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Keywords = topology potential entropy

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21 pages, 781 KB  
Article
A Resilience Entropy-Based Framework for V2G Charging Station Siting and Resilient Reconfiguration of Power Distribution Networks Under Disasters
by Chutao Zheng, Fawen Chen, Zeli Xi, Guowei Guo, Xinsen Yang and Cong Chen
World Electr. Veh. J. 2025, 16(9), 532; https://doi.org/10.3390/wevj16090532 - 19 Sep 2025
Viewed by 404
Abstract
In the post-disaster recovery of power distribution networks (PDNs), electric vehicles (EVs) possess a great potential as mobile energy storage units. When supported by vehicle-to-grid (V2G)-enabled charging stations, EVs can provide effective supplementary power for disaster-stricken areas. However, most existing stations only support [...] Read more.
In the post-disaster recovery of power distribution networks (PDNs), electric vehicles (EVs) possess a great potential as mobile energy storage units. When supported by vehicle-to-grid (V2G)-enabled charging stations, EVs can provide effective supplementary power for disaster-stricken areas. However, most existing stations only support unidirectional charging, limiting the resilience-enhancing potential of V2G. To address this gap, this paper proposes a resilience-oriented restoration optimization model that jointly considers the siting of V2G-enabled charging stations and PDN topology reconfiguration. A novel metric—Resilience Entropy—is introduced to dynamically characterize the recovery process. The model explicitly describes fault propagation and circuit breaker operations, while incorporating power flow and radial topology constraints to ensure secure operation. EV behavioral uncertainty is also considered to enhance model adaptability under real-world post-disaster conditions. The optimal siting scheme is obtained by solving the proposed model. Case studies demonstrate the model’s effectiveness in improving post-disaster supply and recovery efficiency, and analyze the impact of user participation willingness on V2G-based restoration. Full article
(This article belongs to the Section Charging Infrastructure and Grid Integration)
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25 pages, 9610 KB  
Article
Numerical Study of Heat Transfer and Performance in a Hydrogen-Fueled Micro-Combustor with Gyroid, Lidinoid, and Neovius Structures for Thermophotovoltaic Applications
by Faisal Almutairi
Appl. Sci. 2025, 15(18), 10199; https://doi.org/10.3390/app151810199 - 18 Sep 2025
Viewed by 387
Abstract
This work evaluates a hydrogen-fueled planar micro-combustor featuring three triply periodic minimal surface (TPMS) structures, namely, gyroid, lidinoid, and Neovius matrix lattices, aiming to advance heat transfer processes and enhance system efficiency in micro-thermophotovoltaic (MTPV) applications. Through three-dimensional numerical investigations, a series of [...] Read more.
This work evaluates a hydrogen-fueled planar micro-combustor featuring three triply periodic minimal surface (TPMS) structures, namely, gyroid, lidinoid, and Neovius matrix lattices, aiming to advance heat transfer processes and enhance system efficiency in micro-thermophotovoltaic (MTPV) applications. Through three-dimensional numerical investigations, a series of simulations are conducted under varying TPMS lengths, inlet volume flow rate, and inlet equivalence ratios to optimize the design and operating conditions. The outcomes reveal that increasing the length of the TPMS structures is an effective means of improving heat transfer from the combustion zone to the walls, as indicated by significant increases in both mean wall temperature and radiation efficiency. However, longer internal structures reduce the uniformity of wall temperature and slightly increase entropy generation. Of the three topologies, the Neovius lattice demonstrates superior performance in all length scales, exhibiting a marginal improvement over the gyroid and a substantially greater advantage over the lidinoid structure. Increasing the inlet volume flow rate enhances wall temperature and its uniformity; however, the performance parameters decrease for all structures, indicating a limitation of the micro-combustor in benefiting from higher input power. Notably, the gyroid structure shows a lower rate of performance degradation at higher velocities, making it a potentially ideal design under such conditions. Finally, varying the equivalence ratio identifies the stoichiometric condition as optimal, yielding superior performance metrics compared to both lean and rich mixtures. Full article
(This article belongs to the Special Issue Recent Research on Heat and Mass Transfer)
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18 pages, 6001 KB  
Article
A Graph Contrastive Learning Method for Enhancing Genome Recovery in Complex Microbial Communities
by Guo Wei and Yan Liu
Entropy 2025, 27(9), 921; https://doi.org/10.3390/e27090921 - 31 Aug 2025
Viewed by 715
Abstract
Accurate genome binning is essential for resolving microbial community structure and functional potential from metagenomic data. However, existing approaches—primarily reliant on tetranucleotide frequency (TNF) and abundance profiles—often perform sub-optimally in the face of complex community compositions, low-abundance taxa, and long-read sequencing datasets. To [...] Read more.
