arXiv subjects

J. I. Perotti

Publications and source records attributed to J. I. Perotti.

5 recordsLinked to original sources

arXiv2026

Ranking football teams via the higher-order decomposition of performance networks

We propose a unified methodological framework to quantify team performance in elite football by combining event-level performance metrics, higher-order network representations, and algebraic ranking methods. Using data from the 2017--2018 season of the five major European leagues, we construct metric-specific weighted graphs in which teams are connected through relative performance indicators. These graphs are analyzed via Hodge decomposition, and the gradient component is used to derive metric-based team ratings. The resulting rankings are systematically compared with the true league standings using Pearson and Kendall correlation measures, revealing strong metric- and league-dependent effects. Furthermore, by analyzing the ratio between solenoidal and total flow energies, we show that local cyclic dynamics structurally limit the gradient component's capacity to reconstruct the ranking. This topological inconsistency acts as a structural fingerprint of each league's ``competition style'' successfully mapping the studied systems into distinct regimes: highly hierarchical structures (England and Italy), tactical parity driven by generalized loops (Germany), and pockets of localized chaos (France and Spain). Lastly, we introduce a composite rating obtained as a parsimonious linear combination of metric-based ratings, optimized separately for each league. This composite approach significantly improves predictive power and allows the relative importance of different performance indicators to be quantified in a league-specific manner. Our results demonstrate how higher-order network methods provide a flexible and interpretable framework to uncover latent performance structures in football, offering a complementary perspective to outcome-based rankings and a general approach applicable to other oppositional sports.

physics.soc-ph↗

arXiv2021

Stochastic model for football's collective dynamics

In this paper, we study collective interaction dynamics emerging in the game of football-soccer. To do so, we surveyed a database containing body-sensors traces measured during three professional football matches, where we observed statistical patterns that we used to propose a stochastic model for the players' motion in the field. The model, which is based on linear interactions, captures in good approximation the spatiotemporal dynamics of a football team. Our theoretical framework, therefore, becomes an effective analytical tool to uncover the underlying cooperative mechanisms behind the complexity of football plays. Moreover, we showed that it can provide handy theoretical support for coaches to evaluate teams' and players' performances in both training sessions and competitive scenarios.

physics.soc-ph↗

arXiv2020

Modeling ball possession dynamics in the game of football

In this paper, we study interaction dynamics in the game of football-soccer in the context of ball possession intervals. To do so, we analyze a database comprising one season of the five major football leagues of Europe. Using this input, we developed a stochastic model based on three agents: two teammates and one defender. Despite its simplicity, the model is able to capture, in good approximation, the statistical behavior of possession times, pass lengths, and number of passes performed. In the last section, we show that the model's dynamics can be mapped into a Wiener process with drift and an absorbing barrier.

physics.soc-ph↗

arXiv2020

A model for phonetic changes driven by social interactions

We propose a stochastic model to study phonetic changes as an evolutionary process driven by social interactions between two groups of individuals with different phonological systems. Particularly, we focus on the changes in the place of articulation, inspired by the drift /\textphi/$\rightarrow$/h/ observed in some words of Latin root in the Castilian language. In the model, each agent is characterized by a variable of three states, representing the place of articulation used during speech production. In this frame, we propose stochastic rules of interactions among agents which lead to phonetic imitation and consequently to changes in the articulation place. Based on this, we mathematically formalize the model as a problem of population dynamics, derive the equations of evolution in the mean field approximation, and study the emergence of three non--trivial global states, which can be linked to the pattern of phonetic changes observed in the language of Castile and in other Romance languages.

physics.soc-ph↗

arXiv2009

Emergent self-organized complex network topology out of stability constraints

Although most networks in nature exhibit complex topology the origins of such complexity remains unclear. We introduce a model of a growing network of interacting agents in which each new agent's membership to the network is determined by the agent's effect on the network's global stability. It is shown that out of this stability constraint, scale free networks emerges in a self organized manner, offering an explanation for the ubiquity of complex topological properties observed in biological networks.

cond-mat.dis-nn↗