A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

A model updating technique based on FRFs for damped structures

Model updating methods often neglect that in fact all physical structures are damped. Such simplification relies on the structural modelling approach, although it compromises the accuracy of the predictions of the structural dynamic behaviour. In the present work, the authors address the problem of finite element (FE) model updating based on measured frequency response functions (FRFs), considering damping. The proposed procedure is based upon the complex experimental data, which contains information related to the damped FE model parameters and presents the advantage of requiring no prior knowledge about the damping matrix structure or its content, only demanding the definition of the damping type. Numerical simulations are performed in order to establish the applicability of the proposed damped FE model updating technique and its results are discussed in terms of the correlation between the simulated experimental complex FRFs and the ones obtained from the updated FE model.

Machine learning Vasicek model calibration with Gaussian processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.

Creació i transmissió de coneixement als clústers empresarials: un model de simulació

Projecte de recerca elaborat a partir d’una estada a l’Snider Entrepreneurial Research Center de la Wharton School de la University of Pennsilvanya y, EUA entre juliol i desembre del 2007. L’objectiu d’aquest projecte és estudiar la relació entre les estratègies de gestió del coneixement i les tecnologies de la informació i la comunicació (TIC) en l’evolució de les poblacions d’organitzacions i els seus efectes en els patrons industrials d’aglomeració espacial. Per a això s’adopta una aproximació fonamentada en la utilització d'un model basats en agents per a obtenir hipòtesis significatives i provables sobre l’evolució de les poblacions d’organitzacions al si de clústers geogràfics. El model de simulació incorpora les perspectives i supòsits d’un marc conceptual, l’Espai de la Informació o I-Space. Això permet una conceptualització basada en la informació de l’entorn econòmic que té en compte les seves dimensions espacials i temporals. Mitjançant els paràmetres del model es dóna la possibilitat d’assignar estratègies específiques de gestió del coneixement als diversos agents i de localitzar-los en una posició de l’espai físic. La simulació mostra com l'adopció d'estratègies diverses pel que fa a la gestió del coneixement influeix en l'evolució de les organitzacions i de la seva localització espacial, i que aquesta evolució es veu modificada pel desenvolupament de les TIC. A través de la modelització de dos casos ben coneguts de clústers geogràfics d’alta tecnologia, com són Silicon Valley a Califòrnia i la Route 128 als voltants de Boston, s’estudia la interrelació entre les estratègies de gestió del coneixement adoptades per les empreses i la seva tria de localització espacial, i també com això és afectat per l’evolució de les tecnologies de la informació i de la comunicació (TIC). Els resultats obtinguts generen una sèrie d’hipòtesis de rica potencialitat sobre l’impacte del desenvolupament de les TIC en la dinàmica d’aquests clusters geogràfics. Concretament, es troba que la estructuració del coneixement i l’aglomeració espacial co-evolucionen i que aquesta coevolució es veu significativament alterada pel desenvolupament de les TIC.

Uncertainty Quantification Of A Semi-Supervised Support Vector Regression Reservoir Model

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. Recent advances in machine learning offer a novel approach to model spatial distribution of petrophysical properties in complex reservoirs alternative to geostatistics. The approach is based of semisupervised learning, which handles both ?labelled? observed data and ?unlabelled? data, which have no measured value but describe prior knowledge and other relevant data in forms of manifolds in the input space where the modelled property is continuous. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic geological features and describe stochastic variability and non-uniqueness of spatial properties. On the other hand, it is able to capture and preserve key spatial dependencies such as connectivity of high permeability geo-bodies, which is often difficult in contemporary petroleum reservoir studies. Semi-supervised SVR as a data driven algorithm is designed to integrate various kind of conditioning information and learn dependences from it. The semi-supervised SVR model is able to balance signal/noise levels and control the prior belief in available data. In this work, stochastic semi-supervised SVR geomodel is integrated into Bayesian framework to quantify uncertainty of reservoir production with multiple models fitted to past dynamic observations (production history). Multiple history matched models are obtained using stochastic sampling and/or MCMC-based inference algorithms, which evaluate posterior probability distribution. Uncertainty of the model is described by posterior probability of the model parameters that represent key geological properties: spatial correlation size, continuity strength, smoothness/variability of spatial property distribution. The developed approach is illustrated with a fluvial reservoir case. The resulting probabilistic production forecasts are described by uncertainty envelopes. The paper compares the performance of the models with different combinations of unknown parameters and discusses sensitivity issues.

