams, mark (are interpreted as) a birth/death process of cooperation, namely of system elements being recruited into collective states. Finally we discuss a recently discovered form of control (in the form of a new Linear Response Theory), that allows an optimized information transmission between complex systems, named Complexity Matching.

Complex networks form one of the most challenging areas of modern research overarching the traditional scientific disciplines. Of particular importance is the manner in which information is shuttled back and forth between such networks and whether or not there exists general principles that guide the flow of information. Herein we identify Wiener's Law, which determines the information transfer in an information-dominated process. Moreover we show that this law is part of a Principle of Complexity Management (PCM) that determines the efficiency conditions for information exchange between complex networks. Example applications of PCM are made to the phenomenon of habituation and other activities involving the brain. The information transfer between two complex networks is calculated using linear response theory as well as by direct numerical calculation of the master equation dynamics of networks using a two-state decision making model.