Research
At a broad level, my research orbits around the development of mechanistic models in biology within the framework of complex systems. It builds on strong foundations in dynamical systems, statistical mechanics, and the theory of ordinary and partial differential equations, providing tools to capture and analyze emergent behaviors across scales.
Ongoing research 🔬
🦠 Modelling microbiological adaptation in extreme environments
My research focuses on the development of mechanistic mathematical models to understand how archaeal cells adapt to extreme environments. The project combines membrane biophysics with intracellular regulatory dynamics, using tools from nonlinear dynamical systems and partial differential equations to capture processes across spatial and temporal scales.
By explicitly coupling physical constraints with regulatory mechanisms, the models aim to provide predictive insights into the conditions that allow membrane homeostasis and cellular viability to be maintained, lost, or dynamically recovered.
A central challenge lies in formalizing the dynamical interplay between membrane properties and regulatory circuits. Tackling this problem is essential for building a unified understanding of archaeal adaptation under stress, and for explaining complex cellular behaviors such as plasticity, resilience, and evolutionary strategies.
This integrative framework is designed to bridge experimental observations from the M2E team with predictive modeling, ultimately enabling a quantitative exploration of living matter under extreme conditions.
External collaborations
Adaptive neural networks 🧠
A theoretical neuroscience project focused on studying neuronal plasticity models through analytical tools from mathematical physics. The goal is to explore how neurons change and reorganise in response to learning and experience. By employing advanced mathematical physics techniques, this project seeks to gain a deeper understanding of neuronal plasticity processes, ultimately aiming to derive a learning rule that incorporates key characteristics for simulating synaptic activity in a spiking neural network model. The specific objective is to model the connectivity structure of the dorsal striatum, allowing the characterisation of its dynamics and responses to inputs associated with fast learning.
Dynamical systems 🌊
Deterministic chaos. Random dynamical systems. Statistical independence in chaotic dynamics, ergodicity and mixing. Iterated function systems.
Some past projects
📈 Adaptive dynamics. Mathematical and computational modelling of chromosomal rearrangements (inversion mutations in particular) to simulate adaptive walks on fitness landscapes. Graph theoretical representation of accessible mutants to elucidate new evolutionary paths in models of molecular evolution. Time-scales in adaptive dynamics to understand stasis periods punctuated by bursts of fitness as observed in in silico long-term evolution experiments (and perhaps contribute to the debate about gradualism vs punctuated equilibrium). Analysis of population dynamics equations with additional terms describing mutations.
⚛️ Theoretical and computational modelling of granular matter. Kinetic theory of inelastic dense gases (Boltzmann equation; Boltzmann–Enskog approximation; Chapman–Enskog method). Hydrodynamics of granular media. Mathematical models of size segregation in vibro-fluidized granular systems. Elasticity and elastodynamics of granular packings. Elastic wave propagation in granular and heterogeneous materials. Coarse-graining method. Numerical simulations using the discrete element method (DEM).
🛢️ Petroleum science and technology. Rock physics. Dynamic response in rocks. Ultrasonic wave propagation on brine and oil saturated rocks. Well logs analysis. Saturation factors in unconventional oil reservoirs in the Venezuelan Orinoco Oil Belt. Mathematical foundations of seismic waves. Compositional flow in fractured porous media.
🌐 Interdisciplinary applications. Analysis of economic indicators and models to measure and predict business and investments in technology from economic and productive data. Time series analysis. Phase space representation of economic factors.