Interacting multi-class transmissions in large stochastic networks

The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes of the route. Since several classes of connections going through the nodes of the network are considered, an original mean-field result in a multi-class context is established. It is shown that, as the number of connections goes to infinity, the behavior of the different classes of connections can be represented by the solution of an unusual nonlinear stochastic differential equation depending not only on the sample paths of the process, but also on its distribution. Existence and uniqueness results for the solutions of these equations are derived. Properties of their invariant distributions are investigated and it is shown that, under some natural assumptions, they are determined by the solutions of a fixed-point equation in a finite-dimensional space.Comment: Published in at http://dx.doi.org/10.1214/09-AAP614 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Seismic Risk Analysis of Revenue Losses, Gross Regional Product and transportation systems.

Natural threats like earthquakes, hurricanes or tsunamis have shown seri- ous impacts on communities. In the past, major earthquakes in the United States like Loma Prieta 1989, Northridge 1994, or recent events in Italy like L’Aquila 2009 or Emilia 2012 earthquake emphasized the importance of pre- paredness and awareness to reduce social impacts. Earthquakes impacted businesses and dramatically reduced the gross regional product. Seismic Hazard is traditionally assessed using Probabilistic Seismic Hazard Anal- ysis (PSHA). PSHA well represents the hazard at a specific location, but it’s unsatisfactory for spatially distributed systems. Scenario earthquakes overcome the problem representing the actual distribution of shaking over a spatially distributed system. The performance of distributed productive systems during the recovery process needs to be explored. Scenario earthquakes have been used to assess the risk in bridge networks and the social losses in terms of gross regional product reduction. The proposed method for scenario earthquakes has been applied to a real case study: Treviso, a city in the North East of Italy. The proposed method for scenario earthquakes requires three models: one representation of the sources (Italian Seismogenic Zonation 9), one attenuation relationship (Sa- betta and Pugliese 1996) and a model of the occurrence rate of magnitudes (Gutenberg Richter). A methodology has been proposed to reduce thou- sands of scenarios to a subset consistent with the hazard at each location. Earthquake scenarios, along with Mote Carlo method, have been used to simulate business damage. The response of business facilities to earthquake has been obtained from fragility curves for precast industrial building. Fur- thermore, from business damage the reduction of productivity has been simulated using economic data from the National statistical service and a proposed piecewise “loss of functionality model”. To simulate the economic process in the time domain, an innovative businesses recovery function has been proposed. The proposed method has been applied to generate scenarios earthquakes at the location of bridges and business areas. The proposed selection method- ology has been applied to reduce 8000 scenarios to a subset of 60. Subse- quently, these scenario earthquakes have been used to calculate three system performance parameters: the risk in transportation networks, the risk in terms of business damage and the losses of gross regional product. A novel model for business recovery process has been tested. The proposed model has been used to represent the business recovery process and simulate the effects of government aids allocated for reconstruction. The proposed method has efficiently modeled the seismic hazard using scenario earthquakes. The scenario earthquakes presented have been used to assess possible consequences of earthquakes in seismic prone zones and to increase the preparedness. Scenario earthquakes have been used to sim- ulate the effects to economy of the impacted area; a significant Gross Regional Product reduction has been shown, up to 77% with an earthquake with 0.0003 probability of occurrence. The results showed that limited funds available after the disaster can be distributed in a more efficient way

Resonance Transport and Kinetic Entropy

Within the real-time formulation of nonequilibrium field theory, generalized transport equations are derived avoiding the standard quasiparticle approximation. They permit to include unstable particles into the transport scheme. In order to achieve a self-consistent, conserving and thermodynamically consistent description, we generalize the Baym's $\Phi$-functional method to genuine nonequilibrium processes. The developed transport description naturally includes all those quantum features already inherent in the corresponding equilibrium limit. Memory effects appearing in collision term diagrams of higher order are discussed. The variational properties of $\Phi$-functional permit to derive a generalized expression for the non-equilibrium kinetic entropy flow, which includes fluctuations and mass width effects. In special cases an $H$-theorem is demonstrated implying that the entropy can only increase with time. Memory effects in the kinetic terms provide corrections to the kinetic entropy flow that in equilibrium limit recover the famous bosonic type $T^3 \ln T$ correction to the specific heat of Fermi liquids like Helium-3.Comment: 50 pages, submitted to Nucl. Phys.

Soft Modes, Resonances and Quantum Transport

Effects of the propagation of particles, which have a finite life-time and an according width in their mass spectrum, are discussed in the context of transport description. First, the importance of coherence effects (Landau-Pomeranchuk-Migdal effect) on production and absorption of field quanta in non-equilibrium dense matter is considered. It is shown that classical diffusion and Langevin results correspond to re-summation of certain field-theory diagrams formulated in terms of full non-equilibrium Green's functions. Then the general properties of broad resonances in dense and hot systems are discussed in the framework of a self-consistent and conserving Phi-derivable method of Baym at the examples of the rho-meson in hadronic matter and the pion in dilute nuclear matter. Further we address the problem of a transport description that properly accounts for the damping width of the particles. The Phi-derivable method generalized to the real-time contour provides a self-consistent and conserving kinetic scheme. We derive a generalized expression for the non-equilibrium kinetic entropy flow, which includes corrections from fluctuations and mass-width effects. In special cases an H-theorem is proved. Memory effects in collision terms give contributions to the kinetic entropy flow that in the Fermi-liquid case recover the famous bosonic type T^3 ln T correction to the specific heat of liquid Helium-3. At the example of the pion-condensate phase transition in dense nuclear matter we demonstrate important part played by the width effects within the quantum transport.Comment: submitted to Phys. At. Nucl. (Rus.), the volume dedicated to the memory of A.B. Migdal. 31 pages, 5 figure

Oncogenesis- kaleidoscopic and multi-level reality

Oncogenesis is an extremely complex phenomenon. The mechanisms by which cancer is induced is only partially known. Consequently, therapeutic targets may be uncertain and results are often unsatisfactory. The purpose of this paper is to develop a trans-level and multiple transdisciplinary perspective describing the kaleidoscopic reality of oncogenesis. This manner of understanding oncogenesis as a complex process characterized by a non-linear dynamic, far from equilibrium and with unpredictable evolution, transcends the classical perspective and requires a paradigm shift. This approach is also facilitated by recent studies that focus on group phenomena, with emerging behaviors in a continuous phase transition. Biological systems, and obviously the human organism, express this type of behavior with critical self-organizing valences in the context of a genome - mesotope (environment) - phenotype interaction. For example, nature has transposed in the ecosystem, among other things, the performance pattern of its mineral history represented by the dynamic energy-matter-information unit (the principle of invariance). And multi-cell biological systems in the phylogenetic tree crown have multiple directed aerobic metabolisms in accordance with specific functions. Cancers, in turn, have a hybrid (anaerobic and aerobic) and unidirectional metabolism whose only and ultimate reason is the survival of the malignant cell. Understanding the transdisciplinary reality of oncogenesis offers novel development paths for new therapeutic strategies compared to current ones which have relatively limited efficiency

Keldysh Field Theory for Driven Open Quantum Systems

Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in condensed matter. This concerns both their non-thermal flux equilibrium states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.Comment: 73 pages, 13 figure