A novel, coarse-grained, single-framework 'Eulerian' model for blood flow in the microvascular circulation is presented and used to estimate the variations in flow properties that accrue from all of the following: (i) wall position variation, associated with the endothelial cells' (ECs) shape, (ii) glycocalyx layer (GL) effects and (iii) the particulate nature of blood. We stress that our new model is fully coupled and uses only a single Eulerian computational framework to recover complex effects, dispensing altogether with the need for, e.g. re-meshing and advected sets of Lagrangian points. Physically, blood is modelled as a two-component, incompressible fluid - the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets of increased viscosity. Interfacial membrane effects are present to mimic key blood properties and to avoid droplets' coalescence. The model is encapsulated within a multi-component lattice Boltzmann method that uses a sub-lattice 'wavy wall' closure to represent the ECs. Between this boundary and the flow domain, the model incorporates a coarse-grained representation of the endothelial GL, which is known to cover microvessel walls. The endothelial glycocalyx is modelled as a medium of variable and adaptive porosity, with approaching droplets being subject to a repulsive elastic force. Numerical simulations are presented to show the combined and simultaneous influence on fundamental flow properties of the EC wall undulation, the glycocalyx compression and repulsion and the particulate nature of blood. Several characteristic hemodynamical features of microvessel flow are successfully reproduced, including the deformability of particulates and the Fahraeus-Lindqvist effect. Moreover, the importance of modelling the GL is manifest in the magnitude of and the temporal variations in the flow rate and wall shear stresses.

In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the evolution of the cell aggregate.

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.

In this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed of oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is obtained by using energy estimates with suitable transmission conditions at nodes.

Introduction: The brain is a connected network, requiring complex-system measures to describe its organization principles [1,2]. Here, we aim at testing whether the normalized compression distance (NCD) [3] is a suitable quantifier of the functional connectivity between cortical regions. This new measure estimates the information shared by two signals comparing the compression length of one signal given the other, without requiring any representation of the single in harmonics or selecting a specific time window where to compare the two signals. We show that this new measure is a good candidate to estimate the inter-nodes connectivity since it displays features 'expected' for brain connectivity, i.e. it is maximal between homologous cortical areas, it is higher for dominant cortical areas, it depends on age. In order to do it we estimated the NCD between functionally homologous primary somatosensory areas (S1) activities, testing the above-mentioned properties. Methods: Twenty-eight healthy, right-handed volunteers participated in the study. We recorded brain magnetic activity in the left and right Rolandic regions by a 28-channel magnetoencephalographic (MEG) system. We recorded rest activity for 3 min in each hemisphere. MEG activity was also collected during the electrical stimulation of the contralateral median nerve at the wrist delivered via surface disks. Elicited electric pulses were 0.2 ms in duration and 631 ms of inter-stimulus interval. Left and right median nerves were separately stimulated, totaling about 200 artifact-free trials for each. We used the Functional Source Separation (FSS) [4,5] algorithm to identify functionally homologous areas in the two hemispheres devoted to the somatosensory hand representation (FS_S1). Therefore, we calculated NCD between the left and right FS_S1s at rest. NCD is a parameter-free, quasi-universal similarity measure, computed from the lengths of compressed data files, singly and in pairwise concatenation. In other terms, NCD defines that two objects are similar if we can significantly "compress" one given the information of the other. We compared the similarity between the left and right homologous areas in single subjects and across the whole group. In particular, we compared the similarity of the activities in the two hemispheres of the same subject, with that in the same or in the opposite hemisphere of different subjects in the group of people. Results: NCD was minimal (maximal functional connectivity) between the neuronal activities of hemispheric functionally homologous areas in the same subject, i.e the NCD between the left and right FS_S1 of the same person was smaller than across different subjects (p<10 -7 consistently). NCD was smaller within the left dominant hemisphere than within the non dominant right one (p=3o10-7), suggesting that more skilled cortical areas express more tuned neuronal activities. Finally, it became more variable in older than younger people (p=.01), indicating that it is sensitive to proprioceptive and sensorimotor skills degradation typical of aging. Conclusions: NCD displayed an excellent ability in quantifying the similarity among neuronal activities, catching the maximal similarity expected for functionally homologous cortical areas of the two hemispheres. It was also sensitive to dominant- and age-dependent properties of somatosensory representation activities. This ability to catch key features of neuronal activity's dynamics indicates NCD as a good candidate for studies of brain functional connectivity, able to overcome the limitations intrinsic to the classical Fourier or autoregressive estimates in assessing the dynamics of two-nodes functional conections.

