The collisional frequency shift of a trapped-ion optical clock

Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a non-perturbative framework based on a quantum channel description of the scattering process, and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the Sr$^+$ optical atomic clock transition due to elastic collisions with helium

State Dependence and Alternative Explanations for Consumer Inertia

For many consumer packaged goods products, researchers have documented a form of state dependence whereby consumers become "loyal" to products they have consumed in the past. That is, consumers behave as though there is a utility premium from continuing to purchase the same product as they have purchased in the past or, equivalently, there is a psychological cost to switching products. However, it has not been established that this form of state dependence can be identified in the presence of consumer heterogeneity of an unknown form. Most importantly, before this inertia can be given a structural interpretation and used in policy experiments such as counterfactual pricing exercises,alternative explanations which might give rise to similar consumer behavior must be ruled out. We develop a flexible model of heterogeneity which can be given a semi-parametric interpretation and rule out alternative explanations for positive state dependence such as autocorrelated choice errors, consumer search, or consumer learning.

Exact solution of bond percolation on small arbitrary graphs

We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.Comment: 5 pages and 3 figure

Adaptive networks: coevolution of disease and topology

Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low-complexity analytic formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive SIS model of Gross et al. [Phys. Rev. Lett. 96, 208701 (2006)], we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.Comment: 11 pages, 8 figures, 1 appendix. To be published in Physical Review

Different models and single-nucleotide polymorphisms signal the simulated weak gene-gene interaction for a quantitative trait using haplotype-based and mixed models testing

Knowledge of simulated genetic effects facilitates interpretation of methodological studies. Genetic interactions for common disorders are likely numerous and weak. Using the 200 replicates of the Genetic Analysis Workshop 16 (GAW16) Problem 3 simulated data, we compared the statistical power to detect weak gene-gene interactions using a haplotype-based test in the UNPHASED software with genotypic mixed model (GMM) and additive mixed model (AMM) mixed linear regression model in SAS. We assumed a candidate-gene approach where a single-nucleotide polymorphism (SNP) in one gene is fixed and multiple SNPs are at the second gene. We analyzed the quantitative low-density lipoprotein trait (heritability 0.7%), modulated by simulated interaction of rs4648068 from 4q24 and another gene on 8p22, where we analyzed seven SNPs. We generally observed low power calculated per SNP (≤ 37% at the 0.05 level), with the haplotype-based test being inferior. Over all tests, the haplotype-based test performed within chance, while GMM and AMM had low power (~10%). The haplotype-based and mixed models detected signals at different SNPs. The haplotype-based test detected a signal in 50 unique replicates; GMM and AMM featured both shared and distinct SNPs and replicates (65 replicates shared, 41 GMM, 27 AMM). Overall, the statistical signal for the weak gene-gene interaction appears sensitive to the sample structure of the replicates. We conclude that using more than one statistical approach may increase power to detect such signals in studies with limited number of loci such as replications. There were no results significant at the conservative 10-7 genome-wide level

Effet du sérum urémique humain sur le cytochrome P450 hépatique

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Modeling the dynamical interaction between epidemics on overlay networks

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. Exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytic approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g. the spread of preventive information in the context of an emerging infectious disease).Comment: Accepted for publication in Phys. Rev. E. 15 pages, 7 figure