Dynamical complexity of discrete time regulatory networks

Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks which present both discrete and continuous aspects. Our models consist of a network of units, whose states are quantified by a continuous real variable. The state of each unit in the network evolves according to a contractive transformation chosen from a finite collection of possible transformations, according to a rule which depends on the state of the neighboring units. As a first approximation to the complete description of the dynamics of this networks we focus on a global characteristic, the dynamical complexity, related to the proliferation of distinguishable temporal behaviors. In this work we give explicit conditions under which explicit relations between the topological structure of the regulatory network, and the growth rate of the dynamical complexity can be established. We illustrate our results by means of some biologically motivated examples.Comment: 28 pages, 4 figure

The thermonuclear rate for the 19F(a,p)22Ne reaction at stellar temperatures

The $^{19}$F($\alpha$,p)$^{22}$Ne reaction is considered to be one of the main sources of fluorine depletion in AGB and Wolf-Rayet stars. The reaction rate still retains large uncertainties due to the lack of experimental studies available. In this work the yields for both exit channels to the ground state and first excited state of $^{22}$Ne have been measured and several previously unobserved resonances have been found in the energy range E$_{lab}$=792-1993 keV. The level parameters have been determined through a detailed R-matrix analysis of the reaction data and a new reaction rate is provided on the basis of the available experimental information.Comment: Accepted for publication in Phys Rev.

A computational study on the intriguing mechanisms of the gas-phase thermal activation of methane by bare [Ni(H)(OH)](+)

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.A detailed computational study on the reaction mechanisms of the thermal activation of methane by the bare complex [Ni(H)(OH)]+ has been conducted. The experimentally observed reaction features, i.e. the ligand exchange Ni(H) → Ni(CH3), the H/D scrambling between the incoming methane and the hydrido ligand of the nickel complex, the spectator-like behavior of the OH ligand, and the relatively moderate reaction efficiency of 6% relative to the collision rate of the ion/molecule reaction, can be explained by considering three competing mechanisms, and a satisfactory agreement between experiment and theory has been found.DFG, EXC 314, Unifying Concepts in Catalysi

Nucleation and growth mechanism of polycarbazole deposited by electrochemistry

Polycarbazole (PCz) thin films have been deposited by electro-oxidation of carbazole in LiClO4 + anhydrous acetonitrile onto SnO2 coated glass substrates, by potentiostatic method and the nucleation and growth mechanism (NGM) were studied. The obtained current time transients (j-t) were fitted using a mathematical equation with three contributions: instantaneous nucleation with two-dimensional (IN2D) or three-dimensional (IN3D) growth, and also a progressive nucleation with three dimensional (PN3D) growth. At the beginning, the IN2D contribution is predominant but, quickly the IN3D processes become more important. At a deposition time t > 17 s the IN3D corresponds to 80 % of the total current. The visualization by scanning electron microscopy of the surface morphology of the PCz films is in agreement with the NGM proposed by the mathematical method. The film covers very rapidly the SnO2 under layer related to the 2D process, even if some heterogeneities randomly distributed in the films, issued from the 3D processes, are also visible. After two minutes of deposition, the roughness of the whole surface of the films corroborates the 3D processes domination. Therefore, the information directly obtained from the (j-t) transients is a suitable and very useful tool to predict the working conditions in order to control the type of morphology of the film prepared by electropolymerization

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure