Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures

Preasymptotic Convergence of Randomized Kaczmarz Method

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the inverse solution is smooth (e.g., sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.Comment: 20 page

The impact of an intervention to introduce malaria rapid diagnostic tests on fever case management in a high transmission setting in Uganda: A mixed-methods cluster-randomized trial (PRIME).

Rapid diagnostic tests for malaria (mRDTs) have been scaled-up widely across Africa. The PRIME study evaluated an intervention aiming to improve fever case management using mRDTs at public health centers in Uganda. A cluster-randomized trial was conducted from 2010-13 in Tororo, a high malaria transmission setting. Twenty public health centers were randomized in a 1:1 ratio to intervention or control. The intervention included training in health center management, fever case management with mRDTs, and patient-centered services; plus provision of mRDTs and artemether-lumefantrine (AL) when stocks ran low. Three rounds of Interviews were conducted with caregivers of children under five years of age as they exited health centers (N = 1400); reference mRDTs were done in children with fever (N = 1336). Health worker perspectives on mRDTs were elicited through semi-structured questionnaires (N = 49) and in-depth interviews (N = 10). The primary outcome was inappropriate treatment of malaria, defined as the proportion of febrile children who were not treated according to guidelines based on the reference mRDT. There was no difference in inappropriate treatment of malaria between the intervention and control arms (24.0% versus 29.7%, adjusted risk ratio 0.81 95\% CI: 0.56, 1.17 p = 0.24). Most children (76.0\%) tested positive by reference mRDT, but many were not prescribed AL (22.5\% intervention versus 25.9\% control, p = 0.53). Inappropriate treatment of children testing negative by reference mRDT with AL was also common (31.3\% invention vs 42.4\% control, p = 0.29). Health workers appreciated mRDTs but felt that integrating testing into practice was challenging given constraints on time and infrastructure. The PRIME intervention did not have the desired impact on inappropriate treatment of malaria for children under five. In this high transmission setting, use of mRDTs did not lead to the reductions in antimalarial prescribing seen elsewhere. Broader investment in health systems, including infrastructure and staffing, will be required to improve fever case management

High Effective Coverage of Vector Control Interventions in Children After Achieving Low Malaria Transmission in Zanzibar, Tanzania.

\ud \ud Formerly a high malaria transmission area, Zanzibar is now targeting malaria elimination. A major challenge is to avoid resurgence of malaria, the success of which includes maintaining high effective coverage of vector control interventions such as bed nets and indoor residual spraying (IRS). In this study, caretakers' continued use of preventive measures for their children is evaluated, following a sharp reduction in malaria transmission. A cross-sectional community-based survey was conducted in June 2009 in North A and Micheweni districts in Zanzibar. Households were randomly selected using two-stage cluster sampling. Interviews were conducted with 560 caretakers of under-five-year old children, who were asked about perceptions on the malaria situation, vector control, household assets, and intention for continued use of vector control as malaria burden further decreases. Effective coverage of vector control interventions for under-five children remains high, although most caretakers (65%; 363/560) did not perceive malaria as presently being a major health issue. Seventy percent (447/643) of the under-five children slept under a long-lasting insecticidal net (LLIN) and 94% (607/643) were living in houses targeted with IRS. In total, 98% (628/643) of the children were covered by at least one of the vector control interventions. Seasonal bed-net use for children was reported by 25% (125/508) of caretakers of children who used bed nets. A high proportion of caretakers (95%; 500/524) stated that they intended to continue using preventive measures for their under-five children as malaria burden further reduces. Malaria risk perceptions and different perceptions of vector control were not found to be significantly associated with LLIN effective coverage While the majority of caretakers felt that malaria had been reduced in Zanzibar, effective coverage of vector control interventions remained high. Caretakers appreciated the interventions and recognized the value of sustaining their use. Thus, sustaining high effective coverage of vector control interventions, which is crucial for reaching malaria elimination in Zanzibar, can be achieved by maintaining effective delivery of these interventions

Painleve I, Coverings of the Sphere and Belyi Functions

The theory of poles of solutions of Painleve-I is equivalent to the Nevanlinna problem of constructing a meromorphic function ramified over five points - counting multiplicities - and without critical points. We construct such meromorphic functions as limit of rational ones. In the case of the tritronquee solution these rational functions are Belyi functions.Comment: 33 pages, many figures. Version 2: minor corrections and minor changes in the bibliograph

Neuropeptide S alters anxiety, but not depression-like behaviour in Flinders Sensitive Line rats: a genetic animal model of depression

Neuropeptide S (NPS) and its receptor (NPSR) have been implicated in the mediation of anxiolytic-like behaviour in rodents. However, little knowledge is available regarding the NPS system in depression-related behaviours, and whether NPS also exerts anxiolytic effects in an animal model of psychopathology. Therefore, the aim of this work was to characterize the effects of NPS on depression- and anxiety-related parameters, using male and female rats in a well-validated animal model of depression: the Flinders Sensitive Line (FSL), their controls, the Flinders Resistant Line (FRL), and Sprague–Dawley (SD) rats. We found that FSL showed greater immobility in the forced swim test (FST) than FRL, confirming their phenotype. However, NPS did not affect depression-related behaviour in any rat line. No significant differences in baseline anxiety levels between the FSL and FRL strains were observed, but FSL and FRL rats displayed less anxiety-like behaviour compared to SD rats. NPS decreased anxiety-like behaviour on the elevated plus-maze in all strains. The expression of the NPSR in the amygdala, periventricular hypothalamic nucleus, and hippocampus was equal in all male strains, although a trend towards reduced expression within the amygdala was observed in FSL rats compared to SD rats. In conclusion, NPS had a marked anxiolytic effect in FSL, FRL and SD rats, but did not modify the depression-related behaviour in any strain, in spite of the significant differences in innate level between the strains. These findings suggest that NPS specifically modifies anxiety behaviour but cannot overcome/reverse a genetically mediated depression phenotype

The Schwarzian derivative and the Wiman-Valiron property

Consider a transcendental meromorphic function in the plane with finitely many critical values, such that the multiple points have bounded multiplicities and the inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that if the Schwarzian derivative is transcendental then the function has infinitely many multiple points, the inverse function does not have a direct transcendental singularity over infinity, and infinity is not a Borel exceptional value. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method