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Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
Dynamic instability in the cytoskeleton underlies a great many vital cellular processes. In neurons, it is thought to play a role in information processing and the establishment of synaptic connections. It is from this interneuronal…
The collective behavior of biological oscillators has been recognized as an important problem for several decades, but its control has come into limelight only recently. Much of the focus for control has been on desynchronization of an…
Understanding cognitive processes in the brain demands sophisticated models capable of replicating neural dynamics at large scales. We present a physiologically inspired speech recognition architecture, compatible and scalable with deep…
Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their…
We define the ``Pulse Synchronization'' problem that requires nodes to achieve tight synchronization of regular pulse events, in the settings of distributed computing systems. Pulse-coupled synchronization is a phenomenon displayed by a…
Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…
Synchronization is essential for the stability and coordinated operation of complex networked systems. Pinning control, which selectively controls a subset of nodes, provides a scalable solution to enhance network synchronizability.…
Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might…
Diluted neural networks with continuous neurons and nonmonotonic transfer function are studied, with both fixed and dynamic synapses. A noisy stimulus with periodic variance results in a mechanism for controlling chaos in neural systems…
Biological systems use neural circuits to integrate input information and produce outputs. Synaptic convergence, where multiple neurons converge their inputs onto a single downstream neuron, is common in natural neural circuits. However,…
Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…
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,…
The question of controllability of natural and man-made network systems has recently received considerable attention. In the context of the human brain, the study of controllability may not only shed light into the organization and function…
Deep-Brain Stimulation (DBS) is a therapy used in conjunction with medication to help alleviate the motor symptoms of Parkinson's Disease (PD). However, the monitoring and adjustment of DBS settings is tedious and expensive, requiring long…
Correlations between intrinsic dynamics and local topology have become a new trend in the study of synchronization in complex networks. In this paper, we investigate in this paradigm the influence of topology on dynamics of networks made up…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
While traditional feed-forward filter models can reproduce the rate responses of retinal ganglion neurons to simple stimuli, they cannot explain why synchrony between spikes is much higher than expected by Poisson firing [6], and can be…