Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

Who calls the tune? Participation and partnership in research

yesThis paper explores issues of partnership and participation in research and evaluation, drawing on the experiences of evaluating a move from hostel accommodation to independent supported living for people with mental health difficulties or learning disabilities. The service change project involved a partnership between a local authority and a housing association with over 300 people moving into their own tenancies in newly-built flats and bungalows. The accompanying evaluation was designed on a model of service user participation and action research and was specifically concerned to explore the impact of the changes on people’s actual or perceived social inclusion into local communities. Ten service user and carer researchers, some of whom were directly involved in the move from hostel to independent living, were recruited and worked with ‘professional’ researchers to examine both the process and the outcomes of the move. The work will be viewed through the insights offered by feminist, transformative and participatory approaches to research. The ‘positioning’ of the researcher in relation to boundaries and the construction of the ‘other’ will be considered, emphasising an approach grounded in reflexivity and an acknowledgement of the complex ethical issues involved. A key feature of this study has been the negotiation involved between a complex change project and a participatory evaluation design. Learning points from the work so far will also be considered in terms of their wider application in future evaluations of complex change projects that involve multiple stakeholders.Published online Nov 2012

On L2L^2 -functions with bounded spectrum

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$. Only injective affine maps $\varphi$ have this property

Conductance Phases in Aharonov-Bohm Ring Quantum Dots

The regimes of growing phases (for electron numbers N~0-8) that pass into regions of self-returning phases (for N>8), found recently in quantum dot conductances by the Weizmann group are accounted for by an elementary Green function formalism, appropriate to an equi-spaced ladder structure (with at least three rungs) of electronic levels in the quantum dot. The key features of the theory are physically a dissipation rate that increases linearly with the level number (and tentatively linked to coupling to longitudinal optical phonons) and a set of Fano-like meta-stable levels, which disturb the unitarity, and mathematically the change over of the position of the complex transmission amplitude-zeros from the upper-half in the complex gap-voltage plane to the lower half of that plane. The two regimes are identified with (respectively) the Blaschke-term and the Kramers-Kronig integral term in the theory of complex variables.Comment: 20 pages, 4 figure

Photon wave mechanics and position eigenvectors

One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin and orbital angular momentum. While only the Landau-Peierls wave function defines a positive definite photon density, a similarity transformation to a biorthogonal field-potential pair of positive frequency solutions of Maxwell's equations preserves eigenvalues and expectation values. We show that this real space description of photons is compatible with all of the usual rules of quantum mechanics and provides a framework for understanding the relationships amongst different forms of the photon wave function in the literature. It also gives a quantum picture of the optical angular momentum of beams that applies to both one photon and coherent states. According to the rules of qunatum mechanics, this wave function gives the probability to count a photon at any position in space.Comment: 14 pages, to be published in Phys. Rev.

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Phylogenetic and environmental DNA insights into emerging aquatic parasites: implications for risk management.

Species translocation leads to disease emergence in native species of considerable economic importance. Generalist parasites are more likely to be transported, become established and infect new hosts, thus their risk needs to be evaluated. Freshwater systems are particularly at risk from parasite introductions due to the frequency of fish movements, lack of international legislative controls for non-listed pathogens and inherent difficulties with monitoring disease introductions in wild fish populations. Here we used one of the world's most invasive freshwater fish, the topmouth gudgeon, Pseudorasbora parva, to demonstrate the risk posed by an emergent generalist parasite, Sphaerothecum destruens. Pseudorasbora parva has spread to 32 countries from its native range in China through the aquaculture trade and has introduced S. destruens to at least five of these. We systematically investigated the spread of S. destruens through Great Britain and its establishment in native fish communities through a combination of phylogenetic studies of the host and parasite and a novel environmental DNA detection assay. Molecular approaches confirmed that S. destruens is present in 50% of the P. parva communities tested and was also detected in resident native fish communities but in the absence of notable histopathological changes. We identified specific P. parva haplotypes associated with S. destruens and evaluated the risk of disease emergence from this cryptic fish parasite. We provide a framework that can be applied to any aquatic pathogen to enhance detection and help mitigate future disease risks in wild fish populations

On the nonlinearity interpretation of q- and f-deformation and some applications

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.Comment: 11 pages Late