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Applicability of a distributed watershed pollution model in a data-poor environment in Santa Catarina State, Brazil

Intensification of agricultural production without a sound management and regulations can lead to severe environmental problems, as in Western Santa Catarina State, Brazil, where intensive swine production has caused large accumulations of manure and consequently water pollution. Natural resource scientists are asked by decision-makers for advice on management and regulatory decisions. Distributed environmental models are useful tools, since they can be used to explore consequences of various management practices. However, in many areas of the world, quantitative data for model calibration and validation are lacking. The data-intensive distributed environmental model AgNPS was applied in a data-poor environment, the upper catchment (2,520 ha) of the Ariranhazinho River, near the city of Seara, in Santa Catarina State. Steps included data preparation, cell size selection, sensitivity analysis, model calibration and application to different management scenarios. The model was calibrated based on a best guess for model parameters and on a pragmatic sensitivity analysis. The parameters were adjusted to match model outputs (runoff volume, peak runoff rate and sediment concentration) closely with the sparse observed data. A modelling grid cell resolution of 150 m adduced appropriate and computer-fit results. The rainfall runoff response of the AgNPS model was calibrated using three separate rainfall ranges (< 25, 25-60, > 60 mm). Predicted sediment concentrations were consistently six to ten times higher than observed, probably due to sediment trapping along vegetated channel banks. Predicted N and P concentrations in stream water ranged from just below to well above regulatory norms. Expert knowledge of the area, in addition to experience reported in the literature, was able to compensate in part for limited calibration data. Several scenarios (actual, recommended and excessive manure applications, and point source pollution from swine operations) could be compared by the model, using a relative ranking rather than quantitative predictions.

Calibration and application of the MN2D dynamics model to the avalanches of Las Leñas (Argentina)

During the winters of 1999 and 2000 large avalanches occurred in the ski resort of Las Leñas (Los Andes, Mendoza, Argentina). On 8 September 1999 an avalanche of new, dry snow ran over a path with a 1000 m vertical drop. On 30 June and on 1 July 2000 five avalanches of similar vertical drop, which start with new snow, entrained very wet snow during their descent, and evolved into dense snow avalanches. To use the MN2D dynamics model correctly, calibration of model parameters is necessary. Also, no previous works with the use of dynamics models exist in South America. The events used to calibrate the model occurred during the winters of 1999 and 2000 and are a good sample of the kind of avalanches which can occur in this area of the Andes range. By considering the slope morphology and topography, the snow and meteorological conditions and the results of the model simulations, it was estimated that these avalanches were not extreme events with a return period greater than one hundred years. This implies that, in natural conditions, bigger, extreme avalanches could happen. In this work, the MN2D dynamics model is calibrated with two different avalanches of the same magnitude: dry and wet. The importance of the topographic data in the simulation is evaluated. It is concluded that MN2D dynamics model can be used to simulate dry extreme avalanches in Argentinean Andes but not to simulate extreme wet avalanches, which are much more sensitive to the topography.

Estimating parameters for generalized mass action models using constraint propagation.

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

Impact of model complexity on cross-temporal transferability in Maxent species distribution models: An assessment using paleobotanical data

Maximum entropy modeling (Maxent) is a widely used algorithm for predicting species distributions across space and time. Properly assessing the uncertainty in such predictions is non-trivial and requires validation with independent datasets. Notably, model complexity (number of model parameters) remains a major concern in relation to overfitting and, hence, transferability of Maxent models. An emerging approach is to validate the cross-temporal transferability of model predictions using paleoecological data. In this study, we assess the effect of model complexity on the performance of Maxent projections across time using two European plant species (Alnus giutinosa (L.) Gaertn. and Corylus avellana L) with an extensive late Quaternary fossil record in Spain as a study case. We fit 110 models with different levels of complexity under present time and tested model performance using AUC (area under the receiver operating characteristic curve) and AlCc (corrected Akaike Information Criterion) through the standard procedure of randomly partitioning current occurrence data. We then compared these results to an independent validation by projecting the models to mid-Holocene (6000 years before present) climatic conditions in Spain to assess their ability to predict fossil pollen presence-absence and abundance. We find that calibrating Maxent models with default settings result in the generation of overly complex models. While model performance increased with model complexity when predicting current distributions, it was higher with intermediate complexity when predicting mid-Holocene distributions. Hence, models of intermediate complexity resulted in the best trade-off to predict species distributions across time. Reliable temporal model transferability is especially relevant for forecasting species distributions under future climate change. Consequently, species-specific model tuning should be used to find the best modeling settings to control for complexity, notably with paleoecological data to independently validate model projections. For cross-temporal projections of species distributions for which paleoecological data is not available, models of intermediate complexity should be selected.

Development of Furnace Model for Bubbling Fluidized Bed Boiler

The aim of this thesis was to develop a model, which can predict heat transfer, heat release distribution and vertical temperature profile of gas phase in the furnace of a bubbling fluidized bed (BFB) boiler. The model is based on three separate model components that take care of heat transfer, heat release distribution and mass and energy balance calculations taking into account the boiler design and operating conditions. The model was successfully validated by solving the model parameters on the basis of commercial size BFB boiler test run information and by performing parametric studies with the model. Implementation of the developed model for the Foster Wheeler BFB design procedures will require model validation with existing BFB database and possibly more detailed measurements at the commercial size BFB boilers.

