Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A merit of this approach is its flexibility: for example, all compressed sensing problems can be solved via this approach. These include models with objective functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or a combination thereof. In addition, the paper also introduces a number of technical contributions such as a novel continuation scheme, a novel approach for controlling the step size, and some new results showing that the smooth and unsmoothed problems are sometimes formally equivalent. Combined with our framework, these lead to novel, stable and computationally efficient algorithms. For instance, our general implementation is competitive with state-of-the-art methods for solving intensively studied problems such as the LASSO. Further, numerical experiments show that one can solve the Dantzig selector problem, for which no efficient large-scale solvers exist, in a few hundred iterations. Finally, the paper is accompanied with a software release. This software is not a single, monolithic solver; rather, it is a suite of programs and routines designed to serve as building blocks for constructing complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This version has updated reference

Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28])

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Slow relaxation in weakly open vertex-splitting rational polygons

The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two distinct channels for the late-time relaxation of type 1/t^delta are established. The primary channel, associated with the universal relaxation of ''regular'' orbits, with delta = 1, is common for both the closed and open, chaotic and nonchaotic billiards. The secondary relaxation channel, with delta > 1, is originated from ''irregular'' orbits and is due to the rationality of vertices.Comment: Key words: Dynamics of systems of particles, control of chaos, channels of relaxation. 21 pages, 4 figure

The metabolic syndrome and risk of sudden cardiac death: The atherosclerosis risk in communities study

Background--Prior studies have demonstrated a link between the metabolic syndrome and increased risk of cardiovascular mortality. Whether the metabolic syndrome is associated with sudden cardiac death is uncertain. Methods and Results--We characterized the relationship between sudden cardiac death and metabolic syndrome status among participants of the ARIC (Atherosclerosis Risk in Communities) Study (1987-2012) free of prevalent coronary heart disease or heart failure. Among 13 168 participants, 357 (2.7%) sudden cardiac deaths occurred during a median follow-up of 23.6 years. Participants with the metabolic syndrome (n=4444) had a higher cumulative incidence of sudden cardiac death than those without it (n=8724) (4.1% versus 2.3%, P < 0.001). After adjustment for participant demographics and clinical factors other than components of the metabolic syndrome, the metabolic syndrome was independently associated with sudden cardiac death (hazard ratio, 1.70, 95% confidence interval, 1.37-2.12, P < 0.001). This relationship was not modified by sex (interaction P=0.10) or race (interaction P=0.62) and was mediated by the metabolic syndrome criteria components. The risk of sudden cardiac death varied according to the number of metabolic syndrome components (hazard ratio 1.31 per additional component of the metabolic syndrome, 95% confidence interval, 1.19-1.44, P < 0.001). Of the 5 components, elevated blood pressure, impaired fasting glucose, and low high-density lipoprotein were independently associated with sudden cardiac death. Conclusions--We observed that the metabolic syndrome was associated with a significantly increased risk of sudden cardiac death irrespective of sex or race. The risk of sudden cardiac death was proportional to the number of metabolic syndrome components

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Mastocytosis: a Rare Case of Anaphylaxis in Paediatric Age and Literature Review

The term “mastocytosis” denotes a heterogeneous group of disorders characterised by abnormal growth and accumulation of mast cells (MC) in one or more organ systems. Symptoms result from MC chemical mediator’s release, pathologic infiltration of neoplastic MC in tissues or both. Multiple molecular, genetic and chromosomal defects seem to contribute to an autonomous growth, but somatic c-kit D816V mutation is more frequently encountered, especially in systemic disease. We present a literature review of mastocytosis and a rare case report of an 18 month-old-girl with a bullous dermatosis, respiratory distress and anaphylaxis, as clinical manifestations of mastocytosis. The developments of accepted classification systems and novel useful markers allowed a re-evaluation and updating of the classification of mastocytosis. In paediatric age cutaneous forms of disease prevail and may regress spontaneously. SM is more frequently diagnosed in adults and is a persistent(clonal) disease of bone marrow. The clinical course in these patients is variable.Today diagnostic criteria for each disease variant are reasonably well defined. There are, however, peculiarities, namely in paediatric age, that makes the diagnostic approach difficult. Systemic disease may pose differential diagnostic problems resulting from multiple organ systems involvement. Coversly, the “unexplained” appearance of those symptoms with no skin lesions should raise the suspicion of MC disease. This case is reported in order to stress the clinical severity and difficult diagnostic approach that paediatric mastocytosis may assume