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The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper, we present a self-contained and comprehensive introduction to the fractal dimension. We collect and present various numerical estimators and focus on the three most promising ones: generalized entropy, correlation sum, and extreme value theory. We then perform an extensive quantitative evaluation of these estimators, comparing their performance and precision using different datasets and comparing the impact of features like length, noise, embedding dimension, and falsify-ability, among many others. Our analysis shows that for synthetic noiseless data, the correlation sum is the best estimator with extreme value theory following closely. For real experimental data, we found the correlation sum to be more strongly affected by noise vs the entropy and extreme value theory. The recent extreme value theory estimator seems powerful as it has some of the advantages of both alternative methods. However, using four different ways for checking for significance, we found that the method yielded "significant" low-dimensional results for inappropriate data like stock market timeseries. This fact, combined with some ambiguities we found in the literature of the method applications, has implications for both previous and future real-world applications using the extreme value theory approach, as, for example, the argument for small effective dimensionality in the data cannot come from the method itself. All algorithms discussed are implemented as performant and easy to use open source code via the DynamicalSystems.jl library.

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Dynamical systems that are used to model power grids, the brain, and other physical systems can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may "tip" from one stable state to the other, is global stability analysis. It involves identifying the initial conditions that converge to each attractor, known as the basins of attraction, measuring the relative volume of these basins in state space, and quantifying how these fractions change as a system parameter evolves. By improving existing approaches, we present a comprehensive framework that allows for global stability analysis of dynamical systems. Notably, our framework enables the analysis to be made efficiently and conveniently over a parameter range. As such, it becomes an essential tool for stability analysis of dynamical systems that goes beyond local stability analysis offered by alternative frameworks. We demonstrate the effectiveness of our approach on a variety of models, including climate, power grids, ecosystems, and more. Our framework is available as simple-to-use open-source code as part of the DynamicalSystems.jl library.

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BACKGROUND: As technology becomes more sophisticated, more accessible methods of interpretating Big Data become essential. We have continued to develop Complexity and Entropy in Physiological Signals (CEPS) as an open access MATLAB® GUI (graphical user interface) providing multiple methods for the modification and analysis of physiological data. METHODS: To demonstrate the functionality of the software, data were collected from 44 healthy adults for a study investigating the effects on vagal tone of breathing paced at five different rates, as well as self-paced and un-paced. Five-minute 15-s recordings were used. Results were also compared with those from shorter segments of the data. Electrocardiogram (ECG), electrodermal activity (EDA) and Respiration (RSP) data were recorded. Particular attention was paid to COVID risk mitigation, and to parameter tuning for the CEPS measures. For comparison, data were processed using Kubios HRV, RR-APET and DynamicalSystems.jl software. We also compared findings for ECG RR interval (RRi) data resampled at 4 Hz (4R) or 10 Hz (10R), and non-resampled (noR). In total, we used around 190-220 measures from CEPS at various scales, depending on the analysis undertaken, with our investigation focused on three families of measures: 22 fractal dimension (FD) measures, 40 heart rate asymmetries or measures derived from Poincaré plots (HRA), and 8 measures based on permutation entropy (PE). RESULTS: FDs for the RRi data differentiated strongly between breathing rates, whether data were resampled or not, increasing between 5 and 7 breaths per minute (BrPM). Largest effect sizes for RRi (4R and noR) differentiation between breathing rates were found for the PE-based measures. Measures that both differentiated well between breathing rates and were consistent across different RRi data lengths (1-5 min) included five PE-based (noR) and three FDs (4R). Of the top 12 measures with short-data values consistently within ± 5% of their values for the 5-min data, five were FDs, one was PE-based, and none were HRAs. Effect sizes were usually greater for CEPS measures than for those implemented in DynamicalSystems.jl. CONCLUSION: The updated CEPS software enables visualisation and analysis of multichannel physiological data using a variety of established and recently introduced complexity entropy measures. Although equal resampling is theoretically important for FD estimation, it appears that FD measures may also be usefully applied to non-resampled data.

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Clouds are one of the most influential components of Earth's climate system. Specifically, the midlatitude clouds play a vital role in shaping Earth's albedo. This study investigates the connection between baroclinic activity, which dominates the midlatitude climate, and cloud-albedo and how it relates to Earth's existing hemispheric albedo symmetry. We show that baroclinic activity and cloud-albedo are highly correlated. By using Lagrangian tracking of cyclones and anticyclones and analyzing their individual cloud properties at different vertical levels, we explain why their cloud-albedo increases monotonically with intensity. We find that while for anticyclones, the relation between strength and cloudiness is mostly linear, for cyclones, in which clouds are more prevalent, the relation saturates with strength. Using the cloud-albedo strength relationships and the climatology of baroclinic activity, we demonstrate that the observed hemispheric difference in cloud-albedo is well explained by the difference in the population of cyclones and anticyclones, which counter-balances the difference in clear-sky albedo. Finally, we discuss the robustness of the hemispheric albedo symmetry in the future climate. Seemingly, the symmetry should break, as the northern hemisphere's storm track response differs from that of the southern hemisphere due to Arctic amplification. However, we show that the saturation of the cloud response to storm intensity implies that the increase in the skewness of the southern hemisphere storm distribution toward strong storms will decrease future cloud-albedo in the southern hemisphere. This complex response explains how albedo symmetry might persist even with the predicted asymmetric hemispheric change in baroclinicity under climate change.

