Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Local adaptation in moss life histories: population-level variation and a reciprocal transplant experiment

We examine the extent of population-level differentiation in life history traits of Pogonatum aloides, Polytrichum commune and Polytrichum juniperinum (Polytrichaceae) between upland and lowland localities within Britain. Reciprocal transplant studies are used to estimate the relative importance of genetic versus environmental effects on observed differences. We demonstrate significant life history differentiation between moss populations, and show that at least some of these are genetically determined, although environment and phenotypic plasticity are also significant components of the observed variation. The transplant experiments indicate divergence among populations in plasticity of male reproductive effort and of investment in vegetative shoots by females. Two tradeoffs are identified; one between the number and the size of spores, and the second between reproduction by spores versus vegetative reproduction. The patterns of life history variation observed between populations of Polytrichum juniperinum are consistent with selection along these implied tradeoff curves, and we propose that they reflect selective pressures arising from the spatial and demographic distribution of mortality at upland versus lowland sites. The results underscore the need for more studies of intra-specific life history variation in mosses.

Independent and reciprocal accommodation in anisometropic amblyopia

Accommodation is considered to be a symmetrical response and to be driven by the least ametropic and nonamblyopic eye in anisometropia. We report the case of a 4-year-old child with anisometropic amblyopia who accommodates asymmetrically, reliably demonstrating normal accommodation in the nonamblyopic eye and antiaccommodation of the amblyopic eye to near targets. The abnormal accommodation of the amblyopic eye remained largely unchanged during 7 subsequent testing sessions undertaken over the course of therapy. We suggest that a congenital dysinnervation syndrome may result in relaxation of accommodation in relation to near cues and might be a hitherto unconsidered additional etiological factor in anisometropic amblyopia.

A comparison between bond graphs switching modelling techniques implemented on a boost dc-dc converter

A Bond Graph is a graphical modelling technique that allows the representation of energy flow between the components of a system. When used to model power electronic systems, it is necessary to incorporate bond graph elements to represent a switch. In this paper, three different methods of modelling switching devices are compared and contrasted: the Modulated Transformer with a binary modulation ratio (MTF), the ideal switch element, and the Switched Power Junction (SPJ) method. These three methods are used to model a dc-dc Boost converter and then run simulations in MATLAB/SIMULINK. To provide a reference to compare results, the converter is also simulated using PSPICE. Both quantitative and qualitative comparisons are made to determine the suitability of each of the three Bond Graph switch models in specific power electronics applications

Social networks: evolving graphs with memory dependent edges

The plethora, and mass take up, of digital communication tech- nologies has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the ex- istence or otherwise of certain infinite products and series involving age dependent model parameters. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

Ken Thompson's 6-man Statistical Graphs

This note reviews Ken Thompson's statistics on 6-man White wins with Black to move and explains the way in which the statistics have been graphed logarithmically.