Predicting chromosomal compartments directly from the nucleotide sequence with DNA-DDA.

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby.

Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis.

Analytical methods derived from nonlinear dynamical systems, complexity, and chaos theories offer researchers a framework for in-depth analysis of time series data. However, relatively few studies involving time series data obtained from psychological and behavioral research employ such methods. This paucity of application is due to a lack of general analysis frameworks for modeling time series data with strong nonlinear components. In this article, we describe the potential of Hankel alternative view of Koopman (HAVOK) analysis for solving this issue. HAVOK analysis is a unified framework for nonlinear dynamical systems analysis of time series data. By utilizing HAVOK analysis, researchers may model nonlinear time series data in a linear framework while simultaneously reconstructing attractor manifolds and obtaining a secondary time series representing the amount of nonlinear forcing occurring in a system at any given time. We begin by showing the mathematical underpinnings of HAVOK analysis and then show example applications of HAVOK analysis for modeling time series data derived from real psychological and behavioral studies.

Applying dynamic systems theory and complexity theory methods in psychotherapy research: A systematic literature review.

OBJECTIVE: Dynamic systems theory and complexity theory (DST/CT) is a framework explaining how complex systems change and adapt over time. In psychotherapy, DST/CT can be used to understand how a person's mental and emotional state changes during therapy incorporating higher levels of complexity. This study aimed to systematically review the variability of DST/CT methods applied in psychotherapy research. METHODS: A primary studies search was conducted in the EBSCO and Web of Knowledge databases, extracting information about the analyzed DST/CT phenomena, employed mathematical methods to investigate these phenomena, descriptions of specified dynamic models, psychotherapy phenomena, and other information regarding studies with empirical data (e.g., measurement granularity). RESULTS: After screening 38,216 abstracts and 4,194 full texts, N = 41 studies published from 1990 to 2021 were identified. The employed methods typically included measures of dynamic complexity or chaoticity. Computational and simulation studies most often employed first-order ordinary differential equations and typically focused on describing the time evolution of client-therapist dyadic influences. Eligible studies with empirical data were usually based on case studies and focused on data with high time intensity of within-session dynamics. CONCLUSION: This review provides a descriptive synthesis of the current state of the proliferation of DST/CT methods in the psychotherapy research field.

Fractal-Based Hybrid Cryptosystem: Enhancing Image Encryption with RSA, Homomorphic Encryption, and Chaotic Maps.

Protecting digital data, especially digital images, from unauthorized access and malicious activities is crucial in today's digital era. This paper introduces a novel approach to enhance image encryption by combining the strengths of the RSA algorithm, homomorphic encryption, and chaotic maps, specifically the sine and logistic map, alongside the self-similar properties of the fractal Sierpinski triangle. The proposed fractal-based hybrid cryptosystem leverages Paillier encryption for maintaining security and privacy, while the chaotic maps introduce randomness, periodicity, and robustness. Simultaneously, the fractal Sierpinski triangle generates intricate shapes at different scales, resulting in a substantially expanded key space and heightened sensitivity through randomly selected initial points. The secret keys derived from the chaotic maps and Sierpinski triangle are employed for image encryption. The proposed scheme offers simplicity, efficiency, and robust security, effectively safeguarding against statistical, differential, and brute-force attacks. Through comprehensive experimental evaluations, we demonstrate the superior performance of the proposed scheme compared to existing methods in terms of both security and efficiency. This paper makes a significant contribution to the field of digital image encryption, paving the way for further exploration and optimization in the future.

How complex is COVID-19: Spatiotemporal variation of chaotic nature of the virus in Indian states.

Like other pandemics, COVID-19 also created a huge socioeconomic imbalance and distress in people. Often, every pandemic is characterized as chaotic and complex. Hence, the nature of the virus spread and deaths should be analyzed to prepare for the next similar pandemic. In this analysis, the popular and well-known time series in chaos theory is implemented, and the results are deduced for the states of India. The phase space reconstruction algorithm is implemented, and false nearest neighbor (FNN) method is applied to determine the dimensionality, and also Lyapunov exponent of the time series is estimated. The chaotic nature of COVID-19 cases showed a less severe and low complexity, with the FNN dimension range of 3-5, whereas the COVID-19 deaths showed moderate complexity with FNN dimensions 2-7. Policymakers should take action on medical availability in rural states and control people's movement in highly populated areas.

A Chaotic Compressive Sensing Based Data Transmission Method for Sensors within BBNs.