Accurate genome binning is essential for resolving microbial community structure and functional potential from metagenomic data. However, existing approaches—primarily reliant on tetranucleotide frequency (TNF) and abundance profiles—often perform sub-optimally in the face of complex community compositions, low-abundance taxa, and long-read sequencing datasets. To address these limitations, we present MBGCCA, a novel metagenomic binning framework that synergistically integrates graph neural networks (GNNs), contrastive learning, and information-theoretic regularization to enhance binning accuracy, robustness, and biological coherence. MBGCCA operates in two stages: (1) multimodal information integration, where TNF and abundance profiles are fused via a deep neural network trained using a multi-view contrastive loss, and (2) self-supervised graph representation learning, which leverages assembly graph topology to refine contig embeddings. The contrastive learning objective follows the InfoMax principle by maximizing mutual information across augmented views and modalities, encouraging the model to extract globally consistent and high-information representations. By aligning perturbed graph views while preserving topological structure, MBGCCA effectively captures both global genomic characteristics and local contig relationships. Comprehensive evaluations using both synthetic and real-world datasets—including wastewater and soil microbiomes—demonstrate that MBGCCA consistently outperforms state-of-the-art binning methods, particularly in challenging scenarios marked by sparse data and high community complexity. These results highlight the value of entropy-aware, topology-preserving learning for advancing metagenomic genome reconstruction. Full article
(This article belongs to the Special Issue Network-Based Machine Learning Approaches in Bioinformatics)
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30 pages, 9514 KB  
Article
FPGA Implementation of Secure Image Transmission System Using 4D and 5D Fractional-Order Memristive Chaotic Oscillators
by Jose-Cruz Nuñez-Perez, Opeyemi-Micheal Afolabi, Vincent-Ademola Adeyemi, Yuma Sandoval-Ibarra and Esteban Tlelo-Cuautle
Fractal Fract. 2025, 9(8), 506; https://doi.org/10.3390/fractalfract9080506 - 31 Jul 2025
Viewed by 770
Abstract
With the rapid proliferation of real-time digital communication, particularly in multimedia applications, securing transmitted image data has become a vital concern. While chaotic systems have shown strong potential for cryptographic use, most existing approaches rely on low-dimensional, integer-order architectures, limiting their complexity and [...] Read more.
