Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Iowa Civil Rights Commission, 46 Years of Working Toward a State Free of Discrimination Through Enforcement of Civil Rights Laws, Annual Report FY2011

The mission of the Iowa Civil Rights Commission is to end discrimination within the state of Iowa. To achieve this goal, the ICRC must effectively enforce the Iowa Civil Rights Act. The ICRA will be as effective as the Commission is in processing complaints of discrimination. The ICRC undertook significant steps forward in improving the timeliness and competency by which complaints of discrimination are processed. The screening unit was increased with special emphasis on improving the quality and quantity of the analysis of the initial screening decisions. The investigative process for nonhousing cases was completely overhauled. The improved process builds on the screening decision and focuses on the issues raised in that decision. The new process will help the ICRC reduce a significant backlog for non-housing cases. Additionally, we revamped the mediation program by moving to an allvolunteer mediation program. Over 20 Iowa lawyers volunteered to help the ICRC resolve complaints through alternative dispute resolution.

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Preparation, maintenance, and use of serum-free aggregating brain cell cultures.

Serum-free aggregating brain cell cultures are free-floating three-dimensional primary cell cultures able to reconstitute spontaneously a histotypic brain architecture to reproduce critical steps of brain development and to reach a high level of structural and functional maturity. This culture system offers, therefore, a unique model for neurotoxicity testing both during the development and at advanced cellular differentiation, and the high number of aggregates available combined with the excellent reproducibility of the cultures facilitates routine test procedures. This chapter presents a detailed description of the preparation, maintenance, and use of these cultures for neurotoxicity studies and a comparison of the developmental characteristics between cultures derived from the telencephalon and cultures derived from the whole brain. For culture preparation, mechanically dissociated embryonic brain tissue is used. The initial cell suspension, composed of neural stem cells, neural progenitor cells, immature postmitotic neurons, glioblasts, and microglial cells, is kept in a serum-free, chemically defined medium under continuous gyratory agitation. Spherical aggregates form spontaneously and are maintained in suspension culture for several weeks. Within the aggregates, the cells rearrange and mature, reproducing critical morphogenic events, such as migration, proliferation, differentiation, synaptogenesis, and myelination. For experimentation, replicate cultures are prepared by the randomization of aggregates from several original flasks. The high yield and reproducibility of the cultures enable multiparametric endpoint analyses, including "omics" approaches.

Bio-electrical impedance analysis for estimation of fat-free mass and muscle mass in cystic fibrosis patients.

The nutritional status of cystic fibrosis (CF) patients has to be regularly evaluated and alimentary support instituted when indicated. Bio-electrical impedance analysis (BIA) is a recent method for determining body composition. The present study evaluates its use in CF patients without any clinical sign of malnutrition. Thirty-nine patients with CF and 39 healthy subjects aged 6-24 years were studied. Body density and mid-arm muscle circumference were determined by anthropometry and skinfold measurements. Fat-free mass was calculated taking into account the body density. Muscle mass was obtained from the urinary creatinine excretion rate. The resistance index was calculated by dividing the square of the subject's height by the body impedance. We show that fat-free mass, mid-arm muscle circumference and muscle mass are each linearly correlated to the resistance index and that the regression equations are similar for both CF patients and healthy subjects.