A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Coalescent Method in Conjunction with Niche Modeling Reveals Cryptic Diversity among Centipedes in the Western Ghats of South India

Background: There has been growing interest in integrative taxonomy that uses data from multiple disciplines for species delimitation. Typically, in such studies, monophyly is taken as a proxy for taxonomic distinctiveness and these units are treated as potential species. However, monophyly could arise due to stochastic processes. Thus here, we have employed a recently developed tool based on coalescent approach to ascertain the taxonomic distinctiveness of various monophyletic units. Subsequently, the species status of these taxonomic units was further tested using corroborative evidence from morphology and ecology. This inter-disciplinary approach was implemented on endemic centipedes of the genus Digitipes (Attems 1930) from the Western Ghats (WG) biodiversity hotspot of India. The species of the genus Digitipes are morphologically conserved, despite their ancient late Cretaceous origin. Principal Findings: Our coalescent analysis based on mitochondrial dataset indicated the presence of nine putative species. The integrative approach, which includes nuclear, morphology, and climate datasets supported distinctiveness of eight putative species, of which three represent described species and five were new species. Among the five new species, three were morphologically cryptic species, emphasizing the effectiveness of this approach in discovering cryptic diversity in less explored areas of the tropics like the WG. In addition, species pairs showed variable divergence along the molecular, morphological and climate axes. Conclusions: A multidisciplinary approach illustrated here is successful in discovering cryptic diversity with an indication that the current estimates of invertebrate species richness for the WG might have been underestimated. Additionally, the importance of measuring multiple secondary properties of species while defining species boundaries was highlighted given variable divergence of each species pair across the disciplines.

Risk-sensitive control of continuous time Markov chains

We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.

Experimental and theoretical studies on static and dynamic pressure-concentration isotherms of MmNi(5-x)Al(x) (x=0, 0.3, 0.5 and 0.8) hydrides

The static and dynamic pressure concentration isotherms (PCIs) of MmNi(5-x)Al(x). (x = 0, 0.3, 0.5 and 0.8) hydrides were measured at different temperatures using volumetric method. The effect of Al substitution on PCI and thermodynamic properties were studied. The plateau pressure and maximum hydrogen storage capacity decreased with Al content whereas reaction enthalpy increased. The plateau pressure, plateau slope and hysteresis effect was observed more for dynamic PCIs compared to static PCIs. Different mathematical models used for metal hydride-based thermodynamic devices simulation are compared to select suitable model for static and dynamic PCI simulation of MmNi(5)-based hydrides. Few important physical coefficients (partial molar volume, reaction enthalpy, reaction entropy, etc.) useful for development of thermodynamic devices were estimated. A relation has been proposed to correlate aluminium content and physical coefficients for the prediction of unknown PCI. The simulated and experimental PCIs were found matching closely for both static and dynamic conditions. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Role of electrical resistance of electrodes in modeling of discharging and charging of flooded lead-acid batteries

Electrical resistance of both the electrodes of a lead-acid battery increases during discharge due to formation of lead sulfate, an insulator. Work of Metzendorf 1] shows that resistance increases sharply at about 65% conversion of active materials, and battery stops discharging once this critical conversion is reached. However, these aspects are not incorporated into existing mathematical models. Present work uses the results of Metzendorf 1], and develops a model that includes the effect of variable resistance. Further, it uses a reasonable expression to account for the decrease in active area during discharge instead of the empirical equations of previous work. The model's predictions are compared with observations of Cugnet et al. 2]. The model is as successful as the non-mechanistic models existing in literature. Inclusion of variation in resistance of electrodes in the model is important if one of the electrodes is a limiting reactant. If active materials are stoichiometrically balanced, resistance of electrodes can be very large at the end of discharge but has only a minor effect on charging of batteries. The model points to the significance of electrical conductivity of electrodes in the charging of deep discharged batteries. (C) 2014 Elsevier B.V. All rights reserved.

A dynamic view of the spread and intracellular distribution of Salmonella enterica.

The events that determine the dynamics of proliferation, spread and distribution of microbial pathogens within their hosts are surprisingly heterogeneous and poorly understood. We contend that understanding these phenomena at a sophisticated level with the help of mathematical models is a prerequisite for the development of truly novel, targeted preventative measures and drug regimes. We describe here recent studies of Salmonella enterica infections in mice which suggest that bacteria resist the antimicrobial environment inside host cells and spread to new sites, where infection foci develop, and thus avoid local escalation of the adaptive immune response. We further describe implications for our understanding of the pathogenic mechanism inside the host.

