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33 pages, 8203 KB  
Article
Applying Entropic Measures, Spectral Analysis, and EMD to Quantify Ion Channel Recordings: New Insights into Quercetin and Calcium Activation of BK Channels
by Przemysław Borys, Paulina Trybek, Beata Dworakowska, Anna Sekrecka-Belniak, Michał Wojcik and Agata Wawrzkiewicz-Jałowiecka
Entropy 2025, 27(10), 1047; https://doi.org/10.3390/e27101047 - 9 Oct 2025
Viewed by 185
Abstract
Understanding the functional modulation of ion channels by multiple activating substances is critical to grasping stimulus-specific gating mechanisms and possible synergistic or competitive interactions. This study investigates the activation of large-conductance, voltage- and Ca2+-activated potassium channels (BK) in the plasma membrane [...] Read more.
Understanding the functional modulation of ion channels by multiple activating substances is critical to grasping stimulus-specific gating mechanisms and possible synergistic or competitive interactions. This study investigates the activation of large-conductance, voltage- and Ca2+-activated potassium channels (BK) in the plasma membrane of human bronchial epithelial cells by Ca2+ and quercetin (Que), both individually and in combination. Patch-clamp recordings were analyzed using open state probability, dwell-time distributions, Shannon entropy, sample entropy, power spectral density (PSD), and empirical mode decomposition (EMD). Our results reveal concentration-dependent alterations in gating kinetics, particularly at a low concentration of quercetin ([Que] = 10 μM) compared with [Que] = 100 μM, where some Que-related effects are strongly attenuated in the presence of Ca2+. We also identify specific frequency bands where oscillatory components are most sensitive to the considered stimuli. Our findings highlight the complex reciprocal interplay between Ca2+ and Que in modulating BK channel function, and demonstrate the interpretative power of entropic and signal-decomposition approaches in characterizing stimulus-specific gating dynamics. Full article
(This article belongs to the Special Issue Mathematical Modeling for Ion Channels)
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22 pages, 12628 KB  
Article
Physical and Statistical Pattern of the Thiva (Greece) 2020–2022 Seismic Swarm
by Filippos Vallianatos, Eirini Sardeli, Kyriaki Pavlou and Andreas Karakonstantis
Entropy 2025, 27(9), 979; https://doi.org/10.3390/e27090979 - 19 Sep 2025
Viewed by 370
Abstract
On 2 December 2020, an earthquake with a magnitude of Mw 4.5 occurred near the city of Thiva (Greece). The aftershock sequence, triggered by ruptures on or near the Kallithea fault, continued until January 2021. Seven months later, new seismic activity began [...] Read more.
On 2 December 2020, an earthquake with a magnitude of Mw 4.5 occurred near the city of Thiva (Greece). The aftershock sequence, triggered by ruptures on or near the Kallithea fault, continued until January 2021. Seven months later, new seismic activity began a few kilometers west of the initial events, with the swarm displaying a general trend of spatiotemporal migration toward the east–southeast until the middle of 2022. In order to understand the physical and statistical pattern of the swarm, the seismicity was relocated using HypoDD, and the magnitude of completeness was determined using the frequency–magnitude distribution. In order to define the existence of spatiotemporal seismicity clusters in an objective way, the DBSCAN clustering algorithm was applied to the 2020–2022 Thiva earthquake sequence. The extracted clusters permit the analysis of the spatiotemporal scaling properties of the main clusters using the Non-Extensive Statistical Physics (NESP) approach, providing detailed insights into the nature of the long-term correlation of the seismic swarm. The statistical pattern observed aligns with a Q-exponential distribution, with qD values ranging from 0.7 to 0.8 and qT values from 1.44 to 1.50. Furthermore, the frequency–magnitude distributions were analyzed using the fragment–asperity model proposed within the NESP framework, providing the non-additive entropic parameter (qM). The results suggest that the statistical characteristics of earthquake clusters can be effectively interpreted using NESP, highlighting the complexity and non-additive nature of the spatiotemporal evolution of seismicity. In addition, the analysis of the properties of the seismicity clusters extracted using the DBSCAN algorithm permits the suggestion of possible physical mechanisms that drive the evolution of the two main and larger clusters. For the cluster that activated first and is located in the west–northwest part, an afterslip mechanism activated after the 2 September 2021, M 4.0 events seems to predominately control its evolution, while for the second activated cluster located in the east–southeast part, a normal diffusion mechanism is proposed to describe its migration pattern. Concluding, we can state that in the present work the application of the DBSCAN algorithm to recognize the existence of any possible spatiotemporal clustering of seismicity could be helping to provide detailed insight into the statistical and physical patterns in earthquake swarms. Full article
