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Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including…
Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…
A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…
Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in…
Self-organizing memristive networks are physical circuits that dynamically reconfigure their circuitry in response to external input signals. Their adaptive behavior arises from intrinsic neuro-synaptic dynamics combined with a…
An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
A single neuron is known to generate almost identical spike trains when the same fluctuating input is repeatedly applied. Here, we study the reliability of spike firing in a pulse-coupled network of oscillator neurons receiving fluctuating…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural…
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…