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Search Results (1,873)

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Keywords = entropy theory

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21 pages, 6064 KiB  
Article
Study on Steady Flow Force of a Bidirectional Throttling Slide Valve and Its Compensation Optimization
by Qi Mao, Xinying Jia, Zhe Liu, Guang Li, Yichi Cao and Qingjun Yang
Appl. Sci. 2024, 14(23), 11037; https://doi.org/10.3390/app142311037 - 27 Nov 2024
Abstract
This paper focuses on a typical pressure-controlled slide valve, utilizing momentum analysis and computational fluid dynamics to simulate and analyze the asymmetry of steady flow force curves under bidirectional throttling patterns. The entropy production theory is employed to reveal the causes of nonlinearity [...] Read more.
This paper focuses on a typical pressure-controlled slide valve, utilizing momentum analysis and computational fluid dynamics to simulate and analyze the asymmetry of steady flow force curves under bidirectional throttling patterns. The entropy production theory is employed to reveal the causes of nonlinearity in the steady flow force of an inlet throttling slide valve. Based on flow field analysis, a flow force compensation scheme is proposed by adding a guiding shoulder and matching it with a suitably sized inner annular cavity. The study reveals that fluid momentum at the non-throttling valve port is the primary cause of the bidirectional throttling flow force difference, and under large-opening inlet throttling conditions, it may reverse the direction of the flow force. Vortex separation caused by turbulent pulsations is one of the intrinsic reasons for the nonlinearity of steady flow force. Full article
21 pages, 2729 KiB  
Article
Studying the Impact of Diffuser Return Guide Vanes on the Energy Performance of a Multistage Centrifugal Pump
by Jan Górecki, Kliment Klimentov, Gencho Popov, Boris Kostov and Salaf Ibrahim
Appl. Sci. 2024, 14(23), 10991; https://doi.org/10.3390/app142310991 - 26 Nov 2024
Viewed by 248
Abstract
The head, efficiency, and cavitation characteristics of centrifugal pumps are highly dependent on the velocity field in front of the impeller inlet. In multistage pumps, the velocity field in front of the second and each subsequent stage is determined by the shape (design) [...] Read more.
The head, efficiency, and cavitation characteristics of centrifugal pumps are highly dependent on the velocity field in front of the impeller inlet. In multistage pumps, the velocity field in front of the second and each subsequent stage is determined by the shape (design) of the diffuser return guide vanes. This current work presents the results obtained by performing a numerical study using ANSYS CFX 14.0 to determine the impact of the shape (design) of diffuser return guide vanes on the head and coefficient of efficiency of one stage of a multistage centrifugal pump. Three RGVs with different Outlet angles are studied: α6 —original RGV with α6=90deg, RGV1 with α6=110deg and RGV2 with α6=128deg. The results obtained after performing CFD modeling indicate that with one of the studied RGVs, the pump stage head increases by nearly 20%, while the hydraulic coefficient of efficiency remains almost constant. Applying entropy production theory is used to determine the impact of the various components of entropy production on the total head loss in the studied pump stage. The impact of the Outlet angle of the RGV on the velocity field of the flow in front of the next impeller (stage) as well as the RGV head is also analyzed. The numerical results of the original RGV are compared with the experimental data obtained from large-scale studies of pumps performed at the Laboratory of Hydraulic Machines of the University “Angel Kanchev” of Ruse, Bulgaria. When using the modified RGVs, the head curve of the original pump can be obtained by operating at a lower speed or with a smaller impeller diameter. This may lead to an overall increase in the energy efficiency of the machine, which could be explored as a future task. Full article
25 pages, 5960 KiB  
Article
Adaptive Control Parameter Optimization of Permanent Magnet Synchronous Motors Based on Super-Helical Sliding Mode Control
by Lingtao Kong, Hongxin Zhang, Tiezhu Zhang, Junyi Wang, Chaohui Yang and Zhen Zhang
Appl. Sci. 2024, 14(23), 10967; https://doi.org/10.3390/app142310967 - 26 Nov 2024
Viewed by 162
Abstract
Optimizing control rate parameters is one of the key technologies in motor control systems. To address the issues of weak robustness and slow response speed in traditional adaptive control strategies, an adaptive control system based on sliding mode control is proposed to enhance [...] Read more.
