Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Resting-State Functional Connectivity Emerges from Structurally and Dynamically Shaped Slow Linear Fluctuations.

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

External Fluctuations in Front Propagation

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Audit report on the Iowa Water Pollution Control Works Financing Program and the Iowa Drinking Water Facilities Financing Program, joint programs of the Iowa Finance Authority and the Iowa Department of Natural Resources for the year ended June 30, 2012

Audit report on the Iowa Water Pollution Control Works Financing Program and the Iowa Drinking Water Facilities Financing Program, joint programs of the Iowa Finance Authority and the Iowa Department of Natural Resources for the year ended June 30, 2012

Learning wind fields with multiple kernels

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine region.

Linear relations between writhe and minimal crossing number in Conway families of ideal knots and links

We showed earlier how to predict the writhe of any rational knot or link in its ideal geometric configuration, or equivalently the average of the 3D writhe over statistical ensembles of random configurations of a given knot or link (Cerf and Stasiak 2000 Proc. Natl Acad. Sci. USA 97 3795). There is no general relation between the minimal crossing number of a knot and the writhe of its ideal geometric configuration. However, within individual families of knots linear relations between minimal crossing number and writhe were observed (Katritch et al 1996 Nature 384 142). Here we present a method that allows us to express the writhe as a linear function of the minimal crossing number within Conway families of knots and links in their ideal configuration. The slope of the lines and the shift between any two lines with the same

Youthful Offender Programs, 2008

This program is done by CJJP. The programs are sponsored by this department for is risk youths to keep them from making bad choices and give them a place to go.

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.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.