Search Results (54)

Dew constitutes a component of the near-surface water balance, but its large-scale fractal dynamical properties remain poorly documented across Africa. This study estimates dew amounts and investigates their fractal and multifractal behavior under African climatic conditions using gridded ERA5 datasets from 1993 to 2022. The Rescaled-Range (R/S) method, Multifractal Detrended Fluctuation Analysis (MFDFA), and the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) algorithm are used. Hurst exponent (Hu) and the multifractal spectrum width (ω) are evaluated at daily and monthly scales over the full period and two sub-periods (1993–2007 and 2008–2022). The results reveal pronounced spatial heterogeneity in dew distribution. Daily mean amounts range between 0 and 0.18 mm, corresponding to annual accumulations reaching up to ~85 mm·yr⁻¹ in humid coastal, equatorial, and sub-equatorial regions, while remaining below 0.5 mm·yr⁻¹ in hyper-arid deserts. The continental mean annual amount is ~35.5 mm·yr⁻¹. The Hurst exponent exhibits values between zero and one, indicating region-dependent persistent and anti-persistent behaviors. This suggests that prediction schemes based on preceding values may be suitable for dew time series prediction in African regions exhibiting persistent characteristics. The multifractal spectrum width (ω), reaching values of up to 10, highlights strong scaling heterogeneity, particularly at the monthly timescale. These findings indicate that African dew dynamics exhibit significant long-range dependence and multifractal variability, providing new insights into the intrinsic temporal structure of dew and into appropriate approaches for its forecasting. Full article

This paper develops a practical computational framework for the Bayesian Cournot model with bilateral incomplete cost information, where each player is uncertain about the opponent’s marginal cost, drawn from a continuous compact interval $[c_{*}, c^{*}]$ with $0<c_{*}<c^{*}<\infty$. The infinite dimensionality of the functional strategy spaces (mappings from types to production quantities) renders analytical closed-form solutions infeasible in this continuous-type setting. To overcome this challenge, we restrict the strategy spaces to finite-dimensional differentiable sub-manifolds—specifically, one-parameter families of oscillatory functions (cosine, sine, and mixed forms). After suitable affine Q-rescaling to map the oscillatory range into the production interval $[0, Q]$, and with parameter ranges satisfying $\alpha , \beta >(\pi /2)/c_{*}$, these curves ensure near-exhaustivity: the joint production map $(\alpha , \beta )\mapsto (x_{\alpha }\left(s\right), y_{\beta }\left(t\right))$ covers ${[0, Q]}^2$ densely for every fixed cost pair $(s, t)$, thereby recovering (up to density and closure) the full ex-post payoff space. We introduce the ex-post payoff mapping $\Phi (s, t, x, y)=(e_s(x, y)\left(t\right), f_t(x, y)\left(s\right))$, which collects every realizable payoff pair once nature draws the types and players select their strategies. The image of $\Phi$ defines the general payoff space of the game, and its non-dominated points constitute the general ex-post Pareto frontier—all efficient realized outcomes across type-strategy realizations, without dependence on private probability measures over types. Using multi-objective genetic algorithms, we numerically approximate this frontier (and selected collusive compromises) within the restricted but representative sub-manifolds. The resulting frontiers are computationally accessible, robust to parameter variations, and validated through hypervolume convergence, sensitivity analysis, and comparisons with NSGA-II, PSO and scalarization methods. The findings are significant because they provide decision-makers in oligopolistic markets (e.g., electric vehicles) with viable, implementable production policies that explore efficient trade-offs under genuine cost uncertainty, without requiring explicit forecasts of the opponent’s type distribution—a limitation of traditional expected-utility approaches. By focusing on ex-post efficiency, the method reveals belief-independent compromise solutions that may guide tacit coordination or collusive outcomes in real-world strategic settings. Full article

Natural fractures are critical controls on shale oil storage and migration in the Upper Triassic Chang 7 Member of the Ordos Basin. However, conventional identification techniques—such as mud-invasion correction, R/S rescaled range analysis, and radioactive element analysis—are time-consuming, computationally intensive, and highly dependent on specialized logging data, limiting their large-scale application. To overcome these challenges, this study develops a multi-modal deep neural network that integrates conventional well logs with borehole imaging data. A coupled convolutional neural network (CNN) and deep neural network (DNN) architecture was constructed to predict fracture occurrence, dip angle, and aperture. The model achieves dip-angle prediction accuracies of 98.82% for both training and testing datasets, while aperture prediction accuracies reach 95.97% and 95.91%, respectively. Predicted dip angles are concentrated between 65° and 80°, deviating by less than 0.48° from measured values, whereas apertures fall mainly within 0.5–4.5 cm, with deviations below 0.21 cm except in extreme cases. The CNN branch effectively extracts spatial features from imaging logs, while the DNN branch captures nonlinear relationships in conventional logs. The integrated framework substantially improves fracture characterization accuracy and efficiency. This study provides a scalable and cost-effective approach for rapid fracture identification based on conventional logging data, reducing reliance on specialized imaging logs and supporting integrated geological and engineering evaluations in shale oil reservoirs. Full article

Soft-core Coulomb fluids, exemplified by the two-dimensional Gaussian-charge one-component plasma, serve as fundamental benchmarks for both mathematical theory and computational modeling of coarse-grained dynamics, including stochastic density functional theory, dynamical density functional theory, and dissipative particle dynamics. In these systems, the conventional mean-field description, or the random phase approximation (RPA), is frequently employed due to its analytic simplicity; however, its validity is restricted to weak coupling regimes. Here we demonstrate that Coulomb correlations induce a structural crossover to a strongly correlated liquid where the nearest-neighbor distance saturates rather than decreasing monotonically, a behavior fundamentally incompatible with mean-field predictions. Central to our analysis is the emergence of a universal scaling law: when rescaled by the coupling constant, the short-range direct correlation function (DCF) collapses onto a single curve across the strong coupling regime. Exploiting this universality, we construct a closed-form analytic representation of the DCF using a two-Gaussian basis. This compact form accurately reproduces hypernetted-chain radial distribution functions and structure factors while ensuring exact compliance with thermodynamic sum rules. Beyond theoretical elegance, the proposed kernel offers a computationally efficient alternative to RPA-based approximations, enabling real-space dynamical methods to incorporate strong correlations without modifying long-range smoothed-charge electrostatics. Its analytic transparency bridges rigorous integral equation theory and practical dynamical kernels, additionally providing a physics-informed prior for emerging machine-learning models. Collectively, these results establish a mathematically rigorous testbed for advancing the modeling of strongly correlated soft matter systems. Full article

To explore the spatiotemporal evolution of extreme temperature events in Guangxi (1940–2023), reveal regional response mechanisms, and assess future trends of persistence under climate warming, a multi-scale analysis was conducted using ERA5 reanalysis data. Methodologies included RH tests for homogeneity correction, collaborative kriging for data optimisation, Mann–Kendall tests for trend and abrupt change detection, Morlet wavelet analysis for cyclic pattern identification, Exploratory Spatio-Temporal Data Analysis (ESTDA) for spatial heterogeneity quantification, and Rescaled Range (R/S) analysis to calculate Hurst indices for future persistence assessment. Results showed the following: (1) The ERA5 dataset exhibited high applicability in Guangxi (R = 0.9989, RMSE = 1.9492 °C), supporting robust evidence of continuous warming—warm indices (e.g., SU25, TX90p) increased significantly (SU25 at 0.2044 d/10a), while cold indices (e.g., TN10p, FD0) declined (TN10p at −0.0519 d/10a); abrupt changes of cold indices were concentrated in 1942–1950, with warm indices accelerating post-2000 and TXx exhibited the highest warming rate (0.23 °C/decade). (2) Extreme temperature indices displayed a primary 19–21-year oscillation cycle (dominant in warm indices) and a secondary 13-year cycle (prominent in cold indices). (3) Spatial heterogeneity featured northwest–southeast cold–heat inversion, coastal–inland intensity gradients, and latitudinal zonation of extreme indices; ESTDA revealed intensified polarisation, with warm indices clustering in low-latitude regions (e.g., Baise) and cold indices declining homogeneously in mountainous areas (e.g., Guilin), indicating an irreversible transition to a warming steady state. (4) R/S analysis indicated all indices had Hurst indices of 0.65–0.92, reflecting persistent future trends consistent with historical evolution, with warm indices (e.g., TNn, SU25) showing stronger persistence (H > 0.85). This work clarifies the spatial polarisation mechanism and future persistence of extreme temperature dynamics in Guangxi, providing a multi-scale scientific basis for disaster early warning and adaptation planning in climate-sensitive karst-monsoon regions. Full article

Standard correlation analysis is one of the frequently used methods in financial markets. However, this matrix can give erroneous results in the conditions of chaos, fractional systems, entropy, and complexity for the variables. In this study, we employed the time-dependent correlation matrix based on isospectral flow using the Lie group method to assess the price of Bitcoin and gold from 19 July 2010 to 31 December 2024. Firstly, we showed that the variables have a chaotic and fractional structure. Lo’s rescaled range (R/S) and the Mandelbrot–Wallis method were used to determine fractionality and long-term dependence. We estimated and tested the d parameter using GPH and Phillips’ estimators. Renyi, Shannon, Tsallis, and HCT tests determined entropy. The KSC determined the evidence of the complexity of the variables. Hurst exponents determined mean reversion, chaos, and Brownian motion. Largest Lyapunov and Hurst exponents and entropy methods and KSC found evidence of chaos, mean reversion, Brownian motion, entropy, and complexity. The BDS test determined nonlinearity, and later, the time-dependent correlation matrix was obtained by using the stochastic SO(2) Lie group. Finally, we obtained robustness check results. Our results showed that the time-dependent correlation matrix obtained by using the stochastic SO(2) Lie group method yielded more successful results than the ordinary correlation and covariance matrix and the Spearman correlation and covariance matrix. If policymakers, financial managers, risk managers, etc., use the standard correlation method for economy or financial policies, risk management, and financial decisions, the effects of nonlinearity, fractionality, entropy, and chaotic structures may not be fully evaluated or measured. In such cases, this can lead to erroneous investment decisions, bad portfolio decisions, and wrong policy recommendations. Full article

This paper proposes a method for searching for pipeline leaks by analyzing the Hurst exponent of acoustic signals. The investigations conducted on the laboratory setup and the current pipelines of the water supply system. During the experiments, through defects of the round shape-type pipeline with diameters from 1 to 5 mm were modeled. For calculating Hurst exponent, rescaled range analysis (R/S analysis), and detrended fluctuation analysis (DFA) were used. The research results have shown that pipeline leaks are reliably detected by analyzing the Hurst exponent of acoustic signals. The signals of a defect-free pipeline are close to the level of a deterministic signal. When a leak occurs in a pipeline, the Hurst exponent decreases. Pipeline fluctuations are anti-persistent nature. It is shown that a change in the size of the through hole in the pipeline wall does not have a significant effect on the value of the Hurst exponent of acoustic signals. These results are explained by using spectral analysis and CFD modeling (Computational Fluid Dynamics modeling) methods in the Ansys Fluent software (v. 19.2). It has been established that the spectral components that contribute most to the fractal structure of signals are concentrated within the frequency range from 0 to 2 kHz. Full article

This paper presents an integrated robotic trading strategy developed for the day-ahead energy market that includes different methods for time series analysis and forecasting, such as Detrended Fluctuation Analysis (DFA), Rescaled Range Analysis (R/S analysis), fractional derivatives, Long Short-Term Memory (LSTM) Networks, and Seasonal Autoregressive Integrated Moving Average (SARIMA) models. DFA and R/S analysis may capture the long-range dependencies and fractal features inherited by the nature of the electricity price time series and give information about persistence and variability in their behavior. Given this, fractional derivatives can be used to analyze price movements concerning the minor changes in price and time acceleration for that change, which makes the proposed framework more flexible for quickly changing market conditions. LSTM, from their perspective, may capture complex and non-linear dependencies, while SARIMA models may help handle seasonal trends. This integrated approach improves market signal interpretation and optimizes the market risk through adjustable stop-loss and take-profit levels which could lead to better portfolio performance. The proposed integrated strategy is based on actual data from the Bulgarian electricity market for the years 2017–2024. Findings from this research show how the combination of fractals with statistical and machine learning models can improve complex trading strategies implementation for the energy markets. Full article

