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We consider, in this paper, the problem of state estimation for a class of dynamical systems governed via continuous-time McKean-Vlasov stochastic differential equations. The estimation problem is stated and solved under an H2 norm setting. We adopt a Riccati-based approach in order to solve the optimal estimation problem.

Spiking Neural [Formula: see text] Systems are Neural System models characterized by the fact that each neuron mimics a biological cell and the communication between neurons is based on spikes. In the Spiking Neural [Formula: see text] systems investigated so far, the application of evolution rules depends on the contents of a neuron (checked by means of a regular expression). In these [Formula: see text] systems, a specified number of spikes are consumed and a specified number of spikes are produced, and then sent to each of the neurons linked by a synapse to the evolving neuron. [Formula: see text]In the present work, a novel communication strategy among neurons of Spiking Neural [Formula: see text] Systems is proposed. In the resulting models, called Spiking Neural [Formula: see text] Systems with Communication on Request, the spikes are requested from neighboring neurons, depending on the contents of the neuron (still checked by means of a regular expression). Unlike the traditional Spiking Neural [Formula: see text] systems, no spikes are consumed or created: the spikes are only moved along synapses and replicated (when two or more neurons request the contents of the same neuron). [Formula: see text]The Spiking Neural [Formula: see text] Systems with Communication on Request are proved to be computationally universal, that is, equivalent with Turing machines as long as two types of spikes are used. Following this work, further research questions are listed to be open problems.