(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)
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14 pages, 4942 KB  
Article
The Identification of Gyrophoric Acid, a Phytochemical Derived from Lichen, as a Potent Inhibitor for Aggregation of Amyloid Beta Peptide: In Silico and Biochemical Evaluation
by Meixia Yang, Haitao Hu, Jin Gao, Queenie Wing Sze Lai, Farkhod Eshboev, Ka Wing Leung, Tina Tingxia Dong, Qin Xu and Karl Wah Keung Tsim
Int. J. Mol. Sci. 2025, 26(17), 8500; https://doi.org/10.3390/ijms26178500 - 1 Sep 2025
Viewed by 574
Abstract
Alzheimer’s disease (AD) is characterized by amyloid-beta (Aβ) plaque accumulation and neurodegeneration. This study identified gyrophoric acid, a lichen-derived phenolic metabolite, as a dual-action Aβ42 inhibitor preventing aggregation and disassembling of mature Aβ42 fibrils. Integrated in silico studies revealed that gyrophoric acid was [...] Read more.
Alzheimer’s disease (AD) is characterized by amyloid-beta (Aβ) plaque accumulation and neurodegeneration. This study identified gyrophoric acid, a lichen-derived phenolic metabolite, as a dual-action Aβ42 inhibitor preventing aggregation and disassembling of mature Aβ42 fibrils. Integrated in silico studies revealed that gyrophoric acid was a strong thermodynamic stabilizer of Aβ42 (MM–GBSA: −27.3 kcal/mol) via entropically driven hydrophobic interactions and disruption of aggregation-prone conformations (100 ns MD simulations). Through biochemical analysis of the fluorescent dye thioflavin T (ThT), gyrophoric acid induced rapid Aβ42 fibril disassembly within 5 h, with time-lapse confocal microscopy quantitatively confirming the near-complete dissolution of large aggregates by 24 h. ADMET profiling revealed favorable pharmacokinetics (moderate oral absorption: 48.5–57.3%; low toxicity) and Lipinski’s rule compliance. These results establish gyrophoric acid as a promising natural bioactive compound for anti-AD therapeutics with a unique hydrophobic-stabilization mechanism. Full article
(This article belongs to the Section Molecular Pharmacology)
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30 pages, 4353 KB  
Article
Distributionally Robust Bayesian Optimization via Sinkhorn-Based Wasserstein Barycenter
by Iman Seyedi, Antonio Candelieri and Francesco Archetti
Mach. Learn. Knowl. Extr. 2025, 7(3), 90; https://doi.org/10.3390/make7030090 - 28 Aug 2025
Viewed by 915
Abstract
This paper introduces a novel framework for Distributionally Robust Bayesian Optimization (DRBO) with continuous context that integrates optimal transport theory and entropic regularization. We propose the sampling from the Wasserstein Barycenter Bayesian Optimization (SWBBO) method to deal with uncertainty about the context; that [...] Read more.
This paper introduces a novel framework for Distributionally Robust Bayesian Optimization (DRBO) with continuous context that integrates optimal transport theory and entropic regularization. We propose the sampling from the Wasserstein Barycenter Bayesian Optimization (SWBBO) method to deal with uncertainty about the context; that is, the unknown stochastic component affecting the observations of the black-box objective function. This approach captures the geometric structure of the underlying distributional uncertainty and enables robust acquisition strategies without incurring excessive computational costs. The method incorporates adaptive robustness scheduling, Lipschitz regularization, and efficient barycenter construction to balance exploration and exploitation. Theoretical analysis establishes convergence guarantees for the robust Bayesian Optimization acquisition function. Empirical evaluations on standard global optimization problems and real-life inspired benchmarks demonstrate that SWBBO consistently achieves faster convergence, good final regret, and greater stability than other recently proposed methods for DRBO with continuous context. Indeed, SWBBO outperforms all of them in terms of both optimization performance and robustness under repeated evaluations. Full article
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13 pages, 2083 KB  
Article
Avibactam–Cyclodextrin Inclusion Complexes: Computational and Thermodynamic Insights for Drug Delivery, Detection, and Environmental Scavenging
by Jackson J. Alcázar, Paola R. Campodónico and René López
Molecules 2025, 30(16), 3401; https://doi.org/10.3390/molecules30163401 - 18 Aug 2025
Viewed by 845
Abstract
The escalating crisis of multidrug resistance, together with the persistence of antibiotic residues in clinical and environmental matrices, demands integrated strategies that couple sensitive detection, efficient decontamination, and controlled delivery. However, current techniques for quantifying avibactam (AVI)—a broad-spectrum β-lactamase inhibitor—such as HPLC-UV lack [...] Read more.