With the rapid proliferation of real-time digital communication, particularly in multimedia applications, securing transmitted image data has become a vital concern. While chaotic systems have shown strong potential for cryptographic use, most existing approaches rely on low-dimensional, integer-order architectures, limiting their complexity and resistance to attacks. Advances in fractional calculus and memristive technologies offer new avenues for enhancing security through more complex and tunable dynamics. However, the practical deployment of high-dimensional fractional-order memristive chaotic systems in hardware remains underexplored. This study addresses this gap by presenting a secure image transmission system implemented on a field-programmable gate array (FPGA) using a universal high-dimensional memristive chaotic topology with arbitrary-order dynamics. The design leverages four- and five-dimensional hyperchaotic oscillators, analyzed through bifurcation diagrams and Lyapunov exponents. To enable efficient hardware realization, the chaotic dynamics are approximated using the explicit fractional-order Runge–Kutta (EFORK) method with the Caputo fractional derivative, implemented in VHDL. Deployed on the Xilinx Artix-7 AC701 platform, synchronized master–slave chaotic generators drive a multi-stage stream cipher. This encryption process supports both RGB and grayscale images. Evaluation shows strong cryptographic properties: correlation of 6.1081×105, entropy of 7.9991, NPCR of 99.9776%, UACI of 33.4154%, and a key space of 21344, confirming high security and robustness. Full article
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40 pages, 10629 KB  
Article
Methods for Brain Connectivity Analysis with Applications to Rat Local Field Potential Recordings
by Anass B. El-Yaagoubi, Sipan Aslan, Farah Gomawi, Paolo V. Redondo, Sarbojit Roy, Malik S. Sultan, Mara S. Talento, Francine T. Tarrazona, Haibo Wu, Keiland W. Cooper, Norbert J. Fortin and Hernando Ombao
Entropy 2025, 27(4), 328; https://doi.org/10.3390/e27040328 - 21 Mar 2025
Viewed by 957
Abstract
Modeling the brain dependence network is central to understanding underlying neural mechanisms such as perception, action, and memory. In this study, we present a broad range of statistical methods for analyzing dependence in a brain network. Leveraging a combination of classical and cutting-edge [...] Read more.
Modeling the brain dependence network is central to understanding underlying neural mechanisms such as perception, action, and memory. In this study, we present a broad range of statistical methods for analyzing dependence in a brain network. Leveraging a combination of classical and cutting-edge approaches, we analyze multivariate hippocampal local field potential (LFP) time series data concentrating on the encoding of nonspatial olfactory information in rats. We present the strengths and limitations of each method in capturing neural dynamics and connectivity. Our analysis begins with exploratory techniques, including correlation, partial correlation, spectral matrices, and coherence, to establish foundational connectivity insights. We then investigate advanced methods such as Granger causality (GC), robust canonical coherence analysis, spectral transfer entropy (STE), and wavelet coherence to capture dynamic and nonlinear interactions. Additionally, we investigate the utility of topological data analysis (TDA) to extract multi-scale topological features and explore deep learning-based canonical correlation frameworks for connectivity modeling. This comprehensive approach offers an introduction to the state-of-the-art techniques for the analysis of dependence networks, emphasizing the unique strengths of various methodologies, addressing computational challenges, and paving the way for future research. Full article
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18 pages, 5282 KB  
Article
Mechanical and Catalytic Degradation Properties of Porous FeMnCoCr High-Entropy Alloy Structures Fabricated by Selective Laser Melting Additive Manufacturing
by Lyusha Cheng, Cheng Deng, Yushan Huang, Kai Li and Changjun Han
Materials 2025, 18(1), 185; https://doi.org/10.3390/ma18010185 - 4 Jan 2025
Cited by 1 | Viewed by 1279
Abstract
This work investigated the mechanical and catalytic degradation properties of FeMnCoCr-based high-entropy alloys (HEAs) with diverse compositions and porous structures fabricated via selective laser melting (SLM) additive manufacturing for wastewater treatment applications. The effects of Mn content (0, 30 at%, and 50 at%) [...] Read more.
