Modeling and simulation of population balances for particulate processes

This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are property coordinate(s), e.g., the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation, crystallization, polymerization, emulsion and cell dynamics. The semi-discrete high resolution schemes are proposed for solving PBEs modeling one and two-dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two-dimensional cases ...

Modeling resting-state functional networks when the cortex falls asleep: local and global changes.

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized" electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep" due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized network.

Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty

This paper extends the Nelson-Siegel linear factor model by developing a flexible macro-finance framework for modeling and forecasting the term structure of US interest rates. Our approach is robust to parameter uncertainty and structural change, as we consider instabilities in parameters and volatilities, and our model averaging method allows for investors' model uncertainty over time. Our time-varying parameter Nelson-Siegel Dynamic Model Averaging (NS-DMA) predicts yields better than standard benchmarks and successfully captures plausible time-varying term premia in real time. The proposed model has significant in-sample and out-of-sample predictability for excess bond returns, and the predictability is of economic value.

Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula

We investigate the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modelling and forecasting market risk. First, we construct “high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate its usefulness by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for the high-minus-low portfolios. From back-testing, e find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Treeline and climate change : analyzing and modeling patterns and shifts in the Swiss Alps

Summary: Global warming has led to an average earth surface temperature increase of about 0.7 °C in the 20th century, according to the 2007 IPCC report. In Switzerland, the temperature increase in the same period was even higher: 1.3 °C in the Northern Alps anal 1.7 °C in the Southern Alps. The impacts of this warming on ecosystems aspecially on climatically sensitive systems like the treeline ecotone -are already visible today. Alpine treeline species show increased growth rates, more establishment of young trees in forest gaps is observed in many locations and treelines are migrating upwards. With the forecasted warming, this globally visible phenomenon is expected to continue. This PhD thesis aimed to develop a set of methods and models to investigate current and future climatic treeline positions and treeline shifts in the Swiss Alps in a spatial context. The focus was therefore on: 1) the quantification of current treeline dynamics and its potential causes, 2) the evaluation and improvement of temperaturebased treeline indicators and 3) the spatial analysis and projection of past, current and future climatic treeline positions and their respective elevational shifts. The methods used involved a combination of field temperature measurements, statistical modeling and spatial modeling in a geographical information system. To determine treeline shifts and assign the respective drivers, neighborhood relationships between forest patches were analyzed using moving window algorithms. Time series regression modeling was used in the development of an air-to-soil temperature transfer model to calculate thermal treeline indicators. The indicators were then applied spatially to delineate the climatic treeline, based on interpolated temperature data. Observation of recent forest dynamics in the Swiss treeline ecotone showed that changes were mainly due to forest in-growth, but also partly to upward attitudinal shifts. The recent reduction in agricultural land-use was found to be the dominant driver of these changes. Climate-driven changes were identified only at the uppermost limits of the treeline ecotone. Seasonal mean temperature indicators