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The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
Neural networks often have identifiable computational structures - components of the network which perform an interpretable algorithm or task - but the mechanisms by which these emerge and the best methods for detecting these structures are…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
Many experiments have evidenced that electrical and chemical synapses -- hybrid synapses -- coexist in most organisms and brain structures. The role of electrical and chemical synapse connection in diversity of neural activity generation…
The brain forms and stores distributed representations from sparse external input that compete for neuronal resources with already stored memory traces. It is unclear what dynamical properties of neural systems allow formation and…
Understanding the basic operational logics of the nervous system is essential to advancing neuroscientific research. However, theoretical efforts to tackle this fundamental problem are lacking, despite the abundant empirical data about the…
The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. Numerical and analytical calculations show that the network relaxes into a stationary state of…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
In this work, we study the propagation of influence and computation in dynamic distributed systems. We focus on broadcasting models under a worst-case dynamicity assumption which have received much attention recently. We drop for the first…
We consider the theoretical constraints on interactions between coupled cortical columns. Each column comprises a set of neural populations, where each population is modelled as a neural mass. The existence of semi-stable states within a…
Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that…
The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics, and has been widely undertaken. Typically, however, networks employed in theoretical…
In recent years, several studies have provided insight on the functioning of the brain which consists of neurons and form networks via interconnection among them by synapses. Neural networks are formed by interconnected systems of neurons,…
For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…
One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal…
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…