We are excited to share that our last preprint, "A novel mathematical and computational framework of amyloid-beta triggered seizure dynamics in Alzheimer's disease", from C.B. Leimer Saglio, S. Pagani, P.F. Antonietti and me, is now out on ArXiv. 

In this work, we introduce a novel mathematical model that extends the Barreto-Cressman ionic formulation by incorporating multiple mechanisms of calcium dysregulation induced by amyloid-beta. Numerical simulations performed on idealized and realistic brain geometries demonstrate that progressive amyloid-beta accumulation leads to severe alterations in calcium homeostasis, increased neuronal hyperexcitability, and pathological seizure propagation.

Our last preprint "Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems" from P.F. Antonietti, S. Gómez, I. Perugia, and me is now out on ArXiv and MOX Report. 

This work investigates a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. We prove a discrete entropy-stability inequality, which we use to show the existence of discrete solutions, as well as to establish the convergence of the scheme by means of some discrete compactness arguments.

Check out our last article, "Polytopal mesh agglomeration via geometrical deep learning for three-dimensional heterogeneous domains", which has been recently published in Mathematics and Computers in Simulation. 

In this work, we propose a bisection model based on Graph Neural Networks to partition a suitable connectivity graph of computational three-dimensional meshes. Our algorithm can agglomerate meshes of a domain composed of heterogeneous media, automatically respecting the underlying heterogeneities. Moreover, we demonstrate that our algorithm also shows a good level of generalization when applied to complex geometries, such as three-dimensional geometries reconstructed from medical images. Finally, the model’s capability to perform agglomeration in heterogeneous domains is evaluated when integrated into a polytopal discontinuous Galerkin finite element solver.  

Polygonal and Structure-Preserving Methods for PDEs Discretization

Mathematical Modeling of Neurodegenerative Diseases