COMPUTING ANTICIPATORY SYSTEMS: CASYS 2001  Fifth International Conference

Theory of Computing Anticipatory Systems Based on Differential Delayed‐Advanced Difference Equations
View Description Hide DescriptionThis paper introduces some computing anticipatory systems based on differential delayed‐advanced difference equations. Delayed systems are systems which are based on a memory of past states and advanced systems are systems which depend explicitly on their anticipatory future potential states. As any physical actual systems, the laws of evolution must be defined at the current time, so, the past and future states are to be defined by new variables defined at the current time taking into account some hidden mechanisms for their existence and knowledge at the current time, because the past states do no more exist at the current time, and the future states are not yet actualized. Several analytical methods are developed to show properties typical of anticipatory systems. Some delayed‐advanced systems can be transformed to differential equations defined at the current time. Mathematically, new variables, defined by equations at the current time, are introduced in view of computing, by synchronization, past and/or future states. Some other anticipatory systems can be transformed to delayed systems. Numerical simulations of such computing anticipatory systems are presented.

The Evolution of Matter: The Quantal Unity of Evolution
View Description Hide DescriptionThis paper is a brief sketch of the mechanisms that govern the construction of natural systems. Consequently, relatively little will be said about the external circumstances of their diversification. As nature has relatively few tricks in its bag, what follows may be viewed as an overview of the quantal unit of evolution (QUE), modally indexed.

Systems With Emergent Dynamics
View Description Hide DescriptionEvolutionary biologists often reject deterministic models of evolutionary processes because they equate ‘deterministic’ with ‘goal‐seeking’, and have learned the hard way not to trust goal‐seeking explanations of evolutionary adaptations. On the other hand, the general theory of dynamical systems potentially has much to offer for evolutionary biology— for example, as a resolution of the conflict between gradualism and punctuated equilibrium. The concept of a system with emergent dynamics retains the deterministic nature of dynamical systems, while eliminating any goal‐seeking interpretation. Define an emergent property of a complex system to be a property whose computation from the entity‐level rules of the system is intractable (in some reasonable sense). Say that a dynamical system has emergent dynamics if the computation of trajectories is intractable. Then systems with emergent dynamics are deterministic but not goal‐seeking. As such, they offer a sensible way to use dynamical systems as models for evolutionary processes in biology, and in other areas. We discuss these issues and examine a few simple aspects of emergence in dynamical systems.

The Role of Anticipation in Intelligent Systems
View Description Hide DescriptionThe paper explores the relationship between the area of anticipatory systems and the area of intelligent systems. After an overview of these areas, the role of anticipation in intelligent systems is discussed and it is argued that the area of intelligent systems can greatly benefit by importing the various results developed within the area of anticipatory systems. Distinctions between hard and soft systems and between hard and soft computing are then discussed. It is explained why intelligent systems are by necessity soft and why soft computing is essential for their construction. It is finally argued that the area of anticipatory systems can enlarge its scope by importing knowledge regarding soft systems and soft computing from the area of intelligent systems.

Properties of Derived Scalar Anticipatory Systems
View Description Hide DescriptionThe study of anticipatory systems derived from causal systems or recursions has been well established. This paper investigates what happens to the fixed points of a system modelled by a first order recursion when the recursion is replaced by an associated incursion. Results obtained by Dubois with this technique applied to the logistic map are extended to other unimodal maps, typical of a class of population models. Other incursions associated with these maps are also studied, and a paradigm is given for generating a strong anticipatory system from a recursion whose map is of bounded variation. This is done by replacing the recursion with an incursion defined in terms of the variation of the map. The effect of this replacement on the stability properties of the fixed points of the map is examined.

Theoretical Biology: Organisms and Mechanisms
View Description Hide DescriptionThe Theoretical Biology Program initiated by Robert Rosen is intended to identify the key theoretical characteristics of organisms, especially those that distinguish organisms from mechanisms, by looking for the proper abstractions and defining the appropriate relationships. There are strong claims about the distinctions in Rosen’s book “Life Itself”, along with some purported proofs of these assertions. Unfortunately, the Mathematics is incorrect, and the assertions remain unproven (and some of them are simply false). In this paper, we present the ideas of Rosen’s approach, demonstrate that his Mathematical formulations and proofs are wrong, and then show how they might be made more successful.

