The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Risk aversion and HIV/AIDS: Evidence from Senegalese female sex workers

HIV/AIDS is the second cause of mortality globally and there are 5000 new infections each day. Globally, sex workers are 13 times more at risk of HIV than the general population and in Senegal they have an HIV prevalence 16.5 times greater. Therefore, it is urgent to encourage behaviour change, which requires a better understanding of the reasons why sex workers engage in risky behaviours. We provide new evidence of the role of risk preferences on sexual behaviours, health behaviours and health outcomes of 600 female sex workers in Senegal in July and August 2017. We measure risk aversion of sex workers using an incentivised Gneezy and Potters task in addition to specific risk-taking scales in four domains (in general, finance, health and sex). Understanding of the experimental task was high despite low literacy level of participants. Using ordinary least squares, we find that risk aversion is an important predictor of sex workers' sexual behaviours. We find that sex workers with higher level of risk aversion have less sex acts with clients, have less clients at risk of HIV, are more likely to engage in protected sex acts and as a result earn less money per sex act. Furthermore, we find that sex workers exhibiting higher level of risk aversion are less likely to be infected with sexually transmitted infections. Results highlight that some associations between risk preferences and sexual and health behaviours are domain specific. To conclude, our results confirm the role of risk preferences in the spread of HIV/AIDS epidemic and suggest the importance of collecting information on self-reported risk aversion to identify individuals who are at a greater risk of HIV/AIDS. Finally, our results provide some rationale in using lottery-based financial incentives to prevent sexually transmitted infections and HIV/AIDS among high-risk populations

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

Can Self-affirmation Encourage HIV-Prevention? Evidence from Female Sex Workers in Senegal

We test an intervention aiming to increase condom usage and HIV testing in a stigmatized population at high risk of contracting HIV: female sex workers (FSWs) in Senegal. Some sex work is legal in Senegal, and condoms and HIV tests are freely available to registered FSWs-but FSWs may be reluctant to get tested and use condoms, in part because doing so would entail acknowledging their risk of contracting HIV and potentially expose them to stigma. Drawing on self-affirmation theory, we hypothesized that reflecting on a source of personal pride would help participants acknowledge their risk of HIV, intend to use condoms more frequently, and take an HIV test. Prior research suggests that similar self-affirmation interventions can help people acknowledge their health risks and improve their health behavior, especially when paired with information about effectively managing their health (i.e., self-efficacy information). However, such interventions have primarily been tested in the United States and United Kingdom, and their generalizability outside of these contexts is unclear. Our high-powered experiment randomly assigned participants (N = 592 FSWs; N = 563 in the final analysis) to a self-affirmation condition or a control condition and measured their risk perceptions, whether they took condoms offered to them, and whether (after randomly receiving or not receiving self-efficacy information) they took an HIV test. We found no support for any of our hypotheses. We discuss several explanations for these null results based on the stigma attached to sex work and HIV, cross-cultural generalizability of self-affirmation interventions, and robustness of previous findings

On the calculation of finite-gap solutions of the KdV equation

A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the form of rational functions of the elliptic Weierstrass function. The calculation of initial elliptic finite-gap solutions is reduced to the solution of the finite-band equations with respect to the parameters of the representation. The time evolution of these solutions is described via the dynamic equations of their poles, integrated with the help of the finite-gap equations. The proposed approach is applied by calculating the elliptic 1-, 2- and 3-gap solutions of the KdV equations

Lam\'e polynomials, hyperelliptic reductions and Lam\'e band structure

The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion relation, and a previously published l=2 dispersion relation is shown to be partially incorrect. The Hermite-Krichever Ansatz, which expresses Lam\'e equation solutions in terms of l=1 solutions, is the chief tool. It is based on a projection from a genus-l hyperelliptic curve, which parametrizes solutions, to an elliptic curve. A general formula for this covering is derived, and is used to reduce certain hyperelliptic integrals to elliptic ones. Degeneracies between band edges, which can occur if the Lam\'e equation parameters take complex values, are investigated. If the Lam\'e equation is viewed as a differential equation on an elliptic curve, a formula is conjectured for the number of points in elliptic moduli space (elliptic curve parameter space) at which degeneracies occur. Tables of spectral polynomials and Lam\'e polynomials, i.e., band edge solutions, are given. A table in the older literature is corrected.Comment: 38 pages, 1 figure; final revision

Trading HIV for sheep: Risky sexual behavior and the response of female sex workers to Tabaski in Senegal

We use a cohort of female sex workers (FSWs) in Senegal to show how large anticipated economic shocks lead to increased risky sexual behavior. Exploiting the exogenous timing of interviews, we study the effect of Tabaski, the most important Islamic festival celebrated in Senegal, in which most households purchase an expensive animal for sacrifice. Condom use, measured robustly via the list experiment, falls by between 27.3 percentage points (pp) (65.5%) and 43.1 pp (22.7%) in the 9 days before Tabaski, or a maximum of 49.5 pp (76%) in the 7 day period preceding Tabaski. The evidence suggests the economic pressures from Tabaski are key to driving the behavior change observed through the price premium for condomless sex. Those most exposed to the economic pressure from Tabaski were unlikely to be using condoms at all in the week before the festival. Our findings show that Tabaski leads to increased risky behaviors for FSWs, a key population at high risk of HIV infection, for at least 1 week every year and has implications for FSWs in all countries celebrating Tabaski or similar festivals. Because of the scale, frequency, and size of the behavioral response to shocks of this type, policy should be carefully designed to protect vulnerable women against anticipated shocks

Elliptic Solitons and Groebner Bases

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gr\"obner bases method and others. New integrable potentials and corresponding solutions of the Sawada-Kotera, Kaup-Kupershmidt, Boussinesq equations and others are found.Comment: 18 pages, no figures, LaTeX'2

Exact solutions for a class of integrable Henon-Heiles-type systems

We study the exact solutions of a class of integrable Henon-Heiles-type systems (according to the analysis of Bountis et al. (1982)). These solutions are expressed in terms of two-dimensional Kleinian functions. Special periodic solutions are expressed in terms of the well-known Weierstrass function. We extend some of our results to a generalized Henon-Heiles-type system with n+1 degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy

Can Self-affirmation Encourage HIV-Prevention? Evidence from Female Sex Workers in Senegal.

We test an intervention aiming to increase condom usage and HIV testing in a stigmatized population at high risk of contracting HIV: female sex workers (FSWs) in Senegal. Some sex work is legal in Senegal, and condoms and HIV tests are freely available to registered FSWs-but FSWs may be reluctant to get tested and use condoms, in part because doing so would entail acknowledging their risk of contracting HIV and potentially expose them to stigma. Drawing on self-affirmation theory, we hypothesized that reflecting on a source of personal pride would help participants acknowledge their risk of HIV, intend to use condoms more frequently, and take an HIV test. Prior research suggests that similar self-affirmation interventions can help people acknowledge their health risks and improve their health behavior, especially when paired with information about effectively managing their health (i.e., self-efficacy information). However, such interventions have primarily been tested in the United States and United Kingdom, and their generalizability outside of these contexts is unclear. Our high-powered experiment randomly assigned participants (N = 592 FSWs; N = 563 in the final analysis) to a self-affirmation condition or a control condition and measured their risk perceptions, whether they took condoms offered to them, and whether (after randomly receiving or not receiving self-efficacy information) they took an HIV test. We found no support for any of our hypotheses. We discuss several explanations for these null results based on the stigma attached to sex work and HIV, cross-cultural generalizability of self-affirmation interventions, and robustness of previous findings. [Abstract copyright: © 2023. The Author(s).