Deformed quantum mechanics and q-Hermitian operators

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which reproduces at the equilibrium the well-known q-deformed exponential stationary distribution. In this framework, q-deformed adjoint of an operator and q-hermitian operator properties occur in a natural way in order to satisfy the basic quantum mechanics assumptions.Comment: 10 page

Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process

We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebra. We construct all finite dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.Comment: 18 pages, Latex, 1 EPS figur

A systematic review of electronic patient records using the meta-narrative approach: Empirical findings and methodological challenges.

Systematic reviews are central to the enterprise of evidence-based medicine (EBM). However, traditional ‘Cochrane’ reviews have major limitations, especially when dealing with heterogeneous methodologies or an applied setting. The meta-narrative review (see Soc Sci Med 2005; 61: 417-30) is one of several new methods that seek to address pragmatic policy-level questions via broad-based literature reviews. Inspired by Kuhn, meta-narrative review takes a historical and paradigmatic approach to considering different areas of research activity. As an interpretive tool, the approach seeks distinct research traditions, each with its own meta-narrative. We then use these ‘stories of how research unfolded’ as a way of making sense of a diverse literature. Incommensurability between different traditions is seen not as a problem to be lamented or resolved but as a window to higher-order explanations about the nuances of empirical data and what these nuances mean for different applied situations. Having originally developed the meta-narrative method for a study of the diffusion of innovations in healthcare, we are now applying it in a review of the electronic patient record (EPR) in an organizational context. We have collated some 600 papers and books across multiple research traditions including health informatics, information systems research, computer-supported cooperative work (CSCW) and sociology. This very contemporary topic area is raising interesting methodological questions. For example, the EPR literature does not comprise as cleanly delineable traditions for four main reasons: 1. Information and communications technology research is a particularly fast-moving field, so paradigm shifts are relatively common (e.g. the rise of CSCW out of human-computer interaction research). 2. In the electronic age, it is easy for researchers to explore beyond their own discipline and ‘borrow’ theories, ideas and methods from elsewhere. Journal editors may commission overviews from experts in another tradition; authors may explicitly address an audience in another tradition. Research traditions can begin to converge (e.g. papers bringing together CSCW, information systems research and STS). 3. Some researchers are adept ‘boundary spanners’, writing for a number of different academic audiences and adapting their theoretical pedigree to fit (e.g. Marc Berg). 4. Some traditions are characterized not by a single unified paradigm but by active dialogue between competing paradigms (e.g. ‘hard’ versus ‘soft’ perspectives on knowledge management). This work contributes to the STS literature by critically questioning the nature of rigour in secondary research. The EBM movement values ‘Cochrane’ reviews because they meet positivist criteria (e.g. they are rational, objective, replicable, data-led, and transferable across contexts). In contrast, the meta-narrative review is interpretive, reflexive, problem-oriented and work-led, and makes no claim to either replicability or transferability. Rigour is redefined in terms of plausibility, authenticity and usefulness – raising the radical suggestion that the evidence base for key policy decisions can never be set in stone. Systematic reviews are central to the enterprise of evidence-based medicine (EBM). However, traditional ‘Cochrane’ reviews have major limitations, especially when dealing with heterogeneous methodologies or an applied setting. The meta-narrative review (see Soc Sci Med 2005; 61: 417-30) is one of several new methods that seek to address pragmatic policy-level questions via broad-based literature reviews. Inspired by Kuhn, meta-narrative review takes a historical and paradigmatic approach to considering different areas of research activity. As an interpretive tool, the approach seeks distinct research traditions, each with its own meta-narrative. We then use these ‘stories of how research unfolded’ as a way of making sense of a diverse literature. Incommensurability between different traditions is seen not as a problem to be lamented or resolved but as a window to higher-order explanations about the nuances of empirical data and what these nuances mean for different applied situations. Having originally developed the meta-narrative method for a study of the diffusion of innovations in healthcare, we are now applying it in a review of the electronic patient record (EPR) in an organizational context. We have collated some 600 papers and books across multiple research traditions including health informatics, information systems research, computer-supported cooperative work (CSCW) and sociology. This very contemporary topic area is raising interesting methodological questions. For example, the EPR literature does not comprise as cleanly delineable traditions for four main reasons: 1. Information and communications technology research is a particularly fast-moving field, so paradigm shifts are relatively common (e.g. the rise of CSCW out of human-computer interaction research). 2. In the electronic age, it is easy for researchers to explore beyond their own discipline and ‘borrow’ theories, ideas and methods from elsewhere. Journal editors may commission overviews from experts in another tradition; authors may explicitly address an audience in another tradition. Research traditions can begin to converge (e.g. papers bringing together CSCW, information systems research and STS). 3. Some researchers are adept ‘boundary spanners’, writing for a number of different academic audiences and adapting their theoretical pedigree to fit (e.g. Marc Berg). 4. Some traditions are characterized not by a single unified paradigm but by active dialogue between competing paradigms (e.g. ‘hard’ versus ‘soft’ perspectives on knowledge management). This work contributes to the STS literature by critically questioning the nature of rigour in secondary research. The EBM movement values ‘Cochrane’ reviews because they meet positivist criteria (e.g. they are rational, objective, replicable, data-led, and transferable across contexts). In contrast, the meta-narrative review is interpretive, reflexive, problem-oriented and work-led, and makes no claim to either replicability or transferability. Rigour is redefined in terms of plausibility, authenticity and usefulness – raising the radical suggestion that the evidence base for key policy decisions can never be set in stone

Development of a unified tensor calculus for the exceptional Lie algebras

The uniformity of the decomposition law, for a family F of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^n of their adjoint representations ad is now well-known. This paper uses it to embark on the development of a unified tensor calculus for the exceptional Lie algebras. It deals explicitly with all the tensors that arise at the n=2 stage, obtaining a large body of systematic information about their properties and identities satisfied by them. Some results at the n=3 level are obtained, including a simple derivation of the the dimension and Casimir eigenvalue data for all the constituents of ad^3. This is vital input data for treating the set of all tensors that enter the picture at the n=3 level, following a path already known to be viable for a_1. The special way in which the Lie algebra d_4 conforms to its place in the family F alongside the exceptional Lie algebras is described.Comment: 27 pages, LaTeX 2

On factorization of q-difference equation for continuous q-Hermite polynomials

We argue that a customary q-difference equation for the continuous q-Hermite polynomials H_n(x|q) can be written in the factorized form as (D_q^2 - 1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference operator. This means that the polynomials H_n(x|q) are in fact governed by the q-difference equation D_qH_n(x|q)=q^{-n/2}H_n(x|q), which is simpler than the conventional one.Comment: 7 page