The Evolution of complexity in self-maintaining cellular information processing networks

We examine the role of self-maintenance (collective autocatalysis) in the evolution of computational biochemical networks. In primitive proto-cells (lacking separate genetic machinery) self-maintenance is a necessary condition for the direct reproduction and inheritance of what we here term Cellular Information Processing Networks (CIPNs). Indeed, partially reproduced or defective CIPNs may generally lead to malfunctioning or premature death of affected cells. We explore the interaction of this self-maintenance property with the evolution and adaptation of CIPNs capable of distinct information processing abilities. We present an evolutionary simulation platform capable of evolving artificial CIPNs from a bottom-up perspective. This system is an agent-based multi-level selectional Artificial Chemistry (AC) which employs a term rewriting system called the Molecular Classifier System (MCS). The latter is derived from the Holland broadcast language formalism. Using this system, we successfully evolve an artificial CIPN to improve performance on a simple pre-specified information processing task whilst subject to the constraint of continuous self-maintenance. We also describe the evolution of self-maintaining, crosstalking and multitasking, CIPNs exhibiting a higher level of topological and functional complexity. This proof of concept aims at contributing to the understanding of the open-ended evolutionary growth of complexity in artificial systems

Evolution of self-maintaining cellular information processing networks

We examine the role of self-maintenance (collective autocatalysis) in the evolution of computational biochemical networks. In primitive proto-cells (lacking separate genetic machinery) self-maintenance is a necessary condition for the direct reproduction and inheritance of what we here term Cellular Information Processing Networks (CIPNs). Indeed, partially reproduced or defective CIPNs may generally lead to malfunctioning or premature death of affected cells. We explore the interaction of this self-maintenance property with the evolution and adaptation of CIPNs capable of distinct information processing abilities. We present an evolutionary simulation platform capable of evolving artificial CIPNs from a bottom-up perspective. This system is an agent-based multi-level selectional Artificial Chemistry (AC) which employs a term rewriting system called the Molecular Classifier System (MCS). The latter is derived from the Holland broadcast language formalism. Using this system, we successfully evolve an artificial CIPN to improve performance on a simple pre-specified information processing task whilst subject to the constraint of continuous self-maintenance. We also describe the evolution of self-maintaining, crosstalking and multitasking, CIPNs exhibiting a higher level of topological and functional complexity. This proof of concept aims at contributing to the understanding of the open-ended evolutionary growth of complexity in artificial systems

Basics of Modelling the Pedestrian Flow

For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction between the pedestrians on the resulting velocity-density relation. To focus on the role of the required space and remote force we choose a one-dimensional model for this investigation. For those densities, where in two dimensions also passing is no longer possible and the mean value of the velocity depends primarily on the interaction, we obtain the following result: If the model increases the required space of a person with increasing current velocity, the reproduction of the typical form of the fundamental diagram is possible. Furthermore we demonstrate the influence of the remote force on the velocity-density relation.Comment: 9 pages, 3 figures, Changes: Parameter e=0.51 corrected to e =0.07 (see Fig. 2) and prep. for subm. to Phys. Rev.

Free products of operator spaces and free Markov processes

Certain (reduced) free product is introduced in the framework of operator spaces. Under the construction, the free product of preduals of von Neumann algebras agrees with the predual of the free product of von Neumann algebras. This answers a question asked by Effros affirmatively. An example is presented to show that the C*-algebra reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of the operator space reduced free product of the two C*-algebras. Free Markov processes are also investigated in Voiculescu\u27s free probability theory. This highly non-commutative notion generalizes that of free Brownian motion and free Levy processes. Some free Markov processes are realized as solutions to free stochastic differential equations driven by free Levy processes. A special and rather interesting kind of free Markov processes, free Ornstein-Uhlenbeck processes, is studied in some details. It is shown that a probability measure on R is free self-decomposable if and only if it is the stationary distribution of a stationary free Ornstein-Uhlenbeck process (driven by a free Levy process). Finally, the notion of free fractional Brownian motion is introduced. Examples of fractional free Brownian motion are given, which are based on creation and annihilation operators on full Fock spaces. It is proved that the Langevin equation driven by fractional free Brownian motion has a unique solution. We call the solution a fractional free Ornstein-Uhlenbeck process

