In this paper we propose a hybrid model of a neural oscillator, obtained by partially
discretizing a well-known continuous model. Our construction points out that in this case the …

Neural abstractions have been recently introduced as formal approximations of complex,
nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on …

We make the case for neural network objects and extend an already existing neural network
calculus explained in detail in Chapter 2 on\cite {bigbook}. Our aim will be to show that, yes …

In this article we intend to analyze a chaotic system from the standpoint of its computation
capability. to pursue this aim, we refer to a complex chaotic dynamics that we characterize …

We discuss in this short survey article some current mathematical models from
neurophysiology for the computational units of biological neural systems: neurons and …

The behavior of simple recurrent neural networks trained on regular languages is analyzed
in terms of accuracy and interpretability. We use controlled amounts of noise and L1 …

Computation is classically studied in terms of automata, formal languages and algorithms;
yet, the relation between neural dynamics and symbolic representations and operations is …

Recent results have shown that finite state automata can be simulated by recurrent neural
networks composed of synfire rings. The simulation process was shown to work correctly in …

We show that any finite state automaton can be simulated by some neural network of
Izhikevich spiking neurons composed of interconnected synfire rings. The construction turns …

By universal formulas we understand parameterized analytic expressions that have a fixed
complexity, but nevertheless can approximate any continuous function on a compact set …