The escalating crisis of multidrug resistance, together with the persistence of antibiotic residues in clinical and environmental matrices, demands integrated strategies that couple sensitive detection, efficient decontamination, and controlled delivery. However, current techniques for quantifying avibactam (AVI)—a broad-spectrum β-lactamase inhibitor—such as HPLC-UV lack the sensitivity and specificity required for both therapeutic drug monitoring and environmental surveillance. Encapsulation of AVI within cyclodextrins (CDs) may simultaneously enhance its stability, bioavailability, and detectability, while the high binding affinities of CDs position them as molecular traps capable of scavenging residual AVI. In this study, the inclusion complexation of AVI with various CDs was examined through molecular dynamics (MD) simulations, experimental isothermal titration calorimetry (ITC), and non-covalent interaction (NCI) analysis. Stable 1:1 inclusion complexes were observed between AVI and β-cyclodextrin (β-CD), 2,6-dimethyl-β-cyclodextrin (DM-β-CD), and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD), with standard Gibbs free energies of binding (ΔG°) of –3.64, –3.24, and –3.11 kcal/mol, respectively. In contrast, γ-cyclodextrin (γ-CD) exhibited significantly weaker binding (ΔG° = –2.25 kcal/mol). DFT-based NCI analysis revealed that cooperative interaction topology and cavity complementarity, rather than the sheer number of localized contacts, govern complex stability. Combined computational and experimental data establish β-CD derivatives as effective supramolecular hosts for AVI, despite an entropic penalty in the DM-β-CD/AVI complex. These CD–AVI affinities support the development of improved analytical methodologies and pharmaceutical formulations, and they also open avenues for decontamination strategies based on molecular trapping of AVI. Full article
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47 pages, 2189 KB  
Article
The Vicious Cycle Atlas of Fragility: Mapping the Feedback Loops Between Industrial–Urban Metabolism and Earth System Collapse
by Choy Yee Keong
Urban Sci. 2025, 9(8), 320; https://doi.org/10.3390/urbansci9080320 - 14 Aug 2025
Viewed by 1700
Abstract
This study examines how Multi-Scalar Nature-Based Regenerative Solutions (M-NbRS) can realign urban–industrial systems with planetary boundaries to mitigate Earth system destabilization. Using integrated systems analysis, we document three key findings: (1) global material flows show only 9% circularity amid annual extraction of 100 [...] Read more.
