Semigroup formulation and approximation of a linear age-dependent population problem with spatial diffusion.
Semilinear perturbations of Hille-Yosida operators
The semilinear Cauchy problem (1) u’(t) = Au(t) + G(u(t)), , with a Hille-Yosida operator A and a nonlinear operator G: D(A) → X is considered under the assumption that ||G(x) - G(y)|| ≤ ||B(x -y )|| ∀x,y ∈ D(A) with some linear B: D(A) → X, , where V is of suitable small strong variation on some interval [0,ε). We will prove the existence of a semiflow on that provides Friedrichs solutions in L₁ for (1). If X is a Banach lattice, we replace the condition above by |G(x) - G(y)| ≤ Bv whenever...
Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions
The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures....
Sensor network design for the estimation of spatially distributed processes
In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical...
Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method.
Serveis estadístics. Preparant-se per al futur.
El objetivo de este análisis es mirar hacia adelante: cuáles son los retos a los que se enfrentan las agencias de estadística y cómo han de encararlos. Se analiza el contexto dentro del cual han de evolucionar los institutos de estadística: las principales fuerzas que modifican la economía y la sociedad, las medidas políticas nuevas que aparentemente requieren información estadística nueva o adicional y los cambios en la naturaleza de los gobiernos que tienen repercusiones significativas para los...
Shape parametrization of the time-dependent geometry of the heart for steady fluid dynamical analysis.
Significance tests to identify regulated proteins based on a large number of small samples
Modern biology is interested in better understanding mechanisms within cells. For this purpose, products of cells like metabolites, peptides, proteins or mRNA are measured and compared under different conditions, for instance healthy cells vs. infected cells. Such experiments usually yield regulation or expression values – the abundance or absence of a cell product in one condition compared to another one – for a large number of cell products, but with only a few replicates. In order to distinguish...
Simpel modelling of extracellular matrix alignment in dermal wound healing. I: Cell flux induced alignment.
Simulated annealing on uncorrelated energy landscapes.
Simulating Kinetic Processes in Time and Space on a Lattice
We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...
Simulation of electrophysiological waves with an unstructured finite element method
Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.
Simulation of Electrophysiological Waves with an Unstructured Finite Element Method
Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.
Simulation of mathematical models as a tool for the study of reservoirs of American cutaneous leishmaniasis. (Simulación de modelos matemáticos como herramienta para el estudio de los reservorios de la leishmaniasis cutánea Americana.)
Simulation of self-propelled chemotactic bacteria in a stokes flow*
We prescrit a method to simulate the motion of self-propelled rigid particles in a twodimensional Stokesian fluid, taking into account chemotactic behaviour. Self-propulsion is modelled as a point force associated to each particle, placed at a certain distance from its gravity centre. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation on the whole domain, including fluid and particles: rigid...
Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology
We investigate the structure of travelling waves for a model of a fungal disease propagating over a vineyard. This model is based on a set of ODEs of the SIR-type coupled with two reaction-diffusion equations describing the dispersal of the spores produced by the fungus inside and over the vineyard. An estimate of the biological parameters in the model suggests to use a singular perturbation analysis. It allows us to compute the speed and the profile of the travelling waves. The analytical results...
Singular Perturbations For Heart Image Segmentation Tracking
In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.
Singularity patterns in a chemotaxis model.
Skupinové testování – oddělující systémy
Otázkami spojenými s testováním vzorků se v souvislosti s pandemií covid-19 začala zabývat i širší veřejnost. Jednou z otázek, která byla v souvislosti s testováním diskutována, byla i otázka tzv. poolování. Cílem předkládaného článku je představit jeden z matematických nástrojů -- oddělující systémy, který lze při spojování vzorků a jejich následném testování efektivně využít. Všechna odvození jsou realizována jen s využitím elementární matematiky tak, aby bylo možné dosažené výsledky nejen použít...
Skupinový screening
Skupinový screening je nezbytnou součástí boje proti šíření koronaviru. Jak ale čelit možnému nedostatku činidel a materiálu? Tím, že budeme provádět testy na bázi promíchání vzorků a využijeme přitom matematiku.