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The Optional Public Goods Game is a three-strategy game in which an individual can play as a cooperator or defector or decide not to participate. Despite its simplicity, this model can effectively represent many human social dilemmas, such as those found in the use of public services, environmental concerns, or other activities related to society. In this contribution, we present a comprehensive analysis of the conditions under which spontaneous, sustained cooperation emerges and the characteristics of these cooperative states. Through simulations, we demonstrate the conditions leading to the coexistence of the three strategies in a steady equilibrium or the alternate dominance of each strategy in a rock-paper-scissors fashion. The results identify each of the possible scenarios in terms of two key parameters: the multiplication rate of the public good game (reward) and the size of the group of potential players. We also discuss other details of the game that may influence the appearance of cycles, along with relevant characteristics of these cycles, such as the prevalence of cooperation., Comment: 8 pages, 6 figures

Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C, 2350061 (2023)], which is directly reflected in the eigenvalues of these matrices. When these evolutions are analyzed in the mean-field regime, an important question arises: Can the Langevin equation, when translated into maps, perform the same function? Some studies suggest that this method may also capture the chaotic behavior of certain systems. In this work, we propose that the spectral properties of random matrices constructed from maps derived from deterministic or stochastic differential equations can indicate the critical or chaotic behavior of such systems. For chaotic systems, we need only the evolution of iterated Hamiltonian equations, and for spin systems, the Langevin maps obtained from mean-field equations suffice, thus avoiding the need for Monte Carlo (MC) simulations or other techniques., Comment: 19 pages, 5 figures

In this work, we investigate the statistical properties of drink serving in a nightclub bar, utilizing a stochastic model to characterize pedestrian dynamics within the venue. Our model comprises a system of n agents moving across an underlying square lattice of size l representing the nightclub venue. Each agent can exist in one of three states: thirsty, served, or dancing. The dynamics governing the state changes are influenced by a memory time, denoted as {\tau}, which reflects their drinking habits. Agents' movement throughout the lattice is controlled by a parameter {\alpha} which measures the impetus towards/away from the bar. When {\alpha} = 0, a power-law distribution emerges due to the non-objectivity of the agents. As {\alpha} moves into intermediate values, an exponential behavior is observed, as it becomes possible to mitigate the drastic jamming effects in this scenario. However, for higher {\alpha} values, the power-law distribution resurfaces due to increased jamming. We also demonstrate that the average concentration of served, thirsty, and dancing agents provide a reliable indicator of when the system reaches a jammed state. Subsequently, we construct a comprehensive map of the system's stationary state, supporting the idea that for high densities, {\alpha} is not relevant, but for lower densities, the optimal values of measurements occurs at high values of {\alpha}. To complete the analysis, we evaluate the conditional persistence, which measures the probability of an agent failing to receive their drink despite attempting to do so. In addition to contributing to the field of pedestrian dynamics, the present results serve as valuable indicators to assist commercial establishments in providing better services to their clients, tailored to the average drinking habits of their customers.

Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume-Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior., Comment: 30 pages, 15 figures

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapt and apply it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance-overlap criterion for the chaos boundary at $K\approx 2.43$, reinforcing its effectiveness., Comment: 10 pages, 6 figures

Scramble intersections stand as compelling examples of complex systems, shedding light on the pressing challenge of urban mobility. In this paper, we introduce a model aimed at unraveling the statistical intricacies of pedestrian crossing times and their fluctuations in scenarios commonly encountered in major urban centers. Our findings offer snapshots that faithfully mirror real-world situations. Significantly, our results underscore the importance of two key factors: pedestrian flexibility and population density. These factors play a pivotal role in triggering the transition between mobile and immobile behavior in the steady state, a concept expounded upon within this paper through a straightforward order parameter known as directed mobility., Comment: 12 pages, 7 figures

An interesting concept that has been underexplored in the context of time-dependent simulations is the correlation of total magnetization, $C(t)$%. One of its main advantages over directly studying magnetization is that we do not need to meticulously prepare initial magnetizations. This is because the evolutions are computed from initial states with spins that are independent and completely random. In this paper, we take an important step in demonstrating that even for time evolutions from other initial conditions, $C(t_{0},t)$, a suitable scaling can be performed to obtain universal power laws. We specifically consider the significant role played by the second moment of magnetization. Additionally, we complement the study by conducting a recent investigation of random matrices, which are applied to determine the critical properties of the system. Our results show that the aging in the time series of magnetization influences the spectral properties of matrices and their ability to determine the critical temperature of systems., Comment: 14 pages, 6 figures

How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in the spectra of matrices built from time evolutions of magnetization of spin models. In this paper, we show that this method works very accurately in determining the critical temperature in the mean-field Ising model. We show that for Glauber or Metropolis dynamics, the average eigenvalue has a minimum at the critical temperature, which is corroborated by an inflection at eigenvalue dispersion at this same point. Such transition is governed by a gap in the density of eigenvalues similar to short-range spin systems. We conclude that the thermodynamics of this mean-field system can be described by the fluctuations in the spectra of Wishart matrices which suggests a direct relationship between thermodynamic fluctuations and spectral fluctuations., Comment: 14 pages, 4 figures

