One-way quantum computation with four-dimensional photonic qudits

We consider the possibility of performing linear optical quantum computation making use of extra photonic degrees of freedom. In particular we focus on the case where we use photons as quadbits. The basic 2-quadbit cluster state is a hyper-entangled state across polarization and two spatial mode degrees of freedom. We examine the non-deterministic methods whereby such states can be created from single photons and/or Bell pairs, and then give some mechanisms for performing higher-dimensional fusion gates.Comment: 10 figures (typos are corrected

Multiple testing correction in linear mixed models.

BackgroundMultiple hypothesis testing is a major issue in genome-wide association studies (GWAS), which often analyze millions of markers. The permutation test is considered to be the gold standard in multiple testing correction as it accurately takes into account the correlation structure of the genome. Recently, the linear mixed model (LMM) has become the standard practice in GWAS, addressing issues of population structure and insufficient power. However, none of the current multiple testing approaches are applicable to LMM.ResultsWe were able to estimate per-marker thresholds as accurately as the gold standard approach in real and simulated datasets, while reducing the time required from months to hours. We applied our approach to mouse, yeast, and human datasets to demonstrate the accuracy and efficiency of our approach.ConclusionsWe provide an efficient and accurate multiple testing correction approach for linear mixed models. We further provide an intuition about the relationships between per-marker threshold, genetic relatedness, and heritability, based on our observations in real data

SIRS dynamics on random networks: simulations and analytical models

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.Comment: 6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, Chin

Towards an Interaction-based Integration of MKM Services into End-User Applications

The Semantic Alliance (SAlly) Framework, first presented at MKM 2012, allows integration of Mathematical Knowledge Management services into typical applications and end-user workflows. From an architecture allowing invasion of spreadsheet programs, it grew into a middle-ware connecting spreadsheet, CAD, text and image processing environments with MKM services. The architecture presented in the original paper proved to be quite resilient as it is still used today with only minor changes. This paper explores extensibility challenges we have encountered in the process of developing new services and maintaining the plugins invading end-user applications. After an analysis of the underlying problems, I present an augmented version of the SAlly architecture that addresses these issues and opens new opportunities for document type agnostic MKM services.Comment: 14 pages, 7 figure

Revealing the Exciton Fine Structure in PbSe Nanocrystal Quantum Dots

We measure the photoluminescence (PL) lifetime, $\tau$, of excitons in colloidal PbSe nanocrystals (NCs) at low temperatures to 270~mK and in high magnetic fields to 15~T. For all NCs (1.3-2.3~nm radii), $\tau$ increases sharply below 10~K but saturates by 500~mK. In contrast to the usual picture of well-separated ``bright" and ``dark" exciton states (found, e.g., in CdSe NCs), these dynamics fit remarkably well to a system having two exciton states with comparable - but small - oscillator strengths that are separated by only 300-900 $\mu$eV. Importantly, magnetic fields reduce $\tau$ below 10~K, consistent with field-induced mixing between the two states. Magnetic circular dichroism studies reveal exciton g-factors from 2-5, and magneto-PL shows $>$10\% circularly polarized emission.Comment: To appear in Physical Review Letter