This study examines how Multi-Scalar Nature-Based Regenerative Solutions (M-NbRS) can realign urban–industrial systems with planetary boundaries to mitigate Earth system destabilization. Using integrated systems analysis, we document three key findings: (1) global material flows show only 9% circularity amid annual extraction of 100 billion tons of resources; (2) Earth system diagnostics reveal 28 trillion tons of cryosphere loss since 1994 and 372 Zettajoules of oceanic heat accumulation; and (3) meta-analysis identifies accelerating biosphere integrity loss (61.56 million hectares deforested since 2001) and atmospheric CO2 concentrations reaching 424.61 ppm (2024). Our Vicious Cycle Atlas of Fragility framework maps three synergistic disintegration pathways: metabolic overload from linear resource flows exceeding sink capacity, entropic degradation through high-entropy waste driving cryospheric collapse, and planetary boundary transgression. The M-NbRS framework counters these through spatially nested interventions: hyper-local urban tree canopy expansion (demonstrating 0.4–12 °C cooling), regional initiatives like the Heart of Borneo’s 24 million-hectare conservation, and global industrial controls maintaining aragonite saturation (Ωarag > 2.75) for marine resilience. Implementation requires policy innovations including deforestation-free supply chains, sustainability-linked financing, and ecological reciprocity legislation. These findings provide an evidence base for transitioning industrial–urban systems from drivers of Earth system fragility to architects of regeneration within safe operating spaces. Collectively, these findings demonstrate that M-NbRS offer a scientifically grounded, policy-actionable framework for breaking the vicious cycles of Earth system destabilization. By operationalizing nature-based regeneration across spatial scales—from street trees to transboundary conservation—this approach provides measurable pathways to realign human systems with planetary boundaries, offering a timely blueprint for industrial–urban transformation within ecological limits. Full article
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13 pages, 3943 KB  
Proceeding Paper
Emergent Behavior and Computational Capabilities in Nonlinear Systems: Advancing Applications in Time Series Forecasting and Predictive Modeling
by Kárel García-Medina, Daniel Estevez-Moya, Ernesto Estevez-Rams and Reinhard B. Neder
Comput. Sci. Math. Forum 2025, 11(1), 17; https://doi.org/10.3390/cmsf2025011017 - 11 Aug 2025
Viewed by 239
Abstract
Natural dynamical systems can often display various long-term behaviours, ranging from entirely predictable decaying states to unpredictable, chaotic regimes or, more interestingly, highly correlated and intricate states featuring emergent phenomena. That, of course, imposes a level of generality on the models we use [...] Read more.
Natural dynamical systems can often display various long-term behaviours, ranging from entirely predictable decaying states to unpredictable, chaotic regimes or, more interestingly, highly correlated and intricate states featuring emergent phenomena. That, of course, imposes a level of generality on the models we use to study them. Among those models, coupled oscillators and cellular automata (CA) present a unique opportunity to advance the understanding of complex temporal behaviours because of their conceptual simplicity but very rich dynamics. In this contribution, we review the work completed by our research team over the last few years in the development and application of an alternative information-based characterization scheme to study the emergent behaviour and information handling of nonlinear systems, specifically Adler-type oscillators under different types of coupling: local phase-dependent (LAP) coupling and Kuramoto-like local (LAK) coupling. We thoroughly studied the long-term dynamics of these systems, identifying several distinct dynamic regimes, ranging from periodic to chaotic and complex. The systems were analysed qualitatively and quantitatively, drawing on entropic measures and information theory. Measures such as entropy density (Shannon entropy rate), effective complexity measure, and Lempel–Ziv complexity/information distance were employed. Our analysis revealed similar patterns and behaviours between these systems and CA, which are computationally capable systems, for some specific rules and regimes. These findings further reinforce the argument around computational capabilities in dynamical systems, as understood by information transmission, storage, and generation measures. Furthermore, the edge of chaos hypothesis (EOC) was verified in coupled oscillators systems for specific regions of parameter space, where a sudden increase in effective complexity measure was observed, indicating enhanced information processing capabilities. Given the potential for exploiting this non-anthropocentric computational power, we propose this alternative information-based characterization scheme as a general framework to identify a dynamical system’s proximity to computationally enhanced states. Furthermore, this study advances the understanding of emergent behaviour in nonlinear systems. It explores the potential for leveraging the features of dynamical systems operating at the edge of chaos by coupling them with computationally capable settings within machine learning frameworks, specifically by using them as reservoirs in Echo State Networks (ESNs) for time series forecasting and predictive modeling. This approach aims to enhance the predictive capacity, particularly that of chaotic systems, by utilising EOC systems’ complex, sensitive dynamics as the ESN reservoir. Full article
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24 pages, 5811 KB  
Article
Thermodynamics of Molecular Transport Through a Nanochannel: Evidence of Energy–Entropy Compensation
by Changsun Eun
Int. J. Mol. Sci. 2025, 26(15), 7277; https://doi.org/10.3390/ijms26157277 - 28 Jul 2025
Viewed by 382
Abstract
In this work, the thermodynamics of molecular transport between two compartments connected by a nanochannel is investigated through an analysis of internal energy and entropy changes, with a focus on how these changes depend on intermolecular interaction strength. When interactions are weak, resembling [...] Read more.
