Generic identifiability and second-order sufficiency in tame convex optimization

We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, "tame"). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is "partly smooth", ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality conditions hold, guaranteeing smooth behavior of the optimal solution under small perturbations to the objective

Probing The Lower Mass Limit For Supernova Progenitors And The High-Mass End Of The Initial-Final Mass Relation From White Dwarfs In The Open Cluster M35 (NGC 2168)

We present a photometric and spectroscopic study of the white dwarf (WD) population of the populous, intermediate-age open cluster M35 (NGC 2168); this study expands upon our previous study of the WDs in this cluster. We spectroscopically confirm 14 WDs in the field of the cluster: 12 DAs, 1 hot DQ, and 1 db star. For each DA, we determine the WD mass and cooling age, from which we derive each star's progenitor mass. These data are then added to the empirical initial-final mass relation (IFMR), where the M35 WDs contribute significantly to the high-mass end of the relation. The resulting points are consistent with previously published linear fits to the IFMR, modulo moderate systematics introduced by the uncertainty in the star cluster age. Based on this cluster alone, the observational lower limit on the maximum mass of WD progenitors is found to be similar to 5.1M(circle dot) - 5.2M(circle dot) at the 95% confidence level; including data from other young open clusters raises this limit to as high as 7.1M(circle dot), depending on the cluster membership of three massive WDs and the core composition of the most massive WDs. We find that the apparent distance modulus and extinction derived solely from the cluster WDs ((m-M)(V) = 10.45 +/- 0.08 and E(B-V) = 0.185 +/- 0.010, respectively) is fully consistent with that derived from main-sequence fitting techniques. Four M35 WDs may be massive enough to have oxygen - neon cores; the assumed core composition does not significantly affect the empirical IFMR. Finally, the two non-DA WDs in M35 are photometrically consistent with cluster membership; further analysis is required to determine their memberships.NSF AST-0397492, AST-0602288Astronom

Clarke subgradients of stratifiable functions

We establish the following result: if the graph of a (nonsmooth) real-extended-valued function $f:\mathbb{R}^{n}\to \mathbb{R}\cup\{+\infty\}$ is closed and admits a Whitney stratification, then the norm of the gradient of $f$ at $x\in{dom}f$ relative to the stratum containing $x$ bounds from below all norms of Clarke subgradients of $f$ at $x$. As a consequence, we obtain some Morse-Sard type theorems as well as a nonsmooth Kurdyka-\L ojasiewicz inequality for functions definable in an arbitrary o-minimal structure

A Search for Binary Stars at Low Metallicity

We present initial results measuring the companion fraction of metal-poor stars ([Fe/H]$<-$2.0). We are employing the Lick Observatory planet-finding system to make high-precision Doppler observations of these objects. The binary fraction of metal-poor stars provides important constraints on star formation in the early Galaxy (Carney et al. 2003). Although it has been shown that a majority of solar metallicity stars are in binaries, it is not clear if this is the case for metal-poor stars. Is there a metallicity floor below which binary systems do not form or become rare? To test this we are determining binary fractions at metallicities below [Fe/H]$=-2.0$. Our measurments are not as precise as the planet finders', but we are still finding errors of only 50 to 300 m/s, depending on the signal-to-noise of a spectrum and stellar atmosphere of the star. At this precision we can be much more complete than previous studies in our search for stellar companions.Comment: To appear in conference proceedings,"First Stars III", eds. B. O'Shea, A. Heger & T. Abel. 3 pages, 5 figure

An empirical initial-final mass relation from hot, massive white dwarfs in NGC 2168 (M35)

The relation between the zero-age main sequence mass of a star and its white-dwarf remnant (the initial-final mass relation) is a powerful tool for exploration of mass loss processes during stellar evolution. We present an empirical derivation of the initial-final mass relation based on spectroscopic analysis of seven massive white dwarfs in NGC 2168 (M35). Using an internally consistent data set, we show that the resultant white dwarf mass increases monotonically with progenitor mass for masses greater than 4 solar masses, one of the first open clusters to show this trend. We also find two massive white dwarfs foreground to the cluster that are otherwise consistent with cluster membership. These white dwarfs can be explained as former cluster members moving steadily away from the cluster at speeds of <~0.5 km/s since their formation and may provide the first direct evidence of the loss of white dwarfs from open clusters. Based on these data alone, we constrain the upper mass limit of WD progenitors to be >=5.8 solar masses at the 90% confidence level for a cluster age of 150 Myr.Comment: 14 pages, 3 figures. Accepted for publication in the Astrophysical Journal Letters. Contains some acknowledgements not in accepted version (for space reasons), otherwise identical to accepted versio

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Semi-classical Green kernel asymptotics for the Dirac operator

We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator evaluated at two distinct points fulfilling a certain hypothesis can be represented as the product of an exponentially decaying factor involving an associated Agmon distance and some amplitude admitting a complete asymptotic expansion in powers of the semi-classical parameter. Moreover, we find an explicit formula for the leading term in that expansion.Comment: 46 page

Determinants of short-period heart rate variability in the general population

Decreased heart rate variability (HRV) is associated with a worse prognosis in a variety of diseases and disorders. We evaluated the determinants of short-period HRV in a random sample of 149 middle-aged men and 137 women from the general population. Spectral analysis was used to compute low-frequency (LF), high-frequency (HF) and total-frequency power. HRV showed a strong inverse association with age and heart rate in both sexes with a more pronounced effect of heart rate on HRV in women. Age and heart rate-adjusted LF was significantly higher in men and HF higher in women. Significant negative correlations of BMI, triglycerides, insulin and positive correlations of HDL cholesterol with LF and total power occurred only in men. In multivariate analyses, heart rate and age persisted as prominent independent predictors of HRV. In addition, BMI was strongly negatively associated with LF in men but not in women, We conclude that the more pronounced vagal influence in cardiac regulation in middle-aged women and the gender-different influence of heart rate and metabolic factors on HRV may help to explain the lower susceptibility of women for cardiac arrhythmias. Copyright (C) 2001 S. Karger AG, Basel

Chemical Abundances For Evolved Stars In M5: Lithium Through Thorium

We present analysis of high-resolution spectra of a sample of stars in the globular cluster M5 (NGC 5904). The sample includes stars from the red giant branch (RGB; seven stars), the red horizontal branch (two stars), and the asymptotic giant branch (AGB; eight stars), with effective temperatures ranging from 4000 K to 6100 K. Spectra were obtained with the HIRES spectrometer on the Keck I telescope, with a wavelength coverage from 3700 angstrom to 7950 angstrom for the HB and AGB sample, and 5300 angstrom to 7600 angstrom for the majority of the RGB sample. We find offsets of some abundance ratios between the AGB and the RGB branches. However, these discrepancies appear to be due to analysis effects, and indicate that caution must be exerted when directly comparing abundance ratios between different evolutionary branches. We find the expected signatures of pollution from material enriched in the products of the hot hydrogen burning cycles such as the CNO, Ne-Na, and Mg-Al cycles, but no significant differences within these signatures among the three stellar evolutionary branches especially when considering the analysis offsets. We are also able to measure an assortment of neutron-capture element abundances, from Sr to Th, in the cluster. We find that the neutron-capture signature for all stars is the same, and shows a predominately r-process origin. However, we also see evidence of a small but consistent extra s-process signature that is not tied to the light-element variations, pointing to a pre-enrichment of this material in the protocluster gas.National Science Foundation AST-0802292NSF AST-0406988, AST-0607770, AST-0607482DFGW. M. Keck FoundationAstronom

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law