Adaptation Noise And Self Organizing Systems

The aims of this paper are to propose, construct and analyse microscopic kinetic models for the emergence of long chains of RNA from monomeric beta-D-ribonucleotide precursors in prebiotic circumstances. Our theory starts out from similar but more general chemical assumptions to those of Eigen, namely that catalytic replication can lead to a large population of long chains. In particular, our models incorporate the possibility of (i) direct chain growth, (ii) template-assisted synthesis and (iii) catalysis by RNA replicase ribozymes, all with varying degrees of efficiency. However, in our models the reaction mechanisms are kept `open'; we do not assume the existence of closed hypercycles which sustain a population of long chains. Rather it is the feasibility of the initial emergence of a self-sustaining set of RNA chains from monomeric nucleotides which is our prime concern. We confront directly the central nonlinear features of the problem, which have often been overlooked in previous studies. Our detailed microscopic kinetic models lead to kinetic equations which are generalisations of the Becker-Doring system (BD) for the step-wise growth of clusters or polymer chains; they lie within a general theoretical framework which has recently been successfully applied to a wide range of complex chemical problems. In fact, the most accurate model we consider has BD aggregation terms, together with a general Smoluchowski fragmentation term to model the competing hydrolysis of RNA polymer chains. We conclude that, starting from reasonable initial conditions of monomeric nucleotide concentrations within a prebiotic soup and in an acceptable timescale, it is possible for a self-replicating subset of polyribonucleotide chains to be selected, while less efficient replicators become extinct.

In this paper we present results and analyses of a class of games in which heterogeneous agents are rewarded for being in a minority group. Each agent possesses a number of fixed strategies each of which are predictors of the next minority group. The strategies use a set of aggregate, publicly available information (reflecting the agents' collective previous decisions) to make their predictions. An agent chooses which group to join at a given moment by using one of his strategies. These games are adaptive in that agents can choose, at different points of the game, to exercise different strategies in making their choice of which group to join. We find, rather generally, that such systems evidence a phase change from a maladaptive, informationally efficient phase in which the system performs poorly at generating resources, to an inefficient phase in which there is an emergent cooperation among the agents, and the system more effectively generates resources. The best emergent coordination is achieved in a transition region between these two phases. This transition occurs when the dimension of the strategy space is of the order of the number of agents playing the game. We present explanations for this general behavior, based in part on an information theoretic analysis of the system and its publicly available information. We also propose a mean-field like model of the game which is most accurate in the maladaptive, efficient phase. In addition, we show that the best individual agent performance in the two different phases is achieved by sets of strategies with markedly different characteristics. We discuss implications of our results for various aspects of the study of complex adaptive systems.

The study of correlation structure in the primary sequences of DNA is reviewed. The issues reviewed include: symmetries among 16 base-base correlation functions, accurate estimation of correlation measures, the relationship between 1/f and Lorentzian spectra, heterogeneity in DNA sequences, different modeling strategies of the correlation structure of DNA sequences, the difference of correlation structure between coding and non-coding regions (besides the period-3 pattern), and source of broad distribution of domain sizes. Although some of the results remain controversial, a body of work on this topic constitutes a good starting point for future studies.

We consider the covariance matrix G mn (x−y) of the d-dimensional q-states Potts model, rewriting it in terms of the connectivity, the finite-cluster connectivity and the infinite-cluster covariance in the random cluster repre- sentation of Fortuin and Kasteleyn. In any of the q ordered phases, we show that the matrix G mn (x−y) has one tivial eigenvalue 0, one simple eigen- value $G_{\wir}^{(1)}(x-y)$ and one ( q−2 )-fold degenerate eigenvalue $G_{\wir}^{(2)}(x-y)$. Furthermore, we identify the eigenvalues both in terms of representations of the unbroken symmetry group of the model, and in terms of connectivities and cluster covariances, thereby attributing algebraic signifi- cance to these stochastic geometric quantities. In addition to establishing the existence of the correlation lengths $\xi_{\wir}^{(1)}$ and $\xi_{\wir}^{(2)}$ corresponding to $G_{\wir}^{(1)}(x-y)$ and $G_{\wir}^{(2)}(x-y)$, we show that $\xi_{\wir}^{(1)}(\beta)\geq \xi_{\wir}^{(2)}(\beta)$ for all inverse tempera- tures β . For dimension d=2 and q≥1 , we establish a duality relation between $\xi_{\wir}^{(2)}$ and $\xi_{\free}$, the correlation length of the two-point function with free boundary conditions: We show $\xi_{\wir}^{(2)}(\beta) = \frac{1}{2} \xi_{\free}(\beta^\ast)$ for all β≥ β o , where β ∗ is the dual inverse temperature and β o is the self-dual point. In order to prove the above results, we introduce two new inequalities. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing, and replaces independence in the standard percolation model; the second replaces the van den Berg - Kesten inequality.

If p is the probability of a letter of a memoryless source, the length l of the corresponding binary Huffman codeword can be very different from the value -log p. We show that, nevertheless, for a typical letter, l is approximately equal to -log p. More precisely, the probability that l differs from -log p by more than m decreases exponentially with m.

Altruistic behaviour is disadvantageous for the individual while is advantageous for its group. If the target of the selection is the individual, one would expect the selection process to lead to populations formed by wholly homogeneous groups, made up of either altruistic or egoistic individuals, where the winning choice depends on the balance beetwen group advantage and individual disadvantage. We show in a simple model that populations formed by inhomogeneous groups can be stabilized in some circumstances. We argue that this condition is realized when there is a relative advantage conferred by the presence of a few altruists to all the members of the group.

We present a model for biological aging that considers the number of individuals whose (inherited) genetic charge determines the maximum age for death: each individual may die before that age due to some external factor, but never after that limit. The genetic charge of the offspring is inherited from the parent with some mutations, described by a transition matrix. The model can describe different strategies of reproduction and it is exactly soluble. We applied our method to the bit-string model for aging and the results are in perfect agreement with numerical simulations.

We introduce two three sided adaptative systems as toy models to mimic the exchange of commodities between buyers and sellers. These models are simple extensions of the minority game, exhibiting similar behaviour as well as some new features. The main difference between our two models is that in the first the three sides are equivalent while in the second, one choice appears as a compromise between the two other sides. Both models are investigated numerically and compared with the original minority game.

This paper presents description of time evolution of averages of Markov process in wide range of noise intensity. Exact expression of time scale of average evolution has been obtained. It has been demonstrated numerically that for purely noise-induced transitions (transitions over potential barriers) the time evolution of mean coordinate is a simple exponent with a good precision even for the case when the potential barrier height is comparable or smaller than the noise intensity. Also it has been demonstrated that nonlinear system may be "linearized" by a strong noise.

We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average probabilistic totalistic rule'' exhibiting the same periodic behavior.