W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Boundaries and Barriers, pages 56--116. Addison-Wesley, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the other generating a well known algebraic structure called lattice. What follows is the standard definition of a lattice (Rutherford 1966) as well as the definition of a lattice of organizations of an artificial chemistry. Later we shall demonstrate this concept which was already recognized in (Fontana and Buss 1996) on a number of examples and show that it is of importance in understanding the properties of an organization. Definition 2.7. lattice) Let L be a set of elements, where two binary operations are defined by [ and . Let those operations be such that 8x; y; z 2 L the following properties are ....

....and c be an element in O, then c is a replicator in O if there exist d in O such that R(d; c) c or R(c; d) c. An element c is called a self replicator if R(c; c) c. 2. 6 Reformulating Earlier Definitions We now reformulate some of the definitions given in (Fontana and Buss 1994; Fontana and Buss 1996) using our previous terms. Definition 2.12. L0 organization) An organization O = hO; Ri is called an L0 organization if it is finite and if every element c 2 O is a replicator in O. That is, if 8c 2 O there is d 2 O such that R(c; d) c or R(d; c) c Definition 2.13. L1 organization) An ....

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Fontana, W. and L. W. Buss (1996). The barrier of objects: From dynamical systems to bounded organization. In J. Casti and A. Karlqvist (Eds.), Boundaries and Barriers, Redwood City, MA, pp. 56--116. Addison-Wesley.

....applications and March 7, 1997 Page: 5 microwaves) Similarly, self organization is not a property limited to differential equations. Symbol systems can also go to fixed points, show cycles, chaotic behaviour or randomness the exact same classes of behaviour. Giunti, Ch. 18, pp. 557; Ray, 1995; Fontana and Buss, 1996). Slow and fast timescales, indeed, even distance metrics are also definable within other formal systems (Godel used this principle in the 1930s) On pp. 6 9 PVG also go to lengths to describe dynamical systems as statedetermined. But discrete time discrete state machines are also state ....

Fontana, W. and Buss, L. (1996), "The barrier of objects: From dynamical systems to bounded organizations", in J. Casti and A. Karlqvist (eds), Boundaries and Barriers, Addison Wesley, pp. 56-116.

....chemistry is an artificial system, which is similar to a chemical system. Usually, an artificial chemistry consists of: 1. a set of objects S : These objects may be abstract symbols [16] character sequences [1, 12, 14] lambda expressions [8] binary strings [3, 6, 15] numbers [4] or proofs [10]. 2. a set of rules R, describing the interaction among objects: The rules can be defined explicitly [16, 7] or implicitly by using string matching string concatenation [2, 13, 14] lambda calculus [8, 9] Turing machines [15] finite state machines or machine code language [6] proof theory [9] ....

W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Boundaries and Barriers, pages 56--116. Addison-Wesley, 1996.

....and with what strength. Here, we describe an artificial chemistry as a system which consists of the following three parts: 1. a set of objects S : These objects may be abstract symbols [2] character sequences [1, 3, 4] lambda expressions [5] binary strings [6, 7, 8] numbers [9] or proofs [10]. 2. a set of rules R, describing the interaction among objects: The rules can be defined explicitly [2, 11] or implicitly by using string matching string concatenation [1, 4, 12] lambda calculus [5, 13] Turing machines [8] finite state machines or machine code language [7] proof theory [13] ....

....that a selfmaintaining metabolism can emerge in a polymer chemistry without the need of template based replication. The sorting chemistry in [9] can also be considered as a polymer chemistry. 3. 4 Lambda Calculus Fontana applied the lambda calculus to define an abstract constructive chemistry [5, 10, 13, 23, 24]. The lambda calculus is an elegant framework which specifies how character sequences can be interpreted as operators acting on character sequences. Some advantages are the short and implicit definition of the interaction mechanism, the computational universality of the lambda calculus, variable ....

W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, ed., Boundaries and Barriers, 1996.

