Extracting dynamical equations from experimental data is NP-hard

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP-hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70 years).Comment: For mathematical details, see arXiv:0908.2128[math-ph]. v2: final version, accepted in Phys. Rev. Let

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

The usefulness of rapid diagnostic tests in the new context of low malaria transmission in zanzibar.

BACKGROUND\ud \ud We assessed if histidine-rich-protein-2 (HRP2) based rapid diagnostic test (RDT) remains an efficient tool for Plasmodium falciparum case detection among fever patients in Zanzibar and if primary health care workers continue to adhere to RDT results in the new epidemiological context of low malaria transmission. Further, we evaluated the performance of RDT within the newly adopted integrated management of childhood illness (IMCI) algorithm in Zanzibar.\ud \ud METHODS AND FINDINGS\ud \ud We enrolled 3890 patients aged ≥2 months with uncomplicated febrile illness in this health facility based observational study conducted in 12 primary health care facilities in Zanzibar, between May-July 2010. One patient had an inconclusive RDT result. Overall 121/3889 (3.1%) patients were RDT positive. The highest RDT positivity rate, 32/528 (6.1%), was found in children aged 5-14 years. RDT sensitivity and specificity against PCR was 76.5% (95% CI 69.0-83.9%) and 99.9% (95% CI 99.7-100%), and against blood smear microscopy 78.6% (95% CI 70.8-85.1%) and 99.7% (95% CI 99.6-99.9%), respectively. All RDT positive, but only 3/3768 RDT negative patients received anti-malarial treatment. Adherence to RDT results was thus 3887/3889 (99.9%). RDT performed well in the IMCI algorithm with equally high adherence among children <5 years as compared with other age groups.\ud \ud CONCLUSIONS\ud \ud The sensitivity of HRP-2 based RDT in the hands of health care workers compared with both PCR and microscopy for P. falciparum case detection was relatively low, whereas adherence to test results with anti-malarial treatment was excellent. Moreover, the results provide evidence that RDT can be reliably integrated in IMCI as a tool for improved childhood fever management. However, the relatively low RDT sensitivity highlights the need for improved quality control of RDT use in primary health care facilities, but also for more sensitive point-of-care malaria diagnostic tools in the new epidemiological context of low malaria transmission in Zanzibar.\ud \ud TRIAL REGISTRATION\ud \ud ClinicalTrials.gov NCT01002066

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

A Nested Case-Control Study of Intrauterine Exposure to Persistent Organochlorine Pollutants in Relation to Risk of Type 1 Diabetes

BACKGROUND: The incidence of type 1 diabetes in Europe is increasing at a rate of about 3% per year and there is also an increasing incidence throughout the world. Type 1 diabetes is a complex disease caused by multiple genetic and environmental factors. Persistent organochlorine pollutants (POPs) have been suggested as a triggering factor for developing childhood type 1 diabetes. The aim of this case-control study was to assess possible impacts of in utero exposure to POPs on type 1 diabetes. METHODOLOGY/ PRINCIPAL FINDINGS: The study was performed as a case-control study within a biobank in Malmö, a city located in the Southern part of Sweden. The study included 150 cases (children who had their diagnosis mostly before 18 years of age) and 150 controls, matched for gender and day of birth. 2,2',4,4',5,5'-hexachlorobiphenyl (PCB-153) and the major DDT metabolite 1,1-dichloro-2,2-bis (p-chlorophenyl)-ethylene (p,p'-DDE) were used as a biomarkers for POP exposure. When comparing the quartile with the highest maternal serum concentrations of PCB-153 with the other quartiles, an odds ratio (OR) of 0.73 (95% confidence interval [CI] 0.42, 1.27) was obtained. Similar results was obtained for p,p'-DDE (OR 0.56, 95% CI 0.29, 1.08). CONCLUSIONS: The hypothesis that in utero exposure to POPs will trigger the risk for developing type 1 diabetes was not supported by the results. The risk estimates did, although not statistically significant, go in the opposite direction. However, it is not reasonable to believe that exposure to POPs should protect against type 1 diabetes

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