The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Modeling AIDS vaccines: the cellular level

This paper discuses current strategies for the development of AIDS vaccines wich allow immunzation to disturb the natural course of HIV at different detailed stages of its life cycle. Mathematical models describing the main biological phenomena (i.e. virus and vaccine induced T4 cell growth; virus and vaccine induced activation latently infected T4 cells; incremental changes immune response as infection progress; antibody dependent enhancement and neutralization of infection) and allowing for different vaccination strategies serve as a backgroud for computer simulations. The mathematical models reproduce updated information on the behavior of immune cells, antibody concentrations and free viruses. The results point to some controversial outcomes of an AIDS vaccine such as an early increase in virus concentration among vaccinated when compared to nonvaccinated individuals.

Cell-based computational modeling of vascular morphogenesis using Tissue Simulation Toolkit.

Computational modeling has become a widely used tool for unraveling the mechanisms of higher level cooperative cell behavior during vascular morphogenesis. However, experimenting with published simulation models or adding new assumptions to those models can be daunting for novice and even for experienced computational scientists. Here, we present a step-by-step, practical tutorial for building cell-based simulations of vascular morphogenesis using the Tissue Simulation Toolkit (TST). The TST is a freely available, open-source C++ library for developing simulations with the two-dimensional cellular Potts model, a stochastic, agent-based framework to simulate collective cell behavior. We will show the basic use of the TST to simulate and experiment with published simulations of vascular network formation. Then, we will present step-by-step instructions and explanations for building a recent simulation model of tumor angiogenesis. Demonstrated mechanisms include cell-cell adhesion, chemotaxis, cell elongation, haptotaxis, and haptokinesis.

A drug administration decision support system

Drug delivery is one of the most common clinical routines in hospitals, and is critical to patients' health and recovery. It includes a decision making process in which a medical doctor decides the amount (dose) and frequency (dose interval) on the basis of a set of available patients' feature data and the doctor's clinical experience (a priori adaptation). This process can be computerized in order to make the prescription procedure in a fast, objective, inexpensive, non-invasive and accurate way. This paper proposes a Drug Administration Decision Support System (DADSS) to help clinicians/patients with the initial dose computing. The system is based on a Support Vector Machine (SVM) algorithm for estimation of the potential drug concentration in the blood of a patient, from which a best combination of dose and dose interval is selected at the level of a DSS. The addition of the RANdom SAmple Consensus (RANSAC) technique enhances the prediction accuracy by selecting inliers for SVM modeling. Experiments are performed for the drug imatinib case study which shows more than 40% improvement in the prediction accuracy compared with previous works. An important extension to the patient features' data is also proposed in this paper.

Evaluating the influence of spatial uncertainty in locality points for species distributional modeling

1. Species distribution modelling is used increasingly in both applied and theoretical research to predict how species are distributed and to understand attributes of species' environmental requirements. In species distribution modelling, various statistical methods are used that combine species occurrence data with environmental spatial data layers to predict the suitability of any site for that species. While the number of data sharing initiatives involving species' occurrences in the scientific community has increased dramatically over the past few years, various data quality and methodological concerns related to using these data for species distribution modelling have not been addressed adequately. 2. We evaluated how uncertainty in georeferences and associated locational error in occurrences influence species distribution modelling using two treatments: (1) a control treatment where models were calibrated with original, accurate data and (2) an error treatment where data were first degraded spatially to simulate locational error. To incorporate error into the coordinates, we moved each coordinate with a random number drawn from the normal distribution with a mean of zero and a standard deviation of 5 km. We evaluated the influence of error on the performance of 10 commonly used distributional modelling techniques applied to 40 species in four distinct geographical regions. 3. Locational error in occurrences reduced model performance in three of these regions; relatively accurate predictions of species distributions were possible for most species, even with degraded occurrences. Two species distribution modelling techniques, boosted regression trees and maximum entropy, were the best performing models in the face of locational errors. The results obtained with boosted regression trees were only slightly degraded by errors in location, and the results obtained with the maximum entropy approach were not affected by such errors. 4. Synthesis and applications. To use the vast array of occurrence data that exists currently for research and management relating to the geographical ranges of species, modellers need to know the influence of locational error on model quality and whether some modelling techniques are particularly robust to error. We show that certain modelling techniques are particularly robust to a moderate level of locational error and that useful predictions of species distributions can be made even when occurrence data include some error.

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.

Modelització i control d'un reactor de producció d'hidrogen per a l'alimentació de piles de combustible

Les piles de combustible permeten la transformació eficient de l’energia química de certs combustibles a energia elèctrica a través d’un procés electroquímic. De les diferents tecnologies de piles de combustible, les piles de combustible de tipus PEM són les més competitives i tenen una gran varietat d’aplicacions. No obstant, han de ser alimentades únicament per hidrogen. Per altra banda, l’etanol, un combustible interessant en el marc dels combustibles renovables, és una possible font d’hidrogen. Aquest treball estudia la reformació d’etanol per a l’obtenció d’hidrogen per a alimentar piles de combustible PEM. Només existeixen algunes publicacions que tractin l’obtenció d’hidrogen a partir d’etanol, i aquestes no inclouen l’estudi dinàmic del sistema. Els objectius del treball són el modelat i l’estudi dinàmic de reformadors d’etanol de baixa temperatura. Concretament, proposa un model dinàmic d’un reformador catalític d’etanol amb vapor basat en un catalitzador de cobalt. Aquesta reformació permet obtenir valors alts d’eficiència i valors òptims de monòxid de carboni que evitaran l’enverinament d’una la pila de combustible de tipus PEM. El model, no lineal, es basa en la cinètica obtinguda de diferents assaigs de laboratori. El reformador modelat opera en tres etapes: deshidrogenació d’etanol a acetaldehid i hidrogen, reformat amb vapor d’acetaldehid, i la reacció WGS (Water Gas Shift). El treball també estudia la sensibilitat i controlabilitat del sistema, caracteritzant així el sistema que caldrà controlar. L’anàlisi de controlabilitat es realitza sobre la resposta de dinàmica ràpida obtinguda del balanç de massa del reformador. El model no lineal és linealitzat amb la finalitat d’aplicar eines d’anàlisi com RGA, CN i MRI. El treball ofereix la informació necessària per a avaluar la possible implementació en un laboratori de piles de combustibles PEM alimentades per hidrogen provinent d’un reformador d’etanol.

Advanced mapping of environmental data: Geostatistics, Machine Learning and Bayesian Maximum Entropy

This book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.