On multivariate quantiles under partial orders

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order perspective. We also study several statistical aspects of partial quantiles. We provide estimators, associated rates of convergence, and asymptotic distributions that hold uniformly over a continuum of quantile indices. Furthermore, we provide procedures that can restore monotonicity properties that might have been disturbed by estimation error, establish computational complexity bounds, and point out a concentration of measure phenomenon (the latter under independence and the componentwise natural order). Finally, we illustrate the concepts by discussing several theoretical examples and simulations. Empirical applications to compare intake nutrients within diets, to evaluate the performance of investment funds, and to study the impact of policies on tobacco awareness are also presented to illustrate the concepts and their use.Comment: Published in at http://dx.doi.org/10.1214/10-AOS863 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Weak momentum scattering and the conductivity of graphene

Electrical transport in graphene offers a fascinating parallel to spin transport in semiconductors including the spin-Hall effect. In the weak momentum scattering regime the steady-state density matrix contains two contributions, one linear in the carrier number density $n$ and characteristic scattering time $\tau$, the other independent of either. In this paper we take the Liouville equation as our starting point and demonstrate that these two contributions can be identified with pseudospin conservation and non-conservation respectively, and are connected in a non-trivial manner by scattering processes. The scattering term has a distinct form, which is peculiar to graphene and has important consequences in transport. The contribution linear in $\tau$ is analogous to the part of the spin density matrix which yields a steady state spin density, while the contribution independent of $\tau$, is analogous to the part of the spin density matrix which yields a steady state spin current. Unlike in systems with spin-orbit interactions, the $n$ and $\tau$-independent part of the conductivity is reinforced in the weak momentum scattering regime by scattering between the conserved and non-conserved pseudospin distributions.Comment: 10 pages. Accepted for publication in Phys. Rev.

Statistical characterization of phenolic-novolak structures

Three statistical methods of general validity are valuable for characterizing any polymer which results from chain polymerization of multifunctional branching monomers linked through bifunctional monomers

Moving to Diversity

In this brief, authors Richelle Winkler and Kenneth Johnson, using new data and techniques, find that net migration between U.S. counties increased racial diversity in each of the last two decades. However, migration’s influence on diversity was far from uniform: it varied by race, age group, and location, sometimes starkly. Overall, net migration of the population under age 40 increased diversity, while net migration of people over age 60 diminished diversity. Blacks and Hispanics are migrating to predominantly white counties, while white young adults are moving to urban core counties with relatively high proportions of blacks and Hispanics. The movement of older whites is not contributing to the growing diversity, because older whites tend to move to predominantly white counties. Winkler and Johnson conclude that, while migration contributed to the growing diversity of the nation, the process was complex and varied from place to place with significant social, economic, and political implications for both the more diverse and less diverse places

External gates and transport in biased bilayer graphene

We formulate a theory of transport in graphene bilayers in the weak momentum scattering regime in such a way as to take into account contributions to the electrical conductivity to leading and next-to-leading order in the scattering potential. The response of bilayers to an electric field cannot be regarded as a sum of terms due to individual layers. Rather, interlayer tunneling and coherence between positive- and negative-energy states give the main contributions to the conductivity. At low energies, the dominant effect of scattering on transport comes from scattering within each energy band, yet a simple picture encapsulating the role of collisions in a set of scattering times is not applicable. Coherence between positive- and negative-energy states gives, as in monolayers, a term in the conductivity which depends on the order of limits. The application of an external gate, which introduces a gap between positive- and negative-energy states, does not affect transport. Nevertheless the solution to the kinetic equation in the presence of such a gate is very revealing for transport in both bilayers and monolayers.Comment: 6 pages, accepted for publication in Physical Review

Sound predictability as a higher-order cue in auditory scene analysis

A major challenge for the auditory system is to disentangle signals emitted by two or more sound sources that are active in a temporally interleaved manner (sequential stream segregation). Besides distinct characteristics of the individual signals (e.g., their timbre, location, and pitch), one important cue for distinguishing the sound sources is how their emitted signals unfold over time. It seems intuitively plausible that signals that unfold predictably with respect to their acoustic features and time-points of occurrence, such as the repetitive signature of a train moving on the rails, can be more readily identified as originating from one sound source. Based on this rationale, predictive elements have successfully been incorporated into computational models of auditory scene analysis for many years

Reentrant nu = 1 quantum Hall state in a two-dimensional hole system

We report the observation of a reentrant quantum Hall state at the Landau level filling factor nu = 1 in a two-dimensional hole system confined to a 35-nm-wide (001) GaAs quantum well. The reentrant behavior is characterized by a weakening and eventual collapse of the nu = 1 quantum Hall state in the presence of a parallel magnetic field component B||, followed by a strengthening and reemergence as B|| is further increased. The robustness of the nu = 1 quantum Hall state during the transition depends strongly on the charge distribution symmetry of the quantum well, while the magnitude of B|| needed to invoke the transition increases with the total density of the system

Proton-Coupled Electron Flow in Protein Redox Machines

Electron transfer (ET) reactions are fundamental steps in biological redox processes. Respiration is a case in point: at least 15 ET reactions are required to take reducing equivalents from NADH, deposit them in O_2, and generate the electrochemical proton gradient that drives ATP synthesis. Most of these reactions involve quantum tunneling between weakly coupled redox cofactors (ET distances > 10 Å) embedded in the interiors of folded proteins. Here we review experimental findings that have shed light on the factors controlling these distant ET events. We also review work on a sensitizer-modified copper protein photosystem in which multistep electron tunneling (hopping) through an intervening tryptophan is orders of magnitude faster than the corresponding single-step ET reaction.If proton transfers are coupled to ET events, we refer to the processes as proton coupled ET, or PCET, a term introduced by Huynh and Meyer in 1981. Here we focus on two protein redox machines, photosystem II and ribonucleotide reductase, where PCET processes involving tyrosines are believed to be critical for function. Relevant tyrosine model systems also will be discussed