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Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…

We consider a class of spiking neuronal models, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed…

The recent discovered spatial-temporal information processing capability of bio-inspired Spiking neural networks (SNN) has enabled some interesting models and applications. However designing large-scale and high-performance model is yet a…

Modern datasets in neuroscience enable unprecedented inquiries into the relationship between complex behaviors and the activity of many simultaneously recorded neurons. While latent variable models can successfully extract low-dimensional…

In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to targeted spiking times of neurons, where the cases with…

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…

Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with…

Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so…

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…

Behavior results from the integration of ongoing sensory signals and contextual information in various forms, such as past experience, expectations, current goals, etc. Thus, the response to a specific stimulus, say the ringing of a…

Experimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of…

We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample…

Understanding how the dynamics of neural networks is shaped by the computations they perform is a fundamental question in neuroscience. Recently, the framework of efficient coding proposed a theory of how spiking neural networks can compute…

Working memory requires the brain to maintain information from the recent past to guide ongoing behavior. Neurons can contribute to this capacity by slowly integrating their inputs over time, creating persistent activity that outlasts the…

The firing dynamics of biological neurons in mathematical models is often determined by the model's parameters, representing the neurons' underlying properties. The parameter estimation problem seeks to recover those parameters of a single…

The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…

Understanding cognitive flexibility and task-switching mechanisms in neural systems requires biologically plausible computational models. This tutorial presents a step-by-step approach to constructing a spiking neural network (SNN) that…

The apparent stochasticity of in-vivo neural circuits has long been hypothesized to represent a signature of ongoing stochastic inference in the brain. More recently, a theoretical framework for neural sampling has been proposed, which…

A main concern in cognitive neuroscience is to decode the overt neural spike train observations and infer latent representations under neural circuits. However, traditional methods entail strong prior on network structure and hardly meet…