Stochastic resonance in a dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a nonzero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e., when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.

Energy relaxation in nonlinear one-dimensional lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Between manualized treatments and principle-guided psychotherapy: illustration in the case of Caroline

My case study of "Caroline"-a 26 year old presenting with depression, PTSD symptoms, and a history of sexual abuse as a teenager-represents a "third way" between (1) a strict adherence to a manualized treatment, and (2) a principle-guided therapy, in which the therapy follows particular theoretical concepts, but depends on the therapist's clinical judgement to flexibly apply them to the individual case. Specifically, in my therapy with Caroline (Kramer, 2009), I employed Foa and Rothbaum's (1998) cognitive-behavioral, "Prolonged Exposure" (PE) manual for PTSD, but deviated from it in certain ways based upon my evaluation of Caroline's individualized goals and reactions using Grawe and Caspar's "Plan Analysis," which is a cross-theoretical model for assessment and treatment planning. In their commentaries on my case study of Caroline, Caspar (2009) and Haldimann-Balli (see Appendix in Kramer, 2009) support my use of this third way. On the other hand, the other commentators-Muller (2009) and Hembree and Brinen (2009)-critique my handling of the case, arguing that strict adherence to the Foa and Rothbaum manual would have resulted in a more cost-effective therapy. In this article, I respond to the important issues raised by the four commentators.

Zinc adsorption in highly weathered soils

The objective of this work was to assess the effects of pH and ionic strength upon zinc adsorption, in three highly weathered variable charge soils. Adsorption isotherms were elaborated from batch adsorption experiments, with increasing Zn concentrations (0-80 mg L-1), and adsorption envelopes were constructed through soil samples reactions with 0.01, 0.1 and 1 mol L-1 Ca(NO3)2 solutions containing 5 mg L-1 of Zn, with an increasing pH value from 3 to 8. Driving force of reaction was quantified by Gibbs free energy and separation factor. Isotherms were C-, H- and L-type and experimental results were fitted to nonlinear Langmuir model. Maximum adsorption ranged from 59-810 mg kg-1, and Zn affinity was greater in subsoil (0.13-0.81 L kg-1) than in the topsoil samples (0.01-0.34 L kg-1). Zinc adsorption was favorable and spontaneous, and showed sharply increase (20-90%) in the 4-6 pH range. No effect of ionic strength was observed at pH values below 5, because specific adsorption mechanisms predominated in the 3-5 pH range. Above pH 5, and in subsoil samples, Zn was adsorbed by electrostatic mechanisms, since ionic strength effect was observed. Despite depth and ionic strength effects, Zn adsorption depends mainly on the pH.

Simulating maize phenology as a function of air temperature with a linear and a nonlinear model

The objective of this study was to adapt a nonlinear model (Wang and Engel - WE) for simulating the phenology of maize (Zea mays L.), and to evaluate this model and a linear one (thermal time), in order to predict developmental stages of a field-grown maize variety. A field experiment, during 2005/2006 and 2006/2007 was conducted in Santa Maria, RS, Brazil, in two growing seasons, with seven sowing dates each. Dates of emergence, silking, and physiological maturity of the maize variety BRS Missões were recorded in six replications in each sowing date. Data collected in 2005/2006 growing season were used to estimate the coefficients of the two models, and data collected in the 2006/2007 growing season were used as independent data set for model evaluations. The nonlinear WE model accurately predicted the date of silking and physiological maturity, and had a lower root mean square error (RMSE) than the linear (thermal time) model. The overall RMSE for silking and physiological maturity was 2.7 and 4.8 days with WE model, and 5.6 and 8.3 days with thermal time model, respectively.