This paper proposes a deep neural network (DNN) model to estimate the Hurst exponent, a crucial parameter in modelling stock market price movements driven by fractional geometric Brownian motion. We randomly selected 446 indices from the S&P 500 and extracted their price movements over the last 2010 trading days. Using the rescaled range (R/S) analysis and the detrended fluctuation analysis (DFA), we computed the Hurst exponent and related parameters, which serve as the target parameters in the DNN architecture. The DNN model demonstrated remarkable learning capabilities, making accurate predictions even with small sample sizes. This addresses a limitation of R/S analysis, known for biased estimates in such instances. The significance of this model lies in its ability, once trained, to rapidly estimate the Hurst exponent, providing results in a small fraction of a second. Full article

This article presents a new 3D extreme game for virtual reality (VR), which is used to evaluate the impact of generated mental stress on the cardiological state of the playing individuals. The game was developed using Java 3D and Blender. Generated stress is investigated by recording electrocardiograms for 20 min and determining heart rate variability (HRV) parameters in the time and frequency domains and by non-linear visual and quantitative analysis methods, such as the Rescaled Range (R/S) method, Poincarè plot, Recurrence plot, Approximate (ApEn), and Sample Entropy (SampEn). The data of 19 volunteers were analyzed before and immediately after the game, and a comparative analysis was made of two types of VR: immersive and non-immersive. The results show that the application of immersive VR generates higher mental stress levels than non-immersive VR, but in both cases, HRV changes (decreases), but more significantly in immersive VR. The results of this research can provide useful information about the functioning of the autonomic nervous system, which regulates the reactions of the human body during mental stress, to help in the early detection of potential health problems. Full article

Purpose: To assess the possible impact of minor changes in fixation on wavefront measurements as a potential constraint in detecting subtle temporal variations in ocular wavefront error. Methods: Twelve healthy subjects with an average age of 36.3 ± 8.8 were instructed to put their heads in the aberrometer’s chin-rest and look at a fixation target that was embedded in the device. The fixation targets were readily observable to the participants without accommodation, thanks to the aberrometer’s Badal system. When each eye was staring at the target, its wavefront aberration was recorded three times and then averaged for further analysis. The averaged Zernike coefficients were rescaled to the smallest value of the maximum round pupil found among all eyes (4.41 mm), and this procedure was repeated for each target. Results: Alteration of the fixation targets caused changes to the Zernike coefficients of defocus (C(2,0)), vertical trefoil (C(3,–3)), vertical coma (C(3,–1)), horizontal coma (C(3,1)), oblique trefoil (C(3,3)), primary spherical aberration (C(4,0)), and secondary spherical aberration (C(6,0)), but the changes were not statistically significant. Nevertheless, an alteration in the target’s size and shape exhibited a significant correlation across all of the aforementioned coefficients in both eyes (p < 0.05). The total RMS of aberrations and the RMS of the spherical-like aberrations were both lowest while choosing the larger Maltese cross, and the bigger E-letter minimized the RMS of HOA and comatic aberrations. Conclusion: The aberrometric changes occur as a consequence of altering the fixational gaze and are within the range of the changes found after performing a near-vision task, so they might potentially act as a confounding factor when attempting to identify such small variations in the ocular wavefront. Using a smaller E-letter (5 arcmin) as an internal fixation target resulted in the least standard deviation of measurements, fixational stability, and higher accuracy in ocular wavefront measurements. Full article

This research conducted a thorough investigation of Bitcoin volatility patterns using three interrelated methodologies: R/S investigation, simple moving average (SMA), and the relative strength index (RSI). The paper jointly employes the above techniques on volatility range-based estimators to effectively capture the unpredictable volatility patterns of Bitcoin. R/S analysis, SMA, and RSI calculations assess time series data obtained from our volatility estimators. Although Bitcoin is known for its high volatility and price instability, our analysis using R/S analysis and moving averages suggests the existence of underlying patterns. The estimated Hurst exponents for our volatility estimators indicate a level of persistence in these patterns, with some estimators displaying more persistence than others. This persistence underscores the potential of momentum-based trading strategies, reinforcing the expectation of additional price rises after declines and vice versa. However, significant volatility often interrupts this upward movement. The SMA analysis also demonstrates Bitcoin’s susceptibility to external market forces. These observations indicate that traders and investors should modify their risk management approaches in accordance with market circumstances, perhaps integrating a combination of momentum-based and mean-reversion tactics to reduce the risks linked to Bitcoin’s volatility. Furthermore, the existence of robust patterns, as demonstrated by our investigation, presents promising opportunities for investing in Bitcoin. Full article

