On the interaction of adaptive timescales on networks

The dynamics of real-world systems often involve multiple processes that influence system state. The timescales that these processes operate on may be separated by orders of magnitude or may coincide closely. Where timescales are not separable, the way that they relate to each other will be important for understanding system dynamics. In this paper, we present a short overview of how modellers have dealt with multiple timescales and introduce a definition to formalise conditions under which timescales are separable. We investigate timescale separation in a simple model, consisting of a network of nodes on which two processes act. The first process updates the values taken by the network’s nodes, tending to move a node’s value towards that of its neighbours. The second process influences the topology of the network, by rewiring edges such that they tend to more often lie between similar individuals. We show that the behaviour of the system when timescales are separated is very different from the case where they are mixed. When the timescales of the two processes are mixed, the ratio of the rates of the two processes determines the systems equilibrium state. We go on to explore the impact of heterogeneity in the system’s timescales, i.e., where some nodes may update their value and/or neighbourhood faster than others, demonstrating that it can have a significant impact on the equilibrium behaviour of the model

Dynamics and stability of small social networks

The choices and behaviours of individuals in social systems combine in unpredictable ways to create complex, often surprising, social outcomes. The structure of these behaviours, or interactions between individuals, can be represented as a social network. These networks are not static but vary over time as connections are made and broken or change in intensity. Generally these changes are gradual, but in some cases individuals disagree and as a result "fall out" with each other, i.e. , actively end their relationship by ceasing all contact. These "fallouts" have been shown to be capable of fragmenting the social network into disconnected parts. Fragmentation can impair the functioning of social networks and it is thus important to better understand the social processes that have such consequences. In this thesis we investigate the question of how networks fragment: what mechanism drives the changes that ultimately result in fragmentation? To do so, we also aim to understand the necessary conditions for fragmentation to be possible and identify the connections that are most important for the cohesion of the network. To answer these questions, we need a model of social network dynamics that is stable enough such that fragmentation does not occur spontaneously, but is simultaneously dynamic enough to allow the system to react to perturbations (i.e. , disagreements). We present such a model and show that it is able to grow and maintain networks exhibiting the characteristic properties of social networks, and does so using local behavioural rules inspired by sociological theory. We then provide a detailed investigation of fragmentation and confirm basic intuitions on the importance of bridges for network cohesion. Furthermore, we show that this topological feature alone does not explain which points of the network are most vulnerable to fragmentation. Rather, we find that dependencies between edges are crucial for understanding subtle differences between stable and vulnerable bridges. This understandingof the vulnerability of different network components is likely to be valuable for preventing fragmentation and limiting the impact of social fallou

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance

On the interaction of adaptive timescales on networks

The dynamics of real-world systems often involve multiple processes that influence system state. The timescales that these processes operate on may be separated by orders of magnitude or may coincide closely. Where timescales are not separable, the way that they relate to each other will be important for understanding system dynamics. In this paper, we present a short overview of how modellers have dealt with multiple timescales and introduce a definition to formalise conditions under which timescales are separable. We investigate timescale separation in a simple model, consisting of a network of nodes on which two processes act. The first process updates the values taken by the network’s nodes, tending to move a node’s value towards that of its neighbours. The second process influences the topology of the network, by rewiring edges such that they tend to more often lie between similar individuals. We show that the behaviour of the system when timescales are separated is very different from the case where they are mixed. When the timescales of the two processes are mixed, the ratio of the rates of the two processes determines the systems equilibrium state. We go on to explore the impact of heterogeneity in the system’s timescales, i.e., where some nodes may update their value and/or neighbourhood faster than others, demonstrating that it can have a significant impact on the equilibrium behaviour of the model