Our research highlights the effectiveness of utilizing matrices akin to Wishart matrices, derived from magnetization time series data under specific dynamics, to elucidate phase transitions and critical phenomena in the Q-state Potts model. By employing appropriate statistical methods, we not only discern second-order transitions but also differentiate weaker first-order transitions through careful analysis of the density of eigenvalues and their fluctuations. Furthermore, we investigate the method's sensitivity to stronger first-order transition points. Importantly, we establish a robust correlation between the system's actual thermodynamics and the spectral thermodynamics encapsulated within the eigenvalues. Our findings are further substantiated by correlation histograms of the time series data, revealing insightful patterns. Expanding upon our core findings, we present a didactic analysis that draws parallels between the spectral properties of criticality in a spin system and matrices intentionally imbued with correlations (a toy model). Within this framework, we observe a universal behavior characterized by the distribution of eigenvalues into two distinct groups, separated by a gap dependent on the level of correlation, influenced by temperature-induced changes in the spin system., Comment: 29 pages, 14 figures

Generating streams of true random numbers is a critical component of many embedded systems. The design of fully integrated, area and power efficient True Random Number Generators is a challenge. We propose a fully integrated, lightweight implementation, that uses the random telegraph noise (RTN) of standard MOSFET as entropy source. It is not analog-intensive, and without traditional post-processing algorithms, the generated random bit sequence passes the National Institute of Standards and Technology (NIST) tests., Comment: 4 pages, 4 figures, 1 table

In this work, we propose a simple stochastic agent-based model to describe the revenue dynamics of a nightclub venue based on the relationship between profit and spatial occupation. The system consists of an underlying square lattice (nightclub's dance floor) where every attendee (agent) is allowed to move to its first neighboring cells. Each guess has a characteristic delayed time between drinks, denoted as $\tau$, after which it will show an urge to drink. At this moment, the attendee will tend to move towards the bar where a drink will be bought. After it has left the bar zone, $\tau$ time steps should pass so it shows once again the need to drink. Our model among other points show that it is no use filling the bar to obtain profit, and optimization should be analyzed. This can be done in a more secure way taking into consideration the ratio between income and ticket cost., Comment: 13 pages, 6 figures

The earlier times of evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices G of different time evolutions of a simple testbed spin system, as the Ising model, we analyzed the density of eigenvalues of G^{T}G for different temperatures. We observe a transition of the shape of the distribution that presents a gap of eigenvalues from critical temperature with a continuous migration to the Marchenko-Pastur law for the paramagnetic phase. We consider the analysis a promising method to be applied in other spin systems to characterize phase transitions. Our approach is different from alternatives in the literature since it uses the magnetization matrix and not the spatial matrix of spins.

We obtained a semi-analytical treatment obtaining estimators for the sample variance and variance of sample variance for the RTS noise. Our method suggests a way to experimentally determine the constants of capture and emission in the case of a dominant trap and universal behaviors for the superposition from many traps. We present detailed closed-form expressions corroborated by MC simulations. We are sure to have an important tool to guide developers in building and analyzing low-frequency noise in semiconductor devices., Comment: 14 pages, 9 figures

The popularity of social media has created problems such as hate speech and sexism. The identification and classification of sexism in social media are very relevant tasks, as they would allow building a healthier social environment. Nevertheless, these tasks are considerably challenging. This work proposes a system to use multilingual and monolingual BERT and data points translation and ensemble strategies for sexism identification and classification in English and Spanish. It was conducted in the context of the sEXism Identification in Social neTworks shared 2021 (EXIST 2021) task, proposed by the Iberian Languages Evaluation Forum (IberLEF). The proposed system and its main components are described, and an in-depth hyperparameters analysis is conducted. The main results observed were: (i) the system obtained better results than the baseline model (multilingual BERT); (ii) ensemble models obtained better results than monolingual models; and (iii) an ensemble model considering all individual models and the best standardized values obtained the best accuracies and F1-scores for both tasks. This work obtained first place in both tasks at EXIST, with the highest accuracies (0.780 for task 1 and 0.658 for task 2) and F1-scores (F1-binary of 0.780 for task 1 and F1-macro of 0.579 for task 2)., Comment: 18 pages, presented at IberLEF: http://ceur-ws.org/Vol-2943/exist_paper2.pdf, the best scoring system at EXIST

Jansen and Oerding [H. K. Janssen, K. Oerding, J. Phys. A: Math. Gen. 27, 715 (1994)] predicted an interesting anomalous tricritical dynamic behavior in three-dimensional models via renormalization group theory. However, we verify a lack of literature about the computational verification of this universal behavior. Here, we used some tricks to capture the log corrections and the parameters predicted by these authors using the three-dimensional Blume-Capel model. In addition, we also performed a more detailed study of the dynamic localization of the phase diagram via power laws optimization. We quantify the crossover phenomena by computing the critical exponents near the tricritical point., Comment: 6 pages, 6 figures

