arXiv subjects

Erveton P. Pinto

Publications and source records attributed to Erveton P. Pinto.

3 recordsLinked to original sources

arXiv2026

Chaos and Parrondo's paradox: An overview

Parrondo's paradox (PP) is a fundamental principle in nonlinear science where the alternation of individually losing strategies leads to a winning outcome. In this topical review, we provide the first systematic panorama of the synergy between PP and chaos. We observe a bidirectional connection between the two areas. The first direction is the translation of PP into the interplay between Order and Chaos through either Chaos + Chaos $\to$ Order (CCO) or Order + Order $\to$ Chaos (OOC). In this vein, many quantifiers, such as Lyapunov Exponents, $λ$, and entropic measures, are used. Second, we note that chaos can be used to engineer switching protocols that can lead to nontrivial effects in diverse PP cases. Our review clarifies the universality of PP and highlights its robust theoretical and practical applications across several areas of science and technology. Finally, we delineate key open questions, emphasizing the unresolved theoretical limits, the role of high-dimensional maps and continuous flows, and the critical need for more experimental verification of the dynamic PP in chaotic systems. For completeness, we also provide a full Python code that allows the reader to observe the many facets of the PP.

nlin.CD↗

arXiv2025

Cryptocurrency Time Series on the Binary Complexity-Entropy Plane: Ranking Efficiency from the Perspective of Complex Systems

We report the first application of a tailored Complexity-Entropy Plane designed for binary sequences and structures. We do so by considering the daily up/down price fluctuations of the largest cryptocurrencies in terms of capitalization (stable-coins excluded) that are worth $circa \,\, 90 \%$ of the total crypto market capitalization. With that, we focus on the basic elements of price motion that compare with the random walk backbone features associated with mathematical properties of the Efficient Market Hypothesis. From the location of each crypto on the Binary Complexity-Plane (BiCEP) we define an inefficiency score, $\mathcal I$, and rank them accordingly. The results based on the BiCEP analysis, which we substantiate with statistical testing, indicate that only Shiba Inu (SHIB) is significantly inefficient, whereas the largest stake of crypto trading is reckoned to operate in close-to-efficient conditions. Generically, our $\mathcal I$-based ranking hints the design and consensus architecture of a crypto is at least as relevant to efficiency as the features that are usually taken into account in the appraisal of the efficiency of financial instruments, namely canonical fiat money. Lastly, this set of results supports the validity of the binary complexity analysis.

q-fin.ST↗

arXiv2025

Parrondo's effects with aperiodic protocols

In this work, we study the effectiveness of employing archetypal aperiodic sequencing -- namely Fibonacci, Thue-Morse, and Rudin-Shapiro -- on the Parrondian effect. From a capital gain perspective, our results show that these series do yield a Parrondo's Paradox with the Thue-Morse based strategy outperforming not only the other two aperiodic strategies but benchmark Parrondian games with random and periodical ($AABBAABB\ldots$) switching as well. The least performing of the three aperiodic strategies is the Rudin-Shapiro. To elucidate the underlying causes of these results, we analyze the cross-correlation between the capital generated by the switching protocols and that of the isolated losing games. This analysis reveals that a strong anticorrelation with both isolated games is typically required to achieve a robust manifestation of Parrondo's effect. We also study the influence of the sequencing on the capital using the lacunarity and persistence measures. In general, we observe that the switching protocols tend to become less performing in terms of the capital as one increases the persistence and thus approaches the features of an isolated losing game. For the (log-)lacunarity, a property related to heterogeneity, we notice that for small persistence (less than 0.5) the performance increases with the lacunarity with a maximum around 0.4. In respect of this, our work shows that the optimization of a switching protocol is strongly dependent on a fine-tuning between persistence and heterogeneity.

physics.soc-ph↗