A general stochastic model for sporophytic self-incompatibility

Disentangling the processes leading populations to extinction is a major topic in ecology and conservation biology. The difficulty to find a mate in many species is one of these processes. Here, we investigate the impact of self-incompatibility in flowering plants, where several inter-compatible classes of individuals exist but individuals of the same class cannot mate. We model pollen limitation through different relationships between mate availability and fertilization success. After deriving a general stochastic model, we focus on the simple case of distylous plant species where only two classes of individuals exist. We first study the dynamics of such a species in a large population limit and then, we look for an approximation of the extinction probability in small populations. This leads us to consider inhomogeneous random walks on the positive quadrant. We compare the dynamics of distylous species to self-fertile species with and without inbreeding depression, to obtain the conditions under which self-incompatible species could be less sensitive to extinction while they can suffer more pollen limitation

Toddlers' action prediction: statistical learning of continuous action sequences

The current eye-tracking study investigated whether toddlers use statistical information to make anticipatory eye movements while observing continuous action sequences. In two conditions, 19-month-old participants watched either a person performing an action sequence (Agent condition) or a self-propelled visual event sequence (Ghost condition). Both sequences featured a statistical structure in which certain action pairs occurred with deterministic transitional probabilities. Toddlers learned the transitional probabilities between the action steps of the deterministic action pairs and made predictive fixations to the location of the next action in the Agent condition but not in the Ghost condition. These findings suggest that young toddlers gain unique information from the statistical structure contained within action sequences and are able to successfully predict upcoming action steps based on this acquired knowledge. Furthermore, predictive gaze behavior was correlated with reproduction of sequential actions following exposure to statistical regularities. This study extends previous developmental work by showing that statistical learning can guide the emergence of anticipatory eye movements during observation of continuous action sequences

Systems with inheritance: dynamics of distributions with conservation of support, natural selection and finite-dimensional asymptotics

If we find a representation of an infinite-dimensional dynamical system as a nonlinear kinetic system with {\it conservation of supports} of distributions, then (after some additional technical steps) we can state that the asymptotics is finite-dimensional. This conservation of support has a {\it quasi-biological interpretation, inheritance} (if a gene was not presented initially in a isolated population without mutations, then it cannot appear at later time). These quasi-biological models can describe various physical, chemical, and, of course, biological systems. The finite-dimensional asymptotic demonstrates effects of {\it ``natural" selection}. The estimations of asymptotic dimension are presented. The support of an individual limit distribution is almost always small. But the union of such supports can be the whole space even for one solution. Possible are such situations: a solution is a finite set of narrow peaks getting in time more and more narrow, moving slower and slower. It is possible that these peaks do not tend to fixed positions, rather they continue moving, and the path covered tends to infinity at $t \rightarrow \infty$. The {\it drift equations} for peaks motion are obtained. Various types of stability are studied. In example, models of cell division self-synchronization are studied. The appropriate construction of notion of typicalness in infinite-dimensional spaces is discussed, and the ``completely thin" sets are introduced

Asymptotic laws for nonconservative self-similar fragmentations

We consider a self-similar fragmentation process in which the generic particle of size $x$ is replaced at probability rate $x^\alpha$, by its offspring made of smaller particles, where $\alpha$ is some positive parameter. The total of offspring sizes may be both larger or smaller than $x$ with positive probability. We show that under certain conditions the typical size in the ensemble is of the order $t^{-1/\alpha}$ and that the empirical distribution of sizes converges to a random limit which we characterise in terms of the reproduction law.Comment: 17 page

Numerical Analysis of a New Mixed Formulation for Eigenvalue Convection-Diffusion Problems

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization

Selection theorem for systems with inheritance

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of "natural" selection. Estimations of the asymptotic dimension are presented. After some initial time, solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow over time and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t goes to infinity. The drift equations for peak motion are obtained. Various types of distribution stability are studied: internal stability (stability with respect to perturbations that do not extend the support), external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of self-synchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinite-dimensional space is discussed, and the notion of "completely thin" sets is introduced. Key words: Dynamics; Attractor; Evolution; Entropy; Natural selectionComment: 46 pages, the final journal versio