Detailed Chemical Abundances of Globular Clusters in Local Group Dwarf Galaxies

We present detailed chemical abundances of Fe, Ca and Ba for 17 globular clusters (GCs) in 5 Local Group dwarf galaxies: NGC 205, NGC 6822, WLM, the SMC and LMC. These abundances are part of a larger sample of over 20 individual elements measured in GCs in these galaxies using a new analysis method for high resolution, integrated light spectra. Our analysis also provides age and stellar population constraints. The existence of GCs in dwarf galaxies with a range of ages implies that there were episodes of rapid star formation throughout the history of these galaxies; the abundance ratios of these clusters suggest that the duration of these burst varied considerably from galaxy to galaxy. We find evolution of Fe, Ca, and Ba with age in the LMC, SMC, and NGC 6822 that is consistent with extended, lower-efficiency SF between bursts, with an increasing contribution of low-metallicity AGB ejecta at late times. Our sample of GCs in NGC 205 and WLM are predominantly old and metal-poor with high [Ca/Fe] ratios, implying that the early history of these galaxies was marked by consistently high SF rates.Comment: 2 pages, To appear in the proceedings of the conference "A Universe of Dwarf Galaxies" (Lyon, June 14-18, 2010

Future Prospects: Deep Imaging of Galaxy Outskirts using Telescopes Large and Small

The Universe is almost totally unexplored at low surface brightness levels. In spite of great progress in the construction of large telescopes and improvements in the sensitivity of detectors, the limiting surface brightness of imaging observations has remained static for about forty years. Recent technical advances have at last begun to erode the barriers preventing progress. In this Chapter we describe the technical challenges to low surface brightness imaging, describe some solutions, and highlight some relevant observations that have been undertaken recently with both large and small telescopes. Our main focus will be on discoveries made with the Dragonfly Telephoto Array (Dragonfly), which is a new telescope concept designed to probe the Universe down to hitherto unprecedented low surface brightness levels. We conclude by arguing that these discoveries are probably only scratching the surface of interesting phenomena that are observable when the Universe is explored at low surface brightness levels.Comment: 27 pages, 10 figures, Invited review, Book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

What fraction of stars formed in infrared galaxies at high redshift?

Star formation happens in two types of environment: ultraviolet-bright starbursts (like 30 Doradus and HII galaxies at low redshift and Lyman-break galaxies at high redshift) and infrared-bright dust-enshrouded regions (which may be moderately star-forming like Orion in the Galaxy or extreme like the core of Arp 220). In this work I will estimate how many of the stars in the local Universe formed in each type of environment, using observations of star-forming galaxies at all redshifts at different wavelengths and of the evolution of the field galaxy population.Comment: 7 pages, 0 figs, to appear in proceedings of "Starbursts - From 30 Doradus to Lyman break galaxies", edited by Richard de Grijs and Rosa M. Gonzalez Delgado, published by Kluwe

Quantum Algorithms for Learning and Testing Juntas

In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity has no dependence on n, the dimension of the domain the Boolean functions are defined over; - with no access to any classical or quantum membership ("black-box") queries. Instead, our algorithms use only classical examples generated uniformly at random and fixed quantum superpositions of such classical examples; - which require only a few quantum examples but possibly many classical random examples (which are considered quite "cheap" relative to quantum examples). Our quantum algorithms are based on a subroutine FS which enables sampling according to the Fourier spectrum of f; the FS subroutine was used in earlier work of Bshouty and Jackson on quantum learning. Our results are as follows: - We give an algorithm for testing k-juntas to accuracy $\epsilon$ that uses $O(k/\epsilon)$ quantum examples. This improves on the number of examples used by the best known classical algorithm. - We establish the following lower bound: any FS-based k-junta testing algorithm requires $\Omega(\sqrt{k})$ queries. - We give an algorithm for learning $k$-juntas to accuracy $\epsilon$ that uses $O(\epsilon^{-1} k\log k)$ quantum examples and $O(2^k \log(1/\epsilon))$ random examples. We show that this learning algorithms is close to optimal by giving a related lower bound.Comment: 15 pages, 1 figure. Uses synttree package. To appear in Quantum Information Processin

Generalized Bernstein--Reznikov integrals

We find a closed formula for the triple integral on spheres in $\mathbb{R}^{2n}\times\mathbb{R}^{2n}\times\mathbb{R}^{2n}$ whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein--Reznikov integral formula in the $n=1$ case. Our method also applies for linear and conformal structures

Improved Bounds on Quantum Learning Algorithms

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is $O(\frac{\log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$, where $\hat{\gamma}^{C}$ is a combinatorial parameter of the class C. We essentially resolve this conjecture in the affirmative by giving a quantum algorithm that, for any class C, identifies any unknown function from C using $O(\frac{\log |C| \log \log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$ quantum black-box queries. We consider a range of natural problems intermediate between the exact learning problem (in which the learner must obtain all bits of information about the black-box function) and the usual problem of computing a predicate (in which the learner must obtain only one bit of information about the black-box function). We give positive and negative results on when the quantum and classical query complexities of these intermediate problems are polynomially related to each other. Finally, we improve the known lower bounds on the number of quantum examples (as opposed to quantum black-box queries) required for $(\epsilon,\delta)$-PAC learning any concept class of Vapnik-Chervonenkis dimension d over the domain $\{0,1\}^n$ from $\Omega(\frac{d}{n})$ to $\Omega(\frac{1}{\epsilon}\log \frac{1}{\delta}+d+\frac{\sqrt{d}}{\epsilon})$. This new lower bound comes closer to matching known upper bounds for classical PAC learning.Comment: Minor corrections. 18 pages. To appear in Quantum Information Processing. Requires: algorithm.sty, algorithmic.sty to buil

Non-stationary Rayleigh-Taylor instability in supernovae ejecta

The Rayleigh-Taylor instability plays an important role in the dynamics of several astronomical objects, in particular, in supernovae (SN) evolution. In this paper we develop an analytical approach to study the stability analysis of spherical expansion of the SN ejecta by using a special transformation in the co-moving coordinate frame. We first study a non-stationary spherical expansion of a gas shell under the pressure of a central source. Then we analyze its stability with respect to a no radial, non spherically symmetric perturbation of the of the shell. We consider the case where the polytropic constant of the SN shell is $\gamma=5/3$ and we examine the evolution of a arbitrary shell perturbation. The dispersion relation is derived. The growth rate of the perturbation is found and its temporal and spatial evolution is discussed. The stability domain depends on the ejecta shell thickness, its acceleration, and the perturbation wavelength.Comment: 16 page

Time varying α\alpha in N=8 extended Supergravity

There has been some evidence that the fine structure "constant" $\alpha$ may vary with time. We point out that this variation can be described by a scalar field in some supergravity theory in our toy model, for instance, the N=8 extended supergravity in four dimensions which can be accommodated in M-theory.Comment: 5 pages,1 figures. Accepted for publication in JHE

Self-consistent stability analysis of spherical shocks.

In this paper, we study self-similar solutions, and their linear stability as well, describing the flow within a spherical shell with finite thickness, expanding according to a power law of time, t q , where q>0. The shell propagates in a medium with initially uniform density and it is bounded by a strong shock wave at its outer border while the inner face is submitted to a time-dependent uniform pressure. For q=2/5, the well-known Sedov–Taylor solution is recovered. In addition, although both accelerated and decelerated shells can be unstable against dynamic perturbations, they exhibit highly different behaviors. Finally, the dispersion relation derived earlier by Vishniac (Vishniac, E.T. in Astrophys. J. 274:152, 1983) for an infinitely thin shell is obtained in the limit of an isothermal shock wave

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level