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.

Biodegradation of polyethylene glycol (PEG) in three tropical soils using radio labelled PEG

Polyethylene glycol (PEG) may be added to forage based diets rich in tannins for ruminant feeding because it binds to tannins and thus prevent the formation of potentially indigestible tannin-protein complexes. The objective of this work was to determine the in vitro biodegradation (mineralization, i.e., complete breakdown of PEG to CO2) rate of PEG. C-14-Polyethylene glycol (C-14-PEG) was added to three different tropical soils (a sandy clay loam soil, SaCL; a sandy clay soil, SaC; and a sandy loam soil, SaL) and was incubated in Bartha flasks. Free PEG and PEG bound to tannins from a tannin rich local shrub were incubated under aerobic conditions for up to 70 days. The biodegradation assay monitored the (CO2)-C-14 evolved after degradation of the labelled PEG in the soils. After incubation, the amount of (CO2)-C-14 evolved from the C-14-PEG application was low. Higher PEG mineralization values were found for the soils with higher organic matter contents (20.1 and 18.6 g organic matter/kg for SaCL and SaC, respectively) than for the SaL soil (11.9 g organic matter/kg) (P < 0.05). The extent of mineralization of PEG after 70 days of incubation in the soil was significantly lower (P < 0.05) when it was added as bound to the browse tannin than in the free form (0.040 and 0.079, respectively). (c) 2005 Elsevier B.V. All rights reserved.

Synthesis of labelled dihydroartemisinic acid

[15-(CH3)-C-13-H-2]-Dihydroartemisinic acid (2a), [15-(CH3)-H-2]-dihydroartemisinic acid (2b) and [15-(CH3)-C-13]-dihydroartemisinic acid (2c) have been obtained in good yield and high isotopic enrichment by a reconstructive synthesis from artemisinin. These labelled compounds were designed to be used in biosynthetic experiments to determine the origins of artemisinin and other sesquiterpene natural products from Artemisia annua. (C) 2003 Elsevier Ltd. All rights reserved.

Development of a liquid chromatographic time-of-flight mass spectrometric method for the determination of unlabelled and deuterium-labelled alpha-tocopherol in blood components

A method is described for the analysis of deuterated and undeuterated alpha-tocopherol in blood components using liquid chromatography coupled to an orthogonal acceleration time-of-flight (TOF) mass spectrometer. Optimal ionisation conditions for undeuterated (d0) and tri- and hexadeuterated (d3 or d6) alpha-tocopherol standards were found with negative ion mode electrospray ionisation. Each species produced an isotopically resolved single ion of exact mass. Calibration curves of pure standards were linear in the range tested (0-1.5 muM, 0-15 pmol injected). For quantification of d0 and d6 in blood components following a standard solvent extraction, a stable-isotope-labelled internal standard (d3-alpha-tocopherol) was employed. To counter matrix ion suppression effects, standard response curves were generated following identical solvent extraction procedures to those of the samples. Within-day and between-day precision were determined for quantification of d0- and d6-labelled alpha-tocopherol in each blood component and both averaged 3-10%. Accuracy was assessed by comparison with a standard high-performance liquid chromatography (HPLC) method, achieving good correlation (r(2) = 0.94), and by spiking with known concentrations of alpha-tocopherol (98% accuracy). Limits of detection and quantification were determined to be 5 and 50 fmol injected, respectively. The assay was used to measure the appearance and disappearance of deuterium-labelled alpha-tocopherol in human blood components following deuterium-labelled (d6) RRR-alpha-tocopheryl acetate ingestion. The new LC/TOFMS method was found to be sensitive, required small sample volumes, was reproducible and robust, and was capable of high throughput when large numbers of samples were generated. Copyright (C) 2003 John Wiley Sons, Ltd.

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.