were found to be the best for predicting climatic treelines. Applying dynamic seasonal delimitations and the air-to-soil temperature transfer model improved the indicators' applicability for spatial modeling. Reproducing the climatic treelines of the past 45 years revealed regionally different attitudinal shifts, the largest being located near the highest mountain mass. Modeling climatic treelines based on two IPCC climate warming scenarios predicted major shifts in treeline altitude. However, the currently-observed treeline is not expected to reach this limit easily, due to lagged reaction, possible climate feedback effects and other limiting factors. Résumé: Selon le rapport 2007 de l'IPCC, le réchauffement global a induit une augmentation de la température terrestre de 0.7 °C en moyenne au cours du 20e siècle. En Suisse, l'augmentation durant la même période a été plus importante: 1.3 °C dans les Alpes du nord et 1.7 °C dans les Alpes du sud. Les impacts de ce réchauffement sur les écosystèmes - en particuliers les systèmes sensibles comme l'écotone de la limite des arbres - sont déjà visibles aujourd'hui. Les espèces de la limite alpine des forêts ont des taux de croissance plus forts, on observe en de nombreux endroits un accroissement du nombre de jeunes arbres s'établissant dans les trouées et la limite des arbres migre vers le haut. Compte tenu du réchauffement prévu, on s'attend à ce que ce phénomène, visible globalement, persiste. Cette thèse de doctorat visait à développer un jeu de méthodes et de modèles pour étudier dans un contexte spatial la position présente et future de la limite climatique des arbres, ainsi que ses déplacements, au sein des Alpes suisses. L'étude s'est donc focalisée sur: 1) la quantification de la dynamique actuelle de la limite des arbres et ses causes potentielles, 2) l'évaluation et l'amélioration des indicateurs, basés sur la température, pour la limite des arbres et 3) l'analyse spatiale et la projection de la position climatique passée, présente et future de la limite des arbres et des déplacements altitudinaux de cette position. Les méthodes utilisées sont une combinaison de mesures de température sur le terrain, de modélisation statistique et de la modélisation spatiale à l'aide d'un système d'information géographique. Les relations de voisinage entre parcelles de forêt ont été analysées à l'aide d'algorithmes utilisant des fenêtres mobiles, afin de mesurer les déplacements de la limite des arbres et déterminer leurs causes. Un modèle de transfert de température air-sol, basé sur les modèles de régression sur séries temporelles, a été développé pour calculer des indicateurs thermiques de la limite des arbres. Les indicateurs ont ensuite été appliqués spatialement pour délimiter la limite climatique des arbres, sur la base de données de températures interpolées. L'observation de la dynamique forestière récente dans l'écotone de la limite des arbres en Suisse a montré que les changements étaient principalement dus à la fermeture des trouées, mais aussi en partie à des déplacements vers des altitudes plus élevées. Il a été montré que la récente déprise agricole était la cause principale de ces changements. Des changements dus au climat n'ont été identifiés qu'aux limites supérieures de l'écotone de la limite des arbres. Les indicateurs de température moyenne saisonnière se sont avérés le mieux convenir pour prédire la limite climatique des arbres. L'application de limites dynamiques saisonnières et du modèle de transfert de température air-sol a amélioré l'applicabilité des indicateurs pour la modélisation spatiale. La reproduction des limites climatiques des arbres durant ces 45 dernières années a mis en évidence des changements d'altitude différents selon les régions, les plus importants étant situés près du plus haut massif montagneux. La modélisation des limites climatiques des arbres d'après deux scénarios de réchauffement climatique de l'IPCC a prédit des changements majeurs de l'altitude de la limite des arbres. Toutefois, l'on ne s'attend pas à ce que la limite des arbres actuellement observée atteigne cette limite facilement, en raison du délai de réaction, d'effets rétroactifs du climat et d'autres facteurs limitants.

