A5040315282- Mathematical Biology Tumor Growth
- Mathematical and Theoretical Epidemiology and Ecology Models
- Micro and Nano Robotics
- Gene Regulatory Network Analysis
- Cellular Mechanics and Interactions
- Evolution and Genetic Dynamics
- Distributed Control Multi-Agent Systems
- Cancer Cells and Metastasis
- Gas Dynamics and Kinetic Theory
- Advanced Mathematical Modeling in Engineering
- Developmental Biology and Gene Regulation
- Modular Robots and Swarm Intelligence
- Pluripotent Stem Cells Research
- Congenital heart defects research
- Stochastic processes and statistical mechanics
- Microtubule and mitosis dynamics
- Nonlinear Dynamics and Pattern Formation
- Control and Stability of Dynamical Systems
- Numerical methods in inverse problems
- Slime Mold and Myxomycetes Research
- advanced mathematical theories
- Medical Imaging Techniques and Applications
- Evolutionary Game Theory and Cooperation
- Differential Equations and Boundary Problems
- Nonlinear Partial Differential Equations
Centre National de la Recherche Scientifique
2015-2024
Institut de Mathématiques de Toulouse
2017-2024
Université Toulouse III - Paul Sabatier
2021-2024
Institut National des Sciences Appliquées de Toulouse
2021-2024
Université de Toulouse
2019-2024
Center for MathematicaL studies and their Applications
2015-2016
École Normale Supérieure Paris-Saclay
2015-2016
This paper is devoted to the study of systems reaction-cross diffusion equations arising in population dynamics. New results existence weak solutions are presented, allowing treat two which one cross diffusions convex, while other concave. The treatment such cases involves a general structure Lyapunov functionals for systems, and introduction new scheme approximation, provides simplified proofs existence.
The aim of this paper is to analyze a model for chemotaxis based on local sensing mechanism instead the gradient used in celebrated minimal Keller–Segel model. we study has same entropy as model, but different dynamics minimize entropy. Consequently, conditions mass existence stationary solutions or blow-up are same; however, make interesting observation that with case supercritical delayed infinite time. Our made rigorous from mathematical point view via proof global weak arbitrary large...
We introduce a model of multiagent dynamics for self-organized motion; individuals travel at constant speed while trying to adopt the averaged body attitude their neighbors. The attitudes are represented through unitary quaternions. prove correspondence with presented in [P. Degond, A. Frouvelle, and S. Merino-Aceituno, Math. Models Methods Appl. Sci., 27 (2017), pp. 1005--1049], where by rotation matrices. Differently from this previous work, individual-based introduced here is based on...
Although cell-to-cell heterogeneity in gene and protein expression within cell populations has been widely documented, we know little about its biological functions. By studying progenitors of the posterior region bird embryos, found that levels transcription factors Sox2 Bra, respectively involved neural tube (NT) mesoderm specification, display a high degree heterogeneity. combining forced downregulation approaches with time-lapse imaging, demonstrate Sox2-to-Bra ratio guides progenitor’s...
A major challenge in biology is to understand how mechanical interactions and cellular behavior affect the shapes of tissues embryo morphology. The extension neural tube paraxial mesoderm, which form spinal cord musculoskeletal system, respectively, results elongated shape vertebrate embryonic body. Despite our understanding each these elongates independently others, morphogenetic consequences their simultaneous growth are still unclear. Our study investigates differential growth, tissue...
We introduce a model of multi-agent dynamics for self-organised motion; individuals travel at constant speed while trying to adopt the averaged body attitude their neighbours. The attitudes are represented through unitary quaternions. prove correspondance with presented in previous work by three first authors where rotation matrices. Differently from this work, individual based (IBM) introduced here is on nematic (rather than polar) alignment. From IBM, kinetic and macroscopic equations...
We study a nonlinear system of first order partial differential equations describing the macroscopic behavior an ensemble interacting self-propelled rigid bodies. Such may be relevant for modelling bird flocks, fish schools or fleets drones. show that is hyperbolic and can approximated by conservative through relaxation. also derive viscous corrections to model from hydrodynamic limit kinetic model. This analysis prepares future development numerical approximations this system.
Abstract Although cell-to-cell heterogeneity in gene and protein expression within cell populations has been widely documented, we know little about its potential biological functions. We addressed this issue by studying progenitors that populate the posterior region of vertebrate embryos, a population known for capacity to self-renew or contribute formation neural tube paraxial mesoderm tissues. Posterior are characterized co-expression Sox2 Brachyury (Bra), two transcription factors...
Abstract The study of how mechanical interactions and different cellular behaviors affect tissues embryo shaping has been remains an important challenge in biology. Axial extension is a morphogenetic process that results the acquisition elongated shape vertebrate embryonic body. Several adjacent are involved process, including form spinal cord musculoskeletal system: neural tube paraxial mesoderm, respectively. Although we have growing understanding each these elongates, still need to fully...
Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic rate $\phi$ dominates inverse of chemotactic motility function $\gamma$, in sense that $(\phi\gamma)'\ge 0$. This result encompasses complies analysis numerical simulations performed Choi \& Kim (2023). The proof involves two steps: first, Liapunov functional constructed $\phi\gamma$ non-decreasing. convergence relies on detailed study...
In this paper we design, analyze and simulate a finite volume scheme for cross-diffusion system which models chemotaxis with local sensing. This has the same gradient flow structure as celebrated minimal Keller-Segel system, but unlike latter, its solutions are known to exist globally in 2D. The long-time behavior of is only partially understood motivates numerical exploration reliable method. We propose linearly implicit, two-point flux approximation system. show that preserves, at discrete...
While cells typically tend to spread their cytoplasm in a flat and thin lamellipodium when moving on substrate, it is widely observed that the has compact shape micro-channels, tending fulfill cross-section of microchannel. We propose minimal mathematical model for 2D test case which describes cell deformations confined channel. then go through numerical investigation this show allows recover qualitatively physiological characteristics cell.