Body to body networks (BBNs) are a kind of large-scaled sensor network that are composed of several wireless body area networks (WBANs) in the distributed structure, and in recent decades, BBNs have played a key role in medical, aerospace, and military applications. Compared with the traditional WBANs, BBNs have larger scales and longer transmission distances. The sensors within BBNs not only transmit the data they collect, but also forward the data sent by other nodes as relay nodes. Therefore, BBNs have high requirements in energy efficiency, data security, and privacy protection. In this paper, we propose a secure and efficient data transmission method for sensor nodes within BBNs that is based on the perception of chaotic compressive sensing. This method can simultaneously accomplish data compression, encryption, and critical information concealment during the data sampling process and provide various levels of reconstruction qualities according to the authorization level of receivers. Simulation and experimental results demonstrate that the proposed method could realize data compression, encryption, and critical information concealment for images that are transmitted within BBNs. Specifically, the proposed method could enhance the security level of data transmission by breaking the statistical patterns of original data, providing large key space and sensitivity of the initial values, etc.

Sensitivity Optimization and Experimental Study of the Long-Range Metal Detector Based on Chaotic Duffing Oscillator.

Sensors based on chaotic oscillators have a simple design, combined with high sensitivity and energy efficiency. Among many developed schemes of such sensors, the promising one is based on the Duffing oscillator, which possesses a remarkable property of demonstrating chaotic oscillations only in the presence of a weak sine wave at the input. The main goal of this research was to evaluate the maximal sensitivity of a practically implemented metal detector based on the Duffing oscillator and compare its sensitivity with conventional sensors. To achieve high efficiency of the Duffing-based design, we proposed an algorithm which performs a bifurcation analysis of any chaotic system, classifies the oscillation modes and determines the system sensitivity to a change in different parameters. We apply the developed algorithm to improve the sensitivity of the electronic circuit implementing the Duffing oscillator, serving as a key part of a three-coil metal detector. We show that the developed design allows detecting the presence of metal objects near the coils more reliably than the conventional signal analysis techniques, and the developed detector is capable of sensing a large metal plate at distances up to 2.8 of the coil diameter, which can be considered a state-of-the-art result.

Resilience Strategies of Ports against Covid-19 in Terms of Chaos Theory.

During the Covid-19 pandemic, all sectors experienced chaotic dynamics worldwide. For example, maritime transport, particularly ports as one of its main elements, had to continue operating in this chaotic environment. Ports developed their own strategies to provide resilience against these challenges. However, any study in the related literature has not been reached that reveals resilience strategies of ports by combining literature review and interviews with port practitioners. As a novelty of the study, it was tried to evaluate resilience strategies of ports by grounding chaos theory. Therefore, this study had two aims: (1) identifying the Covid-19 strategies of Turkish container ports; (2) prioritizing these strategies in terms of impact level. First, interviews were conducted with Turkish container port representatives to find out their resilience strategies. These strategies were then validated with a literature review and new ones were detected. Second, separate relation analyses of the strategies were conducted for the interviews and literature. Finally, ports' resilience strategies against Covid-19 disruptions were prioritized using Fuzzy Analytic Hierarchy Process (AHP) based on the port managers' evaluations. Fuzzy AHP is widely used and accepted in the maritime business literature. This method also diminishes inconsistencies and subjective evaluations by employing fuzzy logic. The results showed that 'Control Mechanism', 'Hygienic Measures', and 'Information Exchange' were the most effective resilience strategies. By using chaos theory, this study helped to theoretically clarify the role of port management approaches to the challenges of the Covid-19 pandemic. These findings can therefore guide container port practitioners in overcoming pandemic conditions.

A Novel Hyperchaotic 2D-SFCF with Simple Structure and Its Application in Image Encryption.

In this paper, a novel image encryption algorithm is proposed based on hyperchaotic two-dimensional sin-fractional-cos-fractional (2D-SFCF), called sin-fractional-cos-fractional image-encryption (SFCF-IE). The 2D-SFCF is constructed from two one-dimensional cosine fractional (1-DCFs), and it has a more complex chaotic behavior with a larger parameter space than one-dimensional chaotic systems. Compared with the two-dimensional (2D) chaotic system, the 2D-SFCF has a simple structure, and the parameter space in the chaotic state is continuous, which is beneficial to generating the keystream in the cryptosystem. Therefore, in the novel image encryption algorithm, we use the 2D-SFCF to generate the keystream of the cryptosystem. The encryption algorithm is a process of scrambling and diffusion. Different from common diffusion methods, the diffusion starting position of the SFCF-IE is randomly generated, enhancing the algorithm's security. Simulation experiments show that the image encrypted by this algorithm has better distribution characteristics and can resist common attack methods.