Bacterial growth rate and host factors as determinants of intracellular bacterial distributions in systemic Salmonella enterica infections.

Bacteria of the species Salmonella enterica cause a range of life-threatening diseases in humans and animals worldwide. The within-host quantitative, spatial, and temporal dynamics of S. enterica interactions are key to understanding how immunity acts on these infections and how bacteria evade immune surveillance. In this study, we test hypotheses generated from mathematical models of in vivo dynamics of Salmonella infections with experimental observation of bacteria at the single-cell level in infected mouse organs to improve our understanding of the dynamic interactions between host and bacterial mechanisms that determine net growth rates of S. enterica within the host. We show that both bacterial and host factors determine the numerical distributions of bacteria within host cells and thus the level of dispersiveness of the infection.

Theory and Application of the Transient Injection Well Test

Based on the theory of the pumping well test, the transient injection well test was suggested in this paper. The design method and the scope of application are discussed in detail. The mathematical models are developed for the short-time and long-time transient injection test respectively. A double logarithm type curve matching method was introduced for analyzing the field transient injection test data. A set of methods for the transient injection test design, experiment performance and data analysis were established. Some field tests were analyzed, and the results show that the test model and method are suitable for the transient injection test and can be used to deal with the real engineering problems.

Nonlinear Dynamic Response of Tension Leg Platform

Tension Leg Platform (TLP) is a typical compliant offshore structure for oil exploitation in deep water. Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that displacements (translations and rotations) are small magnitude. Herein a theoretical method for analyzing the nonlinear dynamic behavior of TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e. finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Using this theoretical model, we perform the numerical analysis of dynamic response of a representative TLP. The comparison between the degenerative linear solution of the proposed nonlinear model and the published one shows good agreements. Furthermore, numerical results are presented which illustrate that nonlinearities exert a distinct influence on the dynamic responses of the TLP.

Estudio del comportamiento térmico del instrumento TriboLAB durante su estancia en la Estación Espacial Internacional desde la perspectiva del análisis de datos funcionales

[ES]El objetivo principal de esta tesis de máster es el estudio del comportamiento térmico del instrumento TriboLAB durante su estancia en la Estación Espacial Internacional, junto con la comparación de dicho comportamiento con el pronosticado por los modelos térmicos matemáticos empleados en el diseño de su sistema de control térmico. El trabajo realizado ha permitido profundizar de forma importante en el conocimiento del mencionado comportamiento. Ello permitirá poner a disposición de otros experimentadores interesados en ubicar sus instrumentos en los balcones exteriores de la Estación Espacial Internacional, información real acerca del comportamiento térmico de un equipo de las características del TriboLAB en dichas condiciones. Información de gran interés para ser empleada en el diseño del control térmico de sus instrumentos, especialmente ahora que la vida útil de la Estación Espacial Internacional ha sido prorrogada hasta 2020. El control térmico de los equipos espaciales es un aspecto clave para asegurar su supervivencia y correcto funcionamiento bajo las extremas condiciones existentes en el espacio. Su misión es mantener los distintos componentes dentro de su rango de temperaturas admisibles, puesto que en caso contrario no podrían funcionar o incluso ni siquiera sobrevivir más allá de esas temperaturas. Adicionalmente ha sido posible comprobar la aplicabilidad de distintas técnicas de análisis de datos funcionales en lo que respecta al estudio del tipo de datos aquí contemplado. Así mismo, se han comparado los resultados de la campaña de ensayos térmicos con los modelos térmicos matemáticos que han guiado el diseño del control térmico, y que son una pieza fundamental en el diseño del control térmico de cualquier instrumento espacial. Ello ha permitido verificar tanto la validez del sistema de control térmico diseñado para el TriboLAB como con la adecuada similitud existente entre los resultados de los modelos térmicos matemáticos y las temperaturas registradas en el equipo. Todo ello, ha sido realizado desde la perspectiva del análisis de datos funcionales.

The Economics of Gasification: A Market-Based Approach

This paper deals with the economics of gasification facilities in general and IGCC power plants in particular. Regarding the prospects of these systems, passing the technological test is one thing, passing the economic test can be quite another. In this respect, traditional valuations assume constant input and/or output prices. Since this is hardly realistic, we allow for uncertainty in prices. We naturally look at the markets where many of the products involved are regularly traded. Futures markets on commodities are particularly useful for valuing uncertain future cash flows. Thus, revenues and variable costs can be assessed by means of sound financial concepts and actual market data. On the other hand, these complex systems provide a number of flexibility options (e.g., to choose among several inputs, outputs, modes of operation, etc.). Typically, flexibility contributes significantly to the overall value of real assets. Indeed, maximization of the asset value requires the optimal exercise of any flexibility option available. Yet the economic value of flexibility is elusive, the more so under (price) uncertainty. And the right choice of input fuels and/or output products is a main concern for the facility managers. As a particular application, we deal with the valuation of input flexibility. We follow the Real Options approach. In addition to economic variables, we also address technical and environmental issues such as energy efficiency, utility performance characteristics and emissions (note that carbon constraints are looming). Lastly, a brief introduction to some stochastic processes suitable for valuation purposes is provided.

