We consider multi-class systems of interacting nonlinear Hawkes processes modeling
several large families of neurons and study their mean field limits. As the total number of …

Highlights•Balanced networks are widespread in the brain, yet their role in the spinal cord is
unclear.•Respiratory and lumbar circuits show signs of balanced activity.•Network motifs are …

When spinal circuits generate rhythmic movements it is important that the neuronal activity
remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we …

The statistical problem of parameter estimation in partially observed hypoelliptic diffusion
processes is naturally occurring in many applications. However, because of the noise …

Objective. External control of spike times in single neurons can reveal important information
about a neuron's sub-threshold dynamics that lead to spiking, and has the potential to …

Direct measurements of synaptic inhibition (I) and excitation (E) to spinal motoneurons can
provide an important insight into the organization of premotor networks. Such measurements …

Parameter estimation in multidimensional diffusion models with only one coordinate
observed is highly relevant in many biological applications, but a statistically difficult …

Background In this work, we propose to catch the complexity of the membrane potential's
dynamic of a motoneuron between its spikes, taking into account the spikes from other …

In the resting state, cortical neurons can fire action potentials spontaneously but
synchronously (Up state), followed by a quiescent period (Down state) before the cycle …

The rhythmic activity of motoneurons (MNs) that underlies locomotion in mammals is
generated by synaptic inputs from the locomotor network in the spinal cord. Thus, the …