Optimizing control rate parameters is one of the key technologies in motor control systems. To address the issues of weak robustness and slow response speed in traditional adaptive control strategies, an adaptive control system based on sliding mode control is proposed to enhance the overall performance of permanent magnet synchronous motors. The Non-dominated Sorting Genetic Algorithm II and Multi-objective Particle Swarm Optimization are employed to effectively optimize control parameters, thereby mitigating motor torque and speed overshoot. A Partial Sample Shannon Entropy Evaluation method, leveraging entropy theory in conjunction with the Z-score method, is introduced to facilitate the feedback regulation of the optimization process by assessing motor output torque. Simulation results confirm that the proposed control strategy, in combination with the optimized control rate parameters, leads to substantial improvements in motor performance. Compared to traditional adaptive control strategies, the proposed approach improves the motor’s steady-state response speed by 42% and reduces rotor error during system fluctuations by 23%, significantly enhancing the motor’s response speed and robustness. Following parameter optimization, speed and torque overshoot are reduced by 38% and 10%, respectively, resulting in a significant improvement in the stability and precision of the motor control system. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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<p>Equivalent circuit diagram in d-q coordinates.</p>
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<p>Standardized feedback systems.</p>
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<p>Planetary gear and working modes.</p>
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<p>Block diagram of permanent magnet synchronous motor control using the STSM control method.</p>
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<p>Block diagram of the two optimization algorithms NSGA-II and MOPSO.</p>
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<p>The convergence curve of the parameter.</p>
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<p>Motor speed results.</p>
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<p>Motor speed error results.</p>
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<p>Rotor position error results.</p>
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<p>Motor speed error results.</p>
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<p>Motor speed results in sudden speed changes.</p>
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<p>Motor speed results during sudden speed changes.</p>
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<p>The Z-curve plot of standardized evaluation of PSSEE.</p>
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17 pages, 3453 KiB  
Article
Kinetic and Thermodynamic Aspects of the Degradation of Ferritic Steels Immersed in Solar Salt
by Rafael Felix-Contreras, Jonathan de la Vega Olivas, Cinthya Dinorah Arrieta-Gonzalez, Jose Guadalupe Chacon-Nava, Roberto Ademar Rodriguez-Diaz, Jose Gonzalo Gonzalez-Rodriguez and Jesus Porcayo-Calderon
Materials 2024, 17(23), 5776; https://doi.org/10.3390/ma17235776 - 25 Nov 2024
Viewed by 226
Abstract
The study and improvement of the corrosion resistance of materials used in concentrated solar power plants is a permanent field of research. This involves determining their chemical stability when in contact with heat transfer fluids, such as molten nitrate salts. Various studies indicate [...] Read more.
The study and improvement of the corrosion resistance of materials used in concentrated solar power plants is a permanent field of research. This involves determining their chemical stability when in contact with heat transfer fluids, such as molten nitrate salts. Various studies indicate an improvement in the corrosion resistance of iron-based alloys with the incorporation of elements that show high reactivity and solubility in molten nitrate salts, such as Cr and Mo. This study analyzes the kinetic and thermodynamic aspects of the beginning of the corrosion process of ferritic steels immersed in Solar Salt at 400, 500, and 600 °C. The analysis of the kinetic data using the Arrhenius equation and the Transition State Theory shows that an increase in the Cr/Mo ratio reduces the activation energy, the standard formation enthalpy, and the standard formation entropy. This indicates that its incorporation favors the degradation of steel; however, the results show a reduction in the corrosion rate. This effect is possible due to a synergistic effect by the formation of insoluble Fe-oxide layers that favor the formation of a Cr oxide layer at the Fe-oxide-metal interface, which limits the subsequent oxidation of Fe. Full article
22 pages, 5103 KiB  
Article
Spatiotemporal Evolution and Influencing Factors of the Coupling Coordination of Urban Ecological Resilience and New Quality Productivity at the Provincial Scale in China
by Li Yang, Yue Xu, Junqi Zhu and Keyu Sun
Land 2024, 13(12), 1998; https://doi.org/10.3390/land13121998 - 23 Nov 2024
Viewed by 539
Abstract
Enhancing urban ecological resilience (UER) is important in promoting sustainable urban development, and developing new quality productivity (NQP) is an intrinsic requirement to promote industrial change and high-quality development. The coordinated development of UER and NQP can help realize the green transformation and [...] Read more.
