Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir

We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the Hamiltonian Mean Field model and the equilibrium ensemble equivalence. We find that long-lasting quasi-stationary states persist in presence of the interaction with the environment. Our results indicate that quasi-stationary states are indeed reproducible in real physical experiments.Comment: Title changed, throughout revision of the tex

Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics

We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one also unambiguously explains and predicts striking slow algebraic relaxation of the momenta autocorrelation, previously found in numerical simulations. Finally, angular anomalous diffusion are predicted for a large class of initial distributions. Non Extensive Statistical Mechanics is shown to be unnecessary for the interpretation of these phenomena

The role of immune cells, glia and neurons in white and gray matter pathology in multiple sclerosis.

Multiple sclerosis is one of the most common causes of chronic neurological disability beginning in early to middle adult life. Multiple sclerosis is idiopathic in nature, yet increasing correlative evidence supports a strong association between one's genetic predisposition, the environment and the immune system. Symptoms of multiple sclerosis have primarily been shown to result from a disruption in the integrity of myelinated tracts within the white matter of the central nervous system. However, recent research has also highlighted the hitherto underappreciated involvement of gray matter in multiple sclerosis disease pathophysiology, which may be especially relevant when considering the accumulation of irreversible damage and progressive disability. This review aims at providing a comprehensive overview of the interplay between inflammation, glial/neuronal damage and regeneration throughout the course of multiple sclerosis via the analysis of both white and gray matter lesional pathology. Further, we describe the common pathological mechanisms underlying both relapsing and progressive forms of multiple sclerosis, and analyze how current (as well as future) treatments may interact and/or interfere with its pathology. Understanding the putative mechanisms that drive disease pathogenesis will be key in helping to develop effective therapeutic strategies to prevent, mitigate, and treat the diverse morbidities associated with multiple sclerosis.The authors thank Dr. Gillian Tannahill and Prof. Alasdair Coles for critically reviewing the article, and Prof. Kenneth J Smith for the illuminating discussions on MS pathophysiology. We acknowledge the contribution of past and present members of Pluchino laboratory, who have contributed to (or inspired) this manuscript. Research in the author’s laboratory is supported by the National Multiple Sclerosis Society (NMSS; RG-4001-A1), the Italian Multiple Sclerosis Foundation (FISM; RG 2010/R/31), the Italian Ministry of Health (GR08/7) the European Research Council (ERC) 2010-StG (RG 260511-SEM_SEM), the European Community (EC) 7th Framework Program (FP7/2007–2013; RG 280772-iONE), The Evelyn Trust (RG 69865), The Bascule Charitable Trust (RG 75149), The Great Britain Sakakawa Foundation and a core support grant from the Wellcome Trust and MRC to the Wellcome Trust – Medical Research Council Cambridge Stem Cell Institute. GM was supported by an European Neurological Society (ENS) Training fellowship. LPJ was supported by the Wellcome Trust [RRZA/057 RG79423]. JDB was supported by a NIH-OxCam fellowship.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.pneurobio.2015.02.00

Collective Charge Fluctuations in Single-Electron Processes on Nano-Networks

Using numerical modeling we study emergence of structure and structure-related nonlinear conduction properties in the self-assembled nanoparticle films. Particularly, we show how different nanoparticle networks emerge within assembly processes with molecular bio-recognition binding. We then simulate the charge transport under voltage bias via single-electron tunnelings through the junctions between nanoparticles on such type of networks. We show how the regular nanoparticle array and topologically inhomogeneous nanonetworks affect the charge transport. We find long-range correlations in the time series of charge fluctuation at individual nanoparticles and of flow along the junctions within the network. These correlations explain the occurrence of a large nonlinearity in the simulated and experimentally measured current-voltage characteristics and non-Gaussian fluctuations of the current at the electrode.Comment: 10 pages, 7 figure

Analysis of Self-Organized Criticality in the Olami-Feder-Christensen model and in real earthquakes

We perform a new analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears the Probability Density Functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape. This behaviour does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. Such a result can be analytically understood if the sizes (released energies) of the avalanches (earthquakes) have no correlations. Our findings support the hypothesis that a self-organized criticality mechanism with long-range interactions is at the origin of seismic events and indicate that it is not possible to predict the magnitude of the next earthquake knowing those of the previous ones.Comment: 5 pages, 3 figures. New version accepted for publication on PRE Rapid Communication

Mesenchymal stem cells as promoters, enhancers, and playmakers of the translational regenerative medicine

Since their first isolation and characterization by Friedenstein et al. in 1974, mesenchymal stem cells (MSCs) were proven essential for tissue regeneration and homeostasis. Over the years, thanks to a better understanding of the molecular mechanisms underlying the therapeutic effects of MSCs, several approaches with MSC-based therapies have been proposed, in order to treat different human diseases. In this light, MSCs are currently being tested in preclinical in vivo settings as well as in early-stage clinical trials for their ability to modulate immune responses, fostering wound healing and tissue regeneration of various tissue types and organs, including the skin, bone, cartilage, brain, muscle, and tendons

Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation

We here discuss the emergence of Quasi Stationary States (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian Mean Field (HMF) model, numerical simulations are performed based on both the original $N$-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particles correlations.Comment: 5 pages, 3 figure

Incomplete equilibrium in long-range interacting systems

We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution, we find that the Central Limit Theorem implies the Boltzmann expression in Gibbs' $\Gamma$-space. We identify the nonequilibrium sub-manifold of $\Gamma$-space characterizing the anomalous behavior and show that by restricting the Boltzmann-Gibbs approach to this sub-manifold we obtain the statistical mechanics of the quasi-stationary states.Comment: Title changed, throughout revision of the tex

Self-Organized Bottleneck in Energy Relaxation

We study an energy relaxation process after many degrees of freedom are excited in a Hamiltonian system with a large number of degrees of freedom. Bottlenecks of relaxation, where relaxations of the excited elements are drastically slowed down, are discovered. By defining an internal state for the excited degrees of freedom, it is shown that the drastic slowing down occurs when the internal state is in a critical state. The relaxation dynamics brings the internal state into the critical state, and the critical bottleneck of relaxation is self-organized. Relevance of our result to relaxation phenomena in condensed matters or large molecules is briefly discussed.Comment: 4pages, 5 figure