A random hierarchical lattice: the series-parallel graph and its properties

We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability $p$ and $1-p$ respectively. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at $p=1/2$

Dynamic Poisson Factorization

Models for recommender systems use latent factors to explain the preferences and behaviors of users with respect to a set of items (e.g., movies, books, academic papers). Typically, the latent factors are assumed to be static and, given these factors, the observed preferences and behaviors of users are assumed to be generated without order. These assumptions limit the explorative and predictive capabilities of such models, since users' interests and item popularity may evolve over time. To address this, we propose dPF, a dynamic matrix factorization model based on the recent Poisson factorization model for recommendations. dPF models the time evolving latent factors with a Kalman filter and the actions with Poisson distributions. We derive a scalable variational inference algorithm to infer the latent factors. Finally, we demonstrate dPF on 10 years of user click data from arXiv.org, one of the largest repository of scientific papers and a formidable source of information about the behavior of scientists. Empirically we show performance improvement over both static and, more recently proposed, dynamic recommendation models. We also provide a thorough exploration of the inferred posteriors over the latent variables.Comment: RecSys 201

Measurement of Birefringence of Low-Loss, High-Reflectance Coating of M-Axis Sapphire

The birefringence of a low-loss, high-reflectance coating applied to an 8-cm-diameter sapphire crystal grown in the m-axis direction has been mapped. By monitoring the transmission of a high-finesse Fabry-Perot cavity as a function of the polarization of the input light, we find an upper limit for the magnitude of the birefringence of 2.5 x 10^-4 rad and an upper limit in the variation in direction of the birefringence of 10 deg. These values are sufficiently small to allow consideration of m-axis sapphire as a substrate material for the optics of the advanced detector at the Laser Interferometer Gravitational Wave Observatory

Cross-sectional associations between variations in ankle shape by statistical shape modeling, injury history, and race : the Johnston County Osteoarthritis Project

Rheumatology Research Foundation Medical Student Preceptorship Award (Lateef/Nelson), NIAMS K23 AR061406 (Nelson); NIH/NIAMS P60AR064166 and U01DP003206 (Jordan/Renner), NIH/NIAMS R01AR067743 (Golightly). The funders had no role in study design; collection, analysis, or interpretation of data; writing the manuscript or the decision to submit for publication.Peer reviewedPublisher PD

Positive-measure self-similar sets without interior

We recall the problem posed by Peres and Solomyak in Problems on self-similar and self-affine sets; an update. Progr. Prob. 46 (2000), 95–106: can one find examples of self-similar sets with positive Lebesgue measure, but with no interior? The method in Properties of measures supported on fat Sierpinski carpets, this issue, leads to families of examples of such sets

Parity meter for charge qubits: an efficient quantum entangler

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.Comment: 8 pages, 4 figures; v2: discussion of measurement time, references adde

Quantum Discord and Quantum Computing - An Appraisal

We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of nonclassical advantages in computation. Completeness results from computational complexity theory lead to the identification of very disparate problems, and offer a kaleidoscopic view into the realm of quantum enhancements in computation. Emphasis is placed on the `power of one qubit' model, and the boundary between quantum and classical correlations as delineated by quantum discord. A recent result by Eastin on the role of this boundary in the efficient classical simulation of quantum computation is discussed. Perceived drawbacks in the interpretation of quantum discord as a relevant certificate of quantum enhancements are addressed.Comment: To be published in the Special Issue of the International Journal of Quantum Information on "Quantum Correlations: entanglement and beyond." 11 pages, 4 figure

Slope Instability of the Earthen Levee in Boston, UK: Numerical Simulation and Sensor Data Analysis

The paper presents a slope stability analysis for a heterogeneous earthen levee in Boston, UK, which is prone to occasional slope failures under tidal loads. Dynamic behavior of the levee under tidal fluctuations was simulated using a finite element model of variably saturated linear elastic perfectly plastic soil. Hydraulic conductivities of the soil strata have been calibrated according to piezometers readings, in order to obtain correct range of hydraulic loads in tidal mode. Finite element simulation was complemented with series of limit equilibrium analyses. Stability analyses have shown that slope failure occurs with the development of a circular slip surface located in the soft clay layer. Both models (FEM and LEM) confirm that the least stable hydraulic condition is the combination of the minimum river levels at low tide with the maximal saturation of soil layers. FEM results indicate that in winter time the levee is almost at its limit state, at the margin of safety (strength reduction factor values are 1.03 and 1.04 for the low-tide and high-tide phases, respectively); these results agree with real-life observations. The stability analyses have been implemented as real-time components integrated into the UrbanFlood early warning system for flood protection

Interplay between field-induced and frustration-induced quantum criticalities in the frustrated two-leg Heisenberg ladder

The antiferromagnetic Heisenberg two-leg ladder in the presence of frustration and an external magnetic field is a system that is characterized by two sorts of quantum criticalities, not only one. One criticality is the consequence of intrinsic frustration, and the other one is a result of the external magnetic field. So the behaviour of each of them in the presence of the other deserves to be studied. Using the Jordan-Wigner transformation in dimensions higher than one and bond-mean-field theory we examine the interplay between the field-induced and frustration-induced quantum criticalities in this system. The present work could constitute a prototype for those systems showing multiple, perhaps sometimes competing, quantum criticalities. We calculate several physical quantities like the magnetization and spin susceptibility as functions of field and temperature.Comment: 9 pages, 8 figures, submitted to the Canadian Journal of Physic

Entanglement Energetics in the Ground State

We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. A precise relation between entanglement and energy fluctuations is demonstrated in the weak coupling limit. Examples are given with the two-state system and the harmonic oscillator, and energy probability distributions are calculated. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.Comment: 7 pages, 3 figures, Conference proceeding for the Physics of Quantum Electronics; Utah, USA, January 200