In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon-positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: on the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles. © 2009 Springer-Verlag.

In this work the phenomenon of contact inhibition of growth is studied by applying an individual based model and a continuum multiphase model to describe cell colony growth in vitro. The impact of different cell behavior in response to mechanical cues is investigated. The work aims at comparing the results from both models from the qualitative and, whenever possible, also the quantitative point of view. Crown Copyright © 2009.

Neural current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured in the outer space, gives rise to a highly ill-posed and ill-conditioned inverse problem. We use a joint sparsity constraint as a regularization term and we propose an efficient iterative thresholding algorithm to recover the current distribution. Some numerical tests are also displayed.

Neuronal current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured by sophisticated superconducting devices in a noninvasive way, gives rise to a highly ill-posed and ill-conditioned inverse problem. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigned multiscale basis, allows us to apply new regularization techniques to the magnetic inverse problem. In particular, we use a joint sparsity constraint as a regulariza- tion term and we propose an efficient iterative thresholding algorithm to reconstruct the current distribution. Some bidimensional experiments are presented in order to show the algorithm properties.

Direct numerical approximation of a continuous-time infinite horizon control problem, requires to recast the model as a discrete-time, finite-horizon control model. The quality of the optimization results can be heavily degraded if the discretization process does not take into account features of the original model to be preserved. Restricting their attention to optimal growh problems with a steady state, Mercenier and Michel in [1] and [2], studied the conditions to be imposed for ensuring that discrete first-order approximation models have the same steady states as the infinite-horizon continuous-times counterpart. Here we show that Mercenier and Michel scheme is a first order partitioned Runge-Kutta method applied to the state-costate differential system which arises from the Pontryagin maximum principle. The main consequence is that it is possible to consider high order schemes which generalize that algorithm by preserving the steady-growth invariance of the solutions with respect to the discretization process. Numerical examples show the efficiency and accuracy of the proposed methods when applied to the classical Ramsey growth model.

An improvement of a mathematical model of the galvanic iron corrosion, previously presented by one of the authors, is here proposed. The iron(III)-hydroxide formation is, now, considered in addition to the redox reaction. The PDE system, assembled on the basis of the fundamental holding electro-chemistry laws, is numerically solved by a locally refined FD method. For verification purpose we have assembled an experimental galvanic cell; in the present work, we report two tests cases, with acidic and neutral electrolitical solution, where the computed electric potential compares well with the measured experimental one.

The paper investigates a decision criterion for structured bonds portfolio choices. The main issue is the application of risk-adjusted indicators as tools to select either the asset portfolio given a structured bond, or the bond structure given an existing coverage asset portfolio. Such an indicator is suitable for the appraisal of both portfolio management and the potential profits of the structured issue. The selection tool is put into an asset and liability management decision-making context, where the relationship between the expected profit and the capital-at-risk are compared in order to evaluate the issue of the bond and the expected rate of return of the whole portfolio. The case is referred to an equity-linked bond and treated by means of Monte Carlo simulations to identify the best portfolio according to the issuer targets and constraints.

Numerical results on the translocation of long biopolymers through mid-sized and wide pores are presented. The simulations are based on a novel methodology which couples molecular motion to a mesoscopic fluid solvent. Thousands of events of long polymers (up to 8000 monomers) are monitored as they pass through nanopores. Comparison between the different pore sizes shows that wide pores can host a larger number of multiple biopolymer segments, as compared to smaller pores. The simulations provide clear evidence of folding quantization in the translocation process as the biopolymers undertake multi-folded configurations, characterized by a well-defined integer number of folds. Accordingly, the translocation time is no longer represented by a single-exponent power-law dependence on the length, as is the case for single-file translocation through narrow pores. The folding quantization increases with the biopolymer length, while the rate of translocated beads at each time step is linearly correlated with the number of resident beads in the pore. Finally, analysis of the statistics over the translocation work unravels the importance of the hydrodynamic interactions in the process. © 2009 IOP Publishing Ltd.

