Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An introductory informatics theoretical framework, based on an integrable lattice model using quantized function algebras, for studying DNA-ionized gas interaction system

Usually we observe that Bio-physical systems or Bio-chemical systems are many a time based on nanoscale phenomenon in different host environments, which involve many particles can often not be solved explicitly. Instead a physicist, biologist or a chemist has to rely either on approximate or numerical methods. For a certain type of systems, called integrable in nature, there exist particular mathematical structures and symmetries which facilitate the exact and explicit description. Most integrable systems, we come across are low-dimensional, for instance, a one-dimensional chain of coupled atoms in DNA molecular system with a particular direction or exist as a vector in the environment. This theoretical research paper aims at bringing one of the pioneering ‘Reaction-Diffusion’ aspects of the DNA-plasma material system based on an integrable lattice model approach utilizing quantized functional algebras, to disseminate the new developments, initiate novel computational and design paradigms.

A Model-Based Approach for Making Ecological Inference from Distance Sampling Data

We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike’s information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

The Kumaraswamy Gumbel distribution

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

Irreversible spherical model and its stationary entropy production rate

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

Effect of the thermostat in the molecular dynamics simulation on the folding of the model protein chignolin

Molecular dynamics simulations of the model protein chignolin with explicit solvent were carried out, in order to analyze the influence of the Berendsen thermostat on the evolution and folding of the peptide. The dependence of the peptide behavior on temperature was tested with the commonly employed thermostat scheme consisting of one thermostat for the protein and another for the solvent. The thermostat coupling time of the protein was increased to infinity, when the protein is not in direct contact with the thermal bath, a situation known as minimally invasive thermostat. In agreement with other works, it was observed that only in the last situation the instantaneous temperature of the model protein obeys a canonical distribution. As for the folding studies, it was shown that, in the applications of the commonly utilized thermostat schemes, the systems are trapped in local minima regions from which it has difficulty escaping. With the minimally invasive thermostat the time that the protein needs to fold was reduced by two to three times. These results show that the obstacles to the evolution of the extended peptide to the folded structure can be overcome when the temperature of the peptide is not directly controlled.

Independent predictors and a prognostic model for surgical outcome in refractory frontal lobe epilepsy

Purpose: Refractory frontal lobe epilepsy (FLE) remains one of the most challenging surgically remediable epilepsy syndromes. Nevertheless, definition of independent predictors and predictive models of postsurgical seizure outcome remains poorly explored in FLE. Methods: We retrospectively analyzed data from 70 consecutive patients with refractory FLE submitted to surgical treatment at our center from July 1994 to December 2006. Univariate results were submitted to logistic regression models and Cox proportional hazards regression to identify isolated risk factors for poor surgical results and to construct predictive models for surgical outcome in FLE. Results: From 70 patients submitted to surgery, 45 patients (64%) had favorable outcome and 37 (47%) became seizure free. Isolated risk factors for poor surgical outcome are expressed in hazard ratio (H.R.) and were time of epilepsy (H.R.=4.2; 95% C.I.=.1.5-11.7; p=0.006), ictal EEG recruiting rhythm (H.R. = 2.9; 95% C.I. = 1.1-7.7; p=0.033); normal MRI (H.R. = 4.8; 95% C.I. = 1.4-16.6; p = 0.012), and MRI with lesion involving eloquent cortex (H.R. = 3.8; 95% C.I. = 1.2-12.0; p = 0.021). Based on these variables and using a logistic regression model we constructed a model that correctly predicted long-term surgical outcome in up to 80% of patients. Conclusion: Among independent risk factors for postsurgical seizure outcome, epilepsy duration is a potentially modifiable factor that could impact surgical outcome in FLE. Early diagnosis, presence of an MRI lesion not involving eloquent cortex, and ictal EEG without recruited rhythm independently predicted favorable outcome in this series. (C) 2011 Elsevier B.V. All rights reserved.

Solvable model for template coexistence in protocells

Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steadystate probability density of protocell compositions.

A dynamic model of oceanic sulfur (DMOS) applied to the Sargasso Sea: Simulating the dimethylsulfide (DMS) summer paradox

