arXiv subjects

A. Chacoma

Publications and source records attributed to A. Chacoma.

12 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↗

arXiv2024

Emergent Complexity in the Decision-Making Process of Chess Players

In this article, we study the decision-making process of chess players by using a chess engine to evaluate the moves across different pools of games. We quantified the decisiveness of each move during the games using a metric derived from the engine's evaluation of the positions. We then performed a comparative analysis across players of varying competitive levels. Firstly, we observed that players face a wide spectrum of the decisiveness metric, evidencing the complexity of the process. By examining groups of winning and losing players, we found evidence where a decrease in complexity may be associated with a drop in players' performance levels. Secondly, we observed that players' accuracy increases in positions with high values of the decisiveness metric regardless of competitive level. Complementing this information with a null model where players make completely random legal moves allowed us to characterize the decision-making process under the simple strategy of making moves that minimize the decisiveness metric. Finally, based on this idea, we proposed a simple model that approximately replicates the global emergent properties of the system.

physics.soc-ph↗

arXiv2023

Probabilistic model for Padel games dynamics

This study applies complexity sciences to analyze the game of Padel. Data from 18 professional matches were collected, and the probability distributions of the total number of shots and the probability distribution of rallies' duration were analyzed. Based on these empirical observations and previous reports, a probabilistic model with two parameters was proposed to describe the game dynamics. One of them controls the probability of making a shot and the other probability of doing it offensively. The model also considers the offensive advantage of the team serving the ball. Using this model, an analytical expression for the probability distribution of the total number of shots was obtained and fit to the data. The results reveal that the complex dynamics of Padel can be effectively approximated as a stochastic process governed by simple probabilistic rules.

physics.soc-ph↗

arXiv2022

Complexity emerges in measures of the marking dynamics in football games

In this article, we study the dynamics of marking in football matches. To do this, we surveyed and analyzed a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterized a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we proposed a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.

physics.data-an↗

arXiv2022

Simple mechanism rules the dynamics of volleyball

In volleyball games, we define a rally as the succession of events observed since the ball is served until one of the two teams on the court scores the point. In this process, athletes evolve in response to physical and information constraints, spanning several spatiotemporal scales and interplaying co-adaptively with the environment. Aiming to study the emergence of complexity in this system, we carried out a study focused on three steps: data collection, data analysis, and modeling. First, we collected data from 20 high-level professional volleyball games. Then we conducted a data-driven analysis from where we identified fundamental insights that we used to define a parsimonious stochastic model for the dynamics of the game. On these bases, we show that it is possible to give a closed-form expression for the probability that the players perform n hits in a rally using only two stochastic variables. Our results fully agree with the empirical observations and represent a new advance in the comprehension of team-sports competition complexity and dynamics.

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↗

arXiv2021

Word frequency-rank relationship in tagged texts

We analyze the frequency-rank relationship in sub-vocabularies corresponding to three different grammatical classes (nouns, verbs, and others) in a collection of literary works in English, whose words have been automatically tagged according to their grammatical role. Comparing with a null hypothesis which assumes that words belonging to each class are uniformly distributed across the frequency-ranked vocabulary of the whole work, we disclose statistically significant differences between the three classes. This results point to the fact that frequency-rank relationships may reflect linguistic features associated with grammatical function.

cs.CL↗

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

Phase transition induced by traffic lights on a single lane road

In this work we study the effect of a traffic light system on the flow of a single lane road by proposing a traffic model based on a cellular automaton that also includes behavioral considerations. We focus on the macroscopic characterization of the system by studying the changes in vehicle density and the occurrence of jams. In this context we observe and characterize a phase transition between the free flow and jammed states. This transition is induced by the instabilities originated by the vehicles stopping at the traffic lights. Moreover, we analyze the effect of these instabilities on the critical density of vehicles at which the transition occurs as a function of two parameters: (i) the in-flow of cars, (ii) the drivers' behavior. For the latter we observe that the traffic light perturbations feedback on the drivers behavior can lead the system to different scenarios, which are also analyzed.

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↗

arXiv2014

Local character of the highest antiferromagnetic Ce-system CeTi{1-x}Sc{x} Ge

The highest antiferromagnetic (AFM) temperature in Ce based compounds has been reported for CeScGe with Tn=47K, but its local or itinerant nature was not deeply investigated yet. In order to shed more light into this unusually high ordering temperature we have investigated structural, magnetic, transport and thermal properties of CeTi{1-x}Sc{x}Ge alloys within the range of stability of the CeScSi-type structure: 0.25<x<1. Along this concentration range, this strongly anisotropic system presents a complex magnetic phase diagram with a continuous modification of its magnetic behavior, from ferromagnetism (FM)for 0.25<x<0.50 (with 7K<Tc<16K) to AFM for 0.60<x<1 (with 19K<Tn<47K). The onset of the AFM phase is associated to a metamagnetic transition with a critical field increasing from H{cr}=0 at x~0.55 to ~6Tesla at x=1, coincident with an increasing contribution of the first excited crystal electric field doublet. At a critical point x{cr}=0.65 a second transition appears at Tl<Tn. In contrast to observations in itinerant systems like CeRh{2}Si{2} or CeRh{3}B{2}, no evidences for significant hybridization of the 4f electrons at large Sc contents were found. Therefore, the exceptionally large Tn of CeScGe can be attributed to an increasing RKKY inter-layer interaction as Sc content grows.

cond-mat.str-el↗

arXiv2014

Exploring high temperature magnetic order in CeTi_1-xSc_xGe

Most of magnetic transitions related to Ce ordering are found below T_ord~12K. Among the few cases exceeding that temperature, two types of behaviors can be distinguished. One of them is related to the rare cases of Ce binary compounds formed in BCC structures, with a quartet ground state, whose degeneracy is reduced by undergoing different types of transitions mostly structural. The other group shows evidences of itinerant character with the outstanding example of CeRh_3B_2 showing the highest T_ord=115K. The second highest ordering temperature has been reported for CeScGe with T_ord=47K, but the nature of this magnetic state has not been investigated very deeply. In order to shed more light into this unusual high temperature ordering we studied the structural, magnetic, transport and thermal properties of CeTi_1-xSc_xGe alloys in the stability range of the CeScSi-type structure 0.25 0.65, the magnetic phase boundary splits into two transitions, with an intermediate phase presenting incommensurate spin density waves features.

cond-mat.str-el↗