ElectroCOrticoGraphy (ECoG) is an invasive neuroimaging technique that measures electrical potentials produced by brain currents via an electrode grid implanted on the cortical surface. A full interpretation of ECoG data is difficult because it requires solving the inverse problem of reconstructing the spatio-temporal distribution of neural currents responsible of the recorded ECoG signals, which is ill-posed. Only in the last few years novel computational methods to solve this inverse problem have been developed. This study describes a beamformer method for ECoG source modeling. First, we extended the OpenMEEG software with a new method to estimate the lead-field matrix which maps the neural currents onto the sensors space. We further conducted an analysis of the numerical stability of the ECoG inverse problem by computing the condition number of the lead-field matrix for different configurations of the electrodes grid. Finally, we localized sources via a Linear Constraint Minimum Variance (LCMV) beamformer method applied to both synthetic and real data.

Source modeling of EEG data is an important tool for both neuroscience and clinical applications, such as epilepsy. Despite their simplicity, multiple dipole models remain highly desirable to explain neural sources. However, estimating dipole models from EEG time-series remains a difficult task, mainly due to the ill-posedness of the inverse problem and to the fact that the number of dipoles is usually not known a priori. Recently, a Bayesian approach has been presented for multiple dipole estimation of MEG/EEG data [1,2]: the method estimates simultaneously the number of dipoles and the dipole parameters, by exploring a multiple dipole state space with a Monte Carlo procedure combined with a tempering schedule [3]. Here, we present the first validation of this method with experimental EEG data.

We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a bipartite distance hereditary graph. Relations with the class of Ptolemaic graphs are discussed and exploited to give an alternative proof of the result. (C) 2015 Elsevier B.V. All rights reserved.

A {0, 1}-matrix A is balanced if it does not contain a submatrix of odd order having exactly two 1's per row and per column. A graph is balanced if its clique-matrix is balanced. No characterization of minimally unbalanced graphs is known, and even no conjecture on the structure of such graphs has been posed, contrary to what happened for perfect graphs. In this paper, we provide such a characterization for the class of diamond-free graphs and establish a connection between minimally unbalanced diamond-free graphs and Dyck-paths.

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps. In this talk, we consider the numerical approximation of such models. On one hand, due to the non-local nature of the integral term, we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions. On the other hand, we propose a hybrid tree-finite difference method to approximate the Heston model, possibly in the presence of jumps. Numerical tests are presented to show the computational efficiency of the approximation.

We consider the problem of finding a square low-rank correction (?C - B)F to a given square pencil (?E - A) such that the new pencil ?(E - CF) - (A - BF) has all its generalised eigenvalues at the origin. We give necessary and sufficient conditions for this problem to have a solution and we also provide a constructive algorithm to compute F when such a solution exists. We show that this problem is related to the deadbeat control problem of a discrete-time linear system and that an (almost) equivalent formulation is to find a square embedding that has all its finite generalised eigenvalues at the origin.

Financial and activity report - project T.He.T.A. "Technological tools for the Promotion of Transadriatic Archaeological Heritage"

One of the promising frontiers of bioengineering is the controlled release of a therapeutic drug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a two-phase mathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. An eigenvalue problem with discontinuous coefficients is solved and an analytical solution is given in the form of an infinite series expansion. The model points out the role of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers. Drug masses are given and their dependence on the physical parameters is discussed.

We present a general model of drug release from a drug delivery device and the subsequent transport in biological tissue. The model incorporates drug diffusion, dissolution and solubility in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue. Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. One of the novelties is the generality of the model in each layer. Within the drug coating, our model includes diffusion as well as three different models of dissolution. We show that the model may also be used in cases where dissolution is rapid or not relevant, and additionally when drug release is not limited by its solubility. Within the biological tissue, the model can account for nonlinear saturable reversible binding, with lin- ear reversible binding and linear irreversible binding being recovered as special cases.

Bioventing is a technology used to remove some kinds of pollutants from the subsoil and it is based on the capability of some bacteria species to biodegrade contaminants. The biochemical reaction requires, among other things, oxygen and, therefore, oxygen is inflated into the subsoil by wells. The mathematical model describes the movement of the different fluids which are present in the subsoil - air, water, pollutants, oxygen and so on - and the bacteria population dynamics. The presence of source reactive terms in the continuity equations allows the contaminant biodegradation to be described. The design of a subsoil decontamination intervention concerns bioavailability problems and, in particular, the oxygen concentration. Therefore, in order to enhance the biodegradation phenomenon, the optimization of the subsoil oxygen velocity field in the polluted area is required, by an appropriate choice of the well positions and of the well air inflating rates. In mathematical terms, the goal is to obtain the decontamination of the subsoil with an optimal value of an objective function by acting on some control variables which, in this case, are the well positions and the inflating rates. In this paper several kind of objective function are proposed.