[EN]A new one-dimensional model of DMSP/DMS dynamics (DMOS) is developed and applied to the Sargasso Sea in order to explain what drives the observed dimethylsulfide (DMS) summer paradox: a summer DMS concentration maximum concurrent with a minimum in the biomass of phytoplankton, the producers of the DMS precursor dimethylsulfoniopropionate (DMSP). Several mechanisms have been postulated to explain this mismatch: a succession in phytoplankton species composition towards higher relative abundances of DMSP producers in summer; inhibition of bacterial DMS consumption by ultraviolet radiation (UVR); and direct DMS production by phytoplankton due to UVR-induced oxidative stress. None of these hypothetical mechanisms, except for the first one, has been tested with a dynamic model. We have coupled a new sulfur cycle model that incorporates the latest knowledge on DMSP/DMS dynamics to a preexisting nitrogen/carbon-based ecological model that explicitly simulates the microbial-loop. This allows the role of bacteria in DMS production and consumption to be represented and quantified. The main improvements of DMOS with respect to previous DMSP/DMS models are the explicit inclusion of: solar-radiation inhibition of bacterial sulfur uptakes; DMS exudation by phytoplankton caused by solar-radiation-induced stress; and uptake of dissolved DMSP by phytoplankton. We have conducted a series of modeling experiments where some of the DMOS sulfur paths are turned “off” or “on,” and the results on chlorophyll-a, bacteria, DMS, and DMSP (particulate and dissolved) concentrations have been compared with climatological data of these same variables. The simulated rate of sulfur cycling processes are also compared with the scarce data available from previous works. All processes seem to play a role in driving DMS seasonality. Among them, however, solar-radiation-induced DMS exudation by phytoplankton stands out as the process without which the model is unable to produce realistic DMS simulations and reproduce the DMS summer paradox.

Earthquake forecasting and seismic hazard analysis: some insights on the testing phase and the modeling

This thesis is divided in three chapters. In the first chapter we analyse the results of the world forecasting experiment run by the Collaboratory for the Study of Earthquake Predictability (CSEP). We take the opportunity of this experiment to contribute to the definition of a more robust and reliable statistical procedure to evaluate earthquake forecasting models. We first present the models and the target earthquakes to be forecast. Then we explain the consistency and comparison tests that are used in CSEP experiments to evaluate the performance of the models. Introducing a methodology to create ensemble forecasting models, we show that models, when properly combined, are almost always better performing that any single model. In the second chapter we discuss in depth one of the basic features of PSHA: the declustering of the seismicity rates. We first introduce the Cornell-McGuire method for PSHA and we present the different motivations that stand behind the need of declustering seismic catalogs. Using a theorem of the modern probability (Le Cam's theorem) we show that the declustering is not necessary to obtain a Poissonian behaviour of the exceedances that is usually considered fundamental to transform exceedance rates in exceedance probabilities in the PSHA framework. We present a method to correct PSHA for declustering, building a more realistic PSHA. In the last chapter we explore the methods that are commonly used to take into account the epistemic uncertainty in PSHA. The most widely used method is the logic tree that stands at the basis of the most advanced seismic hazard maps. We illustrate the probabilistic structure of the logic tree, and then we show that this structure is not adequate to describe the epistemic uncertainty. We then propose a new probabilistic framework based on the ensemble modelling that properly accounts for epistemic uncertainties in PSHA.

Run-Time Evolution through Explicit Meta-Objects

Software must be constantly adapted due to evolving domain knowledge and unanticipated requirements changes. To adapt a system at run-time we need to reflect on its structure and its behavior. Object-oriented languages introduced reflection to deal with this issue, however, no reflective approach up to now has tried to provide a unified solution to both structural and behavioral reflection. This paper describes Albedo, a unified approach to structural and behavioral reflection. Albedo is a model of fined-grained unanticipated dynamic structural and behavioral adaptation. Instead of providing reflective capabilities as an external mechanism we integrate them deeply in the environment. We show how explicit meta-objects allow us to provide a range of reflective features and thereby evolve both application models and environments at run-time.

Self-organised transients in a neural mass model of epileptogenic tissue dynamics

Stimulation of human epileptic tissue can induce rhythmic, self-terminating responses on the EEG or ECoG. These responses play a potentially important role in localising tissue involved in the generation of seizure activity, yet the underlying mechanisms are unknown. However, in vitro evidence suggests that self-terminating oscillations in nervous tissue are underpinned by non-trivial spatio-temporal dynamics in an excitable medium. In this study, we investigate this hypothesis in spatial extensions to a neural mass model for epileptiform dynamics. We demonstrate that spatial extensions to this model in one and two dimensions display propagating travelling waves but also more complex transient dynamics in response to local perturbations. The neural mass formulation with local excitatory and inhibitory circuits, allows the direct incorporation of spatially distributed, functional heterogeneities into the model. We show that such heterogeneities can lead to prolonged reverberating responses to a single pulse perturbation, depending upon the location at which the stimulus is delivered. This leads to the hypothesis that prolonged rhythmic responses to local stimulation in epileptogenic tissue result from repeated self-excitation of regions of tissue with diminished inhibitory capabilities. Combined with previous models of the dynamics of focal seizures this macroscopic framework is a first step towards an explicit spatial formulation of the concept of the epileptogenic zone. Ultimately, an improved understanding of the pathophysiologic mechanisms of the epileptogenic zone will help to improve diagnostic and therapeutic measures for treating epilepsy.