On the Equivalence of Quadratic APN Functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.Comment: 13 p

Non-positivity of Groenewold operators

A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Liouville densities, leading to what may be termed term Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Liouville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.Comment: 9 pages, 1 figures, submitted to Europhysics Letter

Integrable Electron Model with Correlated Hopping and Quantum Supersymmetry

We give the quantum analogue of a recently introduced electron model which generalizes the Hubbard model with additional correlated hopping terms and electron pair hopping. The model contains two independent parameters and is invariant with respect to the quantum superalgebra $U_q(gl(2|1))$. It is integrable in one dimension by means of the quantum inverse scattering method.Comment: 7 pages, AmsTex fil

A CHAT-based Case Study of Informal Adult Learning and Technology: BarCamp, the Unconference

This paper presents and discusses findings from a pilot case study about Bar Camps. BarCamps are an open technology movement collective learning event. They are gaining momentum as sites of resistance to the idea of ‘owning’ technology knowledge and known for cutting across boundaries to invite learners to learn through shared activities. The findings are organized and discussed based upon constructs of Cultural Historical Activity Theory, CHAT

Group Theory and Quasiprobability Integrals of Wigner Functions

The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0,1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric disks and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in Hilbert space carrying the positive discrete series representations of the algebra su(1,1)or so(2,1). The explicit relation between the spectra of operators associated with disks and circles with proportional radii, is given in terms of the dicrete variable Meixner polynomials.Comment: 11 pages, latex fil

Evaluating the success of public participation in integrated catchment management

Recognition of the need to manage the water environment in more holistic ways has resulted in the global growth of Integrated Catchment Management (ICM). ICM is characterised by horizontal integration, encouraging interdisciplinary working between traditionally disparate management sectors, alongside vertical integration, characterised by the engagement of communities; central is the promotion of participatory governance and management decision-making. ICM has been translated into policy through, for example, the EU Water Framework Directive and at a national level by policies such as the Catchment Based Approach in England. Research exploring the implementation of these policies has reported success at a catchment level, but further research is required to explore practices of management at local level within catchments. This paper presents the findings of participatory research undertaken with a catchment partnership in the northeast of England to explore the integration of top-down policy translation with how local communities interact with management agencies at sub-catchment scale (a bottom-up perspective). The research found that supra-catchment scale drivers dominate the vertical interplay between management systems at more local levels. These drivers embed traditional practices of management, which establishes public participation as a barrier to delivery of top-down management objectives, resulting in practices that exclude communities and participatory movements at the local level. Although collaboration between agencies at the partnership scale offers a potential solution to overcoming these obstacles, the paper recommends changes to supra-catchment governance structures to encourage flexibility in developing local participatory movements as assets. Further research is necessary to develop new practices of management to integrate local people more effectively into the management process

A Chiral Schwinger model, its Constraint Structure and Applications to its Quantization

The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.Comment: 18 page

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 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