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Cluster synchronization is of great importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as…
The search for highly coherent degrees of freedom in noisy solid-state environments is a major challenge in condensed matter. In disordered dipolar systems, such as magnetically doped insulators, compact clusters of two-level systems (TLS)…
Parkinson's Disease (PD) is a chronic, degenerative disorder which leads to a range of motor and cognitive symptoms. PD diagnosis is a challenging task since its symptoms are very similar to other diseases such as normal ageing and…
Cluster analysis aims at separating patients into phenotypically heterogenous groups and defining therapeutically homogeneous patient subclasses. It is an important approach in data-driven disease classification and subtyping. Acute…
In this paper, we provide an overview of a common phenomenon, condensation, observed during the nonlinear training of neural networks: During the nonlinear training of neural networks, neurons in the same layer tend to condense into groups…
Pulsed Dynamic Nuclear Polarization (DNP) is currently receiving substantial interest as a means to enhance the sensitivity of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) by orders of magnitude. It has also…
We study functional activity in the human brain using functional Magnetic Resonance Imaging and recently developed tools from network science. The data arise from the performance of a simple behavioural motor learning task. Unsupervised…
In this paper, we analyze electroencephalograms (EEG) which are recordings of brain electrical activity. We develop new clustering methods for identifying synchronized brain regions, where the EEGs show similar oscillations or waveforms…
Composite pulses are essential for universal manipulation of singlet-triplet spin qubits. In the absence of noise, they are required to perform arbitrary single-qubit operations due to the special control constraint of a singlet-triplet…
Modern neural recording techniques allow neuroscientists to obtain spiking activity of multiple neurons from different brain regions over long time periods, which requires new statistical methods to be developed for understanding structure…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind…
Dipolar spin ensembles with random spin positions attract much attention currently because they help to understand decoherence as it occurs in solid state quantum bits in contact with spin baths. Also, these ensembles are systems which may…
Neural activity in the brain exhibits correlated fluctuations that may strongly influence the properties of neural population coding. However, how such correlated neural fluctuations may arise from the intrinsic neural circuit dynamics and…
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…
Spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle…
Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We…
Motivated by the aim to find new medical strategies to suppress undesirable neural synchronization we study the control of oscillations in a system of inhibitory coupled noisy oscillators. Using dynamical properties of inhibition, we find…
Determining phenotypes of diseases can have considerable benefits for in-hospital patient care and to drug development. The structure of high dimensional data sets such as electronic health records are often represented through an embedding…
We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that unlike a solitary system generating a train of equidistant pulses, an array…