Enhancing urban ecological resilience (UER) is important in promoting sustainable urban development, and developing new quality productivity (NQP) is an intrinsic requirement to promote industrial change and high-quality development. The coordinated development of UER and NQP can help realize the green transformation and upgrading of various industries. This study considered 30 provinces in China as research objects, quantified their UER from nature, economy, and society, and explored the essential connotation of NQP under the guidance of Marx’s productivity theory. The entropy weight-CRITIC method and TOPSIS model were used to comprehensively measure the development levels of the UER and NQP from 2011 to 2022, and their coupling coordination degree (CCD) of UER and NQP was measured by combining the coupling coordination degree model. Consequently, the Global Moran’s I index and Geographical and Temporal Weighted Regression (GTWR) model were used to explore the effects of different influencing factors on the CCD from the spatiotemporal variability perspective. The results indicated the following: (1) UER and NQP improved during the study period but with large differences between the regions. (2) The overall CCD evolved from a mild imbalance to primary coordination. The average CCD values ranged from low to high in the northeastern, western, central, and eastern regions. (3) The GTWR results showed that the levels of economic development, urbanization rate, and technological innovation contributed positively to the CCD, with the urbanization rate having the strongest positive effect. Foreign investment, environmental regulations, and industrial structure generally negatively inhibit the CCD. Full article
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<p>The development level of UER and NQP.</p>
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<p>Overall CCD level.</p>
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<p>CCD distribution in each year and CCD mean value in each province. (<b>a</b>) CCD distribution in each year. (<b>b</b>) CCD mean value in each province.</p>
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<p>Spatial distribution of CCD.</p>
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<p>Box plot of regression coefficients.</p>
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<p>Distribution characteristics of influencing factors. (<b>a</b>) GDPR. (<b>b</b>) OPEN. (<b>c</b>) UBR. (<b>d</b>) IS. (<b>e</b>) TI. (<b>f</b>) ER.</p>
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<p>Distribution characteristics of influencing factors. (<b>a</b>) GDPR. (<b>b</b>) OPEN. (<b>c</b>) UBR. (<b>d</b>) IS. (<b>e</b>) TI. (<b>f</b>) ER.</p>
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18 pages, 1637 KiB  
Article
Study on Emergency Decision-Making of Mine External Fires Based on Deduction of Precursory Scenarios
by Li Wang, Wenrui Huang, Yingnan Huo and Zeyuan Xiao
Fire 2024, 7(12), 429; https://doi.org/10.3390/fire7120429 - 23 Nov 2024
Viewed by 254
Abstract
External mine fires are known for their unpredictability, rapid spread, and difficulty in terms of extinguishment, often resulting in severe casualties and property damage when not managed swiftly. This study examines the progression of coal mine fire incidents through scenario deduction and presents [...] Read more.
