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BACKGROUND: The Confusion, Hubbub, and Order Scale (CHAOS in English Version) was originally developed in the USA by Matheny et al (Bringing order out of chaos: psychometric characteristics of the confusion, hubbub, and order scale. Journal of Applied Developmental Psychology 16(3):429-444, 1995) to measure chaos in the family environment, characterized by confusion, lack of routine, and organization. OBJECTIVE: To present evidence of content validity, internal structure validity, and validity based on relationships with external measures of an adapted version of the CHAOS into Brasilian Portuguese with adolescents sample in São Paulo - Brasil. METHOD: Study 1 involved the translation/back-translation and adaptation of the scale into Brazilian Portuguese [here named "Escala de Confusão, Alvoroço e Ordem no Sistema familiar" (CAOS)], assessed by 5 judges. In Study 2, we conducted an exploratory factor analyses (EFA) to determine the scale's factor structure (N = 180 adults). In Study 3, we carried out confirmatory factor analyses (CFA) to confirm the internal validity of the scale, along with complete structural equation modeling to explore convergent validity in another sample (N = 239 adolescents). RESULTS: The CAOS scale displayed content validity, and the EFA and CFA showed a unifactorial structure (with some scale adjustments) with an acceptable fit. The family chaos latent factor was associated with externalizing symptoms and perceived stress in adolescents. CONCLUSION: Overall, the Brazilian version of the scale presented evidence of construct, internal, and concurrent validity that indicate its usefulness in Brazil.

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Hodgkin lymphoma (HL) is one of the most common lymphomas, with an incidence of 3 per 100,000 persons. Current treatment uses a cocktail of genotoxic agents, including adriamycin, bleomycin, vinblastine, and dacarbazine (ABVD), along with or without radiotherapy. This treatment regimen has proved to be efficient in killing cancer cells, resulting in HL patients having a survival rate of >90% cancer-free survival at five years. However, this therapy does not have a specific cell target, and it can induce damage in the genome of non-cancerous cells. Previous studies have shown that HL survivors often exhibit karyotypes characterized by complex chromosomal abnormalities that are difficult to analyze by conventional banding. Multicolor fluorescence in situ hybridization (M-FISH) is a powerful tool to analyze complex karyotypes; we used M-FISH to investigate the presence of chromosomal damage in peripheral blood lymphocytes from five healthy individuals and five HL patients before, during, and one year after anti-cancer treatment. Our results show that this anti-cancer treatment-induced genomic chaos that persists in the hematopoietic stem cells from HL patients one year after finishing therapy. This chromosomal instability may play a role in the occurrence of second primary cancers that are observed in 10% of HL survivors. This chapter will describe a protocol for utilizing M-FISH to study treatment-induced genome chaos in Hodgkin's lymphoma (HL) patients, following a brief discussion.

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Three-phase induction motors are widely used in various industrial sectors and are responsible for a significant portion of the total electrical energy consumed. To ensure their efficient operation, it is necessary to apply control systems with specific algorithms able to estimate rotation speed accurately and with an adequate response time. However, the angular speed sensors used in induction motors are generally expensive and unreliable, and they may be unsuitable for use in hostile environments. This paper presents an algorithm for speed estimation in three-phase induction motors using the chaotic variable of maximum density. The technique used in this work analyzes the current signals from the motor power supply without invasive sensors on its structure. The results show that speed estimation is achieved with a response time lower than that obtained by classical techniques based on the Fourier Transform. This technique allows for the provision of motor shaft speed values when operated under variable load.

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In this study, we propose a method based on phase space reconstruction to estimate the short-term future behavior of pressure signals in pipelines. The pressure time series data were obtained from an IoT experimental model conducted in the laboratory. The proposed hydraulic system demonstrated the presence of traces of weak chaos in the time series of the pressure signal. Fractal dimension analysis revealed a complex fractal structure in the data, indicating the existence of nonlinear dynamics. Similarly, Lyapunov coefficients, divergent trajectories, and autocorrelation analysis confirmed the presence of weak chaos in the time series. The results demonstrated the existence of apparently chaotic patterns that follow the theory proposed by Kolmogorov for deterministic dynamic systems that exhibit apparently random behaviors. Phase space reconstruction allowed us to show the dynamic characteristics of the signal so that short-term predictions were stable. Finally, the study of strange attractors in pipeline pressure time series can have significant contributions to anomaly detection.•A methodology is proposed for the reconstruction of the phase space to estimate the short-term future behavior of pressure signals in pipelines in real time.•The analysis of the proposed hydraulic system revealed some indications of weak chaos in the time series of the pressure signal obtained experimentally.•The methodology implemented and the results of this study showed that the short-term predictions were very accurate and consistent; Chaotic patterns were also identified that support the theory proposed by Kolmogorov.

