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

Multi-vehicle Control in a Strong Flowfield with Application to Hurricane Sampling

A major obstacle to path-planning and formation-control algorithms in multi-vehicle systems are strong flows in which the ambient flow speed is greater than the vehicle speed relative to the flow. This challenge is espe-cially pertinent in the application of unmanned aircraft used for collecting targeted observations in a hurricane. The presence of such a flowfield may inhibit a vehicle from making forward progress relative to a ground-fixed frame, thus limiting the directions in which it can travel. Using a self-propelled particle model in which each particle moves at constant speed relative to the flow, this paper presents results for motion coordination in a strong, known flowfield. We present the particle model with respect to inertial and rotating reference frames and provide for each case a set of con-ditions on the flowfield that ensure trajectory feasibility. Results from the Lyapunov-based design of decentralized control algorithms are presented for circular, folium, and spirograph trajectories, which are selected for their potential use as hurricane sampling trajectories. The theoretical results are illustrated using numerical simulations in an idealized hurricane model. Nomenclature N Number of particles in the system k Particle index k = 1,..., N rk Position of k th particle with respect to inertial frame r̃k Position of k th particle with respect to rotating fram

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

Weaving Nanoscale Cloth through Electrostatic Templating

Here we disclose a simple route to nanoscopic 2D woven structures reminiscent of the methods used to produce macroscopic textiles. We find that the same principles used in macroscopic weaving can be applied on the nanoscale to create two-dimensional molecular cloth from polymeric strands, a molecular thread. The molecular thread is composed of Co6Se8(PEt3)4L2 superatoms that are bridged with L = benzene bis-1,4-isonitrile to form polymer strands. As the superatoms that make up the polymer chain are electrochemically oxidized, they are electrostatically templated by a nanoscale anion, the tetragonal Lindqvist polyoxometalate Mo6O192–. The tetragonal symmetry of the dianionic template creates a nanoscale version of the box weave. The crossing points in the weave feature π-stacking of the bridging linker. By examining the steps in the weaving process with single crystal X-ray diffraction, we find that the degree of polymerization at the crossing points is crucial in the cloth formation. 2D nanoscale cloth will provide access to a new generation of smart, multifunctional materials, coatings, and surfaces