Seminar Details
2023-03-14 (14h) : Welcome Seminar
At Euler building (room a.002)
Organized by Mathematical Engineering
Section 1: Randomness in Electronic Devices and Circuits
Speaker :
Van Brandt, Léopold
Abstract :
The MOS transistors of smallest dimensions (below 100 nm), universally favoured for the design of digital integrated silicon circuits, are very sensitive to all types of uncertainties, notably statistical process variability. Multiple variability sources of various physical origins introduce random device-to-device fluctuations in the transistor parameters and thereby affect the performance of the circuits. In this presentation, we will mainly focus on the prediction of the failure probability of Static Random Access Memory (SRAM) bitcells. The estimation of probabilities as extremely low as the ppm (i.e. parts-per-million) with limited computational resources and time is a challenge. We will start by emphasising the limitations of the conventional Monte-Carlo simulation approach, before introducing our semi-analytical prediction methodology that turns out to be fast, accurate and insightful. We will close this talk by mentioning some on-going work, where we attempt to apply fundamental physical results to electronic devices and circuits.
Section 2: Lyapunov functions for open multi-agent dynamics
Speaker :
Renato Vizuete (CentraleSupélec and GIPSA-lab, France )
Abstract :
Open multi-agent dynamics are systems characterized by arrivals, departures, or replacements of agents during the evolution of the dynamics. These types of systems are better approximations of modern networks where agents constantly enter and leave the systems, modifying the behavior of the group (e.g., social networks, epidemics, vehicle platoons, swarm of robots). Unfortunately, due to the complexity of the analysis, most of the works have been focused on linear systems, which are limited to few practical applications. In this talk, we present an approach based on Lyapunov functions for the analysis of more complex open multi-agent dynamics where arrivals, departures and replacements are determined by stochastic processes. In the first part, we introduce the techniques based on the formulation of stochastic differential equations with an application to a SIS epidemic subject to replacements of agents. In the second part, by analyzing the Hegselmann-Krause dynamics, we show that some common Lyapunov functions might not be adequate in open scenarios characterized by arrivals and departures of agents.