Alessio Franci

Rodolphe Sepulchre, Guillaume Drion, Alessio Franci

This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection properties rather than closed systems classified by their parameter ranges. Modeling, analysis, and synthesis questions can be formulated in the classical language of circuit theory. The input-output characterization of excitability is in terms of the local sensitivity of the current-voltage relationship. It suggests the formulation of novel questions for non-linear system theory, inspired by questions from experimental neurophysiology.

Kayhan Ozcimder, Biswadip Dey, Alessio Franci et al.

We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modeled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a "dial" in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance.

Loris Mendolia, Chenxi Wen, Elisabetta Chicca et al.

Neuromorphic engineering makes use of mixed-signal analog and digital circuits to directly emulate the computational principles of biological brains. Such electronic systems offer a high degree of adaptability, robustness, and energy efficiency across a wide range of tasks, from edge computing to robotics. Within this context, we investigate a key feature of biological neurons: their ability to carry out robust and reliable computation by adapting their input responses and spiking patterns to context through neuromodulation. Achieving analogous levels of robustness and adaptation in neuromorphic circuits through modulatory mechanisms is a largely unexplored path. We present a novel current-mode neuron design that supports robust neuromodulation with minimal model complexity, compatible with standard CMOS technologies. We first introduce a mathematical model of the circuit and provide tools to analyze and tune the neuron behavior; we then demonstrate both theoretically and experimentally the biologically plausible neuromodulation adaptation capabilities of the circuit over a wide range of parameters. All theoretical predictions were verified in experiments on a low-power 180 nm CMOS implementation of the proposed neuron circuit. Due to the analog underlying feedback structure, the proposed adaptive neuromodulable neuron exhibits a high degree of robustness, flexibility, and scalability across operating ranges of currents and temperatures, making it a perfect candidate for real-world neuromorphic applications.

Gustave Bainier, Antoine Chaillet, Rodolphe Sepulchre et al.

The fading-memory (FM) property captures the progressive loss of influence of past inputs on a system's current output and has originally been formalized by Boyd and Chua in an operator-theoretic framework. Despite its importance for systems approximation, reservoir computing, and recurrent neural networks, its connection with state-space notions of nonlinear stability, especially incremental ones, remains understudied. This paper introduces a state-space definition of FM. In state-space, FM can be interpreted as an extension of incremental input-to-output stability ($δ$IOS) that explicitly incorporates a memory kernel upper-bounding the decay of past input differences. It is also closely related to Boyd and Chua's FM definition, with the sole difference of requiring uniform, instead of general, continuity of the memory functional with respect to an input-fading norm. We demonstrate that incremental input-to-state stability ($δ$ISS) implies FM semi-globally for time-invariant systems under an equibounded input assumption. Notably, Boyd and Chua's approximation theorems apply to delta-ISS state-space models. As a closing application, we show that, under mild assumptions, the state-space model of current-driven memristors possess the FM property.