The full replica symmetry breaking in the Ising spin glass on random regular graph

In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity method, providing a well-defined formulation of the full replica symmetry breaking problem in random regular graphs. Finally, we define the order parameters of the system and get a set of self-consistency equations for the order parameters and the free energy. We face up the problem only from a technical point of view: the physical meaning of this approach and the quantitative evaluation of the solution of the self-consistency equations will be discussed in next works.Comment: 23 page

The full replica symmetry breaking solution in mean-field spin glass models

This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-Mézard cavity method, providing a well-defined formulation of the full replica symmetry breaking problem in random regular graphs. We obtain a variational free energy functional, defined by the sum of two variational functionals (auxiliary variational functionals), that is an extension of the Parisi functional of the Sherrington-Kirkpatrick model. We study the properties of the two variational functionals in detailed, providing representation through the solution of a proper backward stochastic differential equation, that generalize the Parisi partial differential equation. Finally, we define the order parameters of the system and get a set of self-consistency equations for the order parameters and free energy

Further steps in the role of autophagy in methamphetamine toxicity

Methamphetamine (METH) abuse is known to cause a variety of disorders Incluing depression and psychosis. METH induces nigrostriatal damage in animal models and in humans consisting of intracellular alterations in nigral DA cell bodies, degeneration of DA terminals and decreased striatal DA levels. Following METH exposure, the number of nigral cell bodies is quite preserved but autophagy-like vacuoles and cytoplamic accumulation of misfolded proteins are observed. The DA-containing PC12 cell lines represent a simple model of METH toxicity and are commonly used in vitro to understand the pathophysiology of DA neurons. We analyzed at morphological level the effects of plasmid-dependent autophagy modulation on METH toxicity in PC12 cell line. We profited from the high number of authophagic like vacuoles induced by low doses of METH in order to isolate cell fraction in which to study their origin, dynamic structure and molecular composition. We found that authophagy-like vacuoles are positive both for autophagy and proteasome markers. The modulation of autophagy via a p62 containing plasmid protected from METH toxicity, while the inhibition of autophagy machinery worsened METH neurotoxicity. The present data substantiate the protective role of the autophagy machinery in METH-induced DA toxicity where the pro-autophagy protein p62 possesses a key role

Trace ideals for Fourier integral operators with non-smooth symbols II

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann properties of such operators when acting on modulation spaces.Comment: 25 page

The replica symmetric solution for orthogonally constrained Heisenberg model on Bethe lattice

In this paper, we study the thermodynamic properties of a system of D-components classical Heisenberg spins lying on the vertices of a random regular graph, with an unconventional first neighbor non-random interaction J( S_i.S_k)^2. We can consider this model as a continuum version of antiferromagnetic D-states Potts model. We compute the paramagnetic free energy, using a new approach, presented in this paper for the first time, based on the replica method. Through the linear stability analysis, we obtain an instability line on the temperature-connectivity plane that provides a bound to the appearance of a phase transition. We also argue about the character of the instability observed