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Abstract Background The Confusion, Hubbub, and Order Scale (CHAOS in English Version) was originally developed in the USA by Matheny et al (Bringing order out of chaos: psychometric characteristics of the confusion, hubbub, and order scale. Journal of Applied Developmental Psychology 16(3):429-444, 1995) to measure chaos in the family environment, characterized by confusion, lack of routine, and organization. Objective To present evidence of content validity, internal structure validity, and validity based on relationships with external measures of an adapted version of the CHAOS into Brasilian Portuguese with adolescents sample in São Paulo - Brasil. Method Study 1 involved the translation/back-translation and adaptation of the scale into Brazilian Portuguese [here named "Escala de Confusão, Alvoroço e Ordem no Sistema familiar" (CAOS)], assessed by 5 judges. In Study 2, we conducted an exploratory factor analyses (EFA) to determine the scale's factor structure (N= 180 adults). In Study 3, we carried out confirmatory factor analyses (CFA) to confirm the internal validity of the scale, along with complete structural equation modeling to explore convergent validity in another sample (N=239 adolescents). Results The CAOS scale displayed content validity, and the EFA and CFA showed a unifactorial structure (with some scale adjustments) with an acceptable fit. The family chaos latent factor was associated with externalizing symptoms and perceived stress in adolescents. Conclusion Overall, the Brazilian version of the scale presented evidence of construct, internal, and concurrent validity that indicate its usefulness in Brazil.

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The Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics. It is constructed upon the other pillars-classical, quantum, relativistic mechanics and Maxwell equations for electromagnetism-and its foundations are grounded on the optimization of the BG (additive) entropic functional [Formula: see text]. Its use in the realm of classical mechanics is legitimate for vast classes of nonlinear dynamical systems under the assumption that the maximal Lyapunov exponent is positive (currently referred to as strong chaos), and its validity has been experimentally verified in countless situations. It fails however when the maximal Lyapunov exponent vanishes (referred to as weak chaos), which is virtually always the case with complex natural, artificial and social systems. To overcome this type of weakness of the BG theory, a generalization was proposed in 1988 grounded on the non-additive entropic functional [Formula: see text]. The index [Formula: see text] and related ones are to be calculated, whenever mathematically tractable, from first principles and reflect the specific class of weak chaos. We review here the basics of this generalization and illustrate its validity with selected examples aiming to bridge natural and social sciences. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

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Understanding the dynamics of complex systems defined in the sense of Caputo, such as fractional differences, is crucial for predicting their behavior and improving their functionality. In this paper, the emergence of chaos in complex dynamical networks with indirect coupling and discrete systems, both utilizing fractional order, is presented. The study employs indirect coupling to produce complex dynamics in the network, where the connection between the nodes occurs through intermediate fractional order nodes. The temporal series, phase planes, bifurcation diagrams, and Lyapunov exponent are considered to analyze the inherent dynamics of the network. Analyzing the spectral entropy of the chaotic series generated, the complexity of the network is quantified. As a final step, we demonstrate the feasibility of implementing the complex network. It is implemented on a field-programmable gate array (FPGA), which confirms its hardware realizability.

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Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi-Sugeno (T-S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

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A qualitative study of thermal transfers is carried out from a record of measurements (time series) of meteorological variables (temperature, relative humidity and magnitude of wind speeds) and pollutants (PM10, PM2.5 and CO) in six localities located at different heights in the geographic basin of Santiago de Chile. The measurements were made in two periods, 2010-2013 and 2017-2020 (a total of 2,049,336 data), the last period coinciding with a process of intense urbanization, especially high-rise construction. The measurements, in the form of hourly time series, are analyzed on the one hand according to the theory of thermal conduction discretizing the differential equation of the temporal variation in the temperature and, on the other hand, through the theory of chaos that provides the entropies (S). Both procedures demonstrate, comparatively, that the last period of intense urbanization presents an increase in thermal transfers and temperature, which affects urban meteorology and makes it more complex. As shown by the chaotic analysis, there is a faster loss of information for the period 2017-2020. The consequences of the increase in temperature on human health and learning processes are studied.