In this work, the thermodynamics of molecular transport between two compartments connected by a nanochannel is investigated through an analysis of internal energy and entropy changes, with a focus on how these changes depend on intermolecular interaction strength. When interactions are weak, resembling gas-like behavior, entropy dominates and favors configurations in which molecules are evenly distributed between the two compartments, despite an increase in internal energy. In contrast, strong interactions, characteristic of liquid-like behavior, lead to dominant energetic contributions that favor configurations with molecules localized in a single compartment, despite entropy loss. Intermediate interaction strengths yield comparable entropic and energetic contributions that cancel each other out, resulting in oscillatory behavior between evenly distributed and localized configurations, as observed in previous work. This thermodynamic analysis reveals energy–entropy compensation, in which entropic and energetic contributions offset each other across different interaction strengths; notably, this compensatory relationship exhibits a linear trend. These findings provide insight into the thermodynamic origins of molecular transport behavior and highlight fundamental parallels between molecular transport and molecular binding, the latter being particularly relevant to molecular recognition and drug design. Full article
(This article belongs to the Special Issue Research on Molecular Dynamics: 2nd Edition)
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14 pages, 449 KB  
Article
Thermodynamic Study of the Solubility of Triclocarban in Polyethylene Glycol 200 + Water Cosolvent Mixtures at Different Temperatures
by Vanesa Puentes-Lozada, Diego Ivan Caviedes-Rubio, Cristian Rincón-Guio, Nestor Enrique Cerquera, Rossember Edén Cardenas-Torres, Claudia Patricia Ortiz, Fleming Martinez and Daniel Ricardo Delgado
Molecules 2025, 30(12), 2631; https://doi.org/10.3390/molecules30122631 - 17 Jun 2025
Viewed by 554
Abstract
Background: Solubility is a fundamental physicochemical property in pharmaceutical, chemical and environmental industrial processes. Regarding Triclocarban (TCC), a broad-spectrum antimicrobial, solubility is particularly challenging due to its low aqueous solubility and hydrophobic nature; these challenges can be addressed by some effective techniques such [...] Read more.
Background: Solubility is a fundamental physicochemical property in pharmaceutical, chemical and environmental industrial processes. Regarding Triclocarban (TCC), a broad-spectrum antimicrobial, solubility is particularly challenging due to its low aqueous solubility and hydrophobic nature; these challenges can be addressed by some effective techniques such as cosolvency, which allows one to increase the solubility of drugs by several orders of magnitude. This study aims to thermodynamically evaluate the solubility of TCC in cosolvent mixtures of PEG 200 + water at different temperatures. Methods: Experimental solubility data were determined using the shake-flask followed by UV quantification analysis at saturation methods, and thermodynamic functions of the solution processes were calculated using the Gibbs–van’t Hoff–Krug model. Results: The solubility results demonstrate the positive cosolvent effect of PEG 200 on the solubility of TCC, whose solution process is thermodynamically strongly governed by the enthalpy of solution with entropic preference in PEG 200-rich mixtures. Conclusions: The solubility of TCC is an endothermic, thermo-dependent process. The addition of PEG 200 to the cosolvent mixture favors this process and shows a positive cosolvent effect. Full article
(This article belongs to the Special Issue Recent Advances in Chemical Thermodynamics from Theory to Experiment)
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13 pages, 1040 KB  
Article
Texture Analysis of Near-Infrared Vein Images During Reactive Hyperemia in Healthy Subjects
by Henrique Silva and Carlota Rezendes
Appl. Sci. 2025, 15(10), 5702; https://doi.org/10.3390/app15105702 - 20 May 2025
Cited by 1 | Viewed by 716
Abstract
Venous perfusion plays a crucial role in vascular health, yet functional assessment of superficial veins remains limited. Near-infrared reflectance imaging (NIRI) devices, commonly used for vein visualization, may offer untapped potential in this context. We investigated whether texture analysis (TA) applied to NIRI-based [...] Read more.