Importance-Based Key Basic Event Identification and Evolution Mechanism Investigation of Hydraulic Support Failure to Protect Employee Health.

BACKGROUND: Although hydraulic support can help enterprises in their production activities, it can also cause fatal accidents. METHODS: This study established a composite risk-assessment method for hydraulic support failure in the mining industry. The key basic event of hydraulic support failure was identified based on fault tree analysis and gray relational analysis, and the evolution mechanism of hydraulic support failure was investigated based on chaos theory, a synthetic theory model, and cause-and-effect-layer-of-protection analysis (LOPA). RESULTS: After the basic events of hydraulic support failure are identified based on fault tree analysis, structure importance (SI), probability importance (PI), critical importance (CI), and Fussell-Vesely importance (FVI) can be calculated. In this study, we proposed the Fussell-Vesely-Xu importance (FVXI) to reflect the comprehensive impact of basic event occurrence and nonoccurrence on the occurrence probability of the top event. Gray relational analysis was introduced to determine the integrated importance (II) of basic events and identify the key basic events. According to chaos theory, hydraulic support failure is the result of cross-coupling and infinite amplification of faults in the employee, object, environment, and management subsystems, and the evolutionary process has an obvious butterfly effect and inherent randomness. With the help of the synthetic theory model, we investigated the social and organizational factors that may lead to hydraulic support failure. The key basic event, jack leakage, was analyzed in depth based on cause-and-effect-LOPA, and corresponding independent protection layers (IPLs) were identified to prevent jack leakage. IMPLICATIONS: The implications of these findings with respect to hydraulic support failure can be regarded as the foundation for accident prevention in practice.

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints.

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

Dynamical Field Inference and Supersymmetry.

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.

Complexity of COVID-19 Dynamics.

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of "false" neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

Theory of particle transport phenomena during fatigue and time-dependent fracture of materials based on mesoscale dynamics and their practical applications.

In this work, the mesoscale mechanics of metals, which links their microscopic physics and macroscopic mechanics, was established. For practical applications, the laws for quantitatively predicting life of cycle and time-dependent fracture behavior such as fatigue, hydrogen embrittlement, and high-temperature creep were derived using particle transport phenomena theories such as dislocation group dynamics, hydrogen diffusion, and vacancy diffusion. Furthermore, these concepts were also applied for estimating the degree of viscoelastic deterioration of blood vessel walls, which is dominated by a time-dependent mechanism, and for the diagnosis of aneurysm accompanied by the viscoelastic deterioration of the blood vessel wall. In these theories, new mechanical indexes were derived as dominant factors for predicting the life of fatigue crack growth and the time-dependent fracture of notched specimens of materials such as hydrogen embrittlement and high-temperature creep. Furthermore, as an example of a practical application, these theories were applied to estimate the degree of viscoelastic deterioration and chaotic motions of blood vessel walls, which are closely related to blood vessel diseases such as atherosclerosis and aneurysm. Moreover, new indexes to diagnose them were also proposed for clinical applications.

Approaching Adversarial Example Classification with Chaos Theory.

Adversarial examples are one of the most intriguing topics in modern deep learning. Imperceptible perturbations to the input can fool robust models. In relation to this problem, attack and defense methods are being developed almost on a daily basis. In parallel, efforts are being made to simply pointing out when an input image is an adversarial example. This can help prevent potential issues, as the failure cases are easily recognizable by humans. The proposal in this work is to study how chaos theory methods can help distinguish adversarial examples from regular images. Our work is based on the assumption that deep networks behave as chaotic systems, and adversarial examples are the main manifestation of it (in the sense that a slight input variation produces a totally different output). In our experiments, we show that the Lyapunov exponents (an established measure of chaoticity), which have been recently proposed for classification of adversarial examples, are not robust to image processing transformations that alter image entropy. Furthermore, we show that entropy can complement Lyapunov exponents in such a way that the discriminating power is significantly enhanced. The proposed method achieves 65% to 100% accuracy detecting adversarials with a wide range of attacks (for example: CW, PGD, Spatial, HopSkip) for the MNIST dataset, with similar results when entropy-changing image processing methods (such as Equalization, Speckle and Gaussian noise) are applied. This is also corroborated with two other datasets, Fashion-MNIST and CIFAR 19. These results indicate that classifiers can enhance their robustness against the adversarial phenomenon, being applied in a wide variety of conditions that potentially matches real world cases and also other threatening scenarios.

