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

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

Locally Optimal Load Balancing

This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of adjacent nodes differ by at most $1$. If the graph is a path ($\Delta = 2$), it is easy to solve the fractional version of the problem in $O(L)$ communication rounds, independently of the number of nodes. We show that this is tight, and we show that it is possible to solve also the discrete version of the problem in $O(L)$ rounds in paths. For the general case ($\Delta > 2$), we show that fractional load balancing can be solved in $\operatorname{poly}(L,\Delta)$ rounds and discrete load balancing in $f(L,\Delta)$ rounds for some function $f$, independently of the number of nodes.Comment: 19 pages, 11 figure

First record of a non-pollinating fig wasp (Hymenoptera: Sycophaginae) from Dominican amber, with estimation of the size of its host figs

Fig trees and their pollinating fig wasps arose about 75 million years ago in the Cretaceous period. Several other groups of chalcid wasps also utilize figs for larval development, including sycophagines, the putative sister group to pollinating fig wasps. Whereas stone and amber fossil pollinators are known, no fossils representing non-pollinating fig wasp groups have been confirmed previously. Here, we describe the first Sycophaginae from the c.15–20 Ma Dominican amber, Idarnes thanatos sp. nov. Farache, Rasplus, Pereira and Compton, and discuss its relationships within the Idarnes carme species group. Additionally, we use linear regression to compare body size, ovipositor sheaths length, and host fig size data from extant Idarnes species to estimate the size of its host figs. Idarnes thanatos was most likely associated with small to medium sized figs (diameter ≤1.0 cm), that were likely to have been dispersed by birds and primates. The discovery of this close relative of extant non-pollinating fig wasps suggests that early Miocene and modern fig wasp communities may share similar ecological and functional features

Statistical mechanics of budget-constrained auctions

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.Comment: Minor revisio

Singlet Oxygen Chemistry in Water: A Porous Vycor GlassSupported Photosensitizer

Singlet molecular oxygen [1O2 (1Δg)] is generated cleanly in aqueous solution upon irradiation of a heterogeneous complex, meso-tetra(N-methyl-4-pyridyl)porphine (1) adsorbed onto porous Vycor glass (PVG). The cationic photosensitizer 1 tightly binds onto PVG and gives a stable material, which does not dissociate 1 into the surrounding aqueous phase. The production of 1O2 was measured by monitoring the time-resolved 1O2 (1Δg) phosphorescence at 1270 nm. Indirect analysis of 1O2 generation was also carried out with the photooxidation oftrans-2-methyl-2-pentenoate anion, which afforded the corresponding hydroperoxide. Sensitizer-1-impregnated PVG gives rise to a new singlet oxygen generator but more importantly provides a heterogeneous system for use in water

Biomassa e atividade microbiana do solo sob pastagem em sistemas de monocultura e silvipastoril.

A biomassa microbiana é um importante componente do solo que contribui para manutenção do ecossistema de pastagens, principalmente em solos tropicais. Neste sentido, o objetivo do trabalho foi avaliar a biomassa e atividade microbiana do solo sob pastagem em sistemas de monocultura de pasto de Brachiaria brizantha cv. Marandu, e em sistema silvipastoril formado por pasto e coqueiros (Cocos nucifera)