Self-organized criticality and synchronization in a coupled map lattice model of integrate-and-fire oscillators

We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from self-organized criticality, in the sense that the distribution of events (avalanches) obeys a power law, to a macroscopic synchronization of the population of oscillators, with avalanches of the size of the system.

Simple model for nonexponential relaxation in complex fluids

The nonexponential relaxation occurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in any time scale becomes apparent in an effective temperature field, which leads to a hierarchy of relaxation times responsible for the slow relaxation phenomena.

Disordered backgammon model

In this paper we consider an exactly solvable model that displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated with different relaxational time scales. Low-temperature relaxation takes place by partial equilibration of successive lower-energy modes. An adiabatic scaling solution, defined in terms of a threshold energy scale e*, is proposed. For such a solution, modes with energy ee* are equilibrated at the bath temperature, modes with ee* remain out of equilibrium, and relaxation occurs in the neighborhood of the threshold e~e*. The model is presented as a toy example to investigate the conditions related to the existence of an effective temperature in glassy systems and its possible dependence on the energy sector is probed by the corresponding observable.

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.

Dynamical properties of the Zhang model of self-organized criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for d=2 and 3, with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored, and their critical exponents computed. Among other results, it is shown that the three-dimensional exponents do not coincide with the Bak-Tang-Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] (Abelian) model, and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide, as is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed.

Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Integration of local-scale hydrological and regional-scale geophysical based on a nonlinear Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed a downscaling procedure based on a non-linear Bayesian sequential simulation approach. The basic objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity, which is available throughout the model space. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariate kernel density function. This method is then applied to the stochastic integration of low-resolution, re- gional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this downscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the downscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

"Suddenly I get into the zone": Examining discontinuities and nonlinear changes in flow experiences at work

Work-related flow is defined as a sudden and enjoyable merging of action and awareness that represents a peak experience in the daily lives of workers. Employees" perceptions of challenge and skill and their subjective experiences in terms of enjoyment, interest and absorption were measured using the experience sampling method, yielding a total of 6981 observations from a sample of 60 employees. Linear and nonlinear approaches were applied in order to model both continuous and sudden changes. According to the R2, AICc and BIC indexes, the nonlinear dynamical systems model (i.e. cusp catastrophe model) fit the data better than the linear and logistic regression models. Likewise, the cusp catastrophe model appears to be especially powerful for modelling those cases of high levels of flow. Overall, flow represents a nonequilibrium condition that combines continuous and abrupt changes across time. Research and intervention efforts concerned with this process should focus on the variable of challenge, which, according to our study, appears to play a key role in the abrupt changes observed in work-related flow.

Nonlinear Pile Behavior in Integral Abutment Bridges, HR-227, Part 1, 1982

The highway departments of all fifty states were contacted to find the extent of application of integral abutment bridges, to survey the different guidelines used for analysis and design of integral abutment bridges, and to assess the performance of such bridges through the years. The variation in design assumptions and length limitations among the various states in their approach to the use of integral abutments is discussed. The problems associated with lateral displacements at the abutment, and the solutions developed by the different states for most of the ill effects of abutment movements are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure was developed and used to study piling stresses and pile-soil interaction in integral abutment bridges. The finite element idealization consists of beam-column elements with geometric and material nonlinearities for the pile and nonlinear springs for the soil. An idealized soil model (modified Ramberg-Osgood model) was introduced in this investigation to obtain the tangent stiffness of the nonlinear spring elements. Several numerical examples are presented in order to establish the reliability of the finite element model and the computer software developed. Three problems with analytical solutions were first solved and compared with theoretical solutions. A 40 ft H pile (HP 10 X 42) in six typical Iowa soils was then analyzed by first applying a horizontal displacement (to simulate bridge motion) and no rotation at the top and then applying a vertical load V incrementally until failure occurred. Based on the numerical results, the failure mechanisms were generalized to be of two types: (a) lateral type failure and (b) vertical type failure. It appears that most piles in Iowa soils (sand, soft clay and stiff clay) failed when the applied vertical load reached the ultimate soil frictional resistance (vertical type failure). In very stiff clays, however, the lateral type failure occurs before vertical type failure because the soil is sufficiently stiff to force a plastic hinge to form in the pile as the specified lateral displacement is applied. Preliminary results from this investigation showed that the vertical load-carrying capacity of H piles is not significantly affected by lateral displacements of 2 inches in soft clay, stiff clay, loose sand, medium sand and dense sand. However, in very stiff clay (average blow count of 50 from standard penetration tests), it was found that the vertical load carrying capacity of the H pile is reduced by about 50 percent for 2 inches of lateral displacement and by about 20 percent for lateral displacement of 1 inch. On the basis of the preliminary results of this investigation, the 265-feet length limitation in Iowa for integral abutment concrete bridges appears to be very conservative.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations.

BACKGROUND: The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. RESULTS: Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. CONCLUSION: ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Parametric Approach to Blind Deconvolution of Nonlinear Channels

A parametric procedure for the blind inversion of nonlinear channels is proposed, based on a recent method of blind source separation in nonlinear mixtures. Experiments show that the proposed algorithms perform efficiently, even in the presence of hard distortion. The method, based on the minimization of the output mutual information, needs the knowledge of log-derivative of input distribution (the so-called score function). Each algorithm consists of three adaptive blocks: one devoted to adaptive estimation of the score function, and two other blocks estimating the inverses of the linear and nonlinear parts of the channel, (quasi-)optimally adapted using the estimated score functions. This paper is mainly concerned by the nonlinear part, for which we propose two parametric models, the first based on a polynomial model and the second on a neural network, while [14, 15] proposed non-parametric approaches.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Nonequilibrium phase transition in a model for the propagation of innovations among economic agents

We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X. Guardiola et al., Phys. Rev E 66, 026121 (2002)]. We show that the model can be regarded as a nonequilibrium surface growth model. This allows us to demonstrate the presence of a continuous roughening transition between a flat (system size independent fluctuations) and a rough phase (system size dependent fluctuations). Finite-size scaling studies at the transition strongly suggest that the dynamic critical transition does not belong to directed percolation and, in fact, critical exponents do not seem to fit in any of the known universality classes of nonequilibrium phase transitions. Finally, we present an explanation for the occurrence of the roughening transition and argue that avalanche driven dynamics is responsible for the novel critical behavior.

Monte Carlo study of a kinetic lattice model with random diffusion of disorder

We report Monte Carlo results for a nonequilibrium Ising-like model in two and three dimensions. Nearest-neighbor interactions J change sign randomly with time due to competing kinetics. There follows a fast and random, i.e., spin-configuration-independent diffusion of Js, of the kind that takes place in dilute metallic alloys when magnetic ions diffuse. The system exhibits steady states of the ferromagnetic (antiferromagnetic) type when the probability p that J>0 is large (small) enough. No counterpart to the freezing phenomena found in quenched spin glasses occurs. We compare our results with existing mean-field and exact ones, and obtain information about critical behavior.