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.

Entropic risk analysis by a high level decision support system (e-FDSS) for construction SMEs

The method of entropy has been useful in evaluating inconsistency on human judgments. This paper illustrates an entropy-based decision support system called e-FDSS to the solution of multicriterion risk and decision analysis in projects of construction small and medium enterprises (SMEs). It is optimized and solved by fuzzy logic, entropy, and genetic algorithms. A case study demonstrated the use of entropy in e-FDSS on analyzing multiple risk criteria in the predevelopment stage of SME projects. Survey data studying the degree of impact of selected project risk criteria on different projects were input into the system in order to evaluate the preidentified project risks in an impartial environment. Without taking into account the amount of uncertainty embedded in the evaluation process; the results showed that all decision vectors are indeed full of bias and the deviations of decisions are finally quantified providing a more objective decision and risk assessment profile to the stakeholders of projects in order to search and screen the most profitable projects.

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.