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

Quantum Chebyshev Transform: Mapping, Embedding, Learning and Sampling Distributions

We develop a paradigm for building quantum models in the orthonormal space of Chebyshev polynomials. We show how to encode data into quantum states with amplitudes being Chebyshev polynomials with degree growing exponentially in the system size. Similar to the quantum Fourier transform which maps computational basis space into the phase (Fourier) basis, we describe the quantum circuit for the mapping between computational and Chebyshev spaces. We propose an embedding circuit for generating the orthonormal Chebyshev basis of exponential capacity, represented by a continuously-parameterized shallow isometry. This enables automatic quantum model differentiation, and opens a route to solving stochastic differential equations. We apply the developed paradigm to generative modeling from physically- and financially-motivated distributions, and use the quantum Chebyshev transform for efficient sampling of these distributions in extended computational basis.Comment: 6 pages (+ references), 3 figure

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

Neuroplasticity pathways and protein-interaction networks are modulated by vortioxetine in rodents

Additional file 2: Figure S1. Merged mouse and rat network (mapped to human proteins) and summary of biological functions of each sub-network. Biological functions were manually extracted from the Function and Gene Ontology fields of the UniProt protein entries. The genes with dark, bold borders were used to build the network of protein–protein interaction partners. Squares with bold borders represent upregulated targets from the rat network, and circles with bold borders indicate differentially-regulated targets from the mouse network. The arrowheads indicate the common targets found in mouse and rat networks. This network of physically-interacting proteins containing clusters related to synaptic plasticity, synaptic transmission, neurodevelopment, cell growth, metabolism, and apoptosis, was significantly modulated in both mouse and rat

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

Harmonic (Quantum) Neural Networks

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.Comment: 12 pages (main), 7 pages (supplementary), 7 figure

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

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