Well posedness of an angiogenesis related integrodifferential diffusion model

We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded coefficients allow us to generate sequences of approximate solutions. Comparison principles and integral equations provide uniform bounds ensuring some convergence properties for iterative schemes and providing stability bounds. Uniqueness follows from chained integral inequalities

Constructing solutions for a kinetic model of angiogenesis in annular domains

We prove existence and stability of solutions for a model of angiogenesis set in an annular region. Branching, anastomosis and extension of blood vessel tips are described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions and coupled to a diffusion problem with Neumann boundary conditions through the force field created by the tumor induced angiogenic factor and the flux of vessel tips. Our technique exploits balance equations, estimates of velocity decay and compactness results for kinetic operators, combined with gradient estimates of heat kernels for Neumann problems in non convex domains.Comment: to appear in Applied Mathematical Modellin

Dynamic energy budget approach to evaluate antibiotic effects on biofilms

Quantifying the action of antibiotics on biofilms is essential to devise therapies against chronic infections. Biofilms are bacterial communities attached to moist surfaces, sheltered from external aggressions by a polymeric matrix. Coupling a dynamic energy budget based description of cell metabolism to surrounding concentration fields, we are able to approximate survival curves measured for different antibiotics. We reproduce numerically stratified distributions of cell types within the biofilm and introduce ways to incorporate different resistance mechanisms. Qualitative predictions follow that are in agreement with experimental observations, such as higher survival rates of cells close to the substratum when employing antibiotics targeting active cells or enhanced polymer production when antibiotics are administered. The current computational model enables validation and hypothesis testing when developing therapies.Comment: to appear in Communications in Nonlinear Science and Numerical Simulatio

Engineering a QoS Provider Mechanism for Edge Computing with Deep Reinforcement Learning

With the development of new system solutions that integrate traditional cloud computing with the edge/fog computing paradigm, dynamic optimization of service execution has become a challenge due to the edge computing resources being more distributed and dynamic. How to optimize the execution to provide Quality of Service (QoS) in edge computing depends on both the system architecture and the resource allocation algorithms in place. We design and develop a QoS provider mechanism, as an integral component of a fog-to-cloud system, to work in dynamic scenarios by using deep reinforcement learning. We choose reinforcement learning since it is particularly well suited for solving problems in dynamic and adaptive environments where the decision process needs to be frequently updated. We specifically use a Deep Q-learning algorithm that optimizes QoS by identifying and blocking devices that potentially cause service disruption due to dynamicity. We compare the reinforcement learning based solution with state-of-the-art heuristics that use telemetry data, and analyze pros and cons

Hybrid topological derivative-gradient based methods for nondestructive testing

This paper is devoted to the reconstruction of objects buried in a medium and their material properties by hybrid topological derivative-gradient based methods. After illustrating the techniques in time-harmonic acoustic problems with different boundary conditions and in electrical impedance tomography problems with continuous Neumann conditions, we extend the hybrid method for a realistic model in tomography where the boundary conditions are given at a discrete set of electrodes

Atomic models of dislocations and their motion in cubic crystals

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasFALSEunpu

Domain and parameter reconstruction in photothermal imaging

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasFALSEunpu

Pinning and propagation in spatially discrete bistable systems

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasFALSEunpu

Depinning and motion of crystal dislocations

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasFALSEunpu