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This paper describes a relatively simple way of allowing a brain model to self-organise its concept patterns through nested structures. Time is a key element and a simulator would be able to show how patterns may form and then fire in…
How extracellular electric fields, as generated endogenously or through transcranial brain stimulation, affect the dynamics of large neuronal populations is of great interest but not well understood. To study the collective dynamics of…
Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population…
Reverse engineering the brain is proving difficult, perhaps impossible. While many believe that this is just a matter of time and effort, a different approach might help. Here, we describe a very simple idea which explains the power of the…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
Synchronization phenomena are pervasive in biology. In neuronal networks, the mechanisms of synchronization have been extensively studied from both physiological and computational viewpoints. The functional role of synchronization has also…
Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of…
We report measurements of the brain activity of subjects engaged in behavioral exchanges with their environments. We observe brain states which are characterized by coordinated oscillation of populations of neurons that are changing rapidly…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much…
Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models…
Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
We study the impact of noise on a neural population rate model of up and down states. Up and down states are typically observed in neuronal networks as a slow oscillation, where the population switches between high and low firing rates…
A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable…
We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.