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In this work we perform a detailed entropy analysis of some substitutive sequences using the technique of lumping. The basic novelty of the entropy analysis by lumping is that, unlike the Fourier transform or the conventional entropy analysis by gliding, it gives results that can be related to algorithmic aspects of the sequences and in particular with the important property of automaticity. All computations in this paper have been performed with TOOLS FOR SYMBOLIC DYNAMICS a Maple package developed by the authors.

The purpose of this paper is to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map.

At the beginning of the twentieth century, Poincare's recurrence theorem had revolutionized modern mechanics and statistical physics. However, this theorem did not attract considerable attention, at least from a numerical and computational point of view. In a series of relatively recent papers, Balakrishnan, Nicolis and Nicolis have addressed the recurrence time problem in a firm basis, introducing notation, theory, and numerical studies. Motivated by this call, the paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map. The authors propose here in different tests and computations, each one illuminating the many aspects of the problem of recurrence. The paper ends up with a short discussion and conclusions.

In this paper, the authors obtain new results on computations, each one illuminating the many aspects of the problem of recurrence. One striking aspect of this detailed work, is that when the sizes of the cells in the phase space became considerable, then the recurrence times assume ordinary values.

The paper extends previous results on chaotic maps to the logistic map, enhancing comprehension, making possible connections with number theory, combinatorics and cryptography.

The purpose of this paper is to discuss the recognizability of Cantorian stochastic automata by generalized entropy‐like qualities.

The paper gives a necessary entropy condition, valid for all sequences on the alphabet {0, 1} read by lumping and generated by a Cantorian stochastic automaton.

The paper finds that, on this basis, once can determine that a given sequence is not generated by Cantorian stochastic automata and reconstruct the automaton when the sequence is generated by a Cantorian stochastic automaton.

This paper derives a new diagnostic for Cantorian stochastic automata, which could find a direct application to biology, where there is a recent claim that the coding regions of chromosomes form Cantor sets.

Introduction: Blockchain is gaining attention in various industries and sectors. It is described as an emergent technology with immense possibilities similar to how the internet has revolutionised how businesses are currently carried out. Still, various sectors have either not adopted or are in a very nascent stage to adopt blockchain technology in their operations. The current research examines how blockchain can be used in the insurance sector. This industry was chosen as it is extremely relevant in today’s world and directly bears its economy.

Purpose: To determine the current and future path in which the insurance industry is moving about blockchain technology adoption and find synergy between blockchain technology and the insurance business.

Need for study: The insurance industry is highly relevant in today’s world and directly bears the country’s economy. Additionally, blockchain is an emergent technology with immense possibilities similar to how the internet has revolutionised how businesses are done. The current research looks at how blockchain can be used in the insurance business.

Methodology: A systematic literature review was conducted in this study by reviewing literature related to blockchain technology and the insurance sector. Science direct was used as a source of information. For this study, the literature review approach was chosen since it allows us to trace the growth of the subject matter and identify the patterns that have formed through time.

Findings: The study found that the insurance sector has recognised the latent benefits of blockchain technology and has begun to develop its usage in selected cases such as fraud prevention and risk assessment.

Practical implications: The current study can be referred to by academicians, marketers, industry people, and policymakers. The study encourages companies and academicians to further investigate the usage of blockchain in insurance.

The purpose of this paper is to explore new mathematical results to advance the understanding of the picture of a chaotic unimodal map.

Ever since Poicare, deterministic chaos is ultimately connected with exponential divergence of nearby trajectories, unpredictability and erratic behaviour. Here, the authors propose an alternative approach in terms of complexity theory and transcendence.

In this paper, the authors were able to reproduce previous results easily, due to new theorems.

The paper updates previous results and proposes a more complete understanding of the phenomenon of deterministic chaos, also making possible connections with number theory, combinatorics and possibly quantum mechanics, as in quantum mechanics there does not exist the notion on nearby trajectories.

Given a time‐series, what is the best partitioning of the state space in order to obtain reasonable values for the block entropies? The purpose of this paper is to provide a simple answer (an algorithm), although approximative, in connection with symbolic dynamics and statistical properties of 1‐d maps on the interval.

The logistic map is examined as an archetype of a Complex System with different behaviors, namely: periodicity, order‐to‐chaos period‐doubling transition, weak chaos, parametric intermittent chaos, developed chaos and fully developed chaos. For the logistic map the generating partition is known, and allows comparison with other prescriptions in the literature. The partitioning of the phase space with the easy generated bipartition induced by the mean value of a curve in the plane, gives results in good agreement (roughly up to a 20 per cent difference) with the results of the generating partition, if the trajectory of the system is in parametric intermittent chaos and in developed chaos (DC). In the case of fully developed chaos (FDC), the agreement is perfect.

The authors confirm that a statistical partitioning is almost equivalent with the exact partitioning for the logistic map.

The paper updates previous results and proposes a better understanding on the partitioning for symbolic dynamics.

The purpose of this research paper is to review and synthesize the role of blockchain technology (BCT) in various types of illegal activities, including but not limited to fraud, money laundering, ransomware attacks, firearms, drug tracking, cyberattacks, identity theft and scams.

The authors conducted a review of studies related to illegal activities using blockchain from 2015 to 2023. Next, a thematic review of the literature was performed to see how these illegal activities were conducted using BCT.

Through this study, the authors identify the relevant themes that highlight the major illegal activities performed using BCT, its possible steps for prevention and the opportunities for future developments. Finally, the authors provide suggestions for future research using the theory, context and method framework.

No other research has synthesized the illegal activities using BCT through a thematic approach to the best of the authors’ knowledge. Hence, this study will act as a starting point for future research for academic and technical practitioners in this area.