Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation

Copyright © 2011 Springer. The final publication is available at www.springerlink.comWe consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Understanding clinician attitudes towards implementation of guided self-help cognitive behaviour therapy for those who hear distressing voices: using factor analysis to test normalisation process theory

Background The Normalisation Process Theory (NPT) has been used to understand the implementation of physical health care interventions. The current study aims to apply the NPT model to a secondary mental health context, and test the model using exploratory factor analysis. This study will consider the implementation of a brief cognitive behaviour therapy for psychosis (CBTp) intervention. Methods Mental health clinicians were asked to complete a NPT-based questionnaire on the implementation of a brief CBTp intervention. All clinicians had experience of either working with the target client group or were able to deliver psychological therapies. In total, 201 clinicians completed the questionnaire. Results The results of the exploratory factor analysis found partial support for the NPT model, as three of the NPT factors were extracted: (1) coherence, (2) cognitive participation, and (3) reflexive monitoring. We did not find support for the fourth NPT factor (collective action). All scales showed strong internal consistency. Secondary analysis of these factors showed clinicians to generally support the implementation of the brief CBTp intervention. Conclusions This study provides strong evidence for the validity of the three NPT factors extracted. Further research is needed to determine whether participants’ level of seniority moderates factor extraction, whether this factor structure can be generalised to other healthcare settings, and whether pre-implementation attitudes predict actual implementation outcomes

Aerobic Exercise during Pregnancy and Presence of Fetal-Maternal Heart Rate Synchronization

It has been shown that short-term direct interaction between maternal and fetal heart rates may take place and that this interaction is affected by the rate of maternal respiration. The aim of this study was to determine the effect of maternal aerobic exercise during pregnancy on the occurrence of fetal-maternal heart rate synchronization.In 40 pregnant women at the 36th week of gestation, 21 of whom exercised regularly, we acquired 18 min. RR interval time series obtained simultaneously in the mothers and their fetuses from magnetocardiographic recordings. The time series of the two groups were examined with respect to their heart rate variability, the maternal respiratory rate and the presence of synchronization epochs as determined on the basis of synchrograms. Surrogate data were used to assess whether the occurrence of synchronization was due to chance.In the original data, we found synchronization occurred less often in pregnancies in which the mothers had exercised regularly. These subjects also displayed higher combined fetal-maternal heart rate variability and lower maternal respiratory rates. Analysis of the surrogate data showed shorter epochs of synchronization and a lack of the phase coordination found between maternal and fetal beat timing in the original data.The results suggest that fetal-maternal heart rate coupling is present but generally weak. Maternal exercise has a damping effect on its occurrence, most likely due to an increase in beat-to-beat differences, higher vagal tone and slower breathing rates

Modification of Dust Grain Structure by Sputtering

We have applied the SRIM computer code to study the sputtering of some likely astrophysical grain materials, and we have shown that selective embedding of metallic projectiles offers a partial explanation of gas-phase depletions. We show that supernova shockwaves sweep a significantly larger mass of interstellar gas per unit time than the shockwaves generated by outflows in star-forming regions. We apply our sputtering model to the bombardment levels expected in a supernova shock, and show that net embedding may dominate over net sputtering, leading to grain growth under some circumstances, particularly when the bombarding gas is enriched with metals from the supernova progenitor star. A combination of short cooling times and net embedding mean that it is possible for a type II supernova to generate more dust that it destroys, and we conclude that, in general, the sputtering process often leads to a compositional change in the grain material rather than simply to grain erosion.Comment: tex file and nine postscript figure in tar.gz archiv