This work investigated the mechanical and catalytic degradation properties of FeMnCoCr-based high-entropy alloys (HEAs) with diverse compositions and porous structures fabricated via selective laser melting (SLM) additive manufacturing for wastewater treatment applications. The effects of Mn content (0, 30 at%, and 50 at%) and topological structures (gyroid, diamond, and sea urchin-inspired shell) on the compression properties and catalytic efficiency of the Fe80-xMnxCo10Cr10 HEAs were discussed. The results indicated that an increase in the Mn content led to a phase structure transition that optimized mechanical properties and catalytic activities. Among the designed structures, the gyroid HEA structure exhibited the highest compressive yield strength, reaching 197 MPa. Additionally, Fe30Mn50Co10Cr10 HEA exhibited exceptional performance in catalytic degradation experiments by effectively degrading simulated pollutants with a significantly enhanced rate by 22.3% compared to other compositions. The Fe80-xMnxCo10Cr10 HEA catalyst fabricated by SLM demonstrated high stability over multiple cycles. These findings reveal that porous FeMnCoCr-based HEAs have significant potential for catalytic degradation of organic pollutants, providing valuable insights for future catalyst design and development in efficient and sustainable wastewater treatment. Full article
(This article belongs to the Special Issue Fabrication of Advanced Materials)
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16 pages, 17228 KB  
Article
Microstructure and Corrosion Resistance of Laser-Cladded FeCo1.5CrNi1.5Ti0.5 High-Entropy Alloy Coatings
by Sui Wang, Siqi Tian, Renjie Liu, Dengya Chen, Chao Wang, Jing Li and Sen Yang
Coatings 2024, 14(12), 1608; https://doi.org/10.3390/coatings14121608 - 23 Dec 2024
Cited by 1 | Viewed by 1214
Abstract
Due to their excellent mechanical properties and corrosion resistance, high-entropy alloys (HEAs) have the potential to be used as new engineering structures and functional materials. In this study, an FeCo1.5CrNi1.5Ti0.5HEA coating was prepared on the surface of [...] Read more.
Due to their excellent mechanical properties and corrosion resistance, high-entropy alloys (HEAs) have the potential to be used as new engineering structures and functional materials. In this study, an FeCo1.5CrNi1.5Ti0.5HEA coating was prepared on the surface of a 1Cr18Ni9Ti alloy by laser cladding technology. Phase structure and microstructure were characterized by XRD and using an SEM. The corrosion resistance was evaluated by an electrochemical workstation, and the polarization curves were obtained in simulated seawater and 3.5 wt.% NaCl and 5% HCl solutions. The corrosion morphology of the Fe-based HEA coating was further characterized using the SEM, super depth of field observation, and 3D topological images. The results showed that the Fe-based HEA coating had a single-phase FCC structure with a grain size of about 10.7 ± 0.25 μM. Electrochemical analysis results showed that the corrosion resistance of the current Fe-based HEA coating was poor in HCl solutions. However, it exhibited good corrosion properties in simulated seawater and 3.5 wt.% NaCl solutions. Further analysis of the corrosion morphology revealed that in simulated seawater and the 3.5 wt.% NaCl solution, the surface of the current Fe-based HEA coating exhibited a preferential corrosion tendency between dendrites, while in the 5% HCl solution, it exhibited more obvious pitting characteristics. The results indicate that the current Fe-based HEA coating exhibits good comprehensive performance, especially in an acidic Cl corrosion environment. These findings provide a reference for the application of laser cladding prepared Fe HEA coatings. Full article
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13 pages, 10496 KB  
Article
A Method for Fingerprint Edge Enhancement Based on Radial Hilbert Transform
by Baiyang Wu, Shuo Zhang, Weinan Gao, Yong Bi and Xiaosong Hu
Electronics 2024, 13(19), 3886; https://doi.org/10.3390/electronics13193886 - 30 Sep 2024
Cited by 2 | Viewed by 1361
Abstract
Fingerprints play a significant role in various fields due to their uniqueness. In order to effectively utilize fingerprint information, it is necessary to enhance image quality. This paper introduces a method based on Radial Hilbert transform (RHLT), which simulates the vortex filter using [...] Read more.
