Complex Networks Analysis

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Many dynamical systems in physics, biology, ecology and social systems exhibit interesting, rich and complex behavior because their parts interact in a "networked" way. This means that parts (nodes in the network) are connected by links in such a way that only a fraction of possible connections exist. Examples of complex networks are transportation systems in which each node is a location and links correspond to direct traffic between nodes, gene-regulatory networks in which nodes correspond to genes and links represent their regulatory impact on one another, food webs in which nodes are species and links their ecological relationship, or social network where nodes represent people and links their propensity to interact or communicate.

In our group we are particularly interested in understanding topological features of large-scale networks, their evolution and growth, and understanding the imprint that network topologies have on dynamical processes that evolve on them .

Computational Social Science - Pervasive Data Analysis

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The internet, the world wide web, social media in combination with smart devices and sensors has changed the way we can assess human behavior in a qualitative way. Data generated by these technologies allows us to quantify human behavior, measure behavioral aspects with an entirely new precision and statistical reliability.

In our group we analyze pervasive, human generated data to unravel potential hidden regularities and fundamental laws of human behavior. We pioneered this type of analysis in 2006 when we analyzed the geographic movement patterns of millions of banknotes and later the movement patterns of travel bugs, trackable items that play a role in GPS treasure hunt known as geocaching. Currently we are analyzing contagion dynamics in online petition data, and virtual epidemics in a population of smart phones that are part of the large scale SensibleDTU experiment run by our collaborators at DTU Copenhagen in the lab of Sune Lehmann. We also analyze data collected by RFID sensors in hospital settings to better udnerstand hospital acquired diseases.

Computational Epidemiology

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Many non-equilibrium processes in nature are contagion processes that spread though a system after an initial, localized outbreak occurs somewhere. News, fads, fashion and also infectious diseases spread by a combination of replication and propagation. Large scale epidemic events, such as the 2003 worldwide spread of SARS, the 2009 H1N1 pandemic are events that can be understood in terms of mathematical contagion models.

A main focus of our research is the understanding of the dynamics of human infectious diseases. We develop computational models, new analytic and numerical techniques and large-scale quantitative and predictive computer simulations to study various aspects of the dynamics of epidemics. In our research we combine mathematical methods from nonlinear dynamics, stochastic processes, statistical physics, complex network theory, as well as systems biology. We are interested in numerous aspects of disease dynamics, ranging from phenomena related to single populations to the large-scale spatial spread of pandemics.

Anomalous Diffusion

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Many processes in nature can be described by ordinary diffusion processes. Whenever the fundamental laws of diffusion are violated we speak of anomalous diffusion. An increasing body of empirical evidence is accumulating that indicates that many systems that exhibit random motion are anomalous, particularly in biology. When processes spread "faster" than ordinary diffusion they are referred to as superdiffusive, when they are slower, they are called subdiffusive.

We develop and investigate models of anomalous diffusion processes using techniques such as fractional diffusion equations and continuous random walk theory. We are particularly interested when anomalous diffusion processes unfold in heterogeneous environments and when they can be linked to optimal search strategies.
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Robert Koch - Institute & Institute for Theoretical Biology, Humboldt University, Berlin