89 citations · 139 across the 19 of their papers we have counts for
19 papers
Multiscale phase oscillations induced by cluster synchronisation in human connectome core network
Bosiljka Tadic, Marija Mitrovic Dankulov, Roderick Melnik
Brain imaging data mapping onto human connectome networks enables the investigation of global brain dynamics, where the brain hubs play an essential role in transferring activity b…
Spike-timing-dependent plasticity and random inputs shape interspike interval regularity of model STN neurons
Thoa Thieu, Roderick Melnik
Neuronal oscillations are closely related to the symptoms of Parkinson's disease (PD). In this study, we explore how random fluctuations (or "stochastic inputs") affect these oscil…
Fundamental interactions in self-organized critical dynamics on higher-order networks
Bosiljka Tadic, Roderick Melnik
In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-…
Complex non-Markovian dynamics and the dual role of astrocytes in Alzheimer's disease development and propagation
Swadesh Pal, Roderick Melnik
Alzheimer's disease (AD) is a common neurodegenerative disorder nowadays. Amyloid-beta (A) and tau proteins are among the main contributors to the development or propagation of…
Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications
Thi Kim Thoa Thieu, Adrian Muntean, Roderick Melnik
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biolo…
Effects of random inputs and short-term synaptic plasticity in a LIF conductance model for working memory applications
Thi Kim Thoa Thieu, Roderick Melnik
Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitiv…
Effects of noise on leaky integrate-and-fire neuron models for neuromorphic computing applications
Thi Kim Thoa Thieu, Roderick Melnik
Artificial neural networks (ANNs) have been extensively used for the description of problems arising from biological systems and for constructing neuromorphic computing models. The…
Modelling the behavior of human crowds as coupled active-passive dynamics of interacting particle systems
Thi Kim Thoa Thieu, Roderick Melnik
The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psycholog…
Nonlocal Models in the Analysis of Brain Neurodegenerative Protein Dynamics with Application to Alzheimer's Disease
Swadesh Pal, Roderick Melnik
It is well known that today nearly one in six of the world's population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the…
Deep brain stimulation with a computational model for the cortex-thalamus-basal-ganglia system and network dynamics of neurological disorders
Hina Shaheen, Roderick Melnik
Deep brain stimulation (DBS) can alleviate the movement disorders like Parkinson's disease (PD). Indeed, it is known that aberrant beta (13-30Hz)oscillations and the loss of dopami…
Coupled effects of channels and synaptic dynamics in stochastic modelling of healthy and Parkinson's-disease-affected brains
Thi Kim Thoa Thieu, Roderick Melnik
Our brain is a complex information processing network in which the nervous system receives information from the environment to quickly react to incoming events or learns from exper…
Combining Coupled Skorokhod SDEs and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems
Thi Kim Thoa Thieu, Roderick Melnik
To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of t…
The topology of higher-order complexes associated with brain-function hubs in human connectomes
Miroslav Andjelkovic, Bosiljka Tadic, Roderick Melnik
Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial compl…
Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
Marija Mitrovic Dankulov, Bosiljka Tadic, Roderick Melnik
Cooperative self-assembly can result in complex nano-networks with new hyperbolic geometry. However, the relation between the hyperbolicity and spectral and dynamical features of t…
Functional Geometry of Human Connectome and Robustness of Gender Differences
Bosiljka Tadic, Miroslav Andjelkovic, Roderick Melnik
Mapping the brain imaging data to networks, where each node represents a specific area of the brain, has enabled an objective graph-theoretic analysis of human connectome. However,…
The Luttinger-Kohn theory for multiband Hamiltonians: A revision of ellipticity requirements
Dmytro Sytnyk, Roderick Melnik
Modern applications require a robust and theoretically solid tool for the realistic modeling of electronic states in low dimensional nanostructures. The theory has frui…
The mechanisms of self-organised criticality in social processes of knowledge creation
Bosiljka Tadic, Marija Mitrovic Dankulov, Roderick Melnik
In the online social dynamics, a robust scaling behaviour appears as a key feature of many collaborative efforts that lead to the new social value. The underlying empirical data th…
Linear nonlocal problem for the abstract time-dependent non-homogeneous Schrödinger equation
Dmytro Sytnyk, Roderick Melnik
A nonlocal-in-time problem for the abstract Schrödinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solut…
Multiband Hamiltonians of the Luttinger-Kohn Theory and Ellipticity Requirements
Dmytro Sytnyk, Sunil Patil, Roderick Melnik
Modern applications require a robust and theoretically strong tool for the realistic modeling of electronic states in low dimensional nanostructures. The theory has fru…