### ZiF Cooperation Group

# Discrete and Continuous Models in the Theory of Networks

#### October 2012 - September 2017

##### Convenors: Delio Mugnolo (Hagen, GER), Fatihcan M. Atay (Ankara, TUR) und Pavel Kurasov (Stockholm, SWE)

##### Convenors

Fatihcan M. Atay Bilkent University Ankara | Turkey |
Pavel KurasovU Stockholm | Sweden |
Delio
Mugnolo U Hagen | Germany |

##### Members

*Ginestra Bianconi*

Ginestra Bianconi's research interest are fundamental questions in network theory and statistical mechanics
with applications to social networks, neuroscience and
technological communication networks. In 2001 she has found a mapping between evolving networks such as the
World-Wide-Web and a Bose gas able to predict the so called Bose-Einstein condensation in complex networks.
Recently she has been working on entropy measures for complex networks, on classical and quantum phase
transitions in networks, on the characterization of multiplex networks and on evolutionary dynamics.

*Till Becker*

Till Becker is currently Junior Research Group Leader of the Production Systems and Logistic Systems group at the Department of
Production Engineering at University of Bremen. He graduated in Information Systems from University of Münster and received his PhD in International
Logistics from Jacobs University. His research interests include decentralized control approaches in manufacturing and logistics, the investigation of
relations between topology and dynamics in complex manufacturing networks, and robustness in manufacturing systems. He uses methods from queuing theory,
graph theory, computer simulation, and statistics for his research.

*Jonathan Breuer*

Jonathan Breuer is currently senior lecturer at the Einstein Institute of Mathematics at the Hebrew
University of Jerusalem in Israel.
His research focuses on the spectral theory of Schroedinger operators and Jacobi matrices. In the context of
graphs, he has been interested in studying graphs for which the Laplacian has unexpected spectral properties
(such as singular continuous spectrum).
Recently, his research has also focused on understanding various connections with concepts and problems from
random matrix theory.

*Radu Cascaval*

Radu Cascaval's research is focused on the development and analysis of mathematical models arising in the
context of physical and biological applications, through an underlying spatial network, such as the
cardiovascular system. Of special interest are models which capture the nonlinear and dispersive nature of
the wave propagation. Boundary and distributed control problems are also being investigated, with the
ultimate goal of understanding wave phenomena exhibited.

*Mareike Fischer*

Mareike Fischer works as a junior professor for discrete biomathematics at the University of Greifswald, Germany.
Her main research focus is mathematical phylogenetics. In particular, she analyzes and compares methods to derive
evolutionary trees from sequence data such as DNA as well as tree metrics, supertree methods and so forth. She also
works on so-called phylogenetic networks, which are used by biologists to display events like horizontal gene transfer or hybridization.

*Júlia Gallinaro*

Júlia Gallinaro is a PhD student at the Bernstein Center Freiburg, and works with computational neuroscience. The
main topic of her research is neogenesis of neurons and mechanisms of their functional insertion into existing
networks. Her research is being performed with the use of numerical simulation and mathematical analysis of
large-scale spiking neuronal networks that undergo structural changes.

*Jiao Gu*

Jiao Gu is a PhD student in Max-Planck Institute for Mathematics in the Sciences in Leipzig, and mainly
works on bioinformatics. Her research now is centered around the spectral analysis on graphs and looking for
the graph distance between graphs in the sense of structure. She is also working on the analysis on the
networks generated from the database, based on the spectral methods.

*Bobo Hua*

Bobo Hua is working as a Postdoc at Max Planck Institute for Mathematics in the Sciences in Leipzig. His
research interests include discrete geometric analysis and analysis on metric measure spaces. He is now
working on the spectral theory of discrete Laplacians on infinite
graphs. The main methods are from continuous models such as geometric
analysis on manifolds. He also wants to find out the features of
spectral theory on discrete spaces.

*Stojan Jovanovic*

Stojan Jovanovic received his Master's degree in mathematics from the University of Belgrade, Serbia in 2011. The subject of his thesis was the theory of
stochastic integration and stochastic differential equations with respect to general local martingales. In 2012 he became a PhD student in the EuroSPIN joint
European doctoral programme in computational neuroscience. His current research interests include the evolution of statistics of self-exciting point processes and the
emergence of higher-order correlations through synaptic interactions in neural networks.