Satellite-derived soil moisture (SM) observations are widely assimilated in global land data assimilation systems. These systems typically assume zero-mean errors in the land surface model and observations. In practice, systematic differences (biases) exist between the observed and modelled SM. Commonly, the observed SM biases are removed by rescaling techniques or via a machine learning approach. However, these methods do not account for non-stationary biases, which can result from issues with the satellite retrieval algorithms or changes in the land surface model. Therefore, we test a novel application of adaptive SM bias correction (BC) in the European Centre for Medium Range Weather Forecasts (ECMWF) land data assimilation system. A two-stage filter is formulated to dynamically correct biases from satellite-derived active ASCAT C-band and passive L-band SMOS surface SM observations. This complements the operational seasonal rescaling of the ASCAT observations and the SMOS neural network retrieval while allowing the assimilation to correct subseasonal-scale errors. Experiments are performed on the ECMWF stand-alone surface analysis, which is a simplified version of the integrated forecasting system. Over a 3 year test period, the adaptive BC reduces the seasonal-scale (observation−forecast) departures by up to 20% (30%) for the ASCAT (SMOS). The adaptive BC leads to (1) slight improvements in the SM analysis performance and (2) moderate but statistically significant reductions in the 1–5 day relative humidity forecast errors in the boundary layer of the Northern Hemisphere midlatitudes. Future work will test the adaptive SM BC in the full integrated forecasting system. Full article

In this study, we present a novel approach to estimating the Hurst exponent of time series data using a variety of machine learning algorithms. The Hurst exponent is a crucial parameter in characterizing long-range dependence in time series, and traditional methods such as Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) have been widely used for its estimation. However, these methods have certain limitations, which we sought to address by modifying the R/S approach to distinguish between fractional Lévy and fractional Brownian motion, and by demonstrating the inadequacy of DFA and similar methods for data that resembles fractional Lévy motion. This inspired us to utilize machine learning techniques to improve the estimation process. In an unprecedented step, we train various machine learning models, including LightGBM, MLP, and AdaBoost, on synthetic data generated from random walks, namely fractional Brownian motion and fractional Lévy motion, where the ground truth Hurst exponent is known. This means that we can initialize and create these stochastic processes with a scaling Hurst/scaling exponent, which is then used as the ground truth for training. Furthermore, we perform the continuous estimation of the scaling exponent directly from the time series, without resorting to the calculation of the power spectrum or other sophisticated preprocessing steps, as done in past approaches. Our experiments reveal that the machine learning-based estimators outperform traditional R/S analysis and DFA methods in estimating the Hurst exponent, particularly for data akin to fractional Lévy motion. Validating our approach on real-world financial data, we observe a divergence between the estimated Hurst/scaling exponents and results reported in the literature. Nevertheless, the confirmation provided by known ground truths reinforces the superiority of our approach in terms of accuracy. This work highlights the potential of machine learning algorithms for accurately estimating the Hurst exponent, paving new paths for time series analysis. By marrying traditional finance methods with the capabilities of machine learning, our study provides a novel contribution towards the future of time series data analysis. Full article

This paper analyzed the variations of two air temperature indices, diurnal temperature range (DTR) and annual temperature range (ATR), calculated based on observations at the Zagreb Grič Observatory over a period of 133 years (1887–2019). In intense climate changes strongly manifested by the increased air temperature, these two climate indices were determined to significantly impact human health and the environment. This effect is especially evident in urban areas. The Zagreb Grič Observatory is located in the center of Zagreb and has not changed its location during the observed period. It has a long homogeneous series of climatological observations, enabling a detailed study of climate variation in the city, which is strongly influenced by various urbanization processes. In 133 years, both of the analyzed indicators showed a statistically insignificant downward trend. The Rescaled Adjusted Partial Sums (RAPS) method revealed statistically significant differences in DTR’s time series between three sub-periods: 1887–1953, 1954–1989, and 1990–2019. The time series of ATR during 133 years behaved statistically differently in four sub-periods: 1887–1905; 1906–1926; 1927–1964; and 1965–2019. The analysis of monthly values of DTR showed that the DTR values are the highest in the warm part of the year, from May to August, when they are twice as high as those during the cold period from November to December. With an increase in precipitation, the DTR values decrease, while they increase as the mean annual temperature increases. Full article