On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment

In a probabilistic assessment of the performance of structures subjected to uncertain environmental loads such as earthquakes, an important problem is to determine the probability that the structural response exceeds some specified limits within a given duration of interest. This problem is known as the first excursion problem, and it has been a challenging problem in the theory of stochastic dynamics and reliability analysis. In spite of the enormous amount of attention the problem has received, there is no procedure available for its general solution, especially for engineering problems of interest where the complexity of the system is large and the failure probability is small.

The application of simulation methods to solving the first excursion problem is investigated in this dissertation, with the objective of assessing the probabilistic performance of structures subjected to uncertain earthquake excitations modeled by stochastic processes. From a simulation perspective, the major difficulty in the first excursion problem comes from the large number of uncertain parameters often encountered in the stochastic description of the excitation. Existing simulation tools are examined, with special regard to their applicability in problems with a large number of uncertain parameters. Two efficient simulation methods are developed to solve the first excursion problem. The first method is developed specifically for linear dynamical systems, and it is found to be extremely efficient compared to existing techniques. The second method is more robust to the type of problem, and it is applicable to general dynamical systems. It is efficient for estimating small failure probabilities because the computational effort grows at a much slower rate with decreasing failure probability than standard Monte Carlo simulation. The simulation methods are applied to assess the probabilistic performance of structures subjected to uncertain earthquake excitation. Failure analysis is also carried out using the samples generated during simulation, which provide insight into the probable scenarios that will occur given that a structure fails.

Optimal Abandonment of Coal-Fired Stations in the EU

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Modelling the dynamics of phytoplankton with the needs of the end user in mind

How to regulate phytoplankton growth in water supply reservoirs has continued to occupy managers and strategists for some fifty years or so, now, and mathematical models have always featured in their design and operational constraints. In recent years, rather more sophisticated simulation models have begun to be available and these, ideally, purport to provide the manager with improved forecasting of plankton blooms, the likely species and the sort of decision support that might permit management choices to be selected with increased confidence. This account describes the adaptation and application of one such model, PROTECH (Phytoplankton RespOnses To Environmental CHange) to the problems of plankton growth in reservoirs. This article supposes no background knowledge of the main algal types; neither does it attempt to catalogue the problems that their abundance may cause in lakes and reservoirs.

Estimativa do erro de discretização analítico na solução de equações diferenciais utilizando o Método de Volumes Finitos

As análises de erros são conduzidas antes de qualquer projeto a ser desenvolvido. A necessidade do conhecimento do comportamento do erro numérico em malhas estruturadas e não-estruturadas surge com o aumento do uso destas malhas nos métodos de discretização. Desta forma, o objetivo deste trabalho foi criar uma metodologia para analisar os erros de discretização gerados através do truncamento na Série de Taylor, aplicados às equações de Poisson e de Advecção-Difusão estacionárias uni e bidimensionais, utilizando-se o Método de Volumes Finitos em malhas do tipo Voronoi. A escolha dessas equações se dá devido a sua grande utilização em testes de novos modelos matemáticos e função de interpolação. Foram usados os esquemas Central Difference Scheme (CDS) e Upwind Difference Scheme(UDS) nos termos advectivos. Verificou-se a influência do tipo de condição de contorno e a posição do ponto gerador do volume na solução numérica. Os resultados analíticos foram confrontados com resultados experimentais para dois tipos de malhas de Voronoi, uma malha cartesiana e outra triangular comprovando a influência da forma do volume finito na solução numérica obtida. Foi percebido no estudo que a discretização usando o esquema CDS tem erros menores do que a discretização usando o esquema UDS conforme literatura. Também se percebe a diferença nos erros em volumes vizinhos nas malhas triangulares o que faz com que não se tenha uma uniformidade nos gráficos dos erros estudados. Percebeu-se que as malhas cartesianas com nó no centróide do volume tem menor erro de discretização do que malhas triangulares. Mas o uso deste tipo de malha depende da geometria do problema estudado