José A. Carrillo
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View article: Epigenetic control of microglial developmental milestones from proliferative progenitors to efficient phagocytes
Epigenetic control of microglial developmental milestones from proliferative progenitors to efficient phagocytes Open
Early immune perturbations increase the risk of neurodegenerative and neurodevelopmental disorders, yet the mechanisms underlying the maturation of microglia, the resident immune cells of the brain parenchyma, remain poorly defined. Specif…
View article: Finite element scheme for the fractional porous medium equation with fractional pressure
Finite element scheme for the fractional porous medium equation with fractional pressure Open
We construct a finite element method for the numerical solution of a fractional porous medium equation on a bounded open Lipschitz polytopal domain $$\Omega \subset {\mathbb {R}}^{d}$$ , where $$d = 2$$ or 3. The pressure in the model is d…
View article: Epigenetic programming of estrogen receptor in adipocytes by high-fat diet regulates obesity-induced inflammation
Epigenetic programming of estrogen receptor in adipocytes by high-fat diet regulates obesity-induced inflammation Open
Adipose inflammation plays a key role in obesity-induced metabolic abnormalities. Epigenetic regulation, including DNA methylation, is a molecular link between environmental factors and complex diseases. Here we found that high-fat diet (H…
View article: Existence of ground states for free energies on the hyperbolic space
Existence of ground states for free energies on the hyperbolic space Open
We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space ${\mathbb H}^n$ . The free energy consists of two competing terms: an entr…
View article: Long-time behaviour and bifurcation analysis of a two-species aggregation-diffusion system on the torus
Long-time behaviour and bifurcation analysis of a two-species aggregation-diffusion system on the torus Open
We investigate stationary states, including their existence and stability, in a class of nonlocal aggregation-diffusion equations with linear diffusion and symmetric nonlocal interactions. For the scalar case, we extend previous results by…
View article: Epigenetic Programming of Estrogen Receptor in Adipose Tissue by High Fat Diet Regulates Obesity-Induced Inflammation
Epigenetic Programming of Estrogen Receptor in Adipose Tissue by High Fat Diet Regulates Obesity-Induced Inflammation Open
Adipose inflammation plays a key role in obesity-induced metabolic abnormalities. Epigenetic regulation, including DNA methylation, is a molecular link between environmental factors and complex diseases. Here we found that high fat diet (H…
View article: Adaptive tuning of Hamiltonian Monte Carlo methods
Adaptive tuning of Hamiltonian Monte Carlo methods Open
With the recently increased interest in probabilistic models, the efficiency of an underlying sampler becomes a crucial consideration. A Hamiltonian Monte Carlo (HMC) sampler is one popular option for models of this kind. Performance of HM…
View article: Fluid Relaxation Approximation of the Busenberg–Travis Cross-Diffusion System
Fluid Relaxation Approximation of the Busenberg–Travis Cross-Diffusion System Open
The Busenberg–Travis cross-diffusion system for segregating populations is approximated by the compressible Navier–Stokes–Korteweg equations on the torus, including a density-dependent viscosity and drag forces. The Korteweg term can be as…
View article: A minimax method for the spectral fractional Laplacian and related evolution problems
A minimax method for the spectral fractional Laplacian and related evolution problems Open
We present a numerical method for the approximation of the inverse of the fractional Laplacian $(-Δ)^{s}$, based on its spectral definition, using rational functions to approximate the fractional power $A^{-s}$ of a matrix $A$, for $0
View article: Inelastic Boltzmann equation under shear heating
Inelastic Boltzmann equation under shear heating Open
In this paper, we study the spatially homogeneous inelastic Boltzmann equation for the angular cutoff pseudo-Maxwell molecules with an additional term of linear deformation. We establish the existence of non-Maxwellian self-similar profile…
View article: Rate of Convergence for a Nonlocal-to-local Limit in One Dimension
Rate of Convergence for a Nonlocal-to-local Limit in One Dimension Open
We consider a nonlocal approximation of the quadratic porous medium equation where the pressure is given by a convolution with a mollification kernel. It is known that when the kernel concentrates around the origin, the nonlocal equation c…
View article: A Nonlocal-to-Local Approach to Aggregation-Diffusion Equations
A Nonlocal-to-Local Approach to Aggregation-Diffusion Equations Open
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based mode…
View article: A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns
A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns Open
Cell sorting by differential adhesion is one of the basic mechanisms explaining spatial organization of neurons in early stage brain development of fruit flies. The columnar arrangements of neurons determine the large-scale patterns in the…
View article: Evolution equations on co-evolving graphs: long-time behaviour and the graph continuity equation
Evolution equations on co-evolving graphs: long-time behaviour and the graph continuity equation Open
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the so-ca…
View article: Statistical accuracy of the ensemble Kalman filter in the near-linear setting
Statistical accuracy of the ensemble Kalman filter in the near-linear setting Open
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely …
View article: Singular flows with time-varying weights
Singular flows with time-varying weights Open
We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty \cite{duerinckx2020mean} and Bresch-Jabin-Wang \cite{bresch2019modulated}, which consider singular Coulomb …
View article: From Fisher information decay for the Kac model to the Landau-Coulomb hierarchy
From Fisher information decay for the Kac model to the Landau-Coulomb hierarchy Open
We consider the Kac model for the space-homogeneous Landau equation with the Coulomb potential. We show that the Fisher information of the Liouville equation for the unmodified $N$-particle system is monotonically decreasing in time. The m…
View article: Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical Symmetry
Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical Symmetry Open
The compressible Euler-Riesz equations are fundamental with wide applications in astrophysics, plasma physics, and mathematical biology. In this paper, we are concerned with the global existence and nonlinear stability of finite-energy sol…
View article: Collective Transitions from Orbiting to Matrix Invasion in 3D Multicellular Spheroids
Collective Transitions from Orbiting to Matrix Invasion in 3D Multicellular Spheroids Open
Coordinated cell rotation along a curved matrix interface can sculpt epithelial tissues into spherical morphologies. Subsequently, radially-oriented invasion of multicellular strands or branches can occur by local remodeling of the confini…
View article: Sparse identification of nonlocal interaction kernels in nonlinear gradient flow equations via partial inversion
Sparse identification of nonlocal interaction kernels in nonlinear gradient flow equations via partial inversion Open
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation–diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem…
View article: Machine Learning Algorithms for Predictive Maintenance: A Systematic Literature Mapping
Machine Learning Algorithms for Predictive Maintenance: A Systematic Literature Mapping Open
Predictive maintenance is a practice that industrial companies can apply to their processes thanks to technologies such as artificial intelligence and the Internet of Things. Machine Learning algorithms are used in many fields to make pred…
View article: Nonlinear partial differential equations in neuroscience: from modelling to mathematical theory
Nonlinear partial differential equations in neuroscience: from modelling to mathematical theory Open
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the mathema…
View article: Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity
Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity Open
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting …
View article: Corrigendum: Discontinuous Galerkin methods for the Vlasov-Poisson system
Corrigendum: Discontinuous Galerkin methods for the Vlasov-Poisson system Open
In this short note we rectify the error estimates of the discontinuous Galerkin methods for the Vlasov-Poisson system, proposed and analyzed in [1, 2]. The error estimates are now of sub-optimal order.
View article: Positivity-preserving and energy-dissipating discontinuous Galerkin methods for nonlinear nonlocal Fokker–Planck equations
Positivity-preserving and energy-dissipating discontinuous Galerkin methods for nonlinear nonlocal Fokker–Planck equations Open
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker– Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions, represent…