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Survival probability measures the probability that a system taken out of equilibrium has not yet transitioned from its initial state. Inspired by the generalized entropies used to analyze nonergodic states, we introduce a generalized version of the survival probability and discuss how it can assist in studies of the structure of eigenstates and ergodicity.

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PURPOSE: A recently proposed model potential to study quantum scattering of a positron from a hydrogen molecule is used to solve the Hamilton equations for scattering trajectories. In the present classical description, the positron can transfer energy to the vibrational mode of the molecule, remaining trapped for a while before escaping to infinity. Such vibrational resonances may correspond to trajectories which are embedded in phase-space regions of chaotic scattering.

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In this paper we analyze the behavior of the COVID-19 pandemic during a certain period of the year 2020 in the state of Mexico, Mexico. For this, we will use the discrete models obtained by the first, third and fourth authors of this work. The first is a one-dimensional model, and the second is two-dimensional, both non-linear. It is assumed that the population of the state of Mexico is constant and that the parameters used are the infection capacity, which we will initially assume to be constant, and the recovery and mortality parameters in that state. We will show that even when the statistical data obtained are disperse, and the process could be stabilized, this has been slow due to chaotic mitigation, creating situations of economic, social, health and political deterioration in that region of the country. We note that the observed results of the behavior of the epidemic during that period for the first variants of the virus have continued to be observed for the later variants, which has not allowed the eradication of the pandemic.

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The limit of validity of ordinary statistical mechanics and the pertinence of Tsallis statistics beyond it is explained considering the most probable evolution of complex systems processes. To this purpose we employ a dissipative Landau-Ginzburg kinetic equation that becomes a generic one-dimensional nonlinear iteration map for discrete time. We focus on the Renormalization Group (RG) fixed-point maps for the three routes to chaos. We show that all fixed-point maps and their trajectories have analytic closed-form expressions, not only (as known) for the intermittency route to chaos but also for the period-doubling and the quasiperiodic routes. These expressions have the form of q-exponentials, while the kinetic equation's Lyapunov function becomes the Tsallis entropy. That is, all processes described by the evolution of the fixed-point trajectories are accompanied by the monotonic progress of the Tsallis entropy. In all cases the action of the fixed-point map attractor imposes a severe impediment to access the system's built-in configurations, leaving only a subset of vanishing measure available. Only those attractors that remain chaotic have ineffective configuration set reduction and display ordinary statistical mechanics. Finally, we provide a brief description of complex system research subjects that illustrates the applicability of our approach.

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This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of sparse interactions: each firing neuron triggers an instantaneous increase in electric potential to a fixed number of randomly chosen neurons. We prove that, as the number of neurons approaches infinity, the finite network converges to a nonlinear mean-field process characterised by a jump-type stochastic differential equation. We show that this process displays a phase transition: the activity of a typical neuron in the infinite network either rapidly dies out, or persists forever, depending on the global parameters describing the intensity of interconnection. This provides a way to understand the emergence of persistent activity triggered by weak input signals in large neural networks.

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La Teoría del Caos surgió relacionada con las ciencias naturales, pero en la actualidad su campo de aplicación es cada vez más amplio porque el pensamiento complejo ha ofrecido solución a numerosos sistemas en la naturaleza, la biología y otras muy diversas esferas de la vida, como la economía y la lingüística, entre otras. En este artículo se pretende ofrecer una panorámica sobre las principales aplicaciones del caos en medicina, dado que muchos procesos en medicina manifiestan aparente desorden, complejidad y caos. Se analizarán, en particular, las opiniones existentes entre los investigadores sobre la presencia y significado del caos en los procesos metabólicos, las enfermedades cardíacas y la actividad cerebral, ya que son las áreas médicas que expresan los comportamientos más complejos. También se expondrán los resultados de la aplicación de las matemáticas del caos en la epidemiología. Es importante apropiarse de este nuevo enfoque porque comprender el caos confiere al hombre, en cualquier campo que se desempeñe, una visión más clara de la realidad. El abordaje científico aplicando la teoría del caos, conlleva la creación de un equipo multidisciplinario, que enfrente la complejidad desde todas las aristas posibles y del que puedan surgir ideas que rebasen las fronteras del paradigma científico tradicional. Según los expertos sobre el tema, la Teoría del Caos seguirá teniendo un espacio importante en el futuro. Es un reto, una necesidad y un deber para los investigadores de las diferentes ramas y especialidades, estar preparados.