Disentangling the formation of contrasting tree line physiognomies combining model selection and Bayesian parameterization for simulation models.

Alpine tree-line ecotones are characterized by marked changes at small spatial scales that may result in a variety of physiognomies. A set of alternative individual-based models was tested with data from four contrasting Pinus uncinata ecotones in the central Spanish Pyrenees to reveal the minimal subset of processes required for tree-line formation. A Bayesian approach combined with Markov chain Monte Carlo methods was employed to obtain the posterior distribution of model parameters, allowing the use of model selection procedures. The main features of real tree lines emerged only in models considering nonlinear responses in individual rates of growth or mortality with respect to the altitudinal gradient. Variation in tree-line physiognomy reflected mainly changes in the relative importance of these nonlinear responses, while other processes, such as dispersal limitation and facilitation, played a secondary role. Different nonlinear responses also determined the presence or absence of krummholz, in agreement with recent findings highlighting a different response of diffuse and abrupt or krummholz tree lines to climate change. The method presented here can be widely applied in individual-based simulation models and will turn model selection and evaluation in this type of models into a more transparent, effective, and efficient exercise.

Robust Estimates of the Negative Binomial Model

We consider robust parametric procedures for univariate discrete distributions, focusing on the negative binomial model. The procedures are based on three steps: ?First, a very robust, but possibly inefficient, estimate of the model parameters is computed. ?Second, this initial model is used to identify outliers, which are then removed from the sample. ?Third, a corrected maximum likelihood estimator is computed with the remaining observations. The final estimate inherits the breakdown point (bdp) of the initial one and its efficiency can be significantly higher. Analogous procedures were proposed in [1], [2], [5] for the continuous case. A comparison of the asymptotic bias of various estimates under point contamination points out the minimum Neyman's chi-squared disparity estimate as a good choice for the initial step. Various minimum disparity estimators were explored by Lindsay [4], who showed that the minimum Neyman's chi-squared estimate has a 50% bdp under point contamination; in addition, it is asymptotically fully efficient at the model. However, the finite sample efficiency of this estimate under the uncontaminated negative binomial model is usually much lower than 100% and the bias can be strong. We show that its performance can then be greatly improved using the three step procedure outlined above. In addition, we compare the final estimate with the procedure described in

Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

Reaction Kinetics and Viscosity Modelling in the Fusion Syntheses of Ca- and Ca/Mg-resinates

Rosin is a natural product from pine forests and it is used as a raw material in resinate syntheses. Resinates are polyvalent metal salts of rosin acids and especially Ca- and Ca/Mg- resinates find wide application in the printing ink industry. In this thesis, analytical methods were applied to increase general knowledge of resinate chemistry and the reaction kinetics was studied in order to model the non linear solution viscosity increase during resinate syntheses by the fusion method. Solution viscosity in toluene is an important quality factor for resinates to be used in printing inks. The concept of critical resinate concentration, c crit, was introduced to define an abrupt change in viscosity dependence on resinate concentration in the solution. The concept was then used to explain the non-inear solution viscosity increase during resinate syntheses. A semi empirical model with two estimated parameters was derived for the viscosity increase on the basis of apparent reaction kinetics. The model was used to control the viscosity and to predict the total reaction time of the resinate process. The kinetic data from the complex reaction media was obtained by acid value titration and by FTIR spectroscopic analyses using a conventional calibration method to measure the resinate concentration and the concentration of free rosin acids. A multivariate calibration method was successfully applied to make partial least square (PLS) models for monitoring acid value and solution viscosity in both mid-infrared (MIR) and near infrared (NIR) regions during the syntheses. The calibration models can be used for on line resinate process monitoring. In kinetic studies, two main reaction steps were observed during the syntheses. First a fast irreversible resination reaction occurs at 235 °C and then a slow thermal decarboxylation of rosin acids starts to take place at 265 °C. Rosin oil is formed during the decarboxylation reaction step causing significant mass loss as the rosin oil evaporates from the system while the viscosity increases to the target level. The mass balance of the syntheses was determined based on the resinate concentration increase during the decarboxylation reaction step. A mechanistic study of the decarboxylation reaction was based on the observation that resinate molecules are partly solvated by rosin acids during the syntheses. Different decarboxylation mechanisms were proposed for the free and solvating rosin acids. The deduced kinetic model supported the analytical data of the syntheses in a wide resinate concentration region, over a wide range of viscosity values and at different reaction temperatures. In addition, the application of the kinetic model to the modified resinate syntheses gave a good fit. A novel synthesis method with the addition of decarboxylated rosin (i.e. rosin oil) to the reaction mixture was introduced. The conversion of rosin acid to resinate was increased to the level necessary to obtain the target viscosity for the product at 235 °C. Due to a lower reaction temperature than in traditional fusion synthesis at 265 °C, thermal decarboxylation is avoided. As a consequence, the mass yield of the resinate syntheses can be increased from ca. 70% to almost 100% by recycling the added rosin oil.