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A Gentle Introduction to Jensen's Inequality
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Ruger JP: Health and social justice. St Leonards: Routledge; Diez-Roux AV: A glossary for multilevel analysis. Rev Panam Salud Publica , De Maio FG: Income inequality measures. J Epidemiol Community Health , 61 1- Download references. Preliminary findings were presented at the meeting of the Canadian Latin American and Caribbean Studies Association. Correspondence to Fernando G De Maio. FDM and BL conducted the data analysis. FDM wrote the first draft of the paper. All authors contributed to revising the manuscript and to the writing of the final draft.
All authors have read and approved the final manuscript. This article is published under license to BioMed Central Ltd.
Reprints and Permissions. Search all BMC articles Search. Abstract Background Recognition of the global economic and epidemiological burden of chronic non-communicable diseases has increased in recent years. Results Overall, Conclusion The application of the ADI framework enables identification of the regions or groups worst-off for each outcome measure under study. Open Peer Review reports. Background In recent years, the World Health Organization WHO has emphasized the substantial worldwide burden of chronic non-communicable diseases e.
Figure 1. The ADI framework. Full size image. Methods The ENFR is a nationally representative survey with a sample size of 41, adults and a response rate of Demographic and Socioeconomic Measures Along with standard demographic variables sex, age, and marital status , our analysis used four measures of socioeconomic status: employment status employed, unemployed, or not active in the formal labour market , educational attainment, household income, and household unmet basic needs.
Statistical Analysis All analyses were conducted using Stata's survey analysis commands and weighted using survey sampling weights [ 44 ]. Results The demographic and socioeconomic characteristics of the sample are described in table 1.
Electronic Communications in Probability
Table 1 Demographic profile of the sample Full size table. Table 2 Health status by educational attainment N and weighted percentages Full size table. Table 3 Logistic regression analyses for predictors of poor self-rated health and unhealthy diet Full size table. Table 4 Logistic regression analyses for predictors of obesity and diabetes Full size table.
Figure 2. Discussion Our analysis of data from Argentina's first nationally-representative survey of risk factors for chronic non-communicable diseases highlights the social patterning underlying self-reported health status, a common modifiable risk factor unhealthy diet , an intermediate risk factor obesity and a chronic disease outcome diabetes.
Conclusion Incorporating the ADI framework in population health research encourages a move towards a more comprehensive understanding of the underlying social patterning of chronic diseases. References 1. On logarithmic concave measures and functions. Acta Scientiarum Mathematicarum 34 : — Rogers and G. Some extremal problems for convex bodies. Mathematika 5 : 93— A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions. Far East Journal of Theoretical Statistics 48 2 : — Schechtman, Th.
Schlumprecht and J. On the Gaussian measure of the intersection. Annals of Probability 26 1 : — A Gaussian correlation inequality and its applications to the existence of small ball constant. Stochastic Processes and their Applications : — You have access to this content. You have partial access to this content. You do not have access to this content. Volzone and Y. Yao and with V. Calvez and F. As an application, we shall derive a sharp version of a recent result of Hislop and Marx pertaining to the dependence of the integrated density of states of random Schroedinger operators on the distribution of the potential.
Time permitting, we shall also discuss an application to quasiperiodic operators. I will discuss recent joint work with Han Yu, where we prove that such sets must at least approximate arithmetic progressions in a quantifiable sense. Some probabilistic properties still need to be investigated for such channels, which can be seen as a non commutative version of Markov operators. When there exists an invariant normal faithful state, the cyclic properties of quantum channels can be studied passing through the decoherence free algebra and the fixed points domain.
Both these spaces are proved to be images of normal conditional expectations so that their consequent atomic structure is analyzed in order to give a better description of the action of the channel and, for instance, of its Kraus form and invariant densities. The recent computer assisted proof, led by T. Another fascinating case is the computer assisted proof of the Dirac-Schwinger conjecture, by C. Fefferman and L.
Seco, on the asymptotic behaviour of the ground-state energy of certain Schrodinger operators. What may be surprising is that the computational problems used in these proofs are non-computable according to Turing. In this talk we will discuss this paradoxical phenomenon: Not only can non-computable problems be used in computer assisted proofs, they are crucial for proving important conjectures. A key tool for understanding this phenomenon is the Solvability Complexity Index SCI hierarchy, which allows for a classification theory for all types of computational problems.
This classification theory may be of use to pure mathematicians for determining which computational problems that may be used in computer assisted proofs. In particular, there are non-computable problems that can be used and there are non-computable problems that are so difficult that they can never be used in computer assisted proofs. The question is: which ones are safe to utilise?
Examples from mathematical physics and spectral theory will be highlighted. The answer is completely unexpected and depends on the arithmetic properties of the angles of the polygon.http://maisonducalvet.com/cantalapiedra-conocer-gente-por.php
Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory
It appears that a strong two-scale resolvent convergence of associated high-contrast elliptic operators holds under a rather generic decomposition assumption. This implies in particular two-scale convergence of parabolic and hyperbolic semigroups with applications to a wide class of initial value problems. In the end I briefly discuss most recent stronger results with operator-type error estimates for high-contrast problems with Shane Cooper and I. Kamotski , as well as situations where the micro-resonances display certain randomness.
In simplest cases, the resulting two-scale limit behaviour appears to be rather explicit and the macroscopic equations display a form of wave trapping by the micro-resonances due to their randomness. Kamotski, V. Safarov and A. After giving an overview of Quantum Ergodicity results on compact Riemannian manifolds with ergodic geodesic flow due to Shnirelman, Zelditch, Colin de Verdiere and others , we discuss joint work with Yuri Safarov and Alex Strohmaier, which concerns the semiclassical limit of spectral theory on manifolds whose metrics have jump-like discontinuities.
Such systems are quite different from manifolds with smooth Riemannian metrics because the semiclassical limit does not relate to a classical flow but rather to branching ray-splitting billiard dynamics. In order to describe this system we introduce a dynamical system on the space of functions on phase space.
We prove a quantum ergodicity theorem for discontinuous systems. In order to do this we introduce a new notion of ergodicity for the ray-splitting dynamics. If time permits, we outline an example provided by Y. Colin de Verdiere of a system where the ergodicity assumption holds for the discontinuous system. Using a variational principle we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains.