Search Results (1,329)

We examine the estimation of the Kullback–Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate normality. Our starting point is the maximum entropy principle for Shannon entropy: among all distributions with a fixed mean vector and covariance matrix, the multivariate Gaussian distributions uniquely maximize entropy. As a result, the KL divergence from a moment-matched Gaussian distribution to an unknown density can then be written as the entropy difference, which is a suitable information-theoretic measure of divergence from the Gaussian distribution. To estimate, we use k-nearest neighbor (kNN) estimators based on Shannon entropy and KL divergence derived from the Kozachenko–Leonenko approach and subsequent improvements, along with the consistency and $L^2$-convergence results established for these estimators. Motivated by previous entropy-based goodness-of-fit ideas developed for Rényi-type functionals for generalized Gaussian and Student-type models, we describe a KL-based test statistic as being the difference between the entropy of a Gaussian model fitted to the sample mean and covariance and the KL divergence between the unknown entropy and the kNN estimate. The statistic converges to zero for multivariate normality and converges to a strictly positive bound with non-Gaussian alternatives. The results of Monte Carlo simulations conducted across various dimensions and sample sizes indicate that the proposed method provides accurate Type I error control among the alternatives considered and demonstrates promising empirical power. Full article

Background and Objectives: To quantify behavioral complexity in probable Alzheimer’s disease (AD), compare complexity phenotypes, and determine whether behavioral complexity provides clinically meaningful information beyond total neuropsychiatric burden. We also explored whether global amyloid extent and lobar amyloid topography added explanatory value. Methods: In this cross-sectional retrospective study, we analyzed 245 psychotropic drug-naïve patients with probable AD, positive ¹⁸F-FC119S amyloid positron emission tomography (PET), and complete neuropsychiatric, cognitive, functional, and regional PET data. Behavioral complexity was derived from 12 Korean Neuropsychiatric Inventory domains using symptom count, normalized Shannon entropy of the frequency × severity profile, and a composite index. Patients were classified into tertiles. Multivariable regression and burden-stratified analyses examined associations with cognition, dementia severity, function, and amyloid measures. Results: Higher behavioral complexity was associated with lower Korean Mini-Mental State Examination (K-MMSE) scores and higher Clinical Dementia Rating (CDR) and Global Deterioration Scale (GDS) stages. In multivariable analysis, higher CDR, higher GDS, and lower Barthel Index independently predicted greater complexity, whereas amyloid extent did not. After adjustment for total neuropsychiatric burden, higher CDR remained independently associated with the composite complexity index and normalized entropy, while amyloid extent remained non-significant. Complexity-related clinical differences were most evident in the lowest burden stratum and attenuated at higher burden levels. Regional amyloid analyses yielded only selective signals. Conclusions: Behavioral complexity is a clinically meaningful neuropsychiatric phenotype in AD. Although strongly related to total neuropsychiatric burden, it is not fully reducible to it, with its clearest independent association seen for global dementia severity, particularly at lower overall burden. Full article

In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schrödinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel–Duke ordering to obtain exact analytical solutions for the energy spectrum and wave functions. The interplay between the fractal parameter $\alpha$, the effective lattice scale $l_0$, and the harmonic confinement strength $\omega$ is explored. We perform a comprehensive analysis of the Shannon entropy, Fisher information, and Fisher–Shannon complexity in both coordinate and momentum spaces. Our results demonstrate that these parameters directly control the localization–delocalization transition and the informational architecture of the quantum states, while satisfying the entropic and Fisher uncertainty relations. Furthermore, we derive the exact partition function and the corresponding thermodynamic properties (free energy, internal energy, entropy, and specific heat) of the system. The analytical framework presented offers valuable insights into the spectral, information-theoretic, and thermodynamic behavior of quantum systems in fractal semiconductor-like environments. Full article

Optimal coordination of directional overcurrent relays (DOCRs) in medium-to-large power systems constitutes a computationally demanding, mixed-integer, nonlinear optimisation problem whose complexity escalates rapidly with system size, making the simultaneous minimisation of relay operating time and computational cost a critical open challenge. This study presents a two-level hierarchical framework in which Type-2 Fuzzy C-Means (T2FCM) clustering partitions 226 fault scenarios into subproblems at the upper level, while the Hybrid Fractional Entropy Evolution (HFEE) algorithm independently optimises relay settings for each cluster at the lower level. HFEE integrates fractional-order velocity updates—derived from the Grünwald–Letnikov formulation—with a Shannon entropy diversity-control mechanism to prevent premature convergence. T2FCM captures inherent fault-current uncertainty through interval-valued type-2 fuzzy memberships, yielding more robust cluster assignments near protection-zone boundaries than crisp partitioning methods. The framework is validated on the extended IEEE 30-bus system. An ablation study demonstrates that standalone HFEE achieves a 29.19% improvement in $T_{\mathrm{op}}$ over the prior best-reported result; however, a comprehensive parameter sweep over cluster counts $K\in \{2,\dots ,8\}$ and fractional orders $\alpha \in \{0.1,\dots ,0.9\}$ across 50 independent runs per configuration shows that the proposed clustering-decomposed method achieves 3.68–66.67% lower wall-clock computation time while maintaining zero CTI violations across all active relay pairs. The communicationless, entirely offline framework demonstrates scalability for simultaneous sub-transmission and distribution protection coordination and offers a practically deployable strategy for modern power networks. Full article

Feature selection represents a critical step in developing accurate and interpretable models for early breast cancer detection. Despite extensive research in the field of mammographic image analysis, no consensus has yet been reached on the optimal feature subsets that distinguish normal from malignant tissues. To address this gap, the present study aims to identify the most discriminative and significant features through a comprehensive multi-criterion selection framework. The aim is to integrate, as new frameworks, different combinations of t-test, ANOVA, Mutual Information (MI), and Equal Grouping Methods (EGM) to rank 19 linear and nonlinear features extracted from mammographic images. The objective is to maximize feature relevance while minimizing redundancy and enhancing diagnostic and healthcare systems. Linear features were assessed alongside nonlinear descriptors. A framework combining t-test, ANOVA, and EGM, guided by MI relevance, was employed to balance feature contributions across categories. The experimental results demonstrated that hybrid feature selection significantly enhanced diagnostic accuracy using optimal linear and nonlinear attributes. The optimization results suggested using a hybrid of six linear and eight nonlinear features. Linear features were highly accurate for detecting cancer. Haralick entropy obtained the highest average accuracy and performance, 94.14% and 93.45%; followed by kurtosis, 93.49% and 92.59%; perimeter irregularity, 93.43% and 92.65%; skewness, 93.01% and 92.25%; and volume/area, 92.82% and 91.92%. Despite the reliable discriminative power of linear descriptors, their overall effectiveness in representing intricate tissue characteristics was limited. The comparison of statistical characteristics shows a distinct performance benefit of nonlinear descriptors over linear ones for detecting breast cancer. Nonlinear descriptors, however, showcased higher accuracy and performance, with an average accuracy of 97.81% in contrast to 94.43% for linear approaches. Local phase congruency achieved the top average accuracy and performance, 97.81% and 96.61%, respectively; succeeded by wavelet entropy, 97.62% and 96.42%; Laplacian spectrum features, 97.52% and 96.32%; nonlinear diffusion, 97.10% and 95.90%; and clustering coefficient, 96.70% and 95.50%; then Shannon, Tsallis, and Rényi entropies. The results indicate that statistically validated nonlinear characteristics significantly outperform linear ones across accuracy and performance measures. Their combination significantly improves the strength and discriminative power of computer-assisted breast cancer diagnostic systems, affirming their suitability for integration into sophisticated machine learning and deep learning models. The results also show that the new multi-criterion framework’s early detection performance surpassed that of the statistical and deep learning models explored, with an average of 98.6% accuracy, 98% sensitivity, 98.9% precision, and 98.4% F1 score of early detection of breast cancer. The incorporation of statistically validated nonlinear descriptors, particularly local phase congruency and wavelet entropy, improves the discriminative ability, robustness, and clinical understanding of breast cancer computer-assisted diagnostic systems. Overall, the proposed framework confirms that integrating hybrid features substantially enhances robustness and plays a pivotal role in computer-assisted breast cancer detection. These selected features may be fed to more advanced algorithms in the future, potentially yielding improved performance. Full article

Corporate balance sheets report aggregate equity and liability totals but conceal the internal allocation of financing sources across asset categories—an identification problem that conventional econometric methods cannot resolve without additional parametric assumptions. This paper develops a maximum entropy (ME) panel estimator to recover two latent scalar parameters: x ∈ (0,1), the share of equity capital directed toward long-term asset financing, and y ∈ (0,1), the corresponding debt allocation share. Grounded in maximum entropy principle, the estimator selects the unique parameter vector that satisfies the mean-level balance-sheet constraint while maximising joint Shannon entropy—the least-biassed solution consistent with observable data. The closed-form logistic representation yields a scalar Lagrange multiplier λ*, interpreted as a financing pressure index, recoverable via bisection in at most 21 iterations at tolerance ε = 10⁻⁵. Building on the ME estimates, we introduce a continuous matching alignment index M* = x* − y* that measures the degree of compliance with the financial matching principle along a continuous spectrum rather than as a binary categorisation. Applied to a ten-firm, cross-sectoral panel spanning Technology, Finance, Energy, and Automotive sectors over an observation window spanning 2001 to 2025 (with firm-specific subperiods reflecting differences in IPO dates and data availability), the framework reveals substantial heterogeneity in latent financing flows: equity allocation shares range from 30.1% (NVIDIA) to 75.1% (ExxonMobil), while debt allocation shares span 37.1% to 77.5%. Across the panel, only Meta exhibits substantial positive matching alignment, while Microsoft, ExxonMobil, Apple, and Tesla show only very slight differences that fall within the neutral band, and the remaining firms show varying degrees of structural departure from the matching benchmark; the thresholds used to summarise these descriptive labels are interpretive aids rather than re-imposed binary criteria, and the substantive ranking of firms along M* does not depend on the specific threshold values adopted. The ME solution’s entropy H(x*, y*) and the normalised diversification index D(x*, y*) describe allocation balance under the estimator’s information–theoretic criterion rather than independently observed firm complexity; in the present sample, the cross-firm ordering of these values is not recovered by firm size, leverage, or sector classification alone. These findings, based on a ten-firm case-study panel with time-invariant allocation parameters, should be interpreted as descriptive patterns of the present sample rather than statistically validated regularities. They provide a theoretically rigorous and computationally tractable identification of unobservable corporate financing flows, with potential implications for capital structure theory, financial risk assessment, and balance sheet analysis that would benefit from validation on larger and more representative samples in future work. Full article

The Gompertz distribution is a well-known lifetime model in survival and reliability analysis, but its hazard rate is restricted to monotone increasing behavior, which limits its applicability to more complex data structures. In this study, we investigate the New Extended Gompertz (NEG) distribution, which is obtained by applying the existing NE-X generator framework to the classical Gompertz baseline distribution. Thus, the NEG model is a special case within an already established generator family rather than an entirely new family of distributions. The main contribution of this paper is not the introduction of a new generator, but rather a comprehensive and systematic investigation of this particular Gompertz-based extension, including its statistical properties, estimation procedures, and practical applications. The proposed model introduces an additional shape parameter that provides increased flexibility in modeling skewness, tail behavior, and hazard-rate structures, allowing for increasing, decreasing, bathtub-shaped, and unimodal hazard patterns under different parameter configurations. Several mathematical properties of the NEG distribution are derived, including explicit expressions for the density, distribution, survival, and hazard-rate functions, as well as moments, entropy measures, and series representations. Parameter estimation is performed using both maximum likelihood and Bayesian approaches, with numerical optimization and Metropolis–Hastings MCMC procedures employed due to the absence of closed-form estimators. The finite-sample behavior of the estimators is investigated through extensive Monte Carlo simulation studies under three different parameter settings. The practical usefulness of the NEG distribution is illustrated using two real datasets on carbon-fiber tensile strength. Comparative results with several competing Gompertz-type models indicate that the NEG distribution provides competitive performance. However, all comparisons should be interpreted within the context of the considered datasets and parameter settings, rather than as claims of universal superiority. The findings suggest that the NEG distribution offers a flexible and practical extension of the Gompertz model for lifetime data analysis. Full article

Shannon entropy is the most common measure that one could use to check if a data source has random behaviour or not. A value close to the maximum is usually considered as evidence that the source is “random enough”. The present paper shows that this criterion alone is not enough. A deterministic logistic map driven at $r=3.9999$ reaches 94.97% of the Shannon maximum, yet it is fully predictable once we look at the built-in patterns: its permutation entropy drops to 77.01% of the maximum and its sample entropy falls to 0.67, against 2.33 for a high-quality pseudo-random generator (PRNG). Building on this observation, we combine four entropy measures—Shannon, Rényi, permutation, and sample—into a single diagnostic profile of the analyzed source. In order to validate our approach with practical, real life data, we test it on 2538 official draws of the Romanian Loto 6/49 lottery, recorded between August 1993 and April 2026. The lottery historical data set is very close to a high-quality PRNG (pseudo-random number generator) from the point of view of all four measures. We also observe that the entropy deficit of both the lottery and the PRNG decays as a power law with exponent $\alpha \approx -0.96$; in contrast, the logistic map sits at $\alpha \approx -0.07$. A Random Forest classifier trained only on the entropy profile reaches 78% accuracy on the analyzed four-way classification task (lottery, PRNG, logistic map, biased distribution), but scores 55.7% on the binary lottery-versus-PRNG task, consistent with chance. The method introduced in this study is domain-independent and applies directly to RNG certification, cryptographic key auditing, and any setting where structured pseudo-randomness has to be ruled out. Full article

We investigate dynamic weighted fractional information-theoretic measures for linear stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. Motivated by recent constructions of fractional Deng entropy and building upon explicit Gaussian solutions and closed-form fractional moments derived in previous work, we establish fully analytical expressions for the Shannon entropy, Rényi entropy, Tsallis entropy, extropy, and a continuous weighted fractional entropy $\mathbb{E}\left[X_t^p(-\log p_{X_t}\left(X_t\right))\right]$ for $p\ge 0$, expressed directly in terms of known fractional moments without density estimation. All derived measures share a universal asymptotic scaling law growing as $H\log t$, establishing a precise quantitative link between long-memory effects and information dynamics. The weighted fractional entropy further reveals remarkable structural properties as a function of the weighting order p, exposing a dual role of long memory on the system’s informational content. As a concrete application, we characterize anomalous diffusion in aging soft materials through an explicit critical time linking maximal uncertainty to the memory exponent H and the macroscopic aging rate. All results are validated through extensive Monte-Carlo simulations, demonstrating excellent agreement with the closed-form expressions across a wide range of Hurst exponents H and weighting orders p. Full article

This work presents a comprehensive study of entropy-based metrics for evaluating blockchain systems, focusing on on-chain ledger immutability, off-chain data integrity, and computational dynamics within blockchain virtual machines (BVMs). We develop a unified framework that models blockchain states as probabilistic distributions, quantifying uncertainty through Shannon entropy and examining its evolution under varying adversarial fractions. Extensive simulations demonstrate that on-chain entropy exhibits near-exponential decay, reflecting the cumulative reinforcement of honest consensus, while off-chain entropy remains static, highlighting the limitations of conventional data storage. Furthermore, the BVM is analyzed in terms of computation entropy, establishing its Turing completeness and demonstrating that smart-contract state evolution mirrors the information dynamics of arbitrary Turing machines. Our results provide quantitative evidence that entropy serves as both a theoretical and operational measure of immutability, tamper evidence, and protocol resilience. The proposed entropy framework offers practical tools for monitoring ledger integrity, detecting tampering, and assessing computational complexity, bridging the gap between information-theoretic principles and distributed ledger applications. This study advances both the theoretical understanding and practical evaluation of blockchain security, providing a principled methodology for analyzing distributed systems under adversarial conditions. Full article

Grounding connectors critically influence the safety and long-term reliability of earthing systems through coupled electro-thermal, mechanical, and corrosion behaviors, yet no standardized quantitative framework exists for jointly evaluating these performance dimensions across diverse deployment scenarios. This study introduces a unified multi-criteria evaluation framework applied to six grounding connector configurations spanning four alloy families and three joining technologies. Electro-thermal response was characterized by coupled finite element simulations (0–100 A), mechanical reliability by quasi-static tensile testing (n = 10 per configuration), and corrosion durability by accelerated salt-spray exposure with image-based corroded area fraction quantification. Performance metrics were normalized and aggregated using equal-weight, Analytic Hierarchy Process, and Shannon entropy weighting schemes, with the Technique for Order of Preference by Similarity to Ideal Solution applied for multi-scenario ranking. One-way analysis of variance confirmed statistically significant effects of connector type on tensile performance (F(5, 54) = 3154.90, p < 0.001). The exothermic welded joint achieved the highest mean ultimate tensile load (61.5 ± 1.5 kN), while copper mechanical connectors exhibited the lowest steady-state temperature rise (~2 K above ambient at 100 A). Compression-crimped connectors ranked first under both equal and Analytic Hierarchy Process weighting (closeness coefficients 0.737 and 0.807, respectively), while stainless steel connectors ranked first under corrosion-critical deployment scenarios. Scenario-weighted analyses demonstrate that the optimal material–process combination shifts with environmental severity, current duty, and mechanical demand, providing a reproducible, evidence-based basis for context-dependent connector specification. Full article

Forests of Lualaba Province (DR Congo) form a compositionally complex mosaic of dry dense forest, gallery forest, and Miombo woodland. Yet, categorical land-cover maps impose discrete boundaries on these inherently continuous vegetation gradients, systematically discarding subpixel compositional information critical for forest monitoring and carbon accounting. The magnitude of this information loss at the landscape scale, however, remains largely unquantified. In this study, we train a Multi-Output Neural Network (MONN) using Sentinel-2 spectral and textural predictors (2025) to estimate the proportional cover of three forest types across the province. Model performance is benchmarked against a normalised Random Forest (RF) using spatial block cross-validation. Categorical information loss is quantified pixel-wise using two complementary metrics, dominant class proportion and Shannon compositional entropy, alongside a derived interpretive quantity, categorical information loss. The MONN slightly outperformed RF (R² = 0.648 vs. 0.630; RMSE = 0.224 vs. 0.229), yet the results reveal a fundamentally heterogeneous landscape structure. The mean dominant-class proportion was only 56.2%, indicating that categorical maps discard, on average, 43.8% of compositional information per pixel. Only 7.9% of forested pixels exceeded the 75% dominance threshold, while Shannon entropy reached 74.1% of its theoretical maximum, indicating that forest types coexist in near-equal proportions across most pixels. This renders categorical attribution structurally inadequate for most of the forested landscape. Across 92.1% of forested pixels, no single forest type achieved clear dominance. These results show that compositional mixing is the dominant structural condition of the landscape, and that compositional mapping is essential for representing tropical forest structure in heterogeneous drylands. By formally quantifying categorical information loss at the landscape scale, this study shows that continuous compositional mapping converts this structural ambiguity into a spatially explicit ecological signal, with direct implications for monitoring vegetation dynamics and biodiversity, suggesting a structural source of error in carbon stock estimation in tropical dry forests that warrants empirical validation. Full article

Recent land use and land cover (LULC) transformation in Vietnam raises the question of whether recent changes reflect a uniform national trend or differentiated regional patterns. This study assesses provincial LULC dynamics across 34 provinces using nationally consistent remote-sensing data for 2000, 2020, and 2023. We combine annualized intensity analysis, transition matrices, Shannon entropy, dominant transition analysis, and spatial autocorrelation to compare the magnitude, structure, and spatial organization of LULC change before and after 2020. The results show that annualized land-change rates were substantially higher during 2020–2023 than during 2000–2023, with all provinces showing increased rates of transformation. However, this more recent intensification has not been spatially uniform. Higher increases have been concentrated in southern and delta provinces, while several northern and upland provinces showed lower acceleration. Structural responses also varied across provinces: only four of 34 provinces (11.8%) were classified as both accelerated and structurally concentrated, whereas diversified regimes accounted for about two-thirds of the provinces. Population density was moderately associated with post-2020 magnitude of change but only weakly related to structural configuration, indicating that the magnitude and composition of LULC change represent distinct dimensions. By separating change intensity from structural configuration, this study provides a reproducible framework for identifying differentiated provincial land-change regimes. The results show that recent land cover transformation in Vietnam is not a single national process, but a mosaic of spatially and structurally distinct change patterns. Full article