External mine fires are known for their unpredictability, rapid spread, and difficulty in terms of extinguishment, often resulting in severe casualties and property damage when not managed swiftly. This study examines the progression of coal mine fire incidents through scenario deduction and presents an emergency decision-making model based on precursor scenario analysis. We classify precursor elements according to the causes of coal mine fires, organizing scenario elements into states, precursors, and emergency activities using knowledge meta-theory. A dynamic Bayesian network forms the core of the decision-making model, enabling calculation of scenario node probabilities and the development of expert-driven response strategies for critical scenarios. Additionally, we design a comprehensive evaluation index system, utilizing multi-attribute decision-making to establish decision matrices and attribute weights. An improved entropy-weighting TOPSIS method is used to select the optimal emergency decision scheme. The model’s effectiveness is demonstrated through a case study of the “9–27” fire incident at the Chongqing Songzao Coal Mine, where findings affirm the model’s practicality and accuracy in supporting timely, effective emergency responses to external coal mine fires. Full article
(This article belongs to the Special Issue Prevention and Control of Mine Fire)
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<p>Three-level scenario element system of external fire accidents in coal mining.</p>
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<p>Basic unit composition of scenario evolution for external coal mine fire accidents.</p>
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<p>Dynamic Bayesian network for the evolution of external coal mine fire scenarios.</p>
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<p>Flowchart of scenario-based emergency decision-making process.</p>
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<p>Evolution path of fire accident scenario at Songzao coal mine.</p>
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<p>Bayesian network scenario probability.</p>
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21 pages, 472 KiB  
Article
Exploring the Thermodynamic Uncertainty Constant: Insights from a Quasi-Ideal Nano-Gas Model
by Giorgio Sonnino
Entropy 2024, 26(12), 1011; https://doi.org/10.3390/e26121011 - 23 Nov 2024
Viewed by 230
Abstract
In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but [...] Read more.
In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but rather in discrete steps characterized by the quantization constant β. This quantization reflects the underlying discrete nature of the collision process in low-dimensional systems and the essential role played by thermodynamic fluctuations at this scale. Thermodynamic variables conjugate to the forces, along with Glansdorff–Prigogine’s dissipative variable can be discretized, enabling a mesoscopic-scale formulation of canonical commutation rules (CCRs). In this framework, measurements correspond to determining the eigenvalues of operators associated with key thermodynamic quantities. This work investigates the quantization parameter β in the CCRs using a nano-gas model analyzed through classical statistical physics. Our findings suggest that β is not an unknown fundamental constant. Instead, it emerges as the minimum achievable value derived from optimizing the uncertainty relation within the framework of our model. The expression for β is determined in terms of the ratio χ, which provides a dimensionless number that reflects the relative scales of volume and mass between entities at the Bohr (atomic level) and the molecular scales. This latter parameter quantifies the relative influence of quantum effects versus classical dynamics in a given scattering process. Full article
14 pages, 2843 KiB  
Article
User Real Comments Incentive Mechanism Based on Blockchain in E-Commerce Transactions—A Tripartite Evolutionary Game Analysis
by Chengyi Le, Ran Zheng, Ting Lu and Yu Chen
Entropy 2024, 26(12), 1005; https://doi.org/10.3390/e26121005 - 22 Nov 2024
Viewed by 226
Abstract
In response to the widespread issue of fake comments on e-commerce platforms, this study aims to analyze and propose a blockchain-based solution to incentivize authentic user feedback and reduce the prevalence of fraudulent reviews. Specifically, this paper constructs a tripartite evolutionary game model [...] Read more.
In response to the widespread issue of fake comments on e-commerce platforms, this study aims to analyze and propose a blockchain-based solution to incentivize authentic user feedback and reduce the prevalence of fraudulent reviews. Specifically, this paper constructs a tripartite evolutionary game model between sellers, buyers, and e-commerce platforms to study the real comment mechanism of blockchain. The strategy evolution under different incentive factors is simulated using replication dynamic equation analysis and Matlab software simulation. The study found that introducing smart contracts and “tokens” for incentives not only increased incentives for real comments but also reduced the negative experiences caused by “speculative” sellers, thereby influencing buyers to opt for authentic reviews. By structuring interactions through blockchain, the mