Invited speakers

Niloy Ganguly, IIT Kharagpur, IN
Theo Geisel, MPI Göttingen, GE
Annick Lesne, CNRS, LPTMC (Paris) & IGMM (Montpellier), FR
Roeland Merks, Leiden University, NL
Johannes Müller, TU München, GE
Tim Otto Roth, Cologne, GE
Marc Timme, TU Dresden, GE

Titles and abstracts

NeVAE: A Deep Generative Model for Molecular Graphs

Niloy Ganguly, IIT Kharagpur, India

Deep generative models have been praised for their ability to learn smooth latent representation of images, text, and audio, which can then be used to generate new, plausible data. However, current generative models are unable to work with molecular graphs due to their unique characteristics—their underlying structure is not Euclidean or grid-like, they remain isomorphic under permutation of the nodes labels, and they come with a different number of nodes and edges. In this paper, we propose NeVAE, a novel variational autoencoder for molecular graphs, whose encoder and decoder are specially designed to account for the above properties by means of several technical innovations. In addition, by using masking, the decoder is able to guarantee a set of valid properties in the generated molecules. Experiments reveal that our model can discover plausible, diverse and novel molecules more effectively than several state of the art methods. Moreover, by utilizing Bayesian optimization over the continuous latent representation of molecules our model finds, we can also find molecules that maximize certain desirable properties more effectively than alternatives.

Neuronal Networks as Discrete Dynamical Systems and
Dynamical Mechanisms of Information Routing in the Brain

Theo Geisel, Max Planck Institute for Dynamics and Self-Organization, Göttingen & Bernstein Center for Computational Neuroscience Göttingen, Germany.
Work in collaboration with A. Palmigiano, D. Battaglia, and F. Wolf

The collective spiking activity in the neuronal networks of our brain can be modeled in the form of pulse-coupled networks. They lead to complex discrete dynamical systems with peculiar behavior, e.g. a convergence to synchronized states in finite time – i.e. point attractors in phase space. In principle this can allow for fast switching between different states, yet the mechanisms that allow our brain to quickly switch between different information routing states have remained unclear.It is our brain’s ability to flexibly select relevant information and to route it along different paths, e.g. under selective attention, that constitutes part of its efficiency. How can it switch this routing so fast in a fraction of a second, if the neuronal connections can be reconfigured only slowly? We have recently uncovered a highly flexible mechanism which uses transient synchrony to dynamically rewire information paths in a few hundred milliseconds. [1] We show that models of cortical networks near the onset of oscillatory synchrony selectively route input signals despite the short duration of oscillatory bursts and the irregularity of neuronal firing. In multi-area networks with realistic anatomy we find that oscillatory gamma bursts spontaneously arise with matched timing and frequency and that they organize information flow by large-scale routing states.

[1] A. Palmigiano et al., Nature Neurosci. 20, 1014 (2017)

Topological determinants of excitation propagation and self-sustained activity on excitable networks

Annick Lesne, CNRS, LPTMC (Paris) & IGMM (Montpellier), France.
Work done with M.-T. Hütt (Jacobs Univ., Bremen, Germany) and C. Hilgetag (Hamburg Univ., Germany & Boston Univ., USA)

Discrete models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering.  In particular, we have investigated how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe  that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology.  Our findings are interpreted in the context of  self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.

Mathematical modeling of mechanical signaling in biological development

Roeland Merks, Leiden university, Netherlands

To form patterns and shapes during embryonic development, cells must carefully coordinate their behavior. It has become increasingly clear that, alongside exchange of chemical signals, mechanical cell-cell signaling plays a prominent role in biological development. Mechanical signals are often mediated by the extracellular matrix (ECM), the fibrous and jelly materials secreted by the cells that act as mechanical support in many tissues. In this talk I will present mathematical modeling approaches for mechanical regulation of single cell behavior and collective cell behavior by the ECM, showing examples of single cell behavior, blood vessel development, and somitogenesis. After discussing examples involving isotropic contractile cells and isotropic extracellular matrix materials, I will show our more recent attempts to add more biological detail. In particular, I will discuss how focal adhesions, the cells’ “hands” and “feet” by which they adhere to the matrix can help coordinate cellular responses to cell stiffness. Time permitting, I will also discuss anisotropic cell contraction, and our recent attempts to model fibrous ECMs. Altogether, our models help explain how local, cell-ECM interactions assist in coordinating cell behavior during multicellular patterning.