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We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the dynamical system flow. The input to the method is a dynamical system evolution rule and a grid that partitions the state space. No prior knowledge of the number, location, or nature of the attractors is required. The method works for arbitrarily high-dimensional dynamical systems, both discrete and continuous. It also works for stroboscopic maps, Poincaré maps, and projections of high-dimensional dynamics to a lower-dimensional space. The method is accompanied by a performant open-source implementation in the DynamicalSystems.jl library. The performance of the method outclasses the naïve approach of evolving initial conditions until convergence to an attractor, even when excluding the task of first identifying the attractors from the comparison. We showcase the power of our implementation on several scenarios, including interlaced chaotic attractors, high-dimensional state spaces, fractal basin boundaries, and interlaced attracting periodic orbits, among others. The output of our method can be straightforwardly used to calculate concepts, such as basin stability and final state sensitivity.

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Jazz music that swings has the fascinating power to elicit a pleasant sensation of flow in listeners and the desire to synchronize body movements with the music. Whether microtiming deviations (MTDs), i.e. small timing deviations below the bar or phrase level, enhance the swing feel is highly debated in the current literature. Studies on other groove related genres did not find evidence for a positive impact of MTDs. The present study addresses jazz music and swing in particular, as there is some evidence that microtiming patterns are genre-specific. We recorded twelve piano jazz standards played by a professional pianist and manipulated the natural MTDs of the recordings in systematic ways by quantizing, expanding and inverting them. MTDs were defined with respect to a grid determined by the average swing ratio. The original and manipulated versions were presented in an online survey and evaluated by 160 listeners with various musical skill levels and backgrounds. Across pieces the quantized versions (without MTDs) were rated slightly higher and versions with expanded MTDs were rated lower with regard to swing than the original recordings. Unexpectedly, inversion had no impact on swing ratings except for two pieces. Our results suggest that naturally fluctuating MTDs are not an essential factor for the swing feel.

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Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here, the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software on its implementation.

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INTRODUCTION: Quadratus femoris tear is an uncommon injury, which is only rarely reported in the literature. In the majority of cases the correct diagnosis is delayed due to non-specific symptoms and signs. A magnetic resonance imaging scan is crucial in the differential diagnosis since injuries to contiguous soft tissues may present with similar symptoms. Presentation with sciatica is not reported in the few cases existing in the English literature and the reported treatment has always been conservative. CASE PRESENTATION: We report here on a case of quadratus femoris tear in a 22-year-old Greek woman who presented with persistent sciatica. She was unresponsive to conservative measures and so was treated with surgical decompression. CONCLUSION: The correct diagnosis of quadratus muscle tear is a challenge for physicians. The treatment is usually conservative, but in cases of persistent sciatica surgical decompression is an alternative option.

Asunto(s)

Carcinoma de Células Escamosas/patología , Neoplasias Nasofaríngeas/patología , Neoplasias de los Senos Paranasales/patología , Adulto , Carcinoma de Células Escamosas/terapia , Terapia Combinada , Diagnóstico Diferencial , Humanos , Imagen por Resonancia Magnética , Masculino , Neoplasias Nasofaríngeas/terapia , Neoplasias de los Senos Paranasales/terapia , Tomografía Computarizada por Rayos X

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BACKGROUND: The incidence of multiple primary malignant neoplasms increases with age and they are encountered more frequently nowadays than before, the phenomenon is still considered to be rare. CASE PRESENTATION: We report a case of a man in whom urinary bladder transitional cell carcinoma, metachronous prostate adenocarcinoma and small cell lung carcinoma were diagnosed within an eighteen-month period. The only known predisposing factor was that he was heavy smoker (90-100 packets per year). The literature on the phenomenon of multiple primary malignancies in a single patient is reviewed and the data is summarized. CONCLUSION: It is important for the clinicians to keep in mind the possibility of a metachronous (successive) or a synchronous (simultaneous) malignancy in a cancer patient. It is worthy mentioning this case because clustering of three primary malignancies (synchronous and metachronous) is of rare occurrence in a single patient, and, to our knowledge, this is the first report this combination of three carcinomas appearing in the same patient.