Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

Entanglement-free Heisenberg-limited phase estimation

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/sqrt(N) - known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N. It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N <= 6, but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.Comment: Published in Nature. This is the final versio

UK survey of occupational therapist’s and physiotherapist’s experiences and attitudes towards hip replacement precautions and equipment

Background: Total hip replacement (THR) is one of the most common orthopaedic procedures in the United Kingdom (UK). Historically, people following THR have been provided with hip precautions and equipment such as: raised toilet seats and furniture rises, in order to reduce the risks of dislocation post-operation. The purpose of this study was to determine current practices in the provision of these interventions in the UK for people following primary THR. Methods: A 27-question, self-administered online survey was developed and distributed to UK physiotherapists and occupational therapists involved in the management of people following primary THR (target respondents). The survey included questions regarding the current practices in the provision of equipment and hip precautions for THR patients, and physiotherapist’s and occupational therapist’s attitudes towards these practices. The survey was disseminated through print and web-based/social media channels. Results: 170 health professionals (87 physiotherapists and 83 occupational therapists), responded to the survey. Commonly prescribed equipment in respondent’s health trusts were raised toilet seats (95%), toilet frames and rails (88%), furniture raises (79%), helping hands/grabbers (77%), perching stools (75%) and long-handled shoe horns (75%). Hip precautions were routinely prescribed by 97% of respondents. Hip precautions were most frequently taught in a pre-operative group (52% of respondents). Similarly equipment was most frequently provided pre-operatively (61% respondents), and most commonly by occupational therapists (74% respondents). There was variability in the advice provided on the duration of hip precautions and equipment from up to six weeks post-operatively to life-time usage. Conclusions: Current practice on hip precautions and provision of equipment is not full representative of clinician’s perceptions of best care after THR. Future research is warranted to determine whether and to whom hip precautions and equipment should be prescribed post-THR as opposed to the current ‘blanket’ provision of equipment and movement restriction provided in UK practice

Categorical Dimensions of Human Odor Descriptor Space Revealed by Non-Negative Matrix Factorization

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain unclear. Here, we use non-negative matrix factorization (NMF) – a dimensionality reduction technique – to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor dimensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures

People’s understanding of verbal risk descriptors in patient information leaflets : a cross-sectional national survey of 18- to 65-year-olds in England

Introduction Evidence suggests the current verbal risk descriptors used to communicate side effect risk in patient information leaflets (PILs) are overestimated. Objectives The aim was to establish how people understand the verbal risk descriptors recommended for use in PILs by the European Commission (EC), and alternative verbal risk descriptors, in the context of mild and severe side effects. Methods A cross-sectional online survey was carried out by a market research company recruiting participants aged between 18 and 65 years living in England. Data were collected between 18 March and 1 April 2016. Participants were given a hypothetical scenario regarding the risk of mild or severe medication side effects and asked to estimate how many out of 10,000 people would be affected for each of the verbal risk descriptors being tested. Results A total of 1003 participants were included in the final sample. The risks conveyed by the EC recommended verbal risk descriptors were greatly overestimated by participants. Two distinct distributions were apparent for participant estimates of side effect risks: those for ‘high risk’ verbal descriptors (e.g. ‘common’, ‘likely’, ‘high chance’) and those for ‘low risk’ verbal descriptors (e.g. ‘uncommon’, ‘unlikely’, ‘low chance’). Within these two groups, the distributions were near to identical regardless of what adverb (e.g. very, high, fair) or adjective (e.g. common, likely, chance) was used. The EC recommended verbal risk descriptors were more likely to be understood in accordance with their intended meanings when describing severe side effects. Very few demographic or psychological factors were consistently associated with how well participants understood the EC recommended verbal risk descriptors. Discussion The current verbal risk descriptors used in PILs are ineffective at best and misleading at worst. Discontinuing the use of verbal risk descriptors would limit the likelihood of people overestimating the risk of side effects

Associations between age and sleep apnea risk among newborn infants

ObjectiveAmong older children, sleep‐disordered breathing (SDB) is associated with measurable neurocognitive consequences. However, diagnostic SDB thresholds are lacking for infants < 12 months. We sought to evaluate the relationship between SDB indices, gestational age (GA), and postmenstrual age (PMA) for infants who underwent clinically‐indicated polysomnograms at a tertiary care center.MethodsEvery infant < 3‐months chronological age whose first clinically‐indicated polysomnogram was between 2/2012 and 2/2017 was included. Linear regression was used to evaluate associations between apnea‐hypopnea index (AHI), obstructive‐apnea index (OAI), and GA and PMA for infants with and without obvious clinical risk factors for SDB (eg, micrognathia and cleft palate).ResultsFor 53 infants without obvious SDB risk factors (GA 35.6 ± 4.5 weeks; PMA 41.2 ± 4.0 weeks), mean AHI was 27 ± 18 and OAI 2.9 ± 4.5. There was a weak inverse relationship between AHI and PMA (r2 = 0.12, P = 0.01), but AHI was not predicted by GA (r2 = 0.04, P = 0.13). Conversely, OAI was more strongly associated with GA (r2 = 0.33, P < 0.0001) than PMA (r2 = 0.08, P = 0.036). For 28 infants with congenital structural anomalies that predispose to SDB (GA 38.0 ± 3.1 weeks, PMA 43.1 ± 3.3 weeks, AHI 37.7 ± 30, OAI 8.2 ± 11.8), neither AHI nor OAI were related to PMA or GA.ConclusionsAmong infants who received clinically‐indicated polysomnograms but did not have obvious structural risk for SDB, AHI declined with advancing PMA, but obstructive‐apnea was best predicted by prematurity. In contrast, the SDB risk did not improve with increasing GA or PMA for infants with congenital structural risk factors; such infants may not outgrow their risk for SDB.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/150552/1/ppul24354_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150552/2/ppul24354.pd

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

The impact of different DNA extraction kits and laboratories upon the assessment of human gut microbiota composition by 16S rRNA gene sequencing

Peer reviewedPublisher PD

Simulation of the many-body dynamical quantum Hall effect in an optical lattice

We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold-atom experiments with numerical simulations.Comment: 8 pages, 3 figures; accepted in Quantum Information Processin