Chaos Theory arose in connection with the natural sciences, but today its field of application is increasingly broad because complex thinking has offered solutions to numerous systems in nature, biology and other very diverse spheres of life, such as economics and linguistics, among others. This article aims to offer an overview of the main applications of chaos in medicine, given that many processes in medicine show apparent disorder, complexity and chaos. In particular, the existing opinions among researchers about the presence and meaning of chaos in metabolic processes, heart disease and brain activity will be analyzed, since these are the medical areas that express the most complex behaviors. The results of the application of the mathematics of chaos in epidemiology will also be presented. It is important to appropriate this new approach because understanding chaos gives man, in whatever field he works, a clearer vision of reality. The scientific approach applying chaos theory entails the creation of a multidisciplinary team that faces complexity from all possible angles and from which ideas can arise that go beyond the borders of the traditional scientific paradigm. According to experts on the subject, Chaos Theory will continue having an important space in the future. It is a challenge, a necessity and a duty for researchers from different branches and specialties to be prepared.

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From a methodology in the reconstruction scheme, applicable to chaotic time series of economic indices, this paper presents an analysis of the underlying dynamics of stock markets of North America, Europe and Asia. The same global fit model and reconstruction parameters-employed to study the time evolution of S&P 500, NASDAQ Composite, IBEX 35, EURONEXT 100, Nikkei 225 and SSE Composite Index-led a convenient simplification in the analysis. The tools chosen to analyse the time dependence of the level of chaos concerning weeks of economic activity were scatter plots, histograms and sample Spearman correlation coefficients. The results permit to evaluate the impact of the pandemic in the underlying dynamics of different stock markets and to compare them to one another.

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The pandemic outbreak in March 2020 and its associated sanitary regulations and restrictions triggered an abrupt and significant change for society in general and for families' organization in particular. In Chile, the Santiago Metropolitan District was under a strict lockdown that involved the closure of the entire educational system. From a systemic-family stress perspective, the impact of these changes might have consequences not only for each individual family member, but for the parental dynamic and, consequently, for children's well-being. This paper presents the results of a follow-up study showing changes in self-reported parental depression and the perceived home organization of mothers and fathers assessed at three different moments: before the pandemic, at the initial outbreak, and after 1 month of strict lockdown. Relevant moderators were explored using linear mixed models to understand the within-subject changes in mothers' and fathers' self-reports across the different assessment times. Financial strain, personality traits of self-criticism and dependency, previous parent-child quality interaction, recent major stressful events, and number of children are highlighted as relevant factors that moderate changes in home chaos and parental mental health perception. Significant risks and protective factors are described for fathers and mothers. The use of pre-pandemic measures as baseline levels enabled the identification of personal and family characteristics that were related to better outcomes. The results help increase our understanding of the sanitary regulations' impacts on the family system and identify vulnerability indicators that should be considered.

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Resumen Introducción: la teoría del caos se usa para explicación de fenómenos complejos, cuya naturaleza no responde a comportamientos lineales y que a su vez no permite determinar con exactitud medidas y cálculos, pero que a pesar de ello se han logrado avances significativos en la ciencia, pudiéndose expandir además hasta las explicaciones de fenómenos sociales, siendo en este caso la violencia. Materiales y Métodos: se emplearon expresiones matemáticas para validar un modelo de realidad que describa aproximadamente índices de violencia a partir de datos reales. Resultados: se obtuvieron relaciones matemáticas que describen el comportamiento caótico, las cuales dependiendo de la tasa de violencia define si el valor tiende a cero, a un valor constante o un comportamiento caótico. Conclusiones: se obtuvo una relación matemática que describe el comportamiento entrópico de la violencia en sociedad, cuya tendencia caótica describe aproximadamente índices de violencia reales.

