Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation

We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times of those hierarchies. The discrete Toda lattice variable shifts parameters of hypergeometric functions. The role of additional symmetries in generating hypergeometric tau-functions is explained

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(\lambda=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.Comment: 22 pages. 9 figure

Algebraic analysis of a model of two-dimensional gravity

An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian $H_{c}$ are obtained and explicitly written in closed form.Comment: 21 pages, to appear in General Relativity and Gravitatio

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories

Understanding preventive behaviors among mid-Western African-American men: a pilot qualitative study of prostate screening

http://dx.doi.org/10.1016/j.jomh.2011.03.00

A Bayesian Analysis of the Correlations Among Sunspot Cycles

Sunspot numbers form a comprehensive, long-duration proxy of solar activity and have been used numerous times to empirically investigate the properties of the solar cycle. A number of correlations have been discovered over the 24 cycles for which observational records are available. Here we carry out a sophisticated statistical analysis of the sunspot record that reaffirms these correlations, and sets up an empirical predictive framework for future cycles. An advantage of our approach is that it allows for rigorous assessment of both the statistical significance of various cycle features and the uncertainty associated with predictions. We summarize the data into three sequential relations that estimate the amplitude, duration, and time of rise to maximum for any cycle, given the values from the previous cycle. We find that there is no indication of a persistence in predictive power beyond one cycle, and conclude that the dynamo does not retain memory beyond one cycle. Based on sunspot records up to October 2011, we obtain, for Cycle 24, an estimated maximum smoothed monthly sunspot number of 97 +- 15, to occur in January--February 2014 +- 6 months.Comment: Accepted for publication in Solar Physic

National identity predicts public health support during a global pandemic

Changing collective behaviour and supporting non-pharmaceutical interventions is an important component in mitigating virus transmission during a pandemic. In a large international collaboration (Study 1, N = 49,968 across 67 countries), we investigated self-reported factors associated with public health behaviours (e.g., spatial distancing and stricter hygiene) and endorsed public policy interventions (e.g., closing bars and restaurants) during the early stage of the COVID-19 pandemic (April-May 2020). Respondents who reported identifying more strongly with their nation consistently reported greater engagement in public health behaviours and support for public health policies. Results were similar for representative and non-representative national samples. Study 2 (N = 42 countries) conceptually replicated the central finding using aggregate indices of national identity (obtained using the World Values Survey) and a measure of actual behaviour change during the pandemic (obtained from Google mobility reports). Higher levels of national identification prior to the pandemic predicted lower mobility during the early stage of the pandemic (r = −0.40). We discuss the potential implications of links between national identity, leadership, and public health for managing COVID-19 and future pandemics.publishedVersio

Some Aspects of Latent Structure Analysis

Latent structure models involve real, potentially observable variables and latent, unobservable variables. The framework includes various particular types of model, such as factor analysis, latent class analysis, latent trait analysis, latent profile models, mixtures of factor analysers, state-space models and others. The simplest scenario, of a single discrete latent variable, includes finite mixture models, hidden Markov chain models and hidden Markov random field models. The paper gives a brief tutorial of the application of maximum likelihood and Bayesian approaches to the estimation of parameters within these models, emphasising especially the fact that computational complexity varies greatly among the different scenarios. In the case of a single discrete latent variable, the issue of assessing its cardinality is discussed. Techniques such as the EM algorithm, Markov chain Monte Carlo methods and variational approximations are mentioned