....parallel machine Implicit population concentration proportional selection O(log(M) concentration of type i: O(log(M) large infinite populations with low diversity memory efficient easy monitoring Methods for Dynamical Simulation Overview 1. Stochastic molecular collisions e.g. [Fontana and Buss, 1996] 2. Continuous differential or discrete difference equations e.g. Segr and Lancet, 1998, Banzhaf, 1994] 3. Metadynamics e.g. Bagley and Farmer, 1992] 4. Mixed approaches e.g. Zauner and Conrad, 1998] 5. Symbolic analysis of the equations e.g. Farmer et al. 1986] Explicit vs. Implicit ....

....Structure Function Mapping 1. Rewriting or production systems 2. String operations 3. Abstract automata 4. Arithmetic operations 5. Core Wars like systems or assembler automata 6. Lattice molecular systems 7. Others Rewriting or Production Systems Overview 1. Lambda Calculus [Fontana, 1992, Fontana and Buss, 1996] 2. Chemical Abstract Machine (CHAM) Berry and Boudol, 1992] 3. Chemical Rewriting System on Multisets (ARMS) Suzuki and Tanaka, 1997] 4. Chemical Casting Model [Kanada and Hirokawa, 1994] Lambda Calculus and AlChemy (I) Fontana, 1992, Fontana and Buss, 1996] 1. Objects: ffl Molecule : ....

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Fontana, W. and Buss, L. W. (1996). The barrier of objects: From dynamical systems to bounded organization. In Casti, J. and Karlqvist, A., editors, Boundaries and Barriers, pages 56--116. Addison-Wesley.

....system, because the interaction between its elements is specified by an algorithm. It consists of the following three components: 1) a set of objects S: These objects may be abstract symbols [32] character sequences [20] lambda expressions [13] binary strings [4, 30] numbers [5] or proofs [14]. Here, we use binary strings with a constant length of 32 bits, thus, S = f0; 1g 32 . In a basic setting, the soup has no topological structure so that its state can be noted as a concentration vector. 2) a collision or reaction rule: The collision rule defines the interaction among two ....

W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organization. In J. Casti and A. Karlqvist, editors, Boundaries and Barriers, pages 56--116. Addison-Wesley, 1996.

.... But some evolutionary theorists have questioned the adequacy of classical neo Darwinism as either an explanatory or a predictive theory, and argue instead for the primacy of historical contingency (Gould, 1989a) or the self organization of biological structure not due to natural selection (Fontana Buss, 1996; Goodwin, 1990; Kauffman, 1993) These historicists and structuralists are the connectionists of the evolutionary biology community the people questioning the classical orthodoxy. The selectionist historicist structuralist debate has been discussed at length by Gould (1989b) among others. ....

.... what dynamical systems can compute and extending computation theory to continuousvalued computation and two dimensional languages (Moore, 1990, 1996; Lindgren, Moore, Nordahl, 1997) Fontana and Buss s work on self organization and the development of hierarchies in an algorithmic chemistry (Fontana Buss, 1996); and Crutchfield, Mitchell, Das, and others work on the evolution of emergent computation in cellular automata (Crutchfield Mitchell, 1995; Das, Mitchell, Crutchfield, 1994; Mitchell, Crutchfield, Das, 1996) These are only a few examples. Here I will describe this last project as an ....

Fontana, W., & Buss, L. (1996). The barrier of objects: From dynamical systems to bounded organizations. In J. Casti & A. Karlqvist (Eds.), Boundaries and Barriers: On the Limits to Scientific Knowledge. Reading, MA: AddisonWesley.

.... these lines include a quite large collection of papers on the interactions between ontogenetic plasticity and phylogeny (Baldwin effect) the illustration of properties like self repair, self maintenance and autopoiesis in ensembles of formal chemical organizations (Fontana, Wagner, Buss, 1994; Fontana Buss, 1996), the demonstration with very simple evolutionary models showing self organized criticality of the viability of punctuation patterns in the time distribution of species extinction (Bak Paczuski, 1995) and simple models of parapatric speciation (Di Paolo, 1996) In these examples, coming from ....

Fontana, W., & Buss, L. (1996). The barrier of objects: from dynamical systems to bounded organizations.