Short-Time Estimation of Fractionation in Atrial Fibrillation with Coarse-Grained Correlation Dimension for Mapping the Atrial Substrate.

Atrial fibrillation (AF) is currently the most common cardiac arrhythmia, with catheter ablation (CA) of the pulmonary veins (PV) being its first line therapy. Ablation of complex fractionated atrial electrograms (CFAEs) outside the PVs has demonstrated improved long-term results, but their identification requires a reliable electrogram (EGM) fractionation estimator. This study proposes a technique aimed to assist CA procedures under real-time settings. The method has been tested on three groups of recordings: Group 1 consisted of 24 highly representative EGMs, eight of each belonging to a different AF Type. Group 2 contained the entire dataset of 119 EGMs, whereas Group 3 contained 20 pseudo-real EGMs of the special Type IV AF. Coarse-grained correlation dimension (CGCD) was computed at epochs of 1 s duration, obtaining a classification accuracy of 100% in Group 1 and 84.0-85.7% in Group 2, using 10-fold cross-validation. The receiver operating characteristics (ROC) analysis for highly fractionated EGMs, showed 100% specificity and sensitivity in Group 1 and 87.5% specificity and 93.6% sensitivity in Group 2. In addition, 100% of the pseudo-real EGMs were correctly identified as Type IV AF. This method can consistently express the fractionation level of AF EGMs and provides better performance than previous works. Its ability to compute fractionation in short-time can agilely detect sudden changes of AF Types and could be used for mapping the atrial substrate, thus assisting CA procedures under real-time settings for atrial substrate modification.

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial.

Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge is required to understand the methodology.

Early warning biomarkers in major depressive disorder: a strategic approach to a testing question.

PURPOSE: Identification of biomarkers in major depressive disorder (MDD) has proceeded in an extemporised manner. No single biomarker has been identified with utility in screening, diagnosis, prognosis, or monitoring, and screening tests have different characteristics than the other functions. Using chaos, bifurcation, and perturbation (CBP) theories, the aim is to identify biomarkers to aid clinicians in screening for MDD. MATERIALS AND METHODS: MDD is a complex disorder; consequently, a reductionist approach to characterize the complex system changes found in MDD will be inchoate and unreliable. A holistic approach is used to identify biomarkers reflecting the tipping points seen before the catastrophic bifurcation that results in MDD. RESULTS: Applying CBP theories revealed skew, resistance to change, flickering, increased variance and autocorrelation as patterns of biomarkers. Integrals and differentials of extracellular and intracellular biomarkers were identified, specifically focussed on hypothalamo-pituitary axis (HPA) dysfunction, metabolic dysfunction, inflammation and mitochondrial oxidative stress, and tryptophan metabolism. CONCLUSIONS: Applying CBP theories to the dysfunctional complex biological systems in MDD led to development of integrals and differentials of biomarkers that can be used in screening for MDD and planning future biomarker research, targeting intracellular and extracellular inflammation, HPA axis dysfunction, and tryptophan metabolism.

ALUminating the Path of Atherosclerosis Progression: Chaos Theory Suggests a Role for Alu Repeats in the Development of Atherosclerotic Vascular Disease.

Atherosclerosis (ATH) and coronary artery disease (CAD) are chronic inflammatory diseases with an important genetic background; they derive from the cumulative effect of multiple common risk alleles, most of which are located in genomic noncoding regions. These complex diseases behave as nonlinear dynamical systems that show a high dependence on their initial conditions; thus, long-term predictions of disease progression are unreliable. One likely possibility is that the nonlinear nature of ATH could be dependent on nonlinear correlations in the structure of the human genome. In this review, we show how chaos theory analysis has highlighted genomic regions that have shared specific structural constraints, which could have a role in ATH progression. These regions were shown to be enriched with repetitive sequences of the Alu family, genomic parasites that have colonized the human genome, which show a particular secondary structure and are involved in the regulation of gene expression. Here, we show the impact of Alu elements on the mechanisms that regulate gene expression, especially highlighting the molecular mechanisms via which the Alu elements alter the inflammatory response. We devote special attention to their relationship with the long noncoding RNA (lncRNA); antisense noncoding RNA in the INK4 locus (ANRIL), a risk factor for ATH; their role as microRNA (miRNA) sponges; and their ability to interfere with the regulatory circuitry of the (nuclear factor kappa B) NF-κB response. We aim to characterize ATH as a nonlinear dynamic system, in which small initial alterations in the expression of a number of repetitive elements are somehow amplified to reach phenotypic significance.