Venous perfusion plays a crucial role in vascular health, yet functional assessment of superficial veins remains limited. Near-infrared reflectance imaging (NIRI) devices, commonly used for vein visualization, may offer untapped potential in this context. We investigated whether texture analysis (TA) applied to NIRI-based vein finder images can detect dynamic changes in superficial venous structure during reactive hyperemia. Fourteen healthy adults underwent a suprasystolic occlusion protocol, with real-time images acquired from the hand dorsum. From defined regions of interest, we extracted classical texture parameters (e.g., contrast, correlation, entropy, energy, fractal dimension, and lacunarity) and vein width. While vein width significantly increased during occlusion (p < 0.001), most individual texture parameters remained stable. Notably, correlation increased during occlusion (p = 0.023), and lacunarity decreased during recovery (p = 0.024). We developed composite indices combining texture and morphological features. Entropy-to-width and correlation-to-width ratios decreased during occlusion (p < 0.001), while total entropic content rose (p < 0.001). A modest increase in the correlation-to-entropy ratio during recovery (p = 0.026) suggested delayed reorganization of venous texture. These findings indicate that TA of vein finder images captures functional vascular responses beyond morphology alone. Composite parameters enhance sensitivity and may support the development of non-invasive, low-cost tools for assessing venous function. Full article
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22 pages, 4358 KB  
Article
A Study on the Coupled Coordination Between Tourism Efficiency and Economic Development Level in the Beijing–Tianjin–Hebei City Cluster in the Past 10 Years
by Shengxia Wang, Ruiting Liu and Maolan Li
Sustainability 2025, 17(10), 4388; https://doi.org/10.3390/su17104388 - 12 May 2025
Viewed by 632
Abstract
This longitudinal study applies decade-spanning socioeconomic indicators (2013–2022) from the Beijing–Tianjin–Hebei urban agglomeration. An integrated analytical framework was developed, merging the super-efficiency slack-based measurement (SBM) methodology with entropic weighting techniques to quantify tourism efficiency and economic development. Subsequent phases employed a multi-method analytical [...] Read more.
This longitudinal study applies decade-spanning socioeconomic indicators (2013–2022) from the Beijing–Tianjin–Hebei urban agglomeration. An integrated analytical framework was developed, merging the super-efficiency slack-based measurement (SBM) methodology with entropic weighting techniques to quantify tourism efficiency and economic development. Subsequent phases employed a multi-method analytical cascade: coupling coordination assessment modeling for system interaction analysis, standard deviation ellipses for spatial dispersion characterization, and Markovian transition matrices for temporal pattern identification. The investigation concludes with evolutionary trajectory projections using gray system forecasting GM(1,1) modeling. The analytical findings reveal the following patterns: (1) Within the Beijing–Tianjin–Hebei metropolitan cluster, tourism efficiency demonstrates a consistent upward trajectory, manifesting spatial differentiation characteristics characterized by a dual-core structure centered on Tianjin and Baoding, with higher values observed in northwestern areas compared to southeastern regions. Concurrently, regional disparities exhibit progressive convergence over temporal progression. (2) The level of economic development in the Beijing–Tianjin–Hebei city cluster has been rising steadily, demonstrating a geospatial distribution of ‘central concentration with peripheral attenuation, with the north-east being better than the southwest’, and the gap between the regional differences has become broader over time. (3) The coupling between tourism efficiency and the level of economic development in the Beijing–Tianjin–Hebei city cluster has generally improved, with Beijing and Tianjin predominantly in a coordinated regime, and some cities in Hebei Province about to shift from dysfunctional to coordinated, and, spatially, the coupling and coordination in northern sectors demonstrate superior performance compared to southern counterparts nationally. (4) The coupling coordination degree of the Beijing–Tianjin–Hebei city cluster in the next eight years is predicted by the gray GM(1,1) prediction model and the overall continuation of the growth trend of the Beijing–Tianjin–Hebei city cluster over the past ten years, thus verifying the importance of the regional integrated policy frameworks in the system integration of the Beijing–Tianjin–Hebei metropolitan system. Full article
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17 pages, 2106 KB  
Article
Informational Entropy Analysis of Artificial Helium Atoms
by Marcilio N. Guimarães, Rafael N. Cordeiro, Wallas S. Nascimento and Frederico V. Prudente
Atoms 2025, 13(5), 42; https://doi.org/10.3390/atoms13050042 - 12 May 2025
Viewed by 400
Abstract
We use the Shannon informational entropies as a tool to study the artificial helium atom, namely, two electrons confined in a quantum dot. We adopt configurations with spherical and cylindrical symmetries for the physical system of interest. Using the informational quantities, we analyze [...] Read more.
