Equilibrium statistical mechanics and energy partition for the shallow water model

The aim of this paper is to use large deviation theory in order to compute the entropy of macrostates for the microcanonical measure of the shallow water system. The main prediction of this full statistical mechanics computation is the energy partition between a large scale vortical flow and small scale fluctuations related to inertia-gravity waves. We introduce for that purpose a discretized model of the continuous shallow water system, and compute the corresponding statistical equilibria. We argue that microcanonical equilibrium states of the discretized model in the continuous limit are equilibrium states of the actual shallow water system. We show that the presence of small scale fluctuations selects a subclass of equilibria among the states that were previously computed by phenomenological approaches that were neglecting such fluctuations. In the limit of weak height fluctuations, the equilibrium state can be interpreted as two subsystems in thermal contact: one subsystem corresponds to the large scale vortical flow, the other subsystem corresponds to small scale height and velocity fluctuations. It is shown that either a non-zero circulation or rotation and bottom topography are required to sustain a non-zero large scale flow at equilibrium. Explicit computation of the equilibria and their energy partition is presented in the quasi-geostrophic limit for the energy-enstrophy ensemble. The possible role of small scale dissipation and shocks is discussed. A geophysical application to the Zapiola anticyclone is presented.Comment: Journal of Statistical Physics, Springer Verlag, 201

A dynamical approach to von Neumann dimension

Let G be an amenable group and V be a finite dimensional vector space. Gromov pointed out that the von Neumann dimension of linear subspaces of l^2(G;V) (with respect to G) can be obtained by looking at a growth factor for a dynamical (pseudo-)distance. This dynamical point of view (reminiscent of metric entropy) does not requires a Hilbertian structure. It is used in this article to associate to a $\Gamma$-invariant linear subspaces Y of l^p(G;V) a real positive number dim_{l^p} Y (which is the von Neumann dimension when p=2). By analogy with von Neumann dimension, the properties of this quantity are explored to conclude that there can be no injective G-equivariant linear map of finite-type from l^p(G;V) -> l^p(G; V') if dim V > dim V'. A generalization of the Ornstein-Weiss lemma is developed along the way.Comment: 23 pages. Mistake corrected in statement of P

Case study report The view of the EU cultural and science diplomacy from Egypt. EL-CSID Working Paper Issue 2018/12 • April 2018

As a reminder of the framework of this study, it is worth mentioning, even in general terms, a few schemes and figures. A EU-Egypt Association Agreement (2004) and a EU-Egypt Partnership (2017) have been guiding the relationship between the European Union and the Arab Republic of Egypt, which was maintained throughout all the recent historical events and mishaps of this big country. EU assistance to Egypt under the European Neighbourhood and Partnership Instrument (ENPI) for 2007-2013 was over 1 billion €. Under the Single Support Framework for the period 2014-2016 a total amount of 320 million € in EU grants were committed by the EU. For the period 2014-2020, the European Neighbourhood Instrument (ENI) is the main financial instrument for EU cooperation with Egypt. A “Memorandum of Understanding regarding the EU's Single Support Framework 2017-2020” was signed with Egypt (for an amount of 500 million €), defining priority sectors, amongst which economic modernisation, energy and environment, having been consensually determined by both parties. The “Euro-Mediterranean agreement establishing an association between the European communities and their member states and the Arab Republic of Egypt” (2004) already included some articles about culture, science and innovation1

Molecular epidemiological studies of Campylobacter isolated from different sources in New Zealand between 2005 and 2015 : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Massey University, Manawatu, New Zealand

Campylobacteriosis is one of the most important food-borne diseases worldwide, and a significant health burden in New Zealand. C. jejuni is the predominant species worldwide, accounting for approximately 90% of human cases, followed by C. coli. The first study evaluated whether the time elapsing from sampling to culture has an impact on the recovery rate of Campylobacter, and explored whether some sequence types are more likely than others to be missed due to delayed culture. The study revealed that, whereas delayed culture may affect the recovery rate of Campylobacter, there was no evidence of a bias due to specific sequence types being under detected. The second study aimed to analyse the differences in the Campylobacter viable counts and in population genetic structure between chicken drumsticks and whole carcass meat for retail sale. The results indicate that the Campylobacter population genetic structure did not differ between the two types of retail chicken meat. However, the difference in Campylobacter viable counts suggest that consumption of different chicken meat products may pose different risks of campylobacteriosis associated with an exposure to different infection doses. In the third study, we genotyped C. coli isolates collected from different sources between 2005 and 2014, to study their population structure and estimate the contribution of each source to the burden of human C. coli disease. Modelling indicated ruminants and poultry as the main sources of C. coli infection. The fourth study aimed to genotype C. jejuni isolates collected between 2005 and 2015 from different sources, to assess changes in the molecular epidemiology of C. jejuni following the food safety interventions implemented by the New Zealand poultry industry in 2007/2008. Modelling indicated that chicken meat from ‘Supplier A’ was the main source of C. jejuni human infection before the interventions; but after the interventions, ruminants became the main source of infection, followed by chicken meat from Supplier A. This thesis has made us aware of the aetiology of C. coli infections and the change in the attribution of C. jejuni infections. These findings should be used in developing further strategies to reduce the total burden of human campylobacteriosis

Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: LpL^{p} and almost sure rates of convergence

The geometric median, also called $L^{1}$-median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot, Cenac and Zitt. This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The $L^{p}$ rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rate of convergence in quadratic mean of the averaged algorithm is also given

Comment on "Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems"

In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to prove that a new parameter $\theta(0)$ is required to fully characterize the noise of standard collapse models. These two claims are incorrect and motivated by flawed computations. This comment derives the correct transition probabilities exactly from the master equation, explains how they could be computed perturbatively in a safe way and finally shows where the main mistake of the authors of the original article was made.Comment: 4 page

On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone

We show that if $(u,K)$ is a global minimizer for the Mumford-Shah functional in $R^N$, and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1/2. We deduce some applications in $R^3$ as for instance that an angular sector cannot be the singular set of a global minimizer, that if $K$ is a half-plane then $u$ is the corresponding cracktip function of two variables, or that if K is a cone that meets $S^2$ with an union of $C^1$ curvilinear convex polygones, then it is a $P$, $Y$ or $T$.Comment: 28 page