Optimal pricing using online auction experiments: A P\'olya tree approach

We show how a retailer can estimate the optimal price of a new product using observed transaction prices from online second-price auction experiments. For this purpose we propose a Bayesian P\'olya tree approach which, given the limited nature of the data, requires a specially tailored implementation. Avoiding the need for a priori parametric assumptions, the P\'olya tree approach allows for flexible inference of the valuation distribution, leading to more robust estimation of optimal price than competing parametric approaches. In collaboration with an online jewelry retailer, we illustrate how our methodology can be combined with managerial prior knowledge to estimate the profit maximizing price of a new jewelry product.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS503 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Approaching the Ultimate Limits of Photon-Efficient and Bandwidth-Efficient Optical Communication

It is well known that ideal free-space optical communication at the quantum limit can have unbounded photon information efficiency (PIE), measured in bits per photon. High PIE comes at a price of low dimensional information efficiency (DIE), measured in bits per spatio-temporal-polarization mode. If only temporal modes are used, then DIE translates directly to bandwidth efficiency. In this paper, the DIE vs. PIE tradeoffs for known modulations and receiver structures are compared to the ultimate quantum limit, and analytic approximations are found in the limit of high PIE. This analysis shows that known structures fall short of the maximum attainable DIE by a factor that increases linearly with PIE for high PIE. The capacity of the Dolinar receiver is derived for binary coherent-state modulations and computed for the case of on-off keying (OOK). The DIE vs. PIE tradeoff for this case is improved only slightly compared to OOK with photon counting. An adaptive rule is derived for an additive local oscillator that maximizes the mutual information between a receiver and a transmitter that selects from a set of coherent states. For binary phase-shift keying (BPSK), this is shown to be equivalent to the operation of the Dolinar receiver. The Dolinar receiver is extended to make adaptive measurements on a coded sequence of coherent state symbols. Information from previous measurements is used to adjust the a priori probabilities of the next symbols. The adaptive Dolinar receiver does not improve the DIE vs. PIE tradeoff compared to independent transmission and Dolinar reception of each symbol.Comment: 10 pages, 8 figures; corrected a typo in equation 3

Managing Relationship Decay

The final publication is available at Springer via http://dx.doi.org/10.1007/s12110-015-9242-7Relationships are central to human life strategies and have crucial fitness consequences. Yet, at the same time, they incur significant maintenance costs that are rarely considered in either social psychological or evolutionary studies. Although many social psychological studies have explored their dynamics, these studies have typically focused on a small number of emotionally intense ties, whereas social networks in fact consist of a large number of ties that serve a variety of different functions. In this study, we examined how entire active personal networks changed over 18 months across a major life transition. Family relationships and friendships differed strikingly in this respect. The decline in friendship quality was mitigated by increased effort invested in the relationship, but with a striking gender difference: relationship decline was prevented most by increased contact frequency (talking together) for females but by doing more activities together in the case of males

Spin nutation and polarization in ballistic semiconductor nanostructures

The definitions of spin orientation and polarization vectors are introduced within the particle density matrix of scattering states in leads. It is shown that spin-density vector can be defined by the product of the spin orientation vector, being a unit direction vector, and the charge density, corresponding to the amplitude of the spin-density vector, experimentally observable by a spatial charge modulation measurement. When an electron transports through a ballistic semiconductor nanostructure, due to quantum interference of two spin eigenmodes, the electron spin generally undergoes nutation on its precession around the effective magnetic field resulting from spin-orbit interactions. The nutation of electron spin is found to be crucial for spin polarization in the quantum transport. When one of two spin-dependent channels in leads is evanescent, electron spin is shown to be fully polarized for distance from the interface larger than the spin precession length

Gravitational self-torque and spin precession in compact binaries

We calculate the effect of self-interaction on the "geodetic" spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle $\psi$ per radian of orbital revolution for a particle carrying mass $\mu$ and spin $s \ll (G/c) \mu^2$ in a circular orbit around a Schwarzschild black hole of mass $M \gg \mu$. We compute $\psi$ through $O(\mu/M)$ in perturbation theory, i.e, including the correction $\delta\psi$ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for $\delta\psi$, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semi-analytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches.Comment: 5 pages, 1 table, 1 figure. Minor changes to match published versio

Chytrid fungus infection in alpine tree frogs is associated with individual heterozygosity and population isolation but not population-genetic diversity

Chytridiomycosis, a disease caused by the emerging fungus Batrachochytrium dendrobatidis (Bd), has been implicated in the decline of over 500 amphibian species. Population declines could have important genetic consequences, including reduced genetic diversity. We contrasted genetic diversity among both long-Bd-exposed and unexposed populations of the south-east Australian alpine tree frog (Litoria verreauxii alpina) across its range. At the population level, we found no significant differences in genetic diversity between Bd-exposed and unexposed populations. Encouragingly, even Bd-infected remnant populations that are now highly isolated maintain genetic diversity comparable to populations in which Bd is absent. Spatial genetic structure among populations followed an isolation-by-distance pattern, suggesting restricted movement among remnant populations. At the individual level, greater heterozygosity was associated with reduced probability of infection. Loss of genetic diversity in remnant populations that survived chytridiomycosis epidemics does not appear to be a threat to L. v. alpina. We suggest several factors underpinning maintenance of genetic diversity: (1) remnant populations have remained large enough to avoid losses of genetic diversity; (2) many individuals in the population are able to breed once before succumbing to disease; and (3) juveniles in the terrestrial environment have low exposure to Bd, providing an annual ‘reservoir’ of genetic diversity. The association between individual heterozygosity and infection status suggests that, while other work has shown all breeding adults are typically killed by Bd, males with greater heterozygosity may survive longer and obtain fitness benefits through extended breeding opportunities. Our results highlight the critical role of life history in mitigating the impacts of Bd infection for some amphibian species, but we infer that increased isolation as a result of disease-induced population extirpations will enhance population differentiation and thus biogeographic structure