Many problems in applied sciences require to spatially resolve an unknown electrical current distribution from its external magnetic field. Electric currents emit magnetic fields which can be measured by sophisticated superconducting devices in a noninvasive way. Applications of this technique arise in several fields, such as medical imaging and non-destructive testing, and they involve the solution of an inverse problem. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigned multiscale basis, allows us to apply new regularization techniques to the magnetic inverse problem. The solution of linear inverse problems with sparsity constraints can be efficiently obtained by iterative algorithms based on gradient steps intertwined with thresholding operations. We test this algorithms to numerically solve the magnetic inverse problem with a joint sparsity constraint.

Understanding the complexity of the cellular machinery represents a grand challenge in molecular biology. To contribute to the deconvolution of this complexity, a novel inference algorithm based on linear ordinary differential equations is proposed, based on high-throughput gene expression data. The algorithm can infer (i) gene-gene interactions from steady state expression profiles AND (ii) mode-of-action of the components that can trigger changes in the system. Results demonstrate that the proposed algorithm can identify both information with high performances, thus overcoming the limitation of current algorithms that can infer reliably only one.

Background: The aging phenotype in humans is very heterogeneous and can be described as a complex mosaic resulting from the interaction of a variety of environmental, stochastic and genetic-epigenetic variables. Therefore, each old person must be considered as a singleton, and consequently the definition of 'aging phenotype' is very difficult. Objective: We discuss the phenotype of centenarians, the best example of successful aging, as well as other models exploited to study human aging and longevity, such as families enriched in long-living subjects, twins and cohorts of unrelated subjects. Methods: A critical review of literature available until March 2008. Conclusions: No single model can be considered the gold standard for the study of aging and longevity, instead the combination of results obtained from different models must be considered in order to better understand these complex phenomena. We propose that a systems biology concept such as that of 'bow-tie' architecture useful for managing information flow, could help in this demanding task. © 2008 Informa UK Ltd.

Cell death is as important as cell proliferation for cell turn-over, and susceptibility to cell death is affected by a number of parameters that change with time. A time-dependent derangement of such a crucial process, or even the simple cell loss mediated by cell death impinges upon aging and longevity. In this review we will discuss how cell death phenomena are modulated during aging and what is their possible role in the aging process. We will focus on apoptosis and autophagy, which affect mostly proliferating and post-mitotic cells, respectively, and on mitochondrial degradation in long living cells. Since the "decisional process" that leads the cell to death is very complex, we will also discuss the possibility to address this topic with a systems biology approach. © 2008 Bentham Science Publishers Ltd.

Some empirical localized discriminant analysis methods for classifying images are introduced. They use spatial correlation of images in order to improve classification reducing the `pseudo-nuisance' present in pixel-wise discriminant analysis. The result is obtained through an empirical (data driven) and local (pixelwise) choice of the prior class probabilities. Local empirical discriminant analysis is formalized in a framework that focuses on the concept of visibility of a class that is introduced. Numerical experiments are performed on synthetic and real data. In particular, methods are applied to the problem of retrieving the cloud mask from remotely sensed images. In both cases classical and new local discriminant methods are compared to the ICM method.

We investigate the process of biopolymer translocation through a narrow pore using a multiscale approach which explicitly accounts for the hydrodynamic interactions of the molecule with the surrounding solvent. The simulations confirm that the coupling of the correlated molecular motion to hydrodynamics results in significant acceleration of the translocation process. Based on these results, we construct a phenomenological model which incorporates the statistical and dynamical features of the translocation process and predicts a power-law dependence of the translocation time on the polymer length with an exponent alpha approximate to 1.2. The actual value of the exponent from the simulations is alpha=1.28 +/- 0.01, which is in excellent agreement with experimental measurements of DNA translocation through a nanopore, and is not sensitive to the choice of parameters in the simulation. The mechanism behind the emergence of such a robust exponent is related to the interplay between the longitudinal and transversal dynamics of both translocated and untranslocated segments. The connection to the macroscopic picture involves separating the contributions from the blob shrinking and shifting processes, which are both essential to the translocation dynamics.