The Potts Fully Frustrated model: Thermodynamics, percolation and dynamics in 2 dimensions

We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass transition in the high-temperature region. We show that the onset of these phenomena can be related to a thermodynamic transition. Furthermore this transition can be mapped onto a percolation transition. We numerically study the phase diagram in 2 dimensions (2D) for this model with frustration and {\em without} disorder and we compare it to the phase diagram of $i)$ the model with frustration {\em and} disorder and of $ii)$ the ferromagnetic model. Introducing a parameter that connects the three models, we generalize the exact expression of the ferromagnetic Potts transition temperature in 2D to the other cases. Finally, we estimate the dynamic critical exponents related to the Potts order parameter and to the energy.Comment: 10 pages, 10 figures, new result

Vascular dysfunction-The disregarded partner of Alzheimer's disease

Increasing evidence recognizes Alzheimer's disease (AD) as a multifactorial and heterogeneous disease with multiple contributors to its pathophysiology, including vascular dysfunction. The recently updated AD Research Framework put forth by the National Institute on Aging-Alzheimer's Association describes a biomarker-based pathologic definition of AD focused on amyloid, tau, and neuronal injury. In response to this article, here we first discussed evidence that vascular dysfunction is an important early event in AD pathophysiology. Next, we examined various imaging sequences that could be easily implemented to evaluate different types of vascular dysfunction associated with, and/or contributing to, AD pathophysiology, including changes in blood-brain barrier integrity and cerebral blood flow. Vascular imaging biomarkers of small vessel disease of the brain, which is responsible for >50% of dementia worldwide, including AD, are already established, well characterized, and easy to recognize. We suggest that these vascular biomarkers should be incorporated into the AD Research Framework to gain a better understanding of AD pathophysiology and aid in treatment efforts. (C) 2018 the Alzheimer's Association. Published by Elsevier Inc. All rights reserved.Neuro Imaging Researc