Dimitrios Maroulakos, M.Sc

The topic of my dissertation is: „Dynamical disease and localization phenomena”

Mathematical models and methods of the dynamical systems theory are so universal and attractive that afterwards, to a certain extent, they have been applied to the biological models, nervous tissue, and neuron networks in particular.

The main physiological functions, e.g., heartbeat or a negative feedback reflex called recurrent inhibition that limits the firing of motor neurons, are processes that can be modelled through sets of non-linear differential equations. see , for mode details. Bifurcations, the chaos that may appear in periodically driven non-linear models, may cause symptoms of clinical interest.

In a broad sense, dynamical diseases are associated with sudden, qualitative changes in the temporal patterns of physiological variables.

Changes in physiological parameters or anatomical structures can cause such diseases and clinical symptomatics. Therefore, comprehensible therapeutic strategies should be developed based on a deeper understanding of non-linear phenomena. Switching the physiological parameters back into normal mode in the ideal case requires knowledge of the non-linear resonance and synchronization analysis of cooperative behaviour of neurons that mimic sets of coupled and driven non-linear oscillators. Dynamical disease could serve as a unique platform where methods of statistical physics and the theory of dynamical systems meet practical clinical applications.

The main interest of the research, concerns the chaotic recurrent neural networks. In particular we plan to study theoretical aspects of dynamical diseases caused by structural disorders of biological origin, anatomical aspects of prefrontal pathology in particular..

When analyzing artificial neural networks, synaptic dynamics is typically split into two time scales: Short-term plasticity depends on presynaptic activity and is relatively fast. In contrast, long-term plasticity is characterized by a longer timescale and depends not only on presynaptic activity but also on postsynaptic activity. However, consideration of short-term Hebbian plasticity mixes these timescale classifications. Therefore, we will study Hebbian plasticity in a recurrent network without introducing two time scales. We will explore nonlinear aspects of dynamics and focus mainly on the analysis of the Lyapunov spectrum. We analyze two cases, with and without the disorder in the neural network, and compare dynamical characteristics.

Publication:

1.Dimitrios Maroulakos et al. “Local and Non-Local Invasive Measurements on Two Quantum Spins Coupled via Nanomechanical Oscillations”. In: Symmetry 12.7(2020). ISSN: 2073-8994. DOI: 10.3390/sym12071078. URL: https://www.mdpi.com/2073-8994/12/7/1078