In this work, we explore some interesting details of the time-dependent regime of the long-range systems under mean-field approximation in comparison with the critical dynamics of the short-range systems. First, we discuss some mechanisms of the initial anomalous behavior of the magnetization via two-dimensional Monte Carlo simulations to later compare with results from Mean-field simulations in both: spin 1/2 (Ising) and spin 1 (Blume Capel model) Ising models. The distinction between critical and tricritical points is also investigated. For a complete analysis, we performed short-time simulations in the mean-field regime to determine the critical temperatures optimizing power laws and the critical exponents of the different points, which were independently calculated, i.e. without using previous critical exponents estimates from literature/theory. Our investigations corroborate analytical results here also developed., Comment: 10 pages, 9 figures, 2 tables

In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. \textbf{184} 661--670 (2013)] for making predictions instead of only performing a successful characterization of the statistics on the punctuation of the real leagues. Our adaptation considers the advantage of playing at home when considering the potential of the home and away teams. The algorithm predicts the tournament's outcome by using the market value or/and the ongoing team's performance as initial conditions in the context of Monte Carlo simulations. We present and compare our results to the worldwide known SPI predictions performed by the "FiveThirtyEight" project. The results show that the algorithm can deliver good predictions even with a few ingredients and in more complicated seasons like the 2020 editions where the matches were played without fans in the stadiums., Comment: 14 pages, 6 figures, 2 tables

The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color problem. In this paper, we explicitly build the transfer matrix for the 3-color problem in order to calculate the number of possible configurations for finite systems with free, periodic in one direction and toroidal boundary conditions (periodic in both directions), Comment: 18 pages, 7 figures, 6 tables

Metaheuristics, as the simulated annealing used in the optimization of disordered systems, goes beyond physics, and the traveling salesman is a paradigmatic NP-complete problem that allows inferring important theoretical properties of the algorithm in different random environments. Many versions of the algorithm are explored in the literature, but so far the effects of the statistical distribution of the coordinates of the cities on the performance of the algorithm have been neglected. We propose a simple way to explore this aspect by analyzing the performance of a standard version of the simulated annealing (geometric cooling) in correlated systems with a simple and useful method based on a linear combination of independent random variables. Our results suggest that performance depends on the shape of the statistical distribution of the coordinates but not necessarily on its variance corroborated by the cases of uniform and normal distributions. On the other hand, a study with different power laws (different decay exponents) for the coordinates always produces different performances. We show that the performance of the simulated annealing, even in its best version, is not improved when the distribution of the coordinates does not have the first moment. However, surprisingly, we still observe improvements in situations where the second moment is not defined but not where the first one is not defined. Finite-size scaling fits, and universal laws support all of our results. In addition, our study show when the cost must be scaled., Comment: 23 pages, 12 figures, 2 tables

The entropy of the Higgs boson decay probabilities distribution in the Standard Model (SM) is maximized for a Higgs mass value that is less than one standard deviation away from the current experimental measurement. This successful estimate of the Higgs mass encourages us to propose tests of the Maximum Entropy Principle (MEP) as a tool for theoretical inferences in other instances of Higgs physics. In this letter, we show that, irrespective of the extension of the SM predicting a new Higgs boson decay channel, its branching ratio can be inferred to be around 7% in such a way that the new entropy of decays still exhibits a maximum at the experimental Higgs mass. This 7% rule can be tested whenever a new Higgs decay channel is found. In order to illustrate the MEP predictions, we apply the MEP inference to Higgs portal models, Higgs-axion interactions, lepton flavour violating decays of the Higgs boson, and a dark gauge boson model., Comment: 12 pages, 5 figures. Version published in Nuclear Physics B

In this paper, we study the effects of correlated random phases in the intensity of a superposition of $N$ wave-fields. Our results suggest that regardless of whether the phase distribution is continuous or discrete if the phases are random correlated variables, we must observe a heavier tail distribution and the emergence of extreme events as the correlation between phases increases. We believe that such a simple method can be easily applied in other situations to show the existence of extreme statistical events in the context of nonlinear complex systems., Comment: 11 pages, 3 figures

We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of detailed balance leads to entropy production phenomena, which are a hallmark of the irreversibility. By considering that voters can diffuse on the lattice we analyze how the entropy production and how the critical properties are affected by this diffusion. We also explore two important aspects of the diffusion effects on the majority voter model by studying entropy production and entropy flux via time-dependent and steady state simulations. This study is completed by calculating some critical exponents as function of the diffusion probability., Comment: 16 pages, 7 figures

We investigate 17 digital currencies making an analogy with quantum systems and develop the concept of eigenportfolios. We show that the density of states of the correlation matrix of these assets shows a behavior between that of the Wishart ensemble and one whose elements are Cauchy distributed. A metric for the participation matrix based on superposition of Gaussian functions is proposed and we show that small eigenvalues correspond to localized states. Nonetheless, some level of localization is also present for bigger eigenvalues probably caused by the fat tails of the distribution of returns of these assets. We also show through a clustering study that the digital currencies tend to stagger together. We conclude the paper showing that this correlation structure leads to an Epps effect., Comment: 13 pages, 6 figures