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

A new Coniopterygidae from Lebanese amber

We describe the oldest fossil Coniopterygidae, possibly attributable to the Coniopteryginae, in the new genus and species Libanosemidalis hammanaensis, from the outcrop Hammana / Mdeyrij in the Lower Cretaceous amber of Lebanon. This fossil shares with the extant and Cenozoic lineages of Coniopterygidae the presence of only two M branches, unlike other Cretaceous representatives of the family

Improved algorithms for online load balancing

We consider an online load balancing problem and its extensions in the framework of repeated games. On each round, the player chooses a distribution (task allocation) over $K$ servers, and then the environment reveals the load of each server, which determines the computation time of each server for processing the task assigned. After all rounds, the cost of the player is measured by some norm of the cumulative computation-time vector. The cost is the makespan if the norm is $L_\infty$-norm. The goal is to minimize the regret, i.e., minimizing the player's cost relative to the cost of the best fixed distribution in hindsight. We propose algorithms for general norms and prove their regret bounds. In particular, for $L_\infty$-norm, our regret bound matches the best known bound and the proposed algorithm runs in polynomial time per trial involving linear programming and second order programming, whereas no polynomial time algorithm was previously known to achieve the bound.Comment: 16 pages; typos correcte

Structure and Dynamics of the Instantaneous Water/Vapor Interface Revisited by Path-Integral and Ab-Initio Molecular Dynamics Simulations

The structure and dynamics of the water/vapor interface is revisited by means of path-integral and second-generation Car-Parrinello ab-initio molecular dynamics simulations in conjunction with an instantaneous surface definition [A. P. Willard and D. Chandler, J. Phys. Chem. B 114, 1954 (2010)]. In agreement with previous studies, we find that one of the OH bonds of the water molecules in the topmost layer is pointing out of the water into the vapor phase, while the orientation of the underlying layer is reversed. Therebetween, an additional water layer is detected, where the molecules are aligned parallel to the instantaneous water surface.Comment: 9 pages, 5 figure

A new chironomid (Insecta: Diptera) from Wealden amber (Lower Cretaceous) of the Isle of Wight (UK)

The first insect from the Wealden amber of the Isle of Wight (early Barremian) is formally described. Dungeyella gavini n. gen., n. sp. (Diptera: Chironomidae) is a tiny buchonomyiine/podonomian with specialised wing venation and probably lived in an araucarian riparian woodland with seasonal resin production. It is in one of the oldest-known ambers with insect inclusions

The VCG Mechanism for Bayesian Scheduling

We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, in which the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an approximation ratio of O(ln n&frac; ln ln n). This improves significantly on the previously best known bound of O(m/n) for prior-independent mechanisms, given by Chawla et al. [7] under the additional assumption of Monotone Hazard Rate (MHR) distributions. Although we demonstrate that this is tight in general, if we do maintain the MHR assumption, then we get improved, (small) constant bounds for m ≥ n ln n i.i.d. tasks. We also identify a sufficient condition on the distribution that yields a constant approximation ratio regardless of the number of tasks

RNA-Seq identifies genes whose proteins are upregulated during syncytia development in murine C2C12 myoblasts and human BeWo trophoblasts

The fusion of villous cytotrophoblasts into the multinucleated syncytiotrophoblast is critical for the essential functions of the mammalian placenta. Using RNA-Seq gene expression, quantitative protein expression, and siRNA knockdown we identified genes and their cognate proteins which are similarly upregulated in two cellular models of mammalian syncytia development (human BeWo cytotrophoblast to syncytiotrophoblast and murine C2C12 myoblast to myotube). These include DYSF, PDE4DIP, SPIRE2, NDRG1, PLEC, GPR146, HSPB8, DHCR7, and HDAC5. These findings provide avenues for further understanding of the mechanisms underlying mammalian placental syncytiotrophoblast development