Center for Interdisziplinary Research

ZiF Cooperation Group

Discrete and Continuous Models in the Theory of Networks



Fatihcan M. Atay
Bilkent University Ankara | Turkey

Pavel Kurasov
U Stockholm | Sweden

Delio Mugnolo
U Hagen | Germany


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.

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