*Christopher Kaiser-Bunbury*

Christopher Kaiser-Bunbury is an network ecologist with a degree in Biology and PhD in Environmental
Sciences from the University of Zurich, Switzerland. His main research interests lie in the application of a
network approach to the understanding of interaction dynamics in ecological communities and, ultimately, the
conservation and restoration of ecosystems. He aims to identify the drivers of interactions in mutualistic
networks that are key to understanding biodiversity organisation and persistence. Mutualistic networks can
be depicted with bipartite graphs with plants on one level and animals, such as pollinators or seed
dispersers, on the other level. Links between the nodes (i.e., species) represent interaction between plants
and animals. Predicting dynamics in pair-wise interactions based on some general rules on assembly and
disassembly of links between nodes may allow us to use interaction networks as a tool to assess the
functioning and integrity of ecosystems. Chris uses both a stochastic modelling approach and community
experiments in the field to shed light on the complexity of biotic networks. He is currently working with
Nico Blüthgen's group on Ecological Networks at TU Darmstadt.

*Kosmas Kosmidis*

Kosmas Kosmidis is a fesearch fellow in the Computational Systems Biology Lab of Jacobs University Bremen and at at the Computing & Communications Center and the Computational Physics lab at the University of Thessaloniki.

His scientific field is the Computational Physics of Complex Systems. In the past, he has worked on several modern and interdisciplinary physics topics including various aspects of Mathematical and Computational modeling of Complex systems, Percolation, Random walks, Fractals, Applied Diffusion Models and Controlled Drug Release, models of the physics of Language and even Continuum Mechanics with emphasis on Gradient Elasticity. His current research is in Systems Biology and
involves the properties of transcription regulatory networks.

*Annick Lesne*

Annick Lesne is a senior researcher in the Lab. of Theoretical Physics of Condensed Matter (LPTMC, CNRS-University Paris 6)
and at the Institute of Molecular Genetics of Montpellier (IGMM). With a background in mathematics and theoretical physics,
her research focuses since fifteen years on biological questions. In collaboration with experimentalists, she develops
multiscale and network models to understand the functional architecture of living systems and their regulation.

*Wenlian Lu*

Wenlian Lu is a professor in Mathematics at Centre for Computational Systems Biology and School of Mathematical Science, Fudan University,
China. He was a Marie Curie Research Fellow at the Department of Computer Science, The University of Warwick, United Kingdom from October 2012
to September 2014. His research interests focus on modeling and dynamical analysis of neural network, complex network systems and epidemics on
cyber networks, and integrate analysis of brain imaging, biophysical neuronal network model and genetic data.

*Gabriela Malenova*

Gabriela Malenova is currently working as a resercher at Institute of Analysis of Ulm University. Her main
field are quantum graphs, more precisely their spectrum and its correspondence to metric graphs. Spectral
gaps are of central interest. She has also developed numerical tools for computation of the quantum graphs
spectra. She is starting her PhD in Mathematical Modeling at KTH in Stockholm.

*Benjamin Mauroy*

Benjamin Mauroy's research aims to understand oxygen exchange and transport in mammals and the underlying
optimizations of the lungs and vascular network induced by evolution. His research focus on the role of
geometry and physics on such living systems. He is developing mathematical and numerical multi-scale models,
from the organ (bronchi) down to the cells (red blood cell). He is studying lungs and vascular network
morphogenesis and how oxygen is transported, in an efficient way, through the lungs, across the air/blood
barrier and through the vascular network. In parallel, he uses population dynamics to study how the
requirement of robustness in lungs and blood network functions can interact with natural selection.

*Fumito Mori*

Fumito Mori is working as a Postdoc at Fritz Haber Institute of the Max Planck Society.
His research aims to clarify relations between network structure and dynamics on complex networks.
He has derived necessary condition for frequency synchronization in network structure. Recently, he
is investigating evolutionary network design for precise oscillations in fluctuating genetic systems.

*Gabor Pete*

Gabor Pete's interests are currently focused on the following topics: critical two-dimensional random
systems and their continuum scaling limits, with emphasis on near-critical and dynamical behaviour and
noise-sensitivity; random walks, percolation, and other spatial models on graphs; relations between
probabilistic, geometric, and algebraic properties of Cayley graphs of infinite groups and of locally
convergent graph sequences.

