Research Interests



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

(A) Development  of Numerical Analysis methods
(B) Modelling, Simulation and Control
(C) 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: Numerical Analysis, Systems Dynamics, Bifurcation theory, Complex systems Modeling, Statistical Mechanics,  Complex Networks and Control theory.

Numerical Analysis of Large-Scale and Complex Systems

I am interested in studying the dynamics of 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. Thus my research focuses on developing numerical analysis methods for the bridging between microscopic/stochastic models and state-of-the-art numerical methods. The scientific keystones of this direction include Numerical Analysis (Iterative Linear Algebra Methods), Numerical Bifurcation Analysis Theory, Complex Systems and Control theory for experiments and Large-Scale/ Complex problems. 
The idea is based on the Equation-Free framework that bypasses the explicit derivation of closures for the emergent-level equations.  Research focuses  on the development of Numerical Analysis methods for the: 

- Numerical Continuation and Stability Analysis of steady state and time-dependent computations, 

- Computation and Analysis of Self-Similar Solutions and 

- Rare-Events analysis of the complex-emergent dynamics 

-  Adaptive detection of instabilities for experiments and large scale and complex systems, motivated from numerical bifurcation algorithms for critical point detection

- Tracing of Bifurcation diagrams through the development of feedback control schemes, of experiments, microscopic/stochastic simulators, and  large-scale systems,


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.



 

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 Yannick de Decker,
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Belgium,
Professor George Georgiou, Dept. of Mathematics and Statistics, University of Cyprus,
Professor Stefano Mazzoleni, Dipt. di Agraria, University of Naples Federico II, Italy
Professor Geardo Toraldo, Dipt. di  Matematica e Applicazioni, University of Naples Federico II, Italy
Professor Francesco Giannino, Dipt. di Agraria, University of Naples Federico II, Italy
Professor Salvatore Cuomo, Dipt. di  Matematica e Applicazioni, University of Naples Federico II, Italy

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