Prophet Inequalities with Limited Information

In the classical prophet inequality, a gambler observes a sequence of stochastic rewards $V_1,...,V_n$ and must decide, for each reward $V_i$, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value $V_i$. The gambler's goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have been generalized to settings where the gambler can choose $k$ items, and, more generally, where he can choose any independent set in a matroid. However, all the existing algorithms require the gambler to know the distribution from which the rewards $V_1,...,V_n$ are drawn. The assumption that the gambler knows the distribution from which $V_1,...,V_n$ are drawn is very strong. Instead, we work with the much simpler assumption that the gambler only knows a few samples from this distribution. We construct the first single-sample prophet inequalities for many settings of interest, whose guarantees all match the best possible asymptotically, \emph{even with full knowledge of the distribution}. Specifically, we provide a novel single-sample algorithm when the gambler can choose any $k$ elements whose analysis is based on random walks with limited correlation. In addition, we provide a black-box method for converting specific types of solutions to the related \emph{secretary problem} to single-sample prophet inequalities, and apply it to several existing algorithms. Finally, we provide a constant-sample prophet inequality for constant-degree bipartite matchings. We apply these results to design the first posted-price and multi-dimensional auction mechanisms with limited information in settings with asymmetric bidders

Goal setting in sport and exercise: results, methodological issues and future directions for research

El propósito de este artículo es proporcionar una visión general respecto a la investigación en el campo del establecimiento de objetivos y el rendimiento en situaciones deportivas y de ejercicio físico. La mayor parte de las primeras investigaciones en este campo pertenecían al área de la organización y la industria, y únicamente en los últimos diez años los investigadores se han centrado en las situaciones deportivas y en el ejercicio físico. Se han dado a menudo hallazgos controvertidos, debidos en parte al empleo de métodos demasiado directos y en parte a que los dos marcos (organización/industria y deporte) difieren bastante. Estas diferencias se dan respecto a las características de la tarea, el tipo de situación, las dificultades del objetivo, los objetivos personales y la aparición de fijaciones espontáneas de objetivos. Estas variables se consideran como mediadores potenciales de la relación entre las distintos fijaciones de objetivos. Recientemente, Weinberg y cols. han entrevistado atletas universitarios respecto a sus prácticas de establecimiento de objetivos, y han observado que una investigación de tipo más cualitativo nos permitiría saber más acerca de cómo trabajan los objetivos en las situaciones deportivas y en el ejercicio físico. Otras direcciones futuras de investigación incluyen la necesidad de obtener datos longitudinales en el seguimiento de atletas a lo largo de la temporada; incoporar y desarrollar las diferencias socioculturales respecto a los estilos de establecimiento de objetivos y sus preferencias; y la inclusión de las diferencias individuales, tales como las variables situacionales. Si conseguimos empezar a entender mejor de que manera la fijación de objetivos opera en las situaciones deportivas y de ejercicio físico, podremos comenzar a desarrollar programas de intervención que no únicamente irán encaminados a obtener el máximo rendimiento, sino que también mejorarán el crecimiento personal de las personas que toman parte en las actividades deportivasThe purpose of this paper was to provide an overview of research in the area of goal setting and performance in sport and exercise settings. Much of the early research in goal setting has been conducted in industrial/organizational settings as it has only been in the last seven to ten years that researchers have begun to focus on goal setting in sport and exercise settings. This has often produced equivocal findings, in part due to methodological shortcomings and in part due to the fact the sport and exercise environments appear to differ from industrial/organizational settings. These differences were noted and variables such as task characteristics, type of setting, goal difficulty, personal goals, spontaneous goal setting, and competition were discussed as potential mediators of the goal setting performance relationship. Recently, Weinberg and his colleagues have assessed and interviewed collegiate athletes concerning their goal setting practices and more qualitative research would allow us to learn more about how goals operate in sport and exercise settings. Other future directions for research include the need for more longitudinal studies following athletes over the course of a season, the incorporation of developmental and sociocultural differences in goal setting styles and preferences, and the inclusion of individual difference variables as well as situational variables. If we can begin to gain a better understanding of how goal setting operates in sport and exercise environments, then we can begin to develop programs and interventions that will not only maximize performance, but also enhance personal growth of individuals participating in sport and exercis

Derivation of Source-Free Maxwell and Gravitational Radiation Equations by Group Theoretical Methods

We derive source-free Maxwell-like equations in flat spacetime for any helicity "j" by comparing the transformation properties of the 2(2j+1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity "j" states that carry the irreducible representations of this group. The set of constraints so derived involves a pair of curl equations and a pair of divergence equations. These reduce to the free-field Maxwell equations for j=1 and the analogous equations coupling the gravito-electric and the gravito-magnetic fields for j=2.Comment: 15 pages, no figures, to appear in Int. J. Mod. Phys.

Limits on MeV Dark Matter from the Effective Number of Neutrinos

Thermal dark matter that couples more strongly to electrons and photons than to neutrinos will heat the electron-photon plasma relative to the neutrino background if it becomes nonrelativistic after the neutrinos decouple from the thermal background. This results in a reduction in N_eff below the standard-model value, a result strongly disfavored by current CMB observations. Taking conservative lower bounds on N_eff and on the decoupling temperature of the neutrinos, we derive a bound on the dark matter particle mass of m_\chi > 3-9 MeV, depending on the spin and statistics of the particle. For p-wave annihilation, our limit on the dark matter particle mass is stronger than the limit derived from distortions to the CMB fluctuation spectrum produced by annihilations near the epoch of recombination.Comment: 5 pages, 1 figure, discussion added, references added and updated, labels added to figure, to appear in Phys. Rev.

Lensing and CMB Anisotropies by Cosmic Strings at a Junction

The metric around straight arbitrarily-oriented cosmic strings forming a stationary junction is obtained at the linearized level. It is shown that the geometry is flat. The sum rules for lensing by this configuration and the anisotropies of the CMB are obtained.Comment: 17 pages, 2 figure

Radiative Transitions in Charmonium from Lattice QCD

Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the $\eta_c, J/\psi$ and $\chi_{c0}$. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation. With an anisotropy $\xi=3$ at $a_s \sim 0.1 \mathrm{fm}$ we find a reasonable gross spectrum and a hyperfine splitting $\sim 90 \mathrm{MeV}$, which compares favourably with other improved actions. In general, after extrapolation of lattice data at non-zero $Q^2$ to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the $J/\psi$ quadrupole moment. We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.Comment: modified version as publishe