Abstract-- This paper studies targeted opinion formation in multi-agent systems evolving over signed, time-varying directed graphs. The dynamics of each agent's state follow a Laplacian-based update rule driven by both cooperative and antagonistic interactions in the presence of exogenous factors. We formulate these exogenous factors as external control inputs and establish a suitable controller design methodology enabling collective opinion to converge to any desired steady-state configuration, superseding the natural emergent clustering or polarization behavior imposed by persistently structurally balanced influential root nodes. Our approach leverages upper Dini derivative analysis and Gr onwall-type inequalities to establish exponential convergence for opinion magnitude towards the desired steady state configuration on networks with uniform quasi-strong δ-connectivity. Finally, the theoretical results are validated through extensive numerical simulations.

The rise of generative models for scientific research calls for the development of new methods to evaluate their fidelity. A natural framework for addressing this problem is two-sample hypothesis testing, namely the task of determining whether two data sets are drawn from the same distribution. In large-scale and high-dimensional regimes, machine learning offers a set of tools to push beyond the limitations of standard statistical techniques. In this work, we put this claim to the test by comparing a recent proposal from the high-energy physics literature, the New Physics Learning Machine, to perform a classification-based two-sample test against a number of alternative approaches, following the framework presented in Grossi et al. (2025). We highlight the efficiency tradeoffs of the method and the computational costs that come from adopting learning-based approaches. Finally, we discuss the advantages of the different methods for different use cases.

Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so doing numerical operations on big data sets become faster. Sketching algorithms generally use random projections to compress the original dataset and this stochastic generation process makes them amenable to statistical analysis. The statistical properties of sketching algorithms have been widely studied in the context of multiple linear regression. In this paper we propose matrix sketching as a tool for rebalancing class sizes in supervised classification with imbalanced classes. It is well-known in fact that class imbalance may lead to poor classification performances especially as far as the minority class is concerned.