Research Interests



My research focus on Computational Science & Engineering and in particular the development and implementation of computational methods for the analysis of Nonlinear/ Complex systems. There are four directions in this effort to analyze/engineer Large-Scale/ Complex Systems:

(A) Modelling and Simulation
(B) Development and implementation of computational methods
(C) Control algorithms
(D) Linking the above with Machine and Manifold Learning algorithms.

I strive to address emerging interdisciplinary challenging Complex problems with an empahsis in Computational Neuroscience but also Complex Social Networks and their Dynamics,  Mathematical Epidemiology,  Fluid Mechanics, Materials Science, Environmental Modelling and Management, Process Engineering,  Economics and Finance, and Seismology in collaboration with strong and interested colleagues.

The scientific keystones of the research integrates recent advances mainly from: Systems Dynamics, Complex systems Modeling, Statistical MechanicsNumerical Bifurcation theory, Numerical Analysis of larfe-Scale Systems, Complex Networks and Control theory.


Modelling and Simulation of Complex Systems

        For many problems of contemporary practical and research interest in Applied Mathematics, Engineering and Physical Sciences, the closures required to formulate good models in the continuum are not available. Most of them are inherently multi-scale ( interactions of neurons and groups of neurons on complex brain networks, chemical reactions and mass-transfer phenomena on catalytic surfaces,  liquid crystals dynamics, emergence and dynamics of collective phenomena in social systems, evolution of epidemics, the dynamics of fire spread in heterogeneous environments,, dynamics of financial markets).
        My research interest here focuses on the development of microscopic/ individualistic stochastic models using Agent-based, Brownian Dynamics, Molecular Dynamics, Monte-Carlo and Cellular Automata simulation techniques for complex dynamical problems arising across disciplines with important engineering, health, social and environmental im
plications.
        I am also interested in studying the influence of the topology of complex networks on the emergent dynamics of dynamical systems.
The dynamic effects of network heterogeneity are central to fundamental problems in Computational Neuroscience, Biological Systems, Materials Science, Epidemics,  Information Exchange and Social  collective phenomena including Economics and Finance. Towards this aim, the efforts are also focused on the development of computational algorithms for constructing topologies of networks with prescribed characteristics that are able to approximate real-world network structures.

Machine and Manifold Learning Techniques for Systems Identification  and Signal Processing

The aim is mainly focused in Computaional Neuroscience  for the modelling and analysis of Brain activity as recorded from  fMRI, EEG, MEG as coupled with behavioural data (phenotypes) to study the mechanisms that pertain to the cognitive mechanisms of decision making,  working memory and the identification of "biomarkers" of neurological disorders such as Schizophrenia and Epilepsy. Rsearch efforts are focused on the construction of the underlying effective and Functional Connectivity Networks.

Computational Analysis of Large-Scale and Complex Systems

I am interested in studying complex problems for which coarse-grained evolution equation models can be in principle derived in the form of  Ordinary or Partial Differential Equations, however, due to inherent complexity, such models are not explicitly available in a closed form.
My research focuses on the bridging between microscopic/individual-based problem descriptions and state-of-the-art computational methods, in order to provide a systematic approach for analyzing the parametric behaviour of complex/ multi-scale problems. 

The idea is based on the Equation-Free framework that bypasses the explicit derivation of closures for the emergent-level equations. Steady state and time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis and other important tasks such as the computational analysis and continuation of self-similar solutions and rare-events analysis of the complex-emergent dynamics can be performed in a straightforward manner. 

Nonlinear Dynamics, Computational Bifurcation Analysis and Control

        The interface between Bifurcation theory and Control is an active research area. Both disciplines share the goal of accurately locating and efficiently converging on (i.e. stabilizing) steady states computationally or experimentally.

            I aim at developing numerical approaches at the trijunction of Computational Bifurcation analysis, Complex Systems and Control theory for experiments and Large-Scale/ Complex problems as these can be principally described by ordinary or partial differential equations. 

The efforts are mainly focused: 

(a) on the adaptive detection of instabilities for experiments and large scale and complex systems, motivated from numerical bifurcation algorithms for critical point detection

(b) address the development of feedback control schemes, which, can be implemented as a shell around experiments and/or existing microscopic/stochastic simulators, and generally speaking large-scale systems, to enable them to automatically trace their bifurcation diagrams.



 

Research Collaborators

The above directions of research involve extensive collaboration with several interested colleaques including (currently):

Professor Yannis Kevrekidis, Princeton University, USA,
Dr. Bill Gear, Princeton University, USA,
Professor Eleftherios Mylonakis, Medical School, Brown University, USA
Professor Nikos Smyrnis, Medical School, University of Athens, Greece,
Professor Lieven Lagae, Medical School, Section Paediatric Neurology, K.U.Leuven, Belgium,
Dr. Gerasimos Papadopoulos, Institute of Geodynamics, National Observatory of Athens, Greece
Dr. Lucia Russo, Combustion Institute of the C.N.R., Naples, Italy
Professor Paola Russo, Dept. of Chemical Materials and Environmental Engineering, Sapienza University of Rome,
 Italy
Professor Yannick de Decker,
Center for Nonlinear Phenomena and Complex Systems, UniversitÚ Libre de Bruxelles, Belgium,
Professor Dimitris Maroudas,  University of Massachusetts, Amherst, USA
Professor George Georgiou, Dept. of Mathematics and Statistics, University of Cyprus,
Professor Marissa di Matteo, Dept. of Industrial Engineering, University of Salerno, Italy,
Professor Dr. Bj÷rn Reineking, National Institute for Environmental Science and Research at Grenoble, France,
Professor Silvestro Crescitelli, Dept. of Materials Science and Engineering, University of Naples Federico II, Italy,
Professor Dietmar Janetzko, Cologne Business School, Germany
Professor Antonis Zagaris, Dept. Applied Mathematics, University of Twente, The Netherlands
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