We use the Shannon informational entropies as a tool to study the artificial helium atom, namely, two electrons confined in a quantum dot. We adopt configurations with spherical and cylindrical symmetries for the physical system of interest. Using the informational quantities, we analyze the effects of electronic confinement, we validate the entropic uncertainty relation, we identify that the Coulomb interaction potential between the electrons is no longer important for strong confinements, and we indicate/predict the avoided crossing phenomena. Finally, we carried out a density function analysis. When available, the results are compared with those in the literature. Full article
(This article belongs to the Section Atom Based Quantum Technology)
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31 pages, 19278 KB  
Article
Fractal Dimension of Pollutants and Urban Meteorology of a Basin Geomorphology: Study of Its Relationship with Entropic Dynamics and Anomalous Diffusion
by Patricio Pacheco and Eduardo Mera
Fractal Fract. 2025, 9(4), 255; https://doi.org/10.3390/fractalfract9040255 - 17 Apr 2025
Viewed by 392
Abstract
A total of 108 maximum Kolmogorov entropy (SK) values, calculated by means of chaos theory, are obtained from 108 time series (TSs) (each consisting of 28,463 hourly data points). The total TSs are divided into 54 urban meteorological (temperature (T), relative [...] Read more.
A total of 108 maximum Kolmogorov entropy (SK) values, calculated by means of chaos theory, are obtained from 108 time series (TSs) (each consisting of 28,463 hourly data points). The total TSs are divided into 54 urban meteorological (temperature (T), relative humidity (RH) and wind speed magnitude (WS)) and 54 pollutants (PM10, PM2.5 and CO). The measurement locations (6) are located at different heights and the data recording was carried out in three periods, 2010–2013, 2017–2020 and 2019–2022, which determines a total of 3,074,004 data points. For each location, the sum of the maximum entropies of urban meteorology and the sum of maximum entropies of pollutants, SK, MV and SK, P, are calculated and plotted against h, generating six different curves for each of the three data-recording periods. The tangent of each figure is determined and multiplied by the average temperature value of each location according to the period, obtaining, in a first approximation, the magnitude of the entropic forces associated with urban meteorology (FK, MV) and pollutants (FK, P), respectively. It is verified that all the time series have a fractal dimension, and that the fractal dimension of the pollutants shows growth towards the most recent period. The entropic dynamics of pollutants is more dominant with respect to the dynamics of urban meteorology. It is found that this greater influence favors subdiffusion processes (α < 1), which is consistent with a geographic basin with lower atmospheric resilience. By applying a heavy-tailed probability density analysis, it is shown that atmospheric pollution states are more likely, generating an extreme environment that favors the growth of respiratory diseases and low relative humidity, makes heat islands more stable over time, and strengthens heat waves. Full article
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11 pages, 4849 KB  
Article
Analysis of the Relationship Between Enguri Large Dam Monitoring Entropic Features
by Tamaz Chelidze, Teimuraz Matcharashvili, Aleksandre Sborshchikovi, Ekaterine Mepharidze, Dimitri Tepnadze and Levan Laliashvili
Entropy 2025, 27(4), 413; https://doi.org/10.3390/e27040413 - 11 Apr 2025
Viewed by 629
Abstract
In this research, the results of the analysis of Enguri Large Dam (West Georgia) monitoring features, such as foundation displacement data and water level (WL) variation in the reservoir, were investigated. A statistical approach based on calculating time series helps us determine the [...] Read more.
In this research, the results of the analysis of Enguri Large Dam (West Georgia) monitoring features, such as foundation displacement data and water level (WL) variation in the reservoir, were investigated. A statistical approach based on calculating time series helps us determine the research area’s dynamic picture. In this article, we have used various nonlinear analysis methods. Nonlinear dynamics of deformation and filling/reloading near grand dams reflect the complexity of the mentioned time series, connected with the natural agents (regional and local geodynamics), which were presented even before dam erection, and the effects of the water level variation in the reservoir. Both these effects are documented by observations from 1974 to 2024 at the Enguri Large Dam. Modern linear and nonlinear primarily data analysis techniques will be used for analysis of monitoring characteristics of the Enguri Large Dam: Kullback–Leibler divergence, mutual information, Shannon entropy, and Tsallis entropy. The obtained data on the dynamics of deformation and filling/reloading near a large dam can be used for the assessment of the possible risks connected with abrupt changes in the routine dynamics of construction. Full article
(This article belongs to the Section Multidisciplinary Applications)
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