Connection problem for the sine-Gordon/Painlev\'e III tau function and irregular conformal blocks

The short-distance expansion of the tau function of the radial sine-Gordon/Painlev\'e III equation is given by a convergent series which involves irregular $c=1$ conformal blocks and possesses certain periodicity properties with respect to monodromy data. The long-distance irregular expansion exhibits a similar periodicity with respect to a different pair of coordinates on the monodromy manifold. This observation is used to conjecture an exact expression for the connection constant providing relative normalization of the two series. Up to an elementary prefactor, it is given by the generating function of the canonical transformation between the two sets of coordinates.Comment: 18 pages, 1 figur

Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent

Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. The precise description of the exponentially small jump in the dominant solution approaching $\alpha/x$ as $|x|\to\infty$ is given. For the asymptotic power expansion of the dominant solution, the coefficient asymptotics is found.Comment: 19 pages, LaTe

Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlev\'{e} Equation. I

The degenerate third Painlev\'{e} equation, $u^{\prime \prime} = \frac{(u^{\prime})^{2}}{u} - \frac{u^{\prime}}{\tau} + \frac{1}{\tau}(-8 \epsilon u^{2} + 2ab) + \frac{b^{2}}{u}$, where $\epsilon,b \in \mathbb{R}$, and $a \in \mathbb{C}$, and the associated tau-function are studied via the Isomonodromy Deformation Method. Connection formulae for asymptotics of the general as $\tau \to \pm 0$ and $\pm i0$ solution and general regular as $\tau \to \pm \infty$ and $\pm i \infty$ solution are obtained.Comment: 40 pages, LaTeX2

On Airy Solutions of the Second Painleve Equation

In this paper, we discuss Airy solutions of the second Painleve equation and two related equations, the Painleve XXXIV equation and the Jimbo-Miwa-Okamoto sigma form of second Painleve equation, are discussed. It is shown that solutions which depend only on the Airy function Ai(z) have a completely difference structure to those which involve a linear combination of the Airy functions Ai(z) and Bi(z). For all three equations, the special solutions that depend only on inline image are tronquée solutions, i.e., they have no poles in a sector of the complex plane. Further, for both inline image and SII, it is shown that among these tronquée solutions there is a family of solutions that have no poles on the real axis

Stability of the periodic Toda lattice under short range perturbations

We consider the stability of the periodic Toda lattice (and slightly more generally of the algebro-geometric finite-gap lattice) under a short range perturbation. We prove that the perturbed lattice asymptotically approaches a modulated lattice. More precisely, let $g$ be the genus of the hyperelliptic curve associated with the unperturbed solution. We show that, apart from the phenomenon of the solitons travelling on the quasi-periodic background, the $n/t$-pane contains $g+2$ areas where the perturbed solution is close to a finite-gap solution in the same isospectral torus. In between there are $g+1$ regions where the perturbed solution is asymptotically close to a modulated lattice which undergoes a continuous phase transition (in the Jacobian variety) and which interpolates between these isospectral solutions. In the special case of the free lattice ($g=0$) the isospectral torus consists of just one point and we recover the known result. Both the solutions in the isospectral torus and the phase transition are explicitly characterized in terms of Abelian integrals on the underlying hyperelliptic curve. Our method relies on the equivalence of the inverse spectral problem to a matrix Riemann--Hilbert problem defined on the hyperelliptic curve and generalizes the so-called nonlinear stationary phase/steepest descent method for Riemann--Hilbert problem deformations to Riemann surfaces.Comment: 38 pages, 1 figure. This version combines both the original version and arXiv:0805.384

On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation

Using a simple operator-norm estimate we show that the solution to the second Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well defined region of the complex plane of the independent variable. The result is illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit

Temporal-spatial analysis of severe acute respiratory syndrome among hospital inpatients

Background. We report the temporal-spatial spread of severe acute respiratory syndrome (SARS) among inpatients in a hospital ward during a major nosocomial outbreak and discuss possible mechanisms for the outbreak. Methods. All inpatients who had stayed in the same ward as the initial index case patient for any duration before isolation were recruited into a cohort and followed up to document the occurrence of SARS. The normalized concentration of virus-laden aerosols at different locations of the ward was estimated by use of computational fluid dynamics modeling. The attack rates in the various subgroups stratified by bed location were calculated. Multivariate Cox proportional hazards regression was used to document important risk factors. Results. The overall attack rate of SARS was 41% (30 of 74 subjects). It was 65%, 52%, and 18% in the same bay, adjacent bay, and distant bays, respectively (P = .001). Computation fluid dynamics modeling indicated that the normalized concentration of virus-laden aerosols was highest in the same bay and lowest in the distant bays. Cox regression indicated that staying in the ward on 6 or 10 March entailed higher risk, as well as staying in the same or adjacent bays. The epidemic curve showed 2 peaks, and stratified analyses by bed location suggested >1 generation of spread. Conclusions. The temporal-spatial spread of SARS in the ward was consistent with airborne transmission, as modeled by use of computational fluid dynamics. Infected health care workers likely acted as secondary sources in the latter phase of the outbreak. © 2005 by the Infectious Diseases Society of America. All rights reserved.published_or_final_versio

Carbon monoxide and stroke: A time series study of ambient air pollution and emergency hospitalizations

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Who is more vulnerable to death from extremely cold temperatures? A case-only approach in Hong Kong with a temperate climate

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Air pollution and mortality: Effect modification by personal characteristics and specific cause of death in a case-only study

Short-term effects of air pollution on mortality have been well documented in the literature worldwide. Less is known about which subpopulations are more vulnerable to air pollution. We conducted a case-only study in Hong Kong to examine the potential effect modification by personal characteristics and specific causes of death. Individual information of 402,184 deaths of non-external causes and daily mean concentrations of air pollution were collected from 2001 to 2011. For a 10 μg/m3 increase of pollution concentration, people aged ≥∇65 years (compared with younger ages) had a 0.9–1.8% additional increase in mortality related to PM, NO2, and SO2. People dying from cardiorespiratory diseases (compared with other non-external causes) had a 1.6–2.3% additional increase in PM and NO2 related mortality. Other subgroups that were particularly susceptible were females and those economically inactive. Lower socioeconomic status and causes of cardiorespiratory diseases would increase the likelihood of death associated with air pollution.postprin