Anomalous dissipation in a stochastic inviscid dyadic model

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uniqueness for a Stochastic Inviscid Dyadic Model

For the deterministic dyadic model of turbulence, there are examples of initial conditions in $l^2$ which have more than one solution. The aim of this paper is to prove that uniqueness, for all $l^2$-initial conditions, is restored when a suitable multiplicative noise is introduced. The noise is formally energy preserving. Uniqueness is understood in the weak probabilistic sense.Comment: 13 pages, no figures. Submitted to the Proceedings of the American Mathematical Societ

Anomalous dissipation in a stochastic inviscid dyadic model

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Next-Generation SDN and Fog Computing: A New Paradigm for SDN-Based Edge Computing

In the last few years, we have been able to see how terms like Mobile Edge Computing, Cloudlets, and Fog computing have arisen as concepts that reach a level of popularity to express computing towards network Edge. Shifting some processing tasks from the Cloud to the Edge brings challenges to the table that might have been non-considered before in next-generation Software-Defined Networking (SDN). Efficient routing mechanisms, Edge Computing, and SDN applications are challenging to deploy as controllers are expected to have different distributions. In particular, with the advances of SDN and the P4 language, there are new opportunities and challenges that next-generation SDN has for Fog computing. The development of new pipelines along with the progress regarding control-to-data plane programming protocols can also promote data and control plane function offloading. We propose a new mechanism of deploying SDN control planes both locally and remotely to attend different challenges. We encourage researchers to develop new ways to functionally deploying Fog and Cloud control planes that let cross-layer planes interact by deploying specific control and data plane applications. With our proposal, the control and data plane distribution can provide a lower response time for locally deployed applications (local control plane). Besides, it can still be beneficial for a centralized and remotely placed control plane, for applications such as path computation within the same network and between separated networks (remote control plane)

Firms' exporting and importing activities: is there a two-way relationship?

The literature on firm heterogeneity and trade has highlighted that most trading firms tend to engage in both importing and exporting activities. This may be due to some common sunk costs or to a true state dependence. This paper provides some evidence that helps sort this issue out. Using firm level data for a group of 27 Eastern European and Central Asian countries from the World Bank Business Environment and Enterprise Performance Survey (BEEPS) over the period 2002-2008, we estimate a bivariate probit model of exporting and importing. The main finding is that there is a positive correlation between import and export at the level of the firm, but after controlling for size (and other firm level characteristics) importing have a positive effect on exporting, but exporting to not increase the probability of importing. The evidence is thus consistent with the presence of common sunk costs and with a one-way link between importing and exporting. The positive effect of import on export is mainly due to an increase in firm productivity and product innovation.Exports, Imports, Firm heterogeneity, Eastern European and Central Asian countries

A dyadic model on a tree

We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3d Euler and Navier-Stokes equations in a rough approximation of a wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case