Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.Comment: 23 pages, 3 figure

The Metallicity and Reddening of Stars in the Inner Galactic Bulge

We present a preliminary analysis of K, J-K color magnitude diagrams (CMDs) for 7 different positions on or close to the minor axis of the Milky Way at Galactic latitudes between +0.1^\circ and -2.8^\circ. From the slopes of the (linear) giant branches in these CMDs we derive a dependence of on latitude for b between -0.8^\circ and -2.8^\circ of -0.085 \pm 0.033 dex/degree. When combined with the data from Tiede et al. we find for -0.8^\circ \leq b \leq -10.3^\circ the slope in is -0.064 \pm 0.012 dex/degree. An extrapolation to the Galactic Center predicts [Fe/H] = +0.034 \pm 0.053 dex. We also derive average values for the extinction in the K band (A_K) of between 2.15 and 0.27 for the inner bulge fields corresponding to average values of E(J-K) of between 3.46 and 0.44. There is a well defined linear relation between the average extinction for a field and the star-to-star scatter in the extinction for the stars within each field. This result suggests that the typical apparent angular scale size for an absorbing cloud is small compared with the field size (90\arcsec on a side). Finally, from an examination of the luminosity function of bright giants in each field we conclude that the young component of the stellar population observed near the Galactic center declines in density much more quickly than the overall bulge population and is undetectable beyond 1^\circ from the Galactic center.Comment: accepted for publication in Astron. Jour. Compressed file contains the text, 9 figures, and 6 tables prepared with AAS Latex macros v. 4.

Noise Effects on the Complex Patterns of Abnormal Heartbeats

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-hour period and show that the rhythm can be described by a theoretical model consisting of two interacting oscillators with stochastic elements. By varying the magnitude of the noise, we show that for an intermediate level of noise, the model gives best agreement with key statistical features of the dynamics.Comment: 4 pages, 4 figures, RevTe

Computation of microdosimetric distributions for small sites

Object of this study is the computation of microdosimetric functions for sites which are too small to permit experimental determination of the distributions by Rossi-counters. The calculations are performed on simulated tracks generated by Monte-Carlo techniques. The first part of the article deals with the computational procedure. The second part presents numerical results for protons of energies 0.5, 5, 20 MeV and for site diameters of 5, 10, 100 nm

A core genetic module : the Mixed Feedback Loop

The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modelling RNA dynamics explicitly.Comment: To be published in Physical Review

Fractal Scales in a Schwarzschild Atmosphere

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.Comment: to appear in Class. Quantum Gra

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3+1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.Comment: to appear in Gen. Rel. Gra

Synchronous Behavior of Two Coupled Electronic Neurons

We report on experimental studies of synchronization phenomena in a pair of analog electronic neurons (ENs). The ENs were designed to reproduce the observed membrane voltage oscillations of isolated biological neurons from the stomatogastric ganglion of the California spiny lobster Panulirus interruptus. The ENs are simple analog circuits which integrate four dimensional differential equations representing fast and slow subcellular mechanisms that produce the characteristic regular/chaotic spiking-bursting behavior of these cells. In this paper we study their dynamical behavior as we couple them in the same configurations as we have done for their counterpart biological neurons. The interconnections we use for these neural oscillators are both direct electrical connections and excitatory and inhibitory chemical connections: each realized by analog circuitry and suggested by biological examples. We provide here quantitative evidence that the ENs and the biological neurons behave similarly when coupled in the same manner. They each display well defined bifurcations in their mutual synchronization and regularization. We report briefly on an experiment on coupled biological neurons and four dimensional ENs which provides further ground for testing the validity of our numerical and electronic models of individual neural behavior. Our experiments as a whole present interesting new examples of regularization and synchronization in coupled nonlinear oscillators.Comment: 26 pages, 10 figure