Co-evolution of strategy and structure in complex networks with dynamical linking

Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. We provide analytic results for the limiting cases where linking dynamics is much faster than evolutionary dynamics and vice-versa, and show how the individual capacity of forming new links or severing inconvenient ones maps into the problem of strategy evolution in a well-mixed population under a different game. For intermediate ranges, we investigate numerically the detailed interplay determined by these two time-scales and show that the scope of validity of the analytical results extends to a much wider ratio of time scales than expected

'Everyone's so kind and jolly it boosts my spirits, if you know what I mean': A humanising perspective on exercise programme participation.

BACKGROUND: Maintaining a physically active lifestyle across the life course can add to an individual's health and well-being. Many people are insufficiently active to achieve these gains with a trend towards further decreases in activity as people age. Community-based group exercise programmes have been shown to be one means of increasing sustained activity levels for older people. AIM: To understand how and why older people sustain participation to community-based group exercise programmes from a humanising perspective. METHODS: A multiple-case study approach was employed to study three exercise programmes in the South-West of England. Data were collected through participant observation, focus groups and documentation. Data were analysed with deductive thematic analysis and mapped against the humanisation framework. RESULTS: Findings suggest that the humanising nature of these particular exercise programmes supported sustained participation. In these programmes, agency was evidenced in the way participants self-selected their level of exertion with exercises. There was freedom to be their unique selves and exercise within the limits of their insider challenges of an ageing body. Through this non-judgemental exercise environment, there was an embodied understanding of who they were as people. The exercise programme became part of their personal journey. This journey helped inform their future by enabling them to keep active and maintain independence, allowing them to continue engaging in the world. There was a sense of togetherness and belonging which led to feelings of homeliness as they found a sense of place within the group. The friendships they formed helped them make sense and add meaning to their experiences and personal health challenges. CONCLUSIONS: When planning exercise environments to support the long-term adoption of a sustained behaviour change, in the form of physical activity for older people, it is helpful to consider dimensions that make an individual feel human

Disordered Environments in Spatial Games

The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at $\rho^*$, separating a region with spatial chaos from one with localized, stable groups of cooperators.Comment: 6 pages, 5 figure

Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive systems. For well-mixed systems where interactions result in fitness reductions of the losers exceeding fitness gains of the winners, classical theory predicts that two strategies go extinct. The effects of spatial heterogeneity and dispersal rates on this outcome are analyzed using a general framework for evolutionary games in patchy landscapes. The analysis reveals that coexistence is determined by the rates at which dominant strategies invade a landscape occupied by the subordinate strategy (e.g. rock invades a landscape occupied by scissors) and the rates at which subordinate strategies get excluded in a landscape occupied by the dominant strategy (e.g. scissor gets excluded in a landscape occupied by rock). These invasion and exclusion rates correspond to eigenvalues of the linearized dynamics near single strategy equilibria. Coexistence occurs when the product of the invasion rates exceeds the product of the exclusion rates. Provided there is sufficient spatial variation in payoffs, the analysis identifies a critical dispersal rate $d^*$ required for regional persistence. For dispersal rates below $d^*$, the product of the invasion rates exceed the product of the exclusion rates and the rock-paper-scissor metacommunities persist regionally despite being extinction prone locally. For dispersal rates above $d^*$, the product of the exclusion rates exceed the product of the invasion rates and the strategies are extinction prone. These results highlight the delicate interplay between spatial heterogeneity and dispersal in mediating long-term outcomes for evolutionary games.Comment: 31pages, 5 figure

Evolutionary game dynamics in phenotype space

Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of space to evolutionary game dynamics: phenotype space. The population is well-mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies depend on distance in phenotype space. Individuals might behave differently towards those who look similar or dissimilar. Individuals mutate to nearby phenotypes. We study the `phenotypic space walk' of populations. We present analytic calculations that bring together ideas from coalescence theory and evolutionary game dynamics. As a particular example, we investigate the evolution of cooperation in phenotype space. We obtain a precise condition for natural selection to favor cooperators over defectors: for a one-dimensional phenotype space and large population size the critical benefit-to-cost ratio is given by b/c=1+2/sqrt{3}. We derive the fundamental condition for any evolutionary game and explore higher dimensional phenotype spaces.Comment: version 2: minor changes; equivalent to final published versio

Group-based pulmonary telerehabilitation is feasible, safe, beneficial and well-received in patients that have been hospitalised with Covid-19