.... Figure 1: The Essential Components and Interactions reactions between other components see Control of Reaction) As new operators can appear in the world by the aggregation of existing operators, this is the sort of system that Walter Fontana and Leo Buss call a constructive dynamical system [17]. At the risk of getting a bit ahead of myself, the following quotation from Chris Langton demonstrates the relevance of using an aggregative system when studying the evolution of life: The molecular logic of life is a dynamic distributed logic. An initial set of operators and operands goes to ....

....for materials and energy in Nidus, if living organizations do emerge then food webs, trophic levels and hierarchical evolution will also emerge in the long run. Fontana, Buss et al. AlChemy etc. Walter Fontana and colleagues have produced some of the best recent work on artificial chemistry [16, 18, 17]. They argue that a formalism is needed in biology (and other areas) for constructive systems (i.e. those where the components are objects whose structure can change as the result of interactions) This should be coupled with classical dynamic systems approaches to form a constructive dynamic ....

Walter Fontana and Leo W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Boundaries and Barriers, pages 56--116. Addison-Wesley, 1996.

....by Rosen to formalize the functional activities of a living cell metabolism, repair, and replication [9] This system model maintains its metabolic activity through inputs from environments and repair activity. Fontana and Buss suggested the similarity between their study and these systems [5]. In this paper, we try to describe autopoietic systems using a mathematical framework of (M, R) systems. Our attempt may be very thoughtless because of the difficulty in interpreting autopoiesis in the framework of the naive set theory. Accordingly, our description does not strictly reflect pure ....

W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Boundaries and Barriers, pages 56--116. Addison--Wesley, 1996.

.... laws of chemical transformation . The result is a new operator that is fed back to the system. In this way we implement a simple chemical kinetics, where two object species interact with a probability proportional to their concentration. Our metaphor does obvious violence to the chemistry we know [12]. We don t dwell on that here, but one problem needs to be mentioned now. In a calculus, the application of an operator to another produces a single result, rather than two or more. Thus, a key feature of many chemical interactions the feature of producing multiple products in a single event ....

....doubt that expressions are far from molecules and our organizations far from organisms. The extent to which chemical realism can be increased without giving up formalism will determine which further properties of concurrent chemical organization become amenable to theory. It takes another paper [12] to address the major limitations of the present abstraction, and how one might go about them. Let us return to the methodological picture. The mathematical core of current neo Darwinian theory lacks a theory of organization. We have proposed an algebraic notion of molecular organization and a ....

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W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Barriers and Boundaries, pages 56--116. Addison-Wesley, Reading, MA, 1996.

....to see how the connections with recently developed proof systems (e.g. linear logic [11] enable us to address each of the limitations mentioned. Formal logic, it seems, is more appropriate for capturing chemistry than human cognition and reasoning. For an interim report the reader may consult [10]. Further reading Related work that provided important motivation has been published by Bagley, Farmer, Kauffman, Packard and Rasmussen [1, 6, 13, 14, 18] in particular Kauffman s pioneering work on reflexively autocatalytic chemical collectives. Maturana and Varela s concept of autopoiesis ....

....chemical collectives. Maturana and Varela s concept of autopoiesis [15, 16, 17, 19, 20] is of particular relevance. Leo Buss classic [2] was the driving force to go beyond standard formal frameworks in evolutionary biology to address the issue of organization. Our joint work is reported in [8, 9, 10]. Acknowledgement: Thanks to Leo Buss for ironing and starching this text. ....

W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Barriers and Boundaries, pages 56--116. Addison-Wesley, Reading, MA, 1996.

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W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors, Boundaries and Barriers, pages 56--116. Addison-Wesley, 1996.

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FONTANA,W.&BUSS, L. W. (1996). The barrier of objects: from dynamical systems to bounded organizations. In: Boundaries and Barriers (Casti, J. & Karlqvist, A., eds), pp. 56}116. Reading MA: Addison-Wesley.

No context found.

Fontana, W. and L. W: Buss (no year). The barrier of objects: from dynamical systems to bounded organizations. Paper no. 41. New Haven: Center for Computational Ecology, Yale University. Grdenfors, P. (1988). Knowledge in Flux. Modeling the Dynamics of Epistemic States. Cambridge, Mass.: MIT Press.

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