Feature selection is essential for improving classification performance in high-dimensional biomedical data, yet conventional metaheuristic algorithms often suffer from premature convergence and loss of population diversity. To address these issues, this paper proposes a Feature Grouping and Improved Hybrid Breeding Optimization framework (FGIHBO). First, the original feature space is hierarchically partitioned using the Maximum Relevance Minimum Redundancy criterion and Symmetric Uncertainty analysis to alleviate the curse of dimensionality. Then, a Multi-Strategy Synergistic Improved Hybrid Breeding Optimization (MSIHBO) algorithm is developed by incorporating Grey Wolf Optimizer (GWO) guidance and a Shannon entropy-adaptive simulated annealing mechanism to balance exploration and exploitation. Experimental results on the CEC2022 benchmark suite demonstrate that MSIHBO provides robust optimization performance across diverse problem categories. Furthermore, evaluations on eleven high-dimensional biomedical datasets show that FGIHBO achieves average classification accuracies ranging from 92.77% to 97.66%. Compared with representative algorithms, including Multi-strategy Improved Grey Wolf Optimizer (MIGWO), Hybrid Whale Optimization Algorithm based on Gathering strategy (HWOAG), Dynamic Crow Search Algorithm (DCSA), GWO, Hybrid Breeding Optimization (HBO), Hybrid Breeding Optimization based on Lévy flight and Elite Opposition-Based Learning strategy (LEHBO), and MSIHBO, the proposed framework improves average classification accuracy by 1.47–27.46%, with the largest gain observed on dataset D10 relative to HWOAG. These results confirm the effectiveness, robustness, and scalability of the proposed framework for high-dimensional biomedical feature selection. Full article

Protease inhibitors (PIs) remain important components of HIV-2 treatment, but resistance genotyping is frequently challenging in individuals with low or undetectable plasma viremia. Proviral DNA sequencing may provide access to archived viral variants and improve understanding of long-term resistance and clinical evolution. In this retrospective longitudinal study, 27 individuals with HIV-2, both ART-experienced and ART-naïve, followed at a hospital in Lisbon, were analyzed. The HIV-2 protease gene was amplified from peripheral blood mononuclear cell-derived proviral DNA, cloned, and sequenced (Sanger sequencing) at baseline and, for ART-treated participants, after eight years of follow-up. Resistance profiles were interpreted using the Stanford HIVdb, HIV-2EU, and Rega algorithms. Clinical data, including ART history, CD4 counts, and plasma viral load, were collected longitudinally. Amino acid diversity was assessed using Shannon entropy, and longitudinal CD4 dynamics were evaluated using mixed-effects models with time-varying ART exposure. Sensitivity analyses were performed using generalized estimating equations (GEE). A total of 222 clonal HIV-2 protease sequences clustered within group A. Major PI resistance mutations were detected in 21.4% of ART-experienced and 23.1% of ART-naïve individuals at baseline. Longitudinal resistance trajectories varied across participants, including persistence, apparent emergence, and non-detection of previously identified mutations. Mixed-effects modeling revealed substantial inter-individual variability in CD4 trajectories, with no statistically significant associations observed between CD4 evolution and ART status, time, or their interaction. GEE analyses yielded consistent results, supporting robustness across modeling frameworks. Entropy analysis identified localized sequence diversity changes restricted to a small number of protease residues, with positions 60 and 75 differing between groups at baseline and position 21 showing longitudinal variation among treated participants. This study demonstrates that proviral DNA sequencing captures archived HIV-2 protease diversity and reveals persistent and dynamic resistance patterns within the viral reservoir. While no population-level association between ART exposure and CD4 trajectory was observed, marked inter-individual variability highlights the complexity of longitudinal immune recovery in HIV-2 infection. These findings support the value of proviral sequencing as a complementary research tool for characterizing long-term viral evolution in settings where plasma-based genotyping is limited. Full article