-- We show how graphons can be used to model and analyze open multi-agent systems, which are multi-agent systems subject to arrivals and departures, in the specific case of linear consensus. First, we analyze the case of replacements, where under the assumption of a deterministic interval between two replacements, we derive an upper bound for the disagreement in expectation. Then, we study the case of arrivals and departures, where we define a process for the evolution of the number of agents that guarantees a minimum and a maximum number of agents. Next, we derive an upper bound for the disagreement in expectation, and we establish a link with the spectrum of the expected graph used to generate the graph topologies. Finally, for stochastic block model (SBM) graphons, we prove that the computation of the spectrum of the expected graph can be performed based on a matrix whose dimension depends only on the graphon and it is independent of the number of agents. Open multi-agent systems are a framework used to analyze networks subject to arrivals, departures or replacements of agents at a rate similar to the scale time of the process [1], [2]. This type of systems are essentially characterized by the agent internal dynamics, the evolution of the network and the arrivals and departures [3]. This is usually done by considering trivial dynamics like complete graphs [4]-[6], bounds on the algebraic connectivity or diameter [7], [8] or just connectivity at all time instants [9].

While most existing federated learning (FL) approaches assume a fixed set of clients in the system, in practice, clients can dynamically leave or join the system depending on their needs or interest in the specific task. This dynamic FL setting introduces several key challenges: (1) the objective function dynamically changes depending on the current set of clients, unlike traditional FL approaches that maintain a static optimization goal; (2) the current global model may not serve as the best initial point for the next FL rounds and could potentially lead to slow adaptation, given the possibility of clients leaving or joining the system. In this paper, we consider a dynamic optimization objective in FL that seeks the optimal model tailored to the currently active set of clients. Building on our probabilistic framework that provides direct insights into how the arrival and departure of different types of clients influence the shifts in optimal points, we establish an upper bound on the optimality gap, accounting for factors such as stochastic gradient noise, local training iterations, non-IIDness of data distribution, and deviations between optimal points caused by dynamic client pattern. The proposed approach is validated on various datasets and FL algorithms, demonstrating robust performance across diverse client arrival and departure patterns, underscoring its effectiveness in dynamic FL environments. Federated learning (FL) is a decentralized machine learning paradigm that facilitates collaborative model training across multiple clients, such as smartphones and Internet of Things (IoT) clients, without exchanging individual data. Instead of transmitting raw data to the central server, each client performs local training using its proprietary data, sending only model updates to the server.

Satellite imagery is now widely used in the defense sector for monitoring locations of interest. Although the increasing amount of data enables pattern identification and therefore prediction, carrying this task manually is hardly feasible. We hereby propose a cased-based reasoning approach for automatic prediction of rare events on strategic sites. This method allows direct incorporation of expert knowledge, and is adapted to irregular time series and small-size datasets. Experiments are carried out on two use-cases using real satellite images: the prediction of submarines arrivals and departures from a naval base, and the forecasting of imminent rocket launches on two space bases. The proposed method significantly outperforms a random selection of reference cases on these challenging applications, showing its strong potential. Keywords: Predictive analysis · Case-based reasoning · Earth observation · Submarine activity · Space launch.

Nasa has launched a new program that could one day eliminate traffic at the world's busiest airports. The agency plans to create a more efficient method of information sharing, moving away from two-way radio communication toward a computer-based system that connects everybody involved in arrivals and departures. This effort aims to more precisely coordinate an airplane's movements, and over the next five years, Nasa and the Federal Aviation Administration will conduct research and field tests to facilitate the transition. Nasa's Next Generation Air Transportation System plans to use computers to streamline information between air traffic controllers, managers, and flight crews. This would connect everybody involved in arrivals and departures, allowing for more precise coordination of the plane's movement.