Group Leader: Suárez Fernández, Antonio
Description:
The research work of RL2 focuses on the modeling and analysis of biological and health processes, in particular dynamics of living organisms, tumor growth and non-invasive diagnosis of diseases. Our strategy is to build differential models capturing the main characteristics of the biological processes. After studying their analytical properties, the differential model is modified on the feedback provided by the numerical simulations and the medical/biological advice. This allows us to describe the complex interactions present in tumor growth and provide insight to design novel therapies and optimize the current ones.
Our goal is to develop predictive models for the non-invasive diagnosis of diseases and the estimation of the evolution of infectious ones, based on the classification and regression analysis of a learning sample. We also develop pharmacokinetic models to analyze the variability of the pharmacological response depending on physiological characteristics of the patients. For this we develop statistical techniques based upon nonlinear mixed effects models.
Members:
Clara Grima Ruíz
Francisco Guillén González
Juan Vicente Gutiérrez Santacréu
Mª José Jiménez Rodríguez
Research portfolio:
Mathematics of human consciousness: theory, computation and clinical application
A. Dynamical systems
B. Geometrical and topological characterization of attractors of attractors
C. Lotka-Volterra transform
D. Informational structures for brain dynamics
Neuroscience, Psychology, Medical Sciences
Mathematical technology for better understanding of diseases and the control of therapies
A. Partial differential equations
B. Numerical Analysis
C. Dynamical systems
D. Machine learning techniques
E. Complex statistical techniques
Ecology, Medicine, Neuroscience
Mathematical technology for the improvement of healthcare system
A. Partial differential equations
B. Numerical Analysis
C. Dynamical systems
D. Machine learning techniques
E. Complex statistical techniques
Ecology, Medicine, Neuroscience
Long-time behavior of coupled systems with Navier-Stokes
A. Theory of partial differential equations
B. Mathematical modeling through conservation laws
Biology
Bioconvective flows
A. Theory of partial differential equations
Biology
Chemotaxis models and Non-local models applied to Biology
A. Theory of partial differential equations
B. Bifurcation theory
C. Sub-supersolutions methods
D. Semigroup theory
Biology, Medicine
Numerical methods for Biological Models
A. Partial Differential Equations
B. Finite Element Methods
C. Stabilization
D. Discrete Maximum Principle
E. Energy law
Biology, Pharmacy, Medicine
Computational topology and neural networks
A. Computational topology
B. Algebraic topology
C. Machine learning.
D. Deep learning.
E. Topological data analysis
Technology
Topological analysis of biological data
A. Topological data analysis
B. Graph modelling
C. Computational geometry
D. Statistics
Pharmacology, Biomedicine
Theoretical and numerical analysis, and optimal control of biological problems related to the chemotaxis process
A. Theory of partial differential equations
B. Optimal control
C. Numerical approximation using Finite Element Methods
D. Numerical Analysis
Biology, Medicine
Theoretical and numerical analysis, and optimal control of biological problems. Identification of biologiccal parameters and comparision of therapies
A. Theory of partial differential equations
B. Optimal control
C. Numerical approximation using Finite Element Methods (continuous and/or discontinuous)
D. Numerical Analysis
Biology, Medicine
Biological and health systems
A. Theory of Nonlinear Partial Differential Equations
B. Nonlocal Transport terms. Fokker Planck and Porous media equations
C. Solutions arising singularities. Blow-up in finite time
D. Agent Based Models. Mean field equations. Random graphs
E. Statistical Mechanics tools. Boltzmann Equation. Grazing limit.
F. Markov Processes and Hydrodynamic limits
G. Numerical simulations
H. Some nonlocal diffusivities
Biological processes, epidemics , chemotaxis, population dynamics
Modeling and simulation of neuroendocrine processes
A. Theory of Dynamical Systems and bifurcations
B. Mathematical modelling through slow-fast systems
C. Mathematical modelling through non-smooth systems
D. Analysis of complex oscillations and ‘canard’ phenomena
E. Numerical methods for stiff systems.
Biology, Health systems, Engineering
Related projects:
- Deterministic and stochastic dynamics of models from Neuroscience, Epidemiology, Biology and other branches of the Applied Sciences
- PDEs for Biological models with Chemotaxis and Nonlocal effects
- Advances in Computational Topology and Applications
- Computational Algebraic Topology Applied to Computer Vision
- Algebraic Topology for Combinatorial Analysis of Images
Related transfer:
- A dynamical system approach to human consciousness
- Segmentation of images of clinical essays of stem cell colonies by spatial analysis techniques
- Numerical simulation for chemorepulsive and productive models
- Interactions vesicles membranes and liquid crystals
- Opinion formation Models: from individual interactions to the asymptotic behaviour of the whole population
- Some nonlocal diffusivities governing biological processes
- Project for the Valorization of the Crayfish and the Design of Prototypes for the Optimization of its Productive Processes
- Sideview
- Mathematical Modeling of Gonadotropine Neurohormone
