Stochastic oscillations of adaptive networks: application to epidemic modelling

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system's behaviour. In this article we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the structure of the network exhibits stochastic oscillations in response to fluctuations in the disease dynamic.Comment: 11 pages, 4 figure

Patterns of cooperation: fairness and coordination in networks of interacting agents

We study the self-assembly of a complex network of collaborations among self-interested agents. The agents can maintain different levels of cooperation with different partners. Further, they continuously, selectively, and independently adapt the amount of resources allocated to each of their collaborations in order to maximize the obtained payoff. We show analytically that the system approaches a state in which the agents make identical investments, and links produce identical benefits. Despite this high degree of social coordination some agents manage to secure privileged topological positions in the network enabling them to extract high payoffs. Our analytical investigations provide a rationale for the emergence of unidirectional non-reciprocal collaborations and different responses to the withdrawal of a partner from an interaction that have been reported in the psychological literature.Comment: 20 pages, 8 figure

Biocompatibility of Common Implantable Sensor Materials in a Tumor Xenograft Model

Real-time monitoring of tumor microenvironment parameters using an implanted biosensor could provide valuable information on the dynamic nature of a tumor's biology and its response to treatment. However, following implantation biosensors may lose functionality due to biofouling caused by the foreign body response (FBR). This study developed a novel tumor xenograft model to evaluate the potential of six biomaterials (silicon dioxide, silicon nitride, Parylene-C, Nafion, biocompatible EPOTEK epoxy resin, and platinum) to trigger a FBR when implanted into a solid tumor. Biomaterials were chosen based on their use in the construction of a novel biosensor, designed to measure spatial and temporal changes in intra-tumoral O2 , and pH. None of the biomaterials had any detrimental effect on tumor growth or body weight of the murine host. Immunohistochemistry showed no significant changes in tumor necrosis, hypoxic cell number, proliferation, apoptosis, immune cell infiltration, or collagen deposition. The absence of biofouling supports the use of these materials in biosensors; future investigations in preclinical cancer models are required, with a view to eventual applications in humans. To our knowledge this is the first documented investigation of the effects of modern biomaterials, used in the production of implantable sensors, on tumor tissue after implantation. © 2018 The Authors. Journal of Biomedical Materials Research Part B: Applied Biomaterials published by Wiley Periodicals, Inc. J Biomed Mater Res Part B, 2018

Moment-closure approximations for discrete adaptive networks

Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter model. While already the simplest schemes provide reasonable qualitative results, even very complex and sophisticated approximations fail to capture the dynamics quantitatively. We then perform a detailed analysis that identifies the emergence of specific correlations as the reason for the failure of established approaches, before presenting a simple approximation scheme that works best in the parameter range where all other approaches fail. By combining a focused review of published results with new analysis and illustrations, we seek to build up an intuition regarding the situations when existing approaches work, when they fail, and how new approaches can be tailored to specific problems. © 2013 Elsevier B.V. All rights reserved

Reasons for (Non)Participating in a Telephone-Based Intervention Program for Families with Overweight Children

Willingness to participate in obesity prevention programs is low; underlying reasons are poorly understood. We evaluated reasons for (non)participating in a novel telephone-based obesity prevention program for overweight children and their families. percentile) aged 3.5–17.4 years were screened via the CrescNet database, a representative cohort of German children, and program participation (repetitive computer aided telephone counseling) was offered by their local pediatrician. Identical questionnaires to collect baseline data on anthropometrics, lifestyle, eating habits, sociodemographic and psychosocial parameters were analyzed from 433 families (241 participants, 192 nonparticipants). Univariate analyses and binary logistic regression were used to identify factors associated with nonparticipation. percentile) was higher in participants (58.9% vs.38%,p<0.001). Participating girls were younger than boys (8.8 vs.10.4 years, p<0.001). 87.3% and 40% of participants, but only 72.2% and 24.7% of nonparticipants, respectively, reported to have regular breakfasts (p = 0.008) and 5 regular daily meals (p = 0.003). Nonparticipants had a lower household-net-income (p<0.001), but higher subjective physical wellbeing than participants (p = 0.018) and believed that changes in lifestyle can be made easily (p = 0.05).An important reason for nonparticipation was non-awareness of their child's weight status by parents. Nonparticipants, who were often low-income families, believed that they already perform a healthy lifestyle and had a higher subjective wellbeing. We hypothesize that even a low-threshold intervention program does not reach the families who really need it

Adaptive-network models of collective dynamics

Complex systems can often be modelled as networks, in which their basic units are represented by abstract nodes and the interactions among them by abstract links. This network of interactions is the key to understanding emergent collective phenomena in such systems. In most cases, it is an adaptive network, which is defined by a feedback loop between the local dynamics of the individual units and the dynamical changes of the network structure itself. This feedback loop gives rise to many novel phenomena. Adaptive networks are a promising concept for the investigation of collective phenomena in different systems. However, they also present a challenge to existing modelling approaches and analytical descriptions due to the tight coupling between local and topological degrees of freedom. In this work, which is essentially my PhD thesis, I present a simple rule-based framework for the investigation of adaptive networks, using which a wide range of collective phenomena can be modelled and analysed from a common perspective. In this framework, a microscopic model is defined by the local interaction rules of small network motifs, which can be implemented in stochastic simulations straightforwardly. Moreover, an approximate emergent-level description in terms of macroscopic variables can be derived from the microscopic rules, which we use to analyse the system’s collective and long-term behaviour by applying tools from dynamical systems theory. We discuss three adaptive-network models for different collective phenomena within our common framework. First, we propose a novel approach to collective motion in insect swarms, in which we consider the insects’ adaptive interaction network instead of explicitly tracking their positions and velocities. We capture the experimentally observed onset of collective motion qualitatively in terms of a bifurcation in this non-spatial model. We find that three-body interactions are an essential ingredient for collective motion to emerge. Moreover, we show what minimal microscopic interaction rules determine whether the transition to collective motion is continuous or discontinuous. Second, we consider a model of opinion formation in groups of individuals, where we focus on the effect of directed links in adaptive networks. Extending the adaptive voter model to directed networks, we find a novel fragmentation mechanism, by which the network breaks into distinct components of opposing agents. This fragmentation is mediated by the formation of self-stabilizing structures in the network, which do not occur in the undirected case. We find that they are related to degree correlations stemming from the interplay of link directionality and adaptive topological change. Third, we discuss a model for the evolution of cooperation among self-interested agents, in which the adaptive nature of their interaction network gives rise to a novel dynamical mechanism promoting cooperation. We show that even full cooperation can be achieved asymptotically if the networks’ adaptive response to the agents’ dynamics is sufficiently fast

A dynamical mechanism for the evolution and breakdown of cooperation in the snowdrift game in adaptive networks

We present a novel dynamical mechanism promoting cooperation in the snowdrift game on an adaptive network. In infinite systems, asymptotic full cooperation can be achieved, while sudden breakdowns of highly cooperative states are observed in finite systems