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MIRaW - Mathematics Interdisciplinary Research

Monday 18 May 2009
Tasters in complex systems

Organiser: Markus Kirkilionis


Mark Chaplain (Dundee) Multiscale modelling of cancer growth and development

Cancer (i.e. a malignant solid tumour) is a complex multi-scale phenomenon ranging from the genetic to the population levels. Solid tumours, such as carcinoma (which make up over 90% of all cancers), growth through two main growth phases - the avascular phase and the vascular phase. In the initial avascular phase, growth is determined by the diffusion of external nutrients (e.g. oxygen) and the solid tumours grow as small multicellular spheroids up to a size of around 2mm in diameter. At this stage, angiogenic factors are secreted by hypoxic cancer cells and induce the formation of new blood vessels through a process known as angiogenesis. These new blood vessels may connect with the cancer cells, thus providing them with extra nutrients and also an escape route into the main blood system. Thus the second stage of growth - vascular growth - is initiated. Additionally, cancer cells possess the ability to locally degrade and invade the surrounding tissues, thereby facilitating spread. Access to the blood system and lymph system through angiogenesis and invasion provides cancers with the means to spread to distant parts of the host (metastasis) and to set up secondary tumours (metastases). In this talk we will provide a review of several multiscale models for avascular growth, tumour-induced angiogenesis, invasion and metastasis.

Holger Kantz (Dresden) Extreme Events in Complex Systems

Systems with a complex time evolution possess the inherent feature to generate, either in response to tiny perturbations or even autonomously, large fluctuations. Short time large deviations of the system from its normal state are called extreme events. Different dynamical mechanisms lead to different statistical properties and have their implications for prediction and mitigation. We present some phenomena, simple models, and time series approaches.

Jeffrey Johnson (Open Univ) Multilevel Hypernetworks

Networks are increasingly used to investigate relational structure in complex systems. Surprisingly the focus has been mainly on networks of binary relations between pairs of things, when there are many examples of relations between many things. Examples include the combination of piano, violin, viola and cello that form a piano quartet, the eleven players that form a football team, or the words that make a sentence. Relations between n > 2 things form higher dimensional networks with higher dimensional connectivities that constrain the dynamic flows of systems activity. These are called hypernetworks. It will be shown that hypernetworks provide a natural means of representing multilevel structure, supporting bottom-up and top-down flows of influence. Furthermore the structure hypernetworks allow a structural definition of system time related to but different from clock time, and represents some aspects of the dynamics more naturally. The presentation will introduce the main ideas and focus on examples and applications rather than technical details.

Francois Képès (Paris) Epigenomics and Morphodynamics

Biologists are fond of wiring diagrams abstracting the system's components and their interactions. Network-based approaches extend this common viewpoint, while providing a well-paved path to more formal analysis. In particular, a simple topological or dynamical analysis may sometimes allow to reject a biologist's model with little effort. A deeper analysis may shed light on the plausible mechanisms of a well-described and poorly understood phenomenon. Besides this explanatory capacity, the analysis may in different settings be of predictive value or increase the efficiency of subsequent experimental testing. However, what often appears on the biologist's cartoons and is not directly amenable to network-based analysis stricto sensu is the spatial aspect of the biological process under scrutiny. The spatial development of regulatory networks will be emphasized in this talk.

Markus Kirkilionis, Regulation, Feedback, Networks and Stability: Essential Complex Systems?

The talk introduces a couple of concepts and ideas to map 'system components' and their temporal interaction with other such components to different non-spatially explicit mathematical models. Concrete examples are chemical molecular interactions, but on a more abstract level genes, animal species, humans, firms, or supply chains can all be modelled in a very similar fashion. After setting the conceptual framework a number of unsolved problems will be introduced which are highly interesting for applications and mathematically challenging. The discussion will end with the question whether these dynamical network models can serve as 'paradigm' or 'essential' complex systems.

Andras Lórincz (Budapest) The Turing game approach to cognition, serious gaming and social networks

In spite of the tremendous efforts devoted to it, the aim of ‘thinking machines’, that is, machine intelligence comparable to human intelligence has remained a dream. It is also unclear what artificial intelligence is missing and how the progress could be measured. We take a novel approach that elaborates the well known Turing Test by measuring machine intelligence through its participation in a goal oriented framework. Our approach builds on the hypothesis that the emergence of complex interactions requires mind models: participants should theorize about the intentions of the others in order to jointly optimize outcomes in the future. Also, optimization can be easily accomplished by any of the participants if situation specific context dependent ‘language’ appears. To demonstrate these ideas, we replace the classical Turing Test with interactions framed around computer games. We do so by creating virtual worlds we call Turing Games, in which players – human or machine – must collaborate to achieve common goals (Fig. 1).


Figure 1 Example: multiplayer PacMan game

Analyzing the development of collaborative networks will enable us to objectively measure the asymmetries in the roles of human and machine players, this way quantifying the progress of various cognitive architectures. There are indirect potentials in this approach. Technical aspects: the webcam, ECG, dry electrode EEG, Wii remote (accelerometers and infrared pointing devices) can help handicapped and elderly people to interact with the (virtual) environment in various ways. We have been developing tools for severely handicapped, non-speaking but speech understanding children. Serious gaming aspect: We can set up game-like environments for practicing certain situations. Novel wizards can be introduced for software and hardware, including augmented reality using see-through HMD. Social (network) aspect: games can form communities, can entertain people in isolation, can be used for training, enables remote Internet based work of different kinds.

Robert MacKay, The Mathematics of Emergence

"Emergence" has captured the imagination of many, yet arguments about what it is tend to create more heat than light. I propose a mathematical formulation which will allow the subject to develop. A complex system is something with many interdependent components. What emerges from a complex system is one or more probability distributions governing the statistics of typical realisations. I call them "phases", in analogy with the phases of matter. The amount of emergence in a phase is its distance from the set of product distributions over components. An indecomposable system exhibits strong emergence if there is more than one possible phase; the amount of strong emergence is the diameter of the set of phases. Armed with this framework, one can address questions like what are conditions for strong emergence or not, how does the set of phases change with parameters, what correlations are exhibited, how robust is a phase to shocks, how can one design a system to exhibit a phase with desired features...

Felix Reed-Tsochas (Oxford), A bipartite cooperation model for ecological and social networks

The starting point for this talk are some simple stochastic models of ecological networks, which have had great success in accounting for the overall properties of consumer-resource interactions in real food webs. The links in the food webs to which these models have been applied correspond to prey-predator interactions, and are typically treated as unweighted and undirected. More recently, much attention in theoretical ecology has focused on mutualistic interactions, since the co-evolutionary processes generating them are believed to be an important source of biodiversity. We propose a simple stochastic model, the bipartite cooperation model, which generates co-operative relationships between two distinct sets of actors starting from three empirical input parameters. Compared to other (generally more complicated) models that have been proposed, the bipartite cooperation model is able to reproduce a larger number of the structural features observed in plant-animal mutualistic networks obtained from ten empirical pollination datasets. More surprisingly, the bipartite cooperation model does an equally good job accounting for the observed structural features of a network of manufacturer-contractor relationships, based on a dataset of 700,000 transactions over almost 20 years for the New York garment industry. The bipartite co-operation model may therefore provide an explanation for the surprising similarity that we observe for certain organisational and ecological networks, and is likely to apply to other systems as well.