57 citations · 147 across the 13 of their papers we have counts for
14 papers
On the heat kernel of the Rumin complex and Calderón reproducing formula
Paolo Ciatti, Bruno Franchi, Yannick Sire
We derive several properties of the heat equation with the Hodge operator associated with the Rumin complex on Heisenberg groups and prove several properties of the fundamental sol…
The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as…
Exceptional families of measures on Carnot groups
Bruno Franchi, Irina Markina
We study the families of measures on Carnot groups that have vanishing -module, which we call -exceptional families. We found necessary and sufficient condition for the famil…
Cohomology of annuli, duality and -differential forms on Heisenberg groups
Annalisa Baldi, Bruno Franchi, Pierre Pansu
In the last few years the authors proved Poincaré and Sobolev type inequalities in Heisenberg groups for differential forms in the Rumin's complex. The need to subst…
A sensitivity analysis of a mathematical model for the synergistic interplay of Amyloid beta and tau on the dynamics of Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Valentina Meschini +2
We propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We treat brain neurons as a continuous medium and s…
A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation
Bruno Franchi, Martin Heida, Silvia Lorenzani
In this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulation-diffusion equations with non-h…