Local Semantics for the Part‐whole Problem: An Alternative CA Model Based on Unserializable Parallel Processing
View Description Hide DescriptionOn one hand, we can observe and describe behaviors of physical (non‐living) systems as the machinery, where the systems obey certain rules in the time evolutions. On the other hand, many behaviors of living systems can be observed as if they cannot be described as mechanical processes on their own right. Does this confrontation between living and non‐living systems suggest that the process of living systems contains something special that is essentially different from the mechanical (computational) process? In this paper, we propose the concept ‘weak computation’, and argue that processes of living and non‐living systems are not essentially different when we look at both of them from the viewpoint of ‘the weak computation’. We consider that such weak computations are executed in ‘unserializable parallel processing systems (i.e., parallel processing systems irreducible to serial processing systems)’. In order to model ‘the unserializable parallel processing’, we modify the elementary cellular automata [1,2] as their local interaction can be not only reference but also interference.

Scalar Weak Anticipatory Systems
View Description Hide DescriptionWeak anticipatory systems are computing anticipatory systems that use a model to generate predictions of future events, which predictions the system then uses to compute its future states. In this paper we propose an explicit scheme for weak anticipatory systems which are derived from first order causal systems. We investigate their dynamics under various assumptions and compare and contrast their behaviour with the more well known behaviour of the corresponding causal and strong anticipatory systems. We concentrate on unimodal maps, their fixed points and stability properties.

Can Computers be Social?
View Description Hide DescriptionOf main concern in agent based computing is the conception that software agents can attain socially responsible behavior. This idea has its origin in the need for agents to interact with one another in a cooperating manner. Such interplay between several agents can be seen as a combinatorial play where the rules are fixed and the actors are supposed to closely analyze the play in order to behave rational. This kind of rationality has successfully being mathematically described. When the social behavior is extended beyond rational behavior, mere mathematical analysis falls short. For such behavior language is decisive for transferring concepts and language is a holistic entity that cannot be analyzed and defined mathematically. Accordingly, computers cannot be furnished with a language in the sense that meaning can be conveyed and consequently they lack all the necessary properties to be made social. The attempts to postulate mental properties to computer programs are a misconception that is blamed the lack of true understanding of language and especially the relation between formal system and its semantics.

Elimination of Anticipation of Singular Linear Systems
View Description Hide DescriptionThree methods of elimination of the anticipation of singular discrete‐time and continuous‐time linear systems are proposed. The elimination of the anticipation is achieved by connection in series with anticipatory system of a suitable number of delay elements (discrete‐time systems) or integrators (continuous‐time systems) or by suitable choice of gain matrices of state‐derivative feedbacks or state‐feedbacks. Necessary and sufficient conditions for the existence of gain matrices are established.

When Everybody Anticipates in a Different Way …
View Description Hide DescriptionThe paper is oriented to the computer modeling of anticipatory systems in which there are more than one anticipating individuals. The anticipating of each of them can mutually differ. In such a case we can meet four main cases: (1) the anticipating persons make a dialogue to access some agreement and by such a way they can optimize the anticipation, (2) one of the anticipating persons is a teacher of the other ones and can show them where they had to be better in their anticipation, (3) the anticipating persons compete, each of them expecting to make the best anticipation and wishes to apply it in order to make the other ones weaker, (4) the anticipating persons do not mutually communicate. A human often anticipates so that he imagines the possible processes of the future and so he performs a certain “mental simulation”, but nowadays a human uses computer simulation to replace that (insufficient) mental simulation. All the variants were simulated so that the human imagining was transferred to a computer simulation. Thus systems containing several simulating elements were simulated. Experiences with that “nested” simulation and applications of it are described.

Semiosis and Energy Transformation
View Description Hide DescriptionSemiosis is understood as a process of transforming energy to mass via measurement. Measurement is an action of codification, organizing energy within different modes of relation. Measurement is examined within a series of ontological and epistemological cuts that increase asymmetry by first differentiating energy/mass into external and internal realms and then differentiating these realms into formal mind‐models and informal mass‐instances. These realms are examined within the three Peircean modes of Firstness. Secondness and Thirdness to explore five different processes of codification that encode energy to mass within a maturing complexity. Codification within these five processes is examined within classical and quantum mechanics and concludes that we require both mechanics of codification to provide a generative semiosis.

On Anticipatory and Nonanticipatory Properties in Stochastic Differential Systems
View Description Hide DescriptionOne of the aims of this paper is to point out the existence of strong computing anticipatory property and nonanticipatory property in stochastic differential systems, which are characterized by stochastic differential equations (SDEs). Since an SDE is merely a matter of form, its definition sorely depends on the stochastic integrals, not on differentials. Among others Itô and Stratonovich‐Fisk integrals are widely used, and the latter has anticipatory property in its own definition, and hence the systems, which are described by equations including the Stratonovich‐Fisk integrals, are considered to be strong computing anticipatory systems in stochastic type. On the other hand, Itô differential systems are nonanticipatory systems. In computing current states some of numeriacl algorithms for solving the SDE are taking into account predicted states. Hence, such systems are weakly computing anticipatory systems.