*Mats-Erik Pistol*

Mats-Erik Pistol´s research interest are three-fold - optical
spectroscopy of semiconductor nanostructures, numerical simulations of
nanostructures and the basic theory of electron structure calculations.
He is interested in applying pure mathematics to physics problems, for
instance how can the theory of quantum graphs be used in bandstructure
calculations of semiconductors. Another interest is selfadjoint
extensions of operators commonly used in physics, in particular for
those used in bandstructure calculations. Experimentally he is presently investigating the optical response
of periodic arrays of coupled semiconductor nanowires.

*Patricia Alonso Ruiz*

Patricia Alonso Ruiz is currently working as a Postdoc at the Stochastics Department of Ulm University. She
is interested in stochastic modelling, Analysis on fractals via Dirichlet and resistance forms, and the
Einstein relation on such objects. The analytical techniques used come both from discrete and continuous
one-dimensional graph structures. She has recently started also focusing on the stochastic implications of
these fractal models.

*Sadra Sadeh*

Sadra Sadeh is a PhD student of Computational Neuroscience at the Bernstein Center Freiburg and Faculty of Biology, University of
Freiburg. Among the main research interests are link between structure and dynamics in cortical networks, and functional properties of sensory
networks. To address these problems, large-scale simulation of neuronal networks are recruited, and mathematical models are developed to analyze
the dynamics of the complex networks.

*Ruben Sanchez-Garcia*

Ruben Sanchez-Garcia is a Lecturer in Mathematical Sciences at the University of Southampton (UK). He has a pure mathematics background
in Algebraic Topology, although he is currently working in the interface between pure and applied mathematics, particularly mathematical aspects of complex networks, and
topological data analysis. He is interested in symmetries of complex networks and how they relate to the network structure and spectrum, in the stability of dynamical
systems supported by a given network, in certain aspects of spectral clustering, and in the generalisation of some network techniques to higher dimensional analogues.
He has also collaborated with power engineers working on preventing wide-area blackouts of electrical power by a preemptive islanding of the transmission network using graph theoretic techniques.

*Jonathan Schiefer*

Jonathan Schiefer studied mathematics and recently started his PhD in computational neuroscience at the Bernstein Center Freiburg. His current
research interest is the development of cortical networks during a movement. Therefore cortical networks of neural populations are
reconstructed out of data measured during a movement and the development of the connections is studied.

*Liu Shiping*

Shiping Liu is a PhD student in Max-Planck Institute for Mathematics in the Sciences in Leipzig and got his
degree in Mathematics. His research interests are currently focused on the synthetic curvature ideas for
discrete and continuous metric spaces and their applications to the analytic properties of the underlying
spaces. He is working on spectral theory of finite graphs, interaction of curvature and other basic concepts
like local clustering coefficient. The tools include optimal transport, construction of neighborhood graphs,
coupling method, and ideas, intuitions from Riemannian geometry.

*Leszek Sirko*

Leszek Sirko is the head of the Quantum Chaos Group at the Institute of Physics of the Polish Academy of Sciences, which studies manifestations of classical chaos in the corresponding quantum or wave-dynamical systems. Experimental and theoretical investigations of the group include the study of the statistical fluctuation properties of the eigenvalues, the manifestation of periodic orbits in quantum spectra, quantum chaotic scattering and recently isoscattering networks and graphs.

*Dimitri
Volchenkov*

Dimitri Volchenkov obtained his Ph.D. in theoretical physics at the
Saint-Petersburg State University (Russia) and habilitated in CNRS
Centre de Physique Theorique (Marseille, France). He worked in Texas A&M University (USA), Zentrum für
Interdisziplinäre Forschung (Bielefeld, Germany), Centre de Physique Theorique (Marseille, France),
Bielefeld-Bonn Stochastic Research Center (Germany). He is a research
scientist at the Center of Excellence Cognitive Interaction Technology
(Bielefeld, Germany). His research interests are the nonperturbative
quantum-field theory methods in stochastic dynamics and plasma
turbulence, urban spatial networks and their impact on poverty and
environments, stochastic analysis of complex networks, and physics of dance.

*Verena Wolf*

Our research is mainly concerned with stochastic modelling and analysis
techniques where
a particular focus is on Markov models with discrete state spaces and
their applications in quantitative biology, in computer and
communication networks, and in software verification. Current projects
include numerical methods for the estimation of parameters based on
observed data, partial moment closure techniques, and approximations of
rare event probabilities.