Luca Mencarelli | Searcharxiv

arXiv2026

Coarsening and Bifurcations in Wide-Range Two-Dimensional Totalistic Cellular Automata

We investigate Boolean, totalistic cellular automata with a majority or frustrated majority vote rule, and an interaction range of variable span. These two models show a behavior which differs from the mean-field one. The majority vote model is characterized by the presence of absorbing states, and there is a related bifurcation according to the initial density, in agreement with the mean-field approximation. For initial density equal to $0.5$, however, the dynamics is dominated by a coarsening process, which stops when clusters with a definite curvature radius are established. For the frustrated majority vote model, the mean-field approximation gives chaotic oscillations or a limit cycle. Instead, we observe active patterns, with stable density. Above a certain critical value for the interacting radius there is a bifurcation of the asymptotic density as a function of the initial one.

nlin.CG↗

arXiv2021

Time series forecasting from partial observations via Non-negative Matrix Factorization

In modern time series problems, one aims at forecasting multiple time series with possible missing and noisy values. In this paper, we introduce the Sliding Mask Method (SMM) for forecasting multiple nonnegative time series by means of nonnegative matrix completion: observed noisy values and forecast/missing values are collected into matrix form, and learning is achieved by representing its rows as a convex combination of a small number of nonnegative vectors, referred to as the archetypes. We introduce two estimates, the mask Archetypal Matrix factorization (mAMF) and the mask normalized Nonnegative Matrix Factorization (mNMF) which can be combined with the SMM method. We prove that these estimates recover the true archetypes with an error proportional to the noise. We use a proximal alternating linearized method (PALM) to compute the archetypes and the convex combination weights. We compared our estimators with state-of-the-art methods (Transformers, LSTM, SARIMAX...) in multiple time series forecasting on real data and obtain that our method outperforms them in most of the experiments.

cs.LG↗