Fingerprints play a significant role in various fields due to their uniqueness. In order to effectively utilize fingerprint information, it is necessary to enhance image quality. This paper introduces a method based on Radial Hilbert transform (RHLT), which simulates the vortex filter using the point spread function (PSF) of spiral phase plate (SPP) with a topological charge l=1, for fingerprint edge enhancement. The experimental results show that the processed fingerprint image has more distinct edges, with an increase in information entropy and average gradient. Unlike classical edge detection operators, the fingerprint edge image obtained by the RHLT method exhibits a lower mean square error (MSE) and a higher peak signal-to-noise ratio (PSNR). This indicates that the RHLT method provides more accurate edge detection and demonstrates higher noise-resistance capabilities. Due to its ability to highlight edge information while preserving more original features, this method has great application potential in fingerprint image processing. Full article
(This article belongs to the Section Bioelectronics)
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24 pages, 1037 KB  
Article
Inferring Dealer Networks in the Foreign Exchange Market Using Conditional Transfer Entropy: Analysis of a Central Bank Announcement
by Aleksander Janczewski, Ioannis Anagnostou and Drona Kandhai
Entropy 2024, 26(9), 738; https://doi.org/10.3390/e26090738 - 29 Aug 2024
Cited by 1 | Viewed by 1789
Abstract
The foreign exchange (FX) market has evolved into a complex system where locally generated information percolates through the dealer network via high-frequency interactions. Information related to major events, such as economic announcements, spreads rapidly through this network, potentially inducing volatility, liquidity disruptions, and [...] Read more.
The foreign exchange (FX) market has evolved into a complex system where locally generated information percolates through the dealer network via high-frequency interactions. Information related to major events, such as economic announcements, spreads rapidly through this network, potentially inducing volatility, liquidity disruptions, and contagion effects across financial markets. Yet, research on the mechanics of information flows in the FX market is limited. In this paper, we introduce a novel approach employing conditional transfer entropy to construct networks of information flows. Leveraging a unique, high-resolution dataset of bid and ask prices, we investigate the impact of an announcement by the European Central Bank on the information transfer within the market. During the announcement, we identify key dealers as information sources, conduits, and sinks, and, through comparison to a baseline, uncover shifts in the network topology. Full article
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21 pages, 10478 KB  
Article
Identification of Key Risk Hotspots in Mega-Airport Surface Based on Monte Carlo Simulation
by Wen Tian, Xuefang Zhou, Jianan Yin, Yuchen Li and Yining Zhang
Aerospace 2024, 11(4), 254; https://doi.org/10.3390/aerospace11040254 - 25 Mar 2024
Cited by 5 | Viewed by 1787
Abstract
The complex layout of the airport surface, coupled with interrelated vehicle behaviors and densely mixed traffic flows, frequently leads to operational conflict risks. To address this issue, research was conducted on the recognition of characteristics and risk assessment for airport surface operations in [...] Read more.
The complex layout of the airport surface, coupled with interrelated vehicle behaviors and densely mixed traffic flows, frequently leads to operational conflict risks. To address this issue, research was conducted on the recognition of characteristics and risk assessment for airport surface operations in mixed traffic flows. Firstly, a surface topological network model was established based on the analysis of the physical structure features of the airport surface. Based on the Monte Carlo simulation method, the simulation framework for airport surface traffic operations was proposed, enabling the simulation of mixed traffic flows involving aircraft and vehicles. Secondly, from various perspectives, including topological structural characteristics, network vulnerabilities, and traffic complexity, a comprehensive system for feature indices and their measurement methods was developed to identify risk hotspots in mixed traffic flows on the airport surface, which facilitated the extraction of comprehensive risk elements for any node’s operation. Finally, a weighting rule for risk hotspot feature indices based on the CRITIC–entropy method was designed, and a risk assessment method for surface operations based on TOPSIS–gray relational analysis was proposed. This method accurately measured risk indices for airport surface operations hotspots. Simulations conducted at Shenzhen Bao’an International Airport demonstrate that the proposed methods achieve high simulation accuracy. The identified surface risk hotspots closely matched actual conflict areas, resulting in a 20% improvement in the accuracy of direct risk hotspot identification compared to simulation experiments. Additionally, 10.9% of nodes in the airport surface network were identified as risk hotspots, including 3 nodes with potential conflicts between aircraft and ground vehicles and 21 nodes with potential conflicts between aircraft. The proposed methods can effectively provide guidance for identifying potential “aircraft–vehicle” conflicts in complex airport surface layouts and scientifically support informed decisions in airport surface operation safety management. Full article
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18 pages, 2776 KB  
Article
Algal Bloom Ties: Spreading Network Inference and Extreme Eco-Environmental Feedback
by Haojiong Wang, Elroy Galbraith and Matteo Convertino
Entropy 2023, 25(4), 636; https://doi.org/10.3390/e25040636 - 10 Apr 2023
Cited by 6 | Viewed by 2817
Abstract
Coastal marine ecosystems worldwide are increasingly affected by tide alterations and anthropogenic disturbances affecting the water quality and leading to frequent algal blooms. Increased bloom persistence is a serious threat due to the long-lasting impacts on ecological processes and services, such as carbon [...] Read more.