Abstract Introduction: chaos theory is used to explain complex phenomena, whose nature does not respond to linear behavior and which in turn does not allow exact measurements and calculations to be determined, but despite this, significant advances have been made in science, being able to also expand to the explanations of social phenomena, in this case being violence. Materials and Methods: mathematical expressions are used to validate the reality, which describes rates of violence from real data in Colombia. Results: mathematical relationships describing chaotic behavior were obtained, which, depending on the rate of violence, define whether the value tends to zero, a constant value or chaotic behavior. Conclusions: a mathematical relationship was obtained that describes the entropic behavior of violence in society, whose chaotic trend approximately describes real violence values.

Resumo Introdução: a teoria do caos é utilizada para explicar fenômenos complexos, cuja natureza não responde ao comportamento linear e que por sua vez não permite determinar medidas e cálculos exatos, mas apesar disso, avanços significativos foram feitos na ciência, expandindo para as explicações de fenômenos sociais, neste caso a violência. Materiais e Métodos: foram utilizadas expressões matemáticas para validar um modelo de realidade que descreve aproximadamente as taxas de violência a partir de dados reais. Resultados: foram obtidas relações matemáticas que descrevem o comportamento caótico, que, dependendo da taxa de violência, definem-se o valor que tende a zero, um valor constante ou um comportamento caótico. Conclusões: obteve-se uma relação matemática que descreve o comportamento entrópico da violência na sociedade, cuja tendência caótica descreve de forma aproximada os índices reais de violência.

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Systemic blood pressure (BP) may oscillate for homeostatic needs (equilibrium by constancy) or just as shifts in other intrinsic and extrinsic variables known as allostatic changes. This transitory pressure often rises alerts physicians to out-of-control hypertension or even hypertensive crisis. There is a very complex theory underlying these stochastic phenomena, which physicists and mathematicians translate into a single word: chaos. These changes happen according to a stochastic probabilistic pattern that presumes chaotic but somewhat predictable and nonlinear modeling of BP-related dynamics as a mathematical approach. Based on the chaos theory, small changes at the initial BP (baseline overtime) values could disturb the homeostasis leading to extreme BP chaotic shifts. These almost insignificant oscillations may also affect other variables and systems, leading to the misdiagnosis of hypertension, "out-of-control" BP levels, and resistant hypertension (RHT). Thus, these unpredictable and transient increases in BP values may be improperly diagnosed as the white coat and masked or resistant hypertension. Indeed, the interference of the chaos in any phenotype of (true or false) hard to control BP is not considered in clinical settings. This review provides some basic concepts on chaos theory and BP regulation. Besides pseudoresistant hypertension (lack of adherence, circadian variations, and others (white-coat, masked, early morning effects or hypertension), chaotic changes can be responsible for out-of-control hypertension.

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Childhood obesity causes not only medical and psychosocial problems, it also reduces the life expectancy of the adults that they will become. On a large scale, obese adults adversely affect labor markets and the gross domestic product of countries. Monitoring the growth charts of children helps to maintain their body weight within healthy parameters according to the World Health Organization. Modern technologies allow the use of telehealth to carry out weight control programs and monitoring to verify children's compliance with the daily recommendations for risk factors that can be promoters of obesity, such as insufficient physical activity and insufficient sleep hours. In this work, we propose a secure remote monitoring and supervision scheme of physical activity and sleep hours for the children based on telehealth, multi-user networks, chaotic encryption, and spread spectrum, which, to our knowledge, is the first attempt to consider this service for safe pediatric telemedicine. In experimental results, we adapted a recent encryption algorithm in the literature for the proposed monitoring scheme using the assessment of childhood obesity as an application case in a multi-user network to securely send and receive fictitious parameters on childhood obesity of five users through the Internet by using just one communication channel. The results show that all the monitored parameters can be transmitted securely, achieving high sensitivity against secret key, enough secret key space, high resistance against noise interference, and 4.99 Mb/sec in computational simulations. The proposed scheme can be used to monitor childhood obesity in secure telehealth application.

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