85 research outputs found
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 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 , with 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
. 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 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 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
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
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
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, Nâ=â49,968 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 (Nâ=â42 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 (râ=ââ0.40). 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
Cross-cultural inequivalence of dermatology-specific health-related quality of life instruments in psoriasis patients.
Contains fulltext :
52521.pdf (publisher's version ) (Closed access)The dermatology life questionnaire index (DLQI) and the Skindex are the most commonly used dermatology-specific health-related quality of life (HRQOL) instruments. Although these tools are used in international surveys and clinical trials, the cross-cultural equivalence of their items has not been documented. We used differential item functioning (DIF), which is part of the Rasch model, to assess the impact of cultural background on the items of the DLQI and Skindex-29 and-17. The data of the 450 psoriasis patients, who attended in- and outpatient dermatology centers, was collected retrospectively from five European and one US center. The DLQI and Skindex-29 scales did not fit the Rasch model (P<0.0008) and 10/10 of the DLQI and 19/29 of the Skindex-29 items displayed significant DIF. Although the psychosocial scale of the Skindex-17 fitted the Rasch model, half or more of the items of the psychosocial (6/12) and the symptom scale (4/5) showed significant DIF across countries. These findings suggest that psoriasis patients from different countries respond differently to a substantial proportion of DLQI and Skindex items despite having the same level of underlying HRQOL impairment. Therefore, these instruments should not be used in their current form in international studies
Characterization of the probabilistic traveling salesman problem
We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E((L) over bar (pruned))=rootnp(0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np-->infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L-a priori)=rootn/pbeta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05less than or equal topless than or equal to0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required
- âŠ