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

The dynamics of dengue virus serotype 3 introduction and dispersion in the state of Bahia, Brazil

By 2002, dengue virus serotype 1 (DENV-1) and DENV-2 had circulated for more than a decade in Brazil. In 2002, the introduction of DENV-3 in the state of Bahia produced a massive epidemic and the first cases of dengue hemorrhagic fever. Based on the standardized frequency, timing and location of viral isolations by the state's Central Laboratory, DENV-3 probably entered Bahia through its capital, Salvador, and then rapidly disseminated to other cities, following the main roads. A linear regression model that included traffic flow, distance from the capital and DENV-1 circulation (r² = 0.24, p = 0.001) supported this hypothesis. This pattern was not seen for serotypes already in circulation and was not seen for DENV-3 in the following year. Human population density was another important factor in the intensity of viral circulation. Neither DENV-1 nor DENV-2 fit this model for 2001 or 2003. Since the vector has limited flight range and vector densities fail to correlate with intensity of viral circulation, this distribution represents the movement of infected people and to some extent mosquitoes. This pattern may mimic person-to-person spread of a new infection.

Homology modeling and metabolism prediction of human carboxylesterase-2 using docking analyses by GriDock: a parallelized tool based on AutoDock 4.0.

Metabolic problems lead to numerous failures during clinical trials, and much effort is now devoted to developing in silico models predicting metabolic stability and metabolites. Such models are well known for cytochromes P450 and some transferases, whereas less has been done to predict the activity of human hydrolases. The present study was undertaken to develop a computational approach able to predict the hydrolysis of novel esters by human carboxylesterase hCES2. The study involved first a homology modeling of the hCES2 protein based on the model of hCES1 since the two proteins share a high degree of homology (congruent with 73%). A set of 40 known substrates of hCES2 was taken from the literature; the ligands were docked in both their neutral and ionized forms using GriDock, a parallel tool based on the AutoDock4.0 engine which can perform efficient and easy virtual screening analyses of large molecular databases exploiting multi-core architectures. Useful statistical models (e.g., r (2) = 0.91 for substrates in their unprotonated state) were calculated by correlating experimental pK(m) values with distance between the carbon atom of the substrate's ester group and the hydroxy function of Ser228. Additional parameters in the equations accounted for hydrophobic and electrostatic interactions between substrates and contributing residues. The negatively charged residues in the hCES2 cavity explained the preference of the enzyme for neutral substrates and, more generally, suggested that ligands which interact too strongly by ionic bonds (e.g., ACE inhibitors) cannot be good CES2 substrates because they are trapped in the cavity in unproductive modes and behave as inhibitors. The effects of protonation on substrate recognition and the contrasting behavior of substrates and products were finally investigated by MD simulations of some CES2 complexes.

Modeling the biophysical impacts of global change in mountain biosphere reserves

Mountains and mountain societies provide a wide range of goods and services to humanity, but they are particularly sensitive to the effects of global environmental change. Thus, the definition of appropriate management regimes that maintain the multiple functions of mountain regions in a time of greatly changing climatic, economic, and societal drivers constitutes a significant challenge. Management decisions must be based on a sound understanding of the future dynamics of these systems. The present article reviews the elements required for an integrated effort to project the impacts of global change on mountain regions, and recommends tools that can be used at 3 scientific levels (essential, improved, and optimum). The proposed strategy is evaluated with respect to UNESCO's network of Mountain Biosphere Reserves (MBRs), with the intention of implementing it in other mountain regions as well. First, methods for generating scenarios of key drivers of global change are reviewed, including land use/land cover and climate change. This is followed by a brief review of the models available for projecting the impacts of these scenarios on (1) cryospheric systems, (2) ecosystem structure and diversity, and (3) ecosystem functions such as carbon and water relations. Finally, the cross-cutting role of remote sensing techniques is evaluated with respect to both monitoring and modeling efforts. We conclude that a broad range of techniques is available for both scenario generation and impact assessments, many of which can be implemented without much capacity building across many or even most MBRs. However, to foster implementation of the proposed strategy, further efforts are required to establish partnerships between scientists and resource managers in mountain areas.

Bilinear models for spatio-temporal point distribution analysis: application to extrapolation of left ventricular, biventricular and whole heart cardiac dynamics

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart atdifferent points in the same cycle, we can use the bilinearmodel to establish this. Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, weconclude that the dynamics were indeed separated from theinter-subject variability in our dataset.

Pitfalls in the modeling of forward-looking price setting and investment decisions

The present paper makes progress in explaining the role of capital for inflation and output dynamics. We followWoodford (2003, Ch. 5) in assuming Calvo pricing combined with a convex capital adjustment cost at the firm level. Our main result is that capital accumulation affects inflation dynamics primarily through its impact on the marginal cost. This mechanism is much simpler than the one implied by the analysis in Woodford's text. The reason is that his analysis suffers from a conceptual mistake, as we show. The latter obscures the economic mechanism through which capital affects inflation and output dynamics in the Calvo model, as discussed in Woodford (2004).

Inflation and output dynamics with firm-owned capital

We model firm-owned capital in a stochastic dynamic New-Keynesian generalequilibrium model à la Calvo. We find that this structure impliesequilibrium dynamics which are quantitatively di¤erent from the onesassociated with a benchmark case where households accumulate capital andrent it to firms. Our findings therefore stress the importance ofmodeling an investment decision at the firm level in addition to ameaningful price setting decision. Along the way we argue that the problemof modeling firm-owned capital with Calvo price-setting has not been solvedin a correct way in the previous literature.