A mathematical model describing the evolution of the spatial distribution of a bacteria population in a marine environment is described. The hypothesis is that a certain amount of water polluted by bacteria is introduced into the environment due to an accidental event. In particular, the evolution of the spatial bacteria distribution will be described considering the bacteria transport due to the marine currents and the bacteria diffusion, reproduction and death dynamics. In this paper only a short presentation of the partial differential equations of the model will be reported. The final goal of the study will be to describe the environmental scenario following the accident in the short and long term in presence of different tide phase and kind of wind. To this end the numerical approximate resolution of the model it is required.

In the Grande da Pipa river basin, north of Lisbon, 64 % of the total number of landslides inventoried is totally or partially included in a lithological unit composed by marl, clay, and sandstone intercalation complex that is present in 58 % of the study area. The Persistent Scatterer synthetic aperture radar interferometry technique is applied to a data set of TerraSAR-X SAR images, from April of 2010 to March of 2011, firstly to the Laje-Salema test site and further exported to the Grande da Pipa river basin. This work's specific objectives are the following: (i) to assess the potential of the Persistent Scatterer displacement maps to the identification of new landslides/unstable areas and in the redefinition of landslide limits, (ii) to update the landslide state of activity, and (iii) to evaluate the capacity of the Persistent Scatterer deformation maps in assessing landslide susceptibility at the regional scale. Based on this approach, it was possible to increment the number of landslides and to redefine the landslide limits in the test site in 3.8 %. For 39 landslides, it was possible to update the landslide state of activity, in particular from dormant to reactivated or dormant-reactivated (23 landslides) or from stabilized to reactivated (5 landslides). Landslide susceptibility map based in Persistent Scatterer deformation rates, independently validated with a deep rotational slide map, obtained the best value of area under the curve (0.668).

In this work, we exploit the integration of an advanced synthetic aperture radar (SAR) interferometry technique and the application of the finite-element method for the assessment and the interpretation of a localized subsidence phenomenon that took place within a specific area of Lisbon, Portugal. SAR images over the Lisbon city, covering different time intervals in the period of 1995-2010, were acquired and processed by means of the persistent scatterers (PSs) technique. Results clearly reveals a localized subsidence, limited to an area 2 km × 1.5 km wide, which has been confirmed by the leveling performed in 1976, 1996, and 2010. A physical interpretation of the observed ground deformations is provided based on the results of a finite-element model using stratigraphic data, in situ piezometric measurements, and geotechnical properties of the involved soils. The ground subsidence is interpreted as the consequence of a consolidation process affecting the central fine-grained soil layer, which in turn has been driven by water withdrawal from the existing aquifers. The change of the hydraulic boundary conditions was generated by the excavation works for the construction of underground lines and also by the reduction of rainfall water infiltration as an effect of the increase in ground surface impermeable areas due to urbanization. The consequent consolidation process of the compressible fine-grained soil layer is supposed to provide a reasonable explanation of the observed time series of ground displacement in the examined area.

The dynamics of inertial particles in turbulence is modelled and investigated by means of direct numerical simulation of an axisymmetrically expanding homogeneous turbulent strained flow. This flow can mimic the dynamics of particles close to stagnation points. The influence of mean straining flow is explored by varying the dimensionless strain rate parameter Sk(0)/epsilon(0) from 0.2 to 20, where S is the mean strain rate, k(0) and epsilon(0) are the turbulent kinetic energy and energy dissipation rate at the onset of straining. We report results relative to the acceleration variances and probability density functions for both passive and inertial particles. A high mean strain is found to have a significant effect on the acceleration variance both directly by an increase in the frequency of the turbulence and indirectly through the coupling of the fluctuating velocity and the mean flow field. The influence of the strain on the normalized particle acceleration probability distribution functions is more subtle. For the case of a passive particle we can approximate the acceleration variance with the aid of rapid-distortion theory and obtain good agreement with simulation data. For the case of inertial particles we can write a formal expression for the accelerations. The magnitude changes in the inertial particle acceleration variance and the effect on the probability density function are then discussed in a wider context for comparable flows, where the effects of the mean flow geometry and of the anisotropy at small scales are present.