Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle -- with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.Comment: 34 page

Comment on ``Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states''

In a recent paper Coutinho, Nogami and Tomio [Phys. Rev. A 59, 2624 (1999); quant-ph/9812073] presented an example in which, they claim, Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory fails. We show that, contrary to their claim, Feynman's prescription is consistent with the exact solution of their example.Comment: 1 pag

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

Si(111) strained layers on Ge(111): evidence for c(2x4) domains

The tensile strained Si(111) layers grown on top of Ge(111) substrates are studied by combining scanning tunneling microscopy, low energy electron diffraction and first-principles calculations. It is shown that the layers exhibit c(2x4) domains, which are separated by domain walls along directions. A model structure for the c(2x4) domains is proposed, which shows low formation energy and good agreement with the experimental data. The results of our calculations suggest that Ge atoms are likely to replace Si atoms with dangling bonds on the surface (rest-atoms and adatoms), thus significantly lowering the surface energy and inducing the formation of domain walls. The experiments and calculations demonstrate that when surface strain changes from compressive to tensile, the (111) reconstruction converts from dimer-adatom-stacking fault-based to adatom-based structures

Estratégia e planejamento de mercado para produtor de arroz irrigado tropical.

A análise competitiva pode contribuir para o planejamento de mercado do rizicultor e possibilita a visualização de toda a complexidade dos sistemas alternativos à produção tradicional de arroz irrigado e dos requisitos para a mudança de estratégia competitiva do empreendimento rural. A aplicação dessa metodologia a cada safra permite o estabelecimento de indicadores de desempenho e comparações sobre a evolução da competitividade do agricultor

Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems

The irreversibility of a stationary time series can be quantified using the Kullback-Leibler divergence (KLD) between the probability to observe the series and the probability to observe the time-reversed series. Moreover, this KLD is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series. In this paper we introduce analytical and numerical techniques to estimate the KLD between time series generated by several stochastic dynamics with a finite number of states. We examine the accuracy of our estimators for a specific example, a discrete flashing ratchet, and investigate how close is the KLD to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories.Comment: 14 pages, 7 figure

Registo da avaliação da dor em sistema de informação: um projeto em desenvolvimento

Poster apresentado nas I Jornadas do Mestrado em Enfermagem de Saúde Infantil e Pediatria, organizadas pela Escola Superior de Enfermagem do Port