Coastal marine ecosystems worldwide are increasingly affected by tide alterations and anthropogenic disturbances affecting the water quality and leading to frequent algal blooms. Increased bloom persistence is a serious threat due to the long-lasting impacts on ecological processes and services, such as carbon cycling and sequestration. The exploration of eco-environmental feedback and algal bloom patterns remains challenging and poorly investigated, mostly due to the paucity of data and lack of model-free approaches to infer universal bloom dynamics. Florida Bay, taken as an epitome for biodiversity and blooms, has long experienced algal blooms in its central and western regions, and, in 2006, an unprecedented bloom occurred in the eastern habitats rich in corals and vulnerable habitats. With global aims, we analyze the occurrence of blooms in Florida Bay from three perspectives: (1) the spatial spreading networks of chlorophyll-a (CHLa) that pinpoint the source and unbalanced habitats; (2) the fluctuations of water quality factors pre- and post-bloom outbreaks to assess the environmental impacts of ecological imbalances and target the prevention and control of algal blooms; and (3) the topological co-evolution of biogeochemical and spreading networks to quantify ecosystem stability and the likelihood of ecological shifts toward endemic blooms in the long term. Here, we propose the transfer entropy (TE) difference to infer salient dynamical inter actions between the spatial areas and biogeochemical factors (ecosystem connectome) underpinning bloom emergence and spread as well as environmental effects. A Pareto principle, defining the top 20% of areal interactions, is found to identify bloom spreading and the salient eco-environmental interactions of CHLa associated with endemic and epidemic regimes. We quantify the spatial dynamics of algal blooms and, thus, obtain areas in critical need for ecological monitoring and potential bloom control. The results show that algal blooms are increasingly persistent over space with long-term negative effects on water quality factors, in particular, about how blooms affect temperature locally. A dichotomy is reported between spatial ecological corridors of spreading and biogeochemical networks as well as divergence from the optimal eco-organization: randomization of the former due to nutrient overload and temperature increase leads to scale-free CHLa spreading and extreme outbreaks a posteriori. Subsequently, the occurrence of blooms increases bloom persistence, turbidity and salinity with potentially strong ecological effects on highly biodiverse and vulnerable habitats, such as tidal flats, salt-marshes and mangroves. The probabilistic distribution of CHLa is found to be indicative of endemic and epidemic regimes, where the former sets the system to higher energy dissipation, larger instability and lower predictability. Algal blooms are important ecosystem regulators of nutrient cycles; however, chlorophyll-a outbreaks cause vast ecosystem impacts, such as aquatic species mortality and carbon flux alteration due to their effects on water turbidity, nutrient cycling (nitrogen and phosphorus in particular), salinity and temperature. Beyond compromising the local water quality, other socio-ecological services are also compromised at large scales, including carbon sequestration, which affects climate regulation from local to global environments. Yet, ecological assessment models, such as the one presented, inferring bloom regions and their stability to pinpoint risks, are in need of application in aquatic ecosystems, such as subtropical and tropical bays, to assess optimal preventive controls. Full article
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10 pages, 295 KB  
Article
Study of Transformed ηζ Networks via Zagreb Connection Indices
by Muhammad Hussain, Atiq ur Rehman, Andrii Shekhovtsov, Muhammad Asif and Wojciech Sałabun
Information 2022, 13(4), 179; https://doi.org/10.3390/info13040179 - 31 Mar 2022
Viewed by 2366
Abstract
A graph is a tool for designing a system’s required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided ηζ network S(ηζΓ) and discussed their topology. [...] Read more.