Population Genetics and Democratic Elections

Johannes Müller, TU München, Germany. Joint work with Volker Hösel, TUM, and Aurelien Tellier, TUM.

In recent years it became clear that the voter model can be used to model democratic elections. One point needs to be adapted: The Voter model on a connected, finite graph tends in the long run to an absorbing state, where only one opinion/party is left. Therefore, different forms of the noisy voter model have been introduced [1,2], where individuals choose with a certain probability one of the given opinions, without interaction with neighbours.

We propose a slightly different approach, based on the infinite allele model, that is well known in population genetics. With a certain probability, new groups are created, and old groups disappear. We show that this model (with slight adaptations to avoid opinions/parties with only few supporters) on a full graph has properties that are in line with election data from the US, Netherlands, France and Germany [3].
In the present talk we investigate the importance of the graph structure, with the aim to better understand mechanisms behind the variance in election data.
Literature:
1. Granovsky B.L., Madras N. (1995) The noisy voter model. Stoch. Process. Their. Appl. , 55:2343
2. Braha D., de Aguiar M. (2017) Voting contagion: Modeling and analysis of a century of U.S. presidential elections. PLoS ONE, 12:e0177970
3. Hösel, V., Müller, J. Tellier, A. (2019) Universality of neutral models: decision process in politics. Palgrave Comm., in press.

From Pixelsex to Mathematical Socialism – confronting cellular automata with real (artistic) live

Tim Otto Roth, Cologne, GE

Cellular automata (CA) modelling often applies a similar method like art history: visual analogies.  Such analogies are made comparing a pattern generated in silico with patterns in vivo respectively in ‘physica’. An inverse approach is to create physically automata and look for eventual implications of this real world implementation. In my presentation I will introduce a couple of my CA related artistic and composition works revealing a certain shift related to such a material translation by physico-mechanical apparatuses or human agents.
For instance I realized performances with musicians or dancers creating sound or spatiotemporal patterns reacting simply on their neighbours. Human actors reveal special forms of interferences as they can simply fail to execute correctly a neighbourhood rule. Such a failure is not necessarily aleatoric, but can show also certain patterns, as a recent project in India revealed creating hand knotted carpets according to CA rules – this was a very special social experiment at the very same time.
The most challenging task was to use automata for music composition. For a water organ I introduced a special way to analyse the dynamics of the agents: The activity of each pipe is translated into alternating water levels changing also the pipe’s timbre and pitch. Last but not least I will report about some collateral effects of such an artistic approach playing for instance with asymmetric topologies or developing a new way to describe the dynamics and robustness of automata system complementary to the Wolfram classification.

Future Mobility  : Self-Organization, Inefficiencies and Paradoxa

Marc Timme, Chair for Network Dynamics, TU Dresden

Human mobility together with human-centric transport, the transport of the goods humans produce, use and discard fundamentally underlies all aspects of our modern society. How we work, how we spend our free time, how we consume goods and services, how we use and need energy, how we protect our health and ensure environmental sustainability. Besides the large number of challenges existing today, including to contain climate change, to avoid traffic grid locks and to reduce emissions, a vast range of technological innovations impinges on mobility systems today. I highlight how questions on human mobility open up a fascinating research field on self-organization processes described by statistical physics and nonlinear dynamics of coupled multi-dimensional systems.
Models, simulations (and real world data) here bridge the regimes between few, discrete entities and infinite numbers of entities characterized, e.g., by continuous flows. First, I highlight why and how hysteresis persistently causes major inefficiencies across ride-hauling (taxis, ride sharing etc.)systems. Second, I illustrate how ride pooling may enable smoother door-to-door service without the need of owning a private car, also illustrating a recent pilot project we organized. Finally, I point out how tech-enabled routing systems may be optimized not for fastest individual route but for overall effectiveness if the routes of many travelers collectively minimize the total time wasted. I am happy to discuss the long list of open
questions on future mobility.

http://networkdynamics.info
This is work with Malte Schroeder, Philip Marszal, David Storch and others.