Time, Imaginary Value, Paradox, Sign and Space
View Description Hide DescriptionThis paper discusses paradox and imaginary values in relation to the mutuality of sign and space.

Review of Some Recent Results Related to Discrete‐Time Functional Equations
View Description Hide DescriptionThis paper surveys some results on difference equations, mainly of recent date. A parallel with ordinary differential equations is pursued, with the intention to emphasize the role of difference equations as tools to investigate discrete dynamical systems.

Linear Fractionals ‐ Simple Models with Chaotic‐like Behavior
View Description Hide DescriptionWhat are the simplest systems which display chaos ? We consider linear fractionals which are the ratio of two linear functions. While these systems often behave like linear systems, we show that for some parameter values these systems are chaotic‐like displaying sensitive dependence on initial conditions, visiting all open sets, and having a non‐attractive invariant density. Because these systems do not have cycles of every period they are not chaotic in the sense of Devaney [3]. For other parameter values, these systems are periodic, but if the parameters are rationals, the only possible periods are 1,2,3,4, and 6. The period 2 linear fractionals can be used to prove global stability for many of the usual population dynamics models [2]. Because of their simplicity, we are able to give a complete characterization of which linear fractional have which behavior.

Theory of Incursive Synchronization and Application to the Anticipation of Delayed Linear and Nonlinear Systems
View Description Hide DescriptionA general theory of synchronization of systems coupled by an incursive connection is developed. For differential delayed equation systems with a time shift, a slave or driven system anticipates the values of the master or driver system by a future time period, equal to the delay, giving rise to an anticipatory synchronization. Several extensions are successively considered. The anticipation of the synchronization can be modulated between the duration of the delay to a null anticipation. The anticipatory synchronization is extended to differential equation systems without delay. Finally, it is also possible to build a hierarchical anticipatory synchronization, what we call a meta‐anticipatory synchronization. The discrete equation systems corresponding to the differential equation systems are explicitly described in view of numerical simulations. An application is shown in the case of a chaotic delayed Pearl‐Verhulst system. A slave model is incursively synchronized to the master system, the simulation of which showing an anticipation of the slave system by different time durations. Finally, this method is applied to a simple discrete delayed linear system.

An Iterative Solution to the Nonlinear Time‐Discrete TEM Model ‐ The Occurrence of Chaos and a Control Theoretic Algorithmic Approach
View Description Hide DescriptionThis paper is concerned with a mathematical derivation of the nonlinear time‐discrete Technology‐Emissions Means (TEM‐) model. A detailed introduction to the dynamics modelling a Joint Implementation Program concerning Kyoto Protocol is given at the end of the paper. As the nonlinear time‐discrete dynamics tends to chaotic behaviour, the necessary introduction of control parameters in the dynamics of the TEM model leads to new results in the field of time‐discrete control systems. Furthermore the numerical results give new insights into a Joint‐Implementation Program and herewith, they may improve this important economic tool. The iterative solution presented at the end might be a useful orientation to anticipate and support Kyoto Process.

Anticipating the Filtrons of Automata by Complex Discrete Systems Analysis
View Description Hide DescriptionFiltrons of automata are coherent structures (discrete solitons) supported by iterated automata maps (IAMs). They differ from signals of cellular automata. The signals emerge during parallel processing of strings, while IAMs transform strings in serial. We relate the filtron and its supporting automaton with a particular complex discrete system (CDS). This CDS has the form of a processing ring net. Its computation is characterized by four components: instructions of processing nodes (I), inter‐processor communication constraints (C), initial data (D), and synchronization (S). We present an analysis of a computation performed within this CDS. It is useful in the problems of searching for any of the mentioned four components assuming that remaining three are known. We give a technique of anticipating the filtrons with a desired parameter C when I, S and D are given. We show how to decide the synchronization S when I, C and D are assumed, and how to determine instructions I when the desired filtron is described by known C, D and S.

Emergence Processes up to Consciousness Using the Multiplicity Principle and Quantum Physics
View Description Hide DescriptionEvolution is marked by the emergence of new objects and interactions. Pursuing our preceding work on Memory Evolutive Systems (MES; cf. our Internet site), we propose a general mathematical model for this process, based on Category Theory. Its main characteristics is the Multiplicity Principle (MP) which asserts the existence of complex objects with several possible configurations. The MP entails the emergence of non‐reducible more and more complex objects (emergentist reductionism). From the laws of Quantum Physics, it follows that the MP is valid for the category of particles and atoms, hence, by complexification, for any natural autonomous anticipatory complex system, such as biological systems up to neural systems, or social systems. Applying the model to the MES of neurons, we describe the emergence of higher and higher cognitive processes and of a semantic memory. Consciousness is characterized by the development of a permanent ‘personal’ memory, the archetypal core, which allows the formation of extended landscapes with an integration of the temporal dimensions.