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An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable regimes of network activation, typically arising from a limited parameter…

Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

Structural modularity is a pervasive feature of biological neural networks, which have been linked to several functional and computational advantages. Yet, the use of modular architectures in artificial neural networks has been relatively…

Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

The transport capacity of a communication network can be characterized by the transition from a free-flow state to a congested state. Here, we propose a dynamic routing strategy in complex networks based on hierarchical bypass selections.…

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…

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,…

We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…

Neural circuits are able to perform computations under very diverse conditions and requirements. The required computations impose clear constraints on their fine-tuning: a rapid and maximally informative response to stimuli in general…

Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…

Mathematical modeling has broad applications in neuroscience whether modeling the dynamics of a single synapse or an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better…

Construction of neural network architectures suitable for learning from both continuous and discrete tabular data is a challenging research endeavor. Contemporary high-dimensional tabular data sets are often characterized by a relatively…

We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…

For many networks, the connection pattern (often called the topology) can vary in time, depending on the changing state, or mode, of the modules within the network. For example, "airplane mode" is the name for one communicative mode of a…

Activity in coupled systems is often oscillatory, for example, the firing pattern of neuronal populations. Whereas these oscillations have been studied predominantly in local circuits, here we show how the topology of large-scale networks,…

We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their…