A graph is a tool for designing a system’s required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided ηζ network S(ηζΓ) and discussed their topology. In graph theory, there are a variety of invariants to study the topology of a network, but topological indices are designed in such a way that these may transform the graph into a numeric value. In this work, we study S(ηζΓ) via Zagreb connection indices. Due to their predictive potential for enthalpy, entropy, and acentric factor, these indices gain value in the field of chemical graph theory in a very short time. ηζΓ formed by ζ time repeated process which consists ηζ copies of graph Γ along with η2|V(Γ)|ζηζ1 edges which used to join these ηζ copies of Γ. The free hand to choose the initial graph Γ for desired network S(ηζΓ) and its relation with chemical networks along with the repute of Zagreb connection indices enhance the worth of this study. These computations are theoretically innovative and aid topological characterization of S(ηζΓ). Full article
(This article belongs to the Special Issue Artificial Intelligence and Decision Support Systems)
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32 pages, 428 KB  
Article
Rate of Entropy Production in Stochastic Mechanical Systems
by Gregory S. Chirikjian
Entropy 2022, 24(1), 19; https://doi.org/10.3390/e24010019 - 23 Dec 2021
Cited by 2 | Viewed by 3684
Abstract
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., [...] Read more.
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems. Full article
(This article belongs to the Collection Randomness and Entropy Production)
17 pages, 1212 KB  
Article
Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
by Loris Di Cairano, Matteo Gori and Marco Pettini
Entropy 2021, 23(11), 1414; https://doi.org/10.3390/e23111414 - 27 Oct 2021
Cited by 6 | Viewed by 2900
Abstract
Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems [...] Read more.
Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy. Full article
(This article belongs to the Special Issue The Ubiquity of Entropy II)
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22 pages, 16715 KB  
Article
Biomarker Prioritisation and Power Estimation Using Ensemble Gene Regulatory Network Inference
by Furqan Aziz, Animesh Acharjee, John A. Williams, Dominic Russ, Laura Bravo-Merodio and Georgios V. Gkoutos
Int. J. Mol. Sci. 2020, 21(21), 7886; https://doi.org/10.3390/ijms21217886 - 23 Oct 2020
Cited by 5 | Viewed by 3078
Abstract
Inferring the topology of a gene regulatory network (GRN) from gene expression data is a challenging but important undertaking for gaining a better understanding of gene regulation. Key challenges include working with noisy data and dealing with a higher number of genes than [...] Read more.
Inferring the topology of a gene regulatory network (GRN) from gene expression data is a challenging but important undertaking for gaining a better understanding of gene regulation. Key challenges include working with noisy data and dealing with a higher number of genes than samples. Although a number of different methods have been proposed to infer the structure of a GRN, there are large discrepancies among the different inference algorithms they adopt, rendering their meaningful comparison challenging. In this study, we used two methods, namely the MIDER (Mutual Information Distance and Entropy Reduction) and the PLSNET (Partial least square based feature selection) methods, to infer the structure of a GRN directly from data and computationally validated our results. Both methods were applied to different gene expression datasets resulting from inflammatory bowel disease (IBD), pancreatic ductal adenocarcinoma (PDAC), and acute myeloid leukaemia (AML) studies. For each case, gene regulators were successfully identified. For example, for the case of the IBD dataset, the UGT1A family genes were identified as key regulators while upon analysing the PDAC dataset, the SULF1 and THBS2 genes were depicted. We further demonstrate that an ensemble-based approach, that combines the output of the MIDER and PLSNET algorithms, can infer the structure of a GRN from data with higher accuracy. We have also estimated the number of the samples required for potential future validation studies. Here, we presented our proposed analysis framework that caters not only to candidate regulator genes prediction for potential validation experiments but also an estimation of the number of samples required for these experiments. Full article
(This article belongs to the Special Issue OMICs, Data Integration, and Applications in Personalized Medicine)
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