We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the ...fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint $\operatorname{div} B = 0$ to machine precision, both at the spatially and temporally discrete levels.
Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune re-sponse against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the ...percentage of immunogenic cells (i.e. tumour cells that are effectively targeted by immune cells) in a tumour are both expressions of ITH. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8+ T cells, which makes it possible to dissect out the specific impact of these two expressions of ITH on anti-tumour immune response. The set-up of numerical simulations of the model is defined so as to mimic scenarios considered in previous experimental studies. Moreover, the ability of the model to qualitatively reproduce experimental observations of successful and unsuccessful immune surveillance is demonstrated. First, the results of numerical simulations of this model indicate that the presence of a larger number of sub-populations of tumour cells that express different antigens is associated with a reduced ability of CD8+ T cells to mount an effective anti-tumour immune response. Secondly, the presence of a larger percentage of tumour cells that are not effectively targeted by CD8+ T cells may reduce the effectiveness of anti-tumour immunity. Ultimately, the mathematical model presented in this paper may provide a framework to help biologists and clinicians to better understand the mechanisms that are responsible for the emergence of different outcomes of immunotherapy.
Abstract We provide a rigorous mathematical framework to establish the hydrodynamic limit of the Vlasov model introduced in Takata and Noguchi (J. Stat. Phys. 172:880-903, 2018) by Noguchi and Takata ...in order to describe phase transition of fluids by kinetic equations. We prove that, when the scale parameter tends to 0, this model converges to a nonlocal Cahn-Hilliard equation with degenerate mobility. For our analysis, we introduce apropriate forms of the short and long range potentials which allow us to derive Helmhotlz free energy estimates. Several compactness properties follow from the energy, the energy dissipation and kinetic averaging lemmas. In particular we prove a new weak compactness bound on the flux.
We study the Nitsche-based finite element method for contact with Coulomb friction considering both static and dynamic situations. We provide existence and/or uniqueness results for the discretized ...problems under appropriate assumptions on physical and numerical parameters. In the dynamic case, existence and uniqueness of the space semi-discrete problem holds for every value of the friction coefficient and the Nitsche parameter. In the static case, if the Nitsche parameter is large enough, existence is ensured for any friction coefficient, and uniqueness can be obtained provided that the friction coefficient is below a bound that depends on the mesh size. These results are complemented by a numerical study.
We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, 1 − ε > 0 or −(1 + ε) < 0. We study the ...specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the second half of the period, that we refer as the (±1) model. In the absence of migration, the population goes to 0 exponentially fast in each environment. In this paper, we show that, when the period is sufficiently large, a small dispersal between the two patches is able to produce a very high positive exponential growth rate for the whole population, a phenomena called inflation. We prove in particular that the threshold of the dispersal rate at which the inflation appears is exponentially small with the period. We show that inflation is robust to random perturbation, by considering a model where the values of the growth rate in each patch are switched at random times: we prove, using theory of Piecewise Deterministic Markov Processes (PDMP) that inflation occurs for low switching rate and small dispersal. Finally, we provide some extensions to more complicated models, especially epidemiological and density dependent models.
El manuscrito se centra en el desarrollo de un software para optimizar la producción de tilapias, abordando aspectos como el crecimiento, costo y rentabilidad. Utilizando herramientas tecnológicas ...avanzadas, se pretende facilitar la gestión de datos para los piscicultores, permitiendo procesos más eficientes, económicos y precisos. Los factores clave incluyen el peso, la temperatura, el crecimiento absoluto, el crecimiento térmico de los peces, y proyecciones mensuales de costos, producción y rentabilidad. El software, desarrollado en Java y utilizando la plataforma Eclipse, busca equilibrar agilidad y precisión en el tratamiento de datos. El trabajo se apoya en la revisión bibliográfica y entrevistas con piscicultores. Se emplea un enfoque de análisis de componentes principales y correlación de Pearson para asociar variables relevantes. Se evalúa la aplicación mediante datos históricos y pruebas piloto, ajustando funcionalidades para garantizar resultados fiables. Se destaca la importancia de interfaces amigables para usuarios no expertos en tecnología y se propone la expansión a aplicaciones móviles y la adaptación a otras especies de interés zootécnico.
Abstract Due to the fast growth of data that are measured on a continuous scale, functional data analysis has undergone many developments in recent years. Regression models with a functional response ...involving functional covariates, also called "function-on-function", are thus becoming very common. Studying this type of model in the presence of heterogeneous data can be particularly useful in various practical situations. We mainly develop in this work a Function-on-Function Mixture of Experts (FFMoE) regression model. Like most of the inference approach for models on functional data, we use basis expansion (B-splines) both for covariates and parameters. A regularized inference approach is also proposed, it accurately smoothes functional parameters in order to provide interpretable estimators. Numerical studies on simulated data illustrate the good performance of FFMoE as compared with competitors. Usefullness of the proposed model is illustrated on two data sets: the reference Canadian weather data set, in which the precipitations are modeled according to the temperature, and a Cycling data set, in which the developed power is explained by the speed, the cyclist heart rate and the slope of the road.
PDF
