Dynamics of fibered endomorphisms of $\mathbb P^k$

Christophe Dupont (1) , Johan Taflin (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Specific objective of this project is to quantify the neuropathological tau depositions in brain regions and to investigate primary age-related tau pathology and associations with amyloid and glucose-metabolism, neurocognitive tests and MRI metrics. Preliminary results demonstrated higher temporal deposition especially in the hippocampus and the inferior temporal regions compared to mean cortical deposition. Quantitative Braak stage-based regional analyses found highest tau deposition in the Braak stage II in the preclinical samples. There was significant age related higher tau deposition in temporal cortex, while non-significant correlation in mean cortical region. Significant correlations were found between tau deposition and memory as well as executive function scores, especially from middle and inferior temporal cortex; and significant correlations between tau and MRI metrics including diffusion, perfusion, functional and structural connectivities. Our results confirm current notion of this new tau tracer for reliably and consistently labeling and quantifying human taupathy in early dementia.

Mots clés: Bifurcation current MSC 2010 : 32H50; Lyapunov exponents; Equilibrium measure; 37F10

Domaines: Variables complexes [math.CV]; Systèmes dynamiques [math.DS]

Christophe Dupont, Johan Taflin. Dynamics of fibered endomorphisms of $\mathbb P^k$. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2021, 22 (1), pp.53-78. ⟨10.2422/2036-2145.201811_017⟩. ⟨hal-01925373⟩