The quantum state vector in phase space and Gabor's windowed Fourier transform

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed `window state vector'. Here aspects of this construction are explored, with emphasis on the connection with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of window are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schr\"odinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and further references adde

Deep Bilevel Learning

We present a novel regularization approach to train neural networks that enjoys better generalization and test error than standard stochastic gradient descent. Our approach is based on the principles of cross-validation, where a validation set is used to limit the model overfitting. We formulate such principles as a bilevel optimization problem. This formulation allows us to define the optimization of a cost on the validation set subject to another optimization on the training set. The overfitting is controlled by introducing weights on each mini-batch in the training set and by choosing their values so that they minimize the error on the validation set. In practice, these weights define mini-batch learning rates in a gradient descent update equation that favor gradients with better generalization capabilities. Because of its simplicity, this approach can be integrated with other regularization methods and training schemes. We evaluate extensively our proposed algorithm on several neural network architectures and datasets, and find that it consistently improves the generalization of the model, especially when labels are noisy.Comment: ECCV 201

Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides--coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.Comment: LaTeX, 22 pages, 2 figure

Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras

We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.Comment: 13 pages, AmsTex file; to appear in Lett. Math. Phy

Reproductive and developmental effects of disinfection by-products in drinking water.

Recent epidemiologic studies have reported associations between the consumption of chlorinated drinking water and reproductive and developmental effects. Here we review the available epidemiologic data, assess the hazard potential posed by exposure to disinfection by-products, identify critical data gaps, and offer recommendations for further research. The epidemiologic evidence supporting associations between exposure to water disinfection by-products (DBPs) and adverse pregnancy outcomes is sparse, and positive findings should be interpreted cautiously. The methods used during the early stages of research in this area have been diverse. Variability in exposure assessment and endpoints makes it difficult to synthesize or combine the available data. Exposure misclassification and unmeasured confounding may have lead to bias in risk estimation. Future studies of reproductive outcome and exposure to chlorinated water should use improved methods for exposure assessment to 1) assure selection of appropriate exposure markers, 2) assess seasonal and annual fluctuations in DBPs, 3) assess variability within the distribution system, and 4) assess exposure through multiple routes such as bathing and showering, as well as consumption. Population-based studies should be conducted to evaluate male and female fertility, conception delay, growth retardation, and specific birth defects. The reproductive and developmental effects of exposure to DBPs could be efficiently explored in ongoing investigations by incorporating valid exposure markers and relevant questionnaire information. Future studies should make use of naturally occurring variability in the concentrations of DBPs and may incorporate biomarkers of exposure and effect in their design. Epidemiologic investigations should be conducted in parallel with laboratory-based and animal studies in a coordinated, multidisciplinary approach

Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations

The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as Feynman's approach. This allows us to go beyond the standard case and discover non-trivial results. In fact, while the first formulation gives rise to the static Maxwell equations, the second formulation is based on the following assumption $m[x_{j},\dot{x_{k}}]=i\hbar \delta_{jk}+im\theta_{jk}f.$ The results extracted from the second formulation are more significant since they are associated to a non trivial $\theta$-extension of the Bianchi-set of Maxwell equations. We find $div_{\theta}B=\eta_{\theta}$ and $\frac{\partial B_{s}}{\partial t}+\epsilon_{kjs}\frac{\partial E_{j}}{\partial x_{k}}=A_{1}\frac{d^{2}f}{dt^{2}}+A_{2}\frac{df}{dt}+A_{3},$ where $\eta_{\theta}$, $A_{1}$, $A_{2}$ and $A_{3}$ are local functions depending on the NC $\theta$-parameter. The novelty of this proof in the NC space is revealed notably at the level of the corrections brought to the previous Maxwell equations. These corrections correspond essentially to the possibility of existence of magnetic charges sources that we can associate to the magnetic monopole since $div_{\theta}B=\eta_{\theta}$ is not vanishing in general.Comment: LaTeX file, 16 page

On the solution of a supersymmetric model of correlated electrons

We consider the exact solution of a model of correlated electrons based on the superalgebra $Osp(2|2)$. The corresponding Bethe ansatz equations have an interesting form. We derive an expression for the ground state energy at half filling. We also present the eigenvalue of the transfer matrix commuting with the Hamiltonian.Comment: Palin latex , 8 page

ADRIC: Adverse Drug Reactions In Children - a programme of research using mixed methods