Impact of increasing mean air temperature on the development of rice and red rice

The objective of this study was to assess the development response of cultivated rice and red rice to different increases in minimum and maximum daily air temperatures, in Santa Maria, Rio Grande do Sul State, Brazil. One hundred years climate scenarios of temperatures 0, +1, +2, +3, +4, and +5ºC, with symmetric and asymmetric increases in minimum and maximum daily air temperatures were created, using the LARS-WG Weather Generator, and a 1969-2003 database. Nine cultivated rice genotypes (IRGA 421, IRGA 416, IRGA 417, IRGA 420, BRS 7 TAIM, BR-IRGA 409, EPAGRI 109, EEA 406 and a hybrid), and two red rice biotypes (awned black hull-ABHRR, and awned yellow hull-AYHRR) were used. The dates of panicle differentiation (R1), anthesis (R4), and all grains with brown hulls (R9) were estimated with a nonlinear simulation model. Overall, the duration of the emergence-R1 phase decreased, whereas the duration of the R1-R4 and R4-R9 phases most often increased, as temperature increased in the climate change scenarios. The simulated rice development response to elevated temperature was not the same, when the increase in minimum and maximum temperature was symmetric or asymmetric.

Improving node number simulation in soybean

The objective of this study was to improve the simulation of node number in soybean cultivars with determinate stem habits. A nonlinear model considering two approaches to input daily air temperature data (daily mean temperature and daily minimum/maximum air temperatures) was used. The node number on the main stem data of ten soybean cultivars was collected in a three-year field experiment (from 2004/2005 to 2006/2007) at Santa Maria, RS, Brazil. Node number was simulated using the Soydev model, which has a nonlinear temperature response function [f(T)]. The f(T) was calculated using two methods: using daily mean air temperature calculated as the arithmetic average among daily minimum and maximum air temperatures (Soydev tmean); and calculating an f(T) using minimum air temperature and other using maximum air temperature and then averaging the two f(T)s (Soydev tmm). Root mean square error (RMSE) and deviations (simulated minus observed) were used as statistics to evaluate the performance of the two versions of Soydev. Simulations of node number in soybean were better with the Soydev tmm version, with a 0.5 to 1.4 node RMSE. Node number can be simulated for several soybean cultivars using only one set of model coefficients, with a 0.8 to 2.4 node RMSE.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

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.

On the inefficiency of the restricted maximum likelihood

The restricted maximum likelihood is preferred by many to the full maximumlikelihood for estimation with variance component and other randomcoefficientmodels, because the variance estimator is unbiased. It is shown that thisunbiasednessis accompanied in some balanced designs by an inflation of the meansquared error.An estimator of the cluster-level variance that is uniformly moreefficient than the fullmaximum likelihood is derived. Estimators of the variance ratio are alsostudied.

Características anatômicas e morfofisiológicas de lâminas foliares de genótipos de Panicum maximum

O objetivo deste trabalho foi avaliar as características anatômicas e morfofisiológicas de lâminas foliares de genótipos de Panicum maximum e determinar quais as mais relevantes para a discriminação precoce do valor nutritivo de genótipos promissores. O experimento foi realizado entre janeiro de 2006 e novembro de 2007, em Dourados, MS. Foram avaliados 23 genótipos de P. maximum pré-selecionados do programa de melhoramento da Embrapa Gado de Corte. Utilizou-se o delineamento experimental de blocos ao acaso, com três repetições. Foram avaliadas 27 características anatômicas e morfofisiológicas de lâminas foliares em cada genótipo. Para cada característica estudada, os resultados foram agrupados pelo teste de Scott-Knott. A importância relativa das características avaliadas para a avaliação da divergência genética foi determinada pelo método de Singh. As características que melhor discriminaram os genótipos foram as proporções - na seção transversal das lâminas - das epidermes adaxial, abaxial, adaxial + abaxial, do mesofilo e do tecido vascular + esclerênquima. A área foliar específica, a área foliar e o comprimento de lâmina foram as características morfofisiológicas que mais contribuíram para a discriminação dos genótipos; porém, sua importância relativa foi muito menor que a das características anatômicas. A proporção ocupada pela bainha parenquimática dos feixes e a largura das lâminas apresentam instabilidade fenotípica.