ORGANIZERS: Óscar Angulo, Eduardo Cuesta, Ángel Durán (Department of Applied Mathematics, University of Valladolid)
DATE. 16-17 MAY 2016
LOCATION: Faculty of Science, University of Valladolid
TOPICS: The workshop is devoted to the introduction and mathematical treatment of evolution models with applications to Nonlinear Waves, Population Dynamics and Image Processing.
1. Mostafa Adimy, Université Claude Bernard Lyon 1. (mostafa.adimy@inria.fr)
2. Didier Clamond, Université de Nice Sophia-Antipolis. (Didier.clamond@unice.fr)
3. Fabien Crauste, Université Claude Bernard Lyon 1. (crauste@math.univ-lyon1.fr)
4. Ángel Durán, University of Valladolid. (angel@mac.uva.es)
5. Denys Dutykh, Université Savoie Mont Blanc. (Denys.Dutykh@univ-savoie.fr)
6. Carmen Quintano, University of Valladolid. (menchu@tele.uva.es)

• Modelización, análisis y simulación numérica de la dinámica de poblaciones estructuradas (MASNUPES): MTM2014-56022-C2-2-P. (IP: Miguel Ángel López Marcos, Óscar Angulo)
• Análisis numérico de problemas de evolución no lineales y no locales (ANPENLNL): MTM2014-54710-P. (IP: César Palencia, Ángel Durán)
• Estudio numérico de modelos complejos descritos mediante ecuaciones en derivadas parciales y sus aplicaciones en Biología, Ecología y Finanzas: VA191U13. (IP: Óscar Angulo)
• Métodos Numéricos para Ecuaciones en Derivadas Parciales con Difusión: Modelos con Múltiples Escalas en Matemáticas Financieras y en Dinámica de Poblaciones. (Grupo de Investigación de Excelencia de la Junta de Castilla y León, GR-137. Director: Luis Abia)
• Análisis Numérico de Problemas de Evolución. Aplicaciones en Biomatemática. (Grupo de Investigación Reconocido, Universidad de Valladolid. Coordinador: Luis Abia)
• Análisis Numérico de Problemas de Evolución. (Grupo de Investigación Reconocido, Universidad de Valladolid. Coordinador: César Palencia)
• Unidad de Investigación Consolidada de Castilla y León UIC 033. (Director: Miguel Ángel López Marcos)

• 16/05/2016. Nonlinear Waves (Organized by Angel Durán).
Speaker: Didier Clamond, Université de Nice Sophia-Antipolis.
Title: Modelling water waves beyond perturbations.
Abstract: In this presentation, I will focus on the practical use of variational principles for modelling water waves. In particular, a "relaxed" variational principle will be introduced and the advantages of this formulation will be discussed, specially when there are no small parameters in the problem to be modeled.
Speaker: Denys Dutykh, Université Savoie Mont Blanc.
Title: Energy-consistent shallow water models derivation.
Abstract: The present talk is a natural continuation of the lecture given by D. Clamond. Namely, in this second, more specialized, talk we shall illustrate the power and great flexibility of the relaxed Lagrangian formulation. More precisely, we shall use the relaxed variational principle in order to derive various approximate models in shallow and in deep waters. Some of derived models being already known and some of them seem to be completely new

• 16/05/2016. Population Dynamics (Organized by Óscar Angulo).
Speaker: Mostafa Adimy, Université Claude Bernard Lyon 1.
Title: Traveling waves in a coupled reaction-diffusion and difference model of hematopoiesis (with A. Chekroun and B. Kazmierczak).
Abstract: The formation and development of blood cells (red blood cells, white cells and platelets) is a very complex process, called hematopoiesis. This process involves a small population of cells called hematopoietic stem cells (HSCs). We propose a mathematical model describing the dynamics of HSC population, taking into account their spatial distribution and diffusion. The resulting model is an age-structured reaction-diffusion system. The method of characteristics can be used to reduce this model to an unstructured time-delayed reaction-diffusion equation coupled with a difference equation. We investigated mathematical studies of the model and showed the existence of traveling wave front solutions connecting the zero steady state with the unique positive uniform one. We used the classical monotone iteration technique coupled with the upper- and lower-solutions method. A numerical simulation is carried out to show the propagation of the solution in a traveling wave front.
Speaker: Fabien Crauste, Université Claude Bernard Lyon 1.
Title: Multiscale models of the immune response: mathematical and modeling challenges.
Abstract: The immune response is a complex process tightly regulating cell differentiation, proliferation and death, in a very short time scale in order to fight pathogens. By focusing on the description of an acute CD8 T cell immune response (against influenza virus for instance), I will discuss multiscale models of the immune response, describing both molecular and cellular scale dynamics through coupled dynamical models, using deterministic ordinary differential systems for the description of intracellular regulation, and either partial differential equations or stochastic agent-based models for the description of cell population dynamics. I will focus on the relevance of such models, from a modeling, a mathematical, and an immunological point of view, and illustrate discussions with concrete achievements obtained using in silico models.

• 17/05/2016. Image Processing (Organized by Eduardo Cuesta).

Speaker: Carmen Quintano, University of Valladolid.
Title: Advanced mathematical methods to estimate forest fire damage from satellite images.
Abstract: Forest fires are an annually recurring phenomenon in Mediterranean countries having important management and research implications. Though fieldwork is still needed, at present satellite data is widely used to map the extent of areas affected by fire. A brief summary of traditional remote sensing –based methods to map burned area and burn severity is presented, focusing on their limitations. New methodologies based on advance mathematical methods (data mining, fractional type convolution filtering, spectral mixture analysis, multiple endmember spectral mixture analysis) are being developed. Accuracy of burned area / burn severity estimates using the new methodologies is measured and an increase versus the accuracy from traditional remote sensing –based methods is observed.
Speaker: Ángel Durán, University of Valladolid.
Title: Cross-diffusion models for image processing (with A. Araújo, S. Barbeiro and E. Cuesta).
Abstract: The present talk will introduce the use of cross diffusion systems to model different phenomena in image processing. The most common continuous representation of a grey-scale image is given by a real valued function standing for the grey-scale value of the image at the pixels. The use of two scalar fields may have the goal of distributing the features of the image and governing their relations. The discussion will start with the linear cross-diffusion filtering, in order to determine those kernels that ensure relevant scale-space properties to the model. A second part of the talk will be devoted to study the effect of introducing nonlinearities in the system by way of a cross-diffusion matrix that depend on the image.