Aims To comprehensively investigate the incidence, nature and risk factors of adverse drug reactions (ADRs) in a hospital-based population of children, with rigorous assessment of causality, severity and avoidability, and to assess the consequent impact on children and families. We aimed to improve the assessment of ADRs by development of new tools to assess causality and avoidability, and to minimise the impact on families by developing better strategies for communication. Review methods Two prospective observational studies, each over 1 year, were conducted to assess ADRs in children associated with admission to hospital, and those occurring in children who were in hospital for longer than 48 hours. We conducted a comprehensive systematic review of ADRs in children. We used the findings from these studies to develop and validate tools to assess causality and avoidability of ADRs, and conducted interviews with parents and children who had experienced ADRs, using these findings to develop a leaflet for parents to inform a communication strategy about ADRs. Results The estimated incidence of ADRs detected in children on admission to hospital was 2.9% [95% confidence interval (CI) 2.5% to 3.3%]. Of the reactions, 22.1% (95% CI 17% to 28%) were either definitely or possibly avoidable. Prescriptions originating in the community accounted for 44 out of 249 (17.7%) of ADRs, the remainder originating from hospital. A total of 120 out of 249 (48.2%) reactions resulted from treatment for malignancies. Off-label and/or unlicensed (OLUL) medicines were more likely to be implicated in an ADR than authorised medicines [relative risk (RR) 1.67, 95% CI 1.38 to 2.02; p  48 hours, the overall incidence of definite and probable ADRs based on all admissions was 15.9% (95% CI 15.0 to 16.8). Opiate analgesic drugs and drugs used in general anaesthesia (GA) accounted for > 50% of all drugs implicated in ADRs. The odds ratio of an OLUL drug being implicated in an ADR compared with an authorised drug was 2.25 (95% CI 1.95 to 2.59; p < 0.001). Risk factors identified were exposure to a GA, age, oncology treatment and number of medicines. The systematic review estimated that the incidence rates for ADRs causing hospital admission ranged from 0.4% to 10.3% of all children [pooled estimate of 2.9% (95% CI 2.6% to 3.1%)] and from 0.6% to 16.8% of all children exposed to a drug during hospital stay. New tools to assess causality and avoidability of ADRs have been developed and validated. Many parents described being dissatisfied with clinician communication about ADRs, whereas parents of children with cancer emphasised confidence in clinician management of ADRs and the way clinicians communicated about medicines. The accounts of children and young people largely reflected parents’ accounts. Clinicians described using all of the features of communication that parents wanted to see, but made active decisions about when and what to communicate to families about suspected ADRs, which meant that communication may not always match families’ needs and expectations. We developed a leaflet to assist clinicians in communicating ADRs to parents. Conclusion The Adverse Drug Reactions In Children (ADRIC) programme has provided the most comprehensive assessment, to date, of the size and nature of ADRs in children presenting to, and cared for in, hospital, and the outputs that have resulted will improve the management and understanding of ADRs in children and adults within the NHS. Recommendations for future research: assess the values that parents and children place on the use of different medicines and the risks that they will find acceptable within these contexts; focusing on high-risk drugs identified in ADRIC, determine the optimum drug dose for children through the development of a gold standard practice for the extrapolation of adult drug doses, alongside targeted pharmacokinetic/pharmacodynamic studies; assess the research and clinical applications of the Liverpool Causality Assessment Tool and the Liverpool Avoidability Assessment Tool; evaluate, in more detail, morbidities associated with anaesthesia and surgery in children, including follow-up in the community and in the home setting and an assessment of the most appropriate treatment regimens to prevent pain, vomiting and other postoperative complications; further evaluate strategies for communication with families, children and young people about ADRs; and quantify ADRs in other settings, for example critical care and neonatology

Multivortex Solutions of the Weierstrass Representation

The connection between the complex Sine and Sinh-Gordon equations on the complex plane associated with a Weierstrass type system and the possibility of construction of several classes of multivortex solutions is discussed in detail. We perform the Painlev\'e test and analyse the possibility of deriving the B\"acklund transformation from the singularity analysis of the complex Sine-Gordon equation. We make use of the analysis using the known relations for the Painlev\'{e} equations to construct explicit formulae in terms of the Umemura polynomials which are $\tau$-functions for rational solutions of the third Painlev\'{e} equation. New classes of multivortex solutions of a Weierstrass system are obtained through the use of this proposed procedure. Some physical applications are mentioned in the area of the vortex Higgs model when the complex Sine-Gordon equation is reduced to coupled Riccati equations.Comment: 27 pages LaTeX2e, 1 encapsulated Postscript figur

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. This provides us with a basis for computing the finite size corrections to the low lying energies in the system.Comment: 4 pages, RevTex. Some cosmetic changes. The version to appear in Phys. Rev.