Introduction Covid-19 has caused worldwide mass hospitalisation. The need for multi-disciplinary post-hospitalisation rehabilitation is becoming increasingly apparent and telerehabilitation has been endorsed. The aim of study was to investigate the feasibility and efficacy of pulmonary telerehabilitation for Covid-19 survivors.Methods A single centre, mixed-methods, fast-track (wait-list), randomised controlled trial of telerehabilitation for patients who have been hospitalised with Covid-19.Participants Forty patients discharged from two University Teaching Hospitals in the North of England. Interventions: Telerehabilitation consisted of twelve exercise classes, six education events and opportunity for peer support. Patients commenced telerehabilitation 14 days after randomisation in the fast-track group and 56 days after randomisation in the wait-list group.Outcome measures and results Descriptive and statistical improvements were noted is several clinical outcome measures. Exercise capacity increased from a median (Q1–Q3) 20 (14–24) sit-to-stand repetitions in one-minute at baseline to 25 (24–30) post-telerehabilitation. Breathlessness rated using the MRC changed from 3.5 (3–4) at baseline to 2 (1.5–3) post-telerehabilitation, with additional favourable outcomes noted in respiratory symptoms measured using numerical rating scales and visual analogue scales (VAS). Quality of life measured using the EQ-VAS improved from 55 (60–70) units at baseline to 70 (55–80) units following telerehabilitation. Improvements in fatigue (FACIT-F) and mood (HADS-D) were also observed. Natural recovery was observed in the wait-list group prior to receiving telerehabilitation, however, improvements were accelerated by early telerehabilitation in the fast-track group.Conclusions We have shown that group-based telerehabilitation is feasible, safe, beneficial and well-received in this population

Telerehabilitation for patients who have been hospitalised with covid-19: a qualitative study

PurposeThe aim of this qualitative study was to explore the views of participants of a group-based, supervised, telerehabilitation programme, following discharge from hospital with Covid-19. This study was part of a single-centre, fast-track (wait-list), randomised, mixed-methods, feasibility trial of telerehabilitation (Registration: Clinicaltrials.gov reference:285205).MethodsSemi-structured interviews were conducted over a virtual teleconference platform with 10 participants who took part in a telerehabilitation programme following Covid-19 after discharge from an acute hospital. Data were transcribed verbatim and analysed using thematic analysis.ResultsFive themes were important from the participant perspective: telerehabilitation programme as part of the Covid-19 journey; the telerehabilitation programme design and delivery; peer aspects; the role of the instructor; and the role of technology and online delivery.ConclusionsOverall, the telerehabilitation programme was a positive experience for participants. The instructors were central to this positive view as was the group nature of the programme. The group aspect was particularly important in supporting the broader perceived wellbeing gains, such as the sense of enjoyment and reduced social isolation. Several participants would have liked to have continued with the exercises beyond the six-week intervention indicating that the programme could be a way to help people sustain a physically active lifestyle.IMPLICATIONS FOR REHABILITATIONParticipants who were recovering from Covid-19 following hospital admission perceived the telerehabilitation to be a positive experience overall.The group aspect of the telerehabilitation programme was important in supporting the broader perceived wellbeing gains such as the sense of enjoyment and reduced social isolation.Telerehabilitation programmes for Covid-19 may need to include pathways for participants to continue to engage in exercise beyond the time-limited six-week intervention to support ongoing self-management

L-infinity algebra connections and applications to String- and Chern-Simons n-transport

We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L-infinity algebras and use it to study the obstruction theory of lifts through higher String-like extensions of Lie algebras. We find (generalized) Chern-Simons and BF-theory functionals this way and describe aspects of their parallel transport and quantization. It is known that over a D-brane the Kalb-Ramond background field of the string restricts to a 2-bundle with connection (a gerbe) which can be seen as the obstruction to lifting the PU(H)-bundle on the D-brane to a U(H)-bundle. We discuss how this phenomenon generalizes from the ordinary central extension U(1) -> U(H) -> PU(H) to higher categorical central extensions, like the String-extension BU(1) -> String(G) -> G. Here the obstruction to the lift is a 3-bundle with connection (a 2-gerbe): the Chern-Simons 3-bundle classified by the first Pontrjagin class. For G = Spin(n) this obstructs the existence of a String-structure. We discuss how to describe this obstruction problem in terms of Lie n-algebras and their corresponding categorified Cartan-Ehresmann connections. Generalizations even beyond String-extensions are then straightforward. For G = Spin(n) the next step is "Fivebrane structures" whose existence is obstructed by certain generalized Chern-Simons 7-bundles classified by the second Pontrjagin class.Comment: 100 pages, references and clarifications added; correction to section 5.1 and further example to 9.3.1 adde

Higher Structures, Self-Dual Strings and 6d Superconformal Field Theories

I summarize and discuss some recent results on formulating actions of six-dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review crucial aspects of this framework, such as $L_\infty$-algebras and corresponding kinematical data given by higher connections. We then show that there is a mathematically consistent non-Abelian extension of the self-dual string equation which satisfies many physical expectations. Our construction favors a particular higher gauge group leading us to higher principal bundles known as string structures. Using these, we manage to formulate a six-dimensional action which shares many properties with the famous $(2,0)$-theory but also still differs from it in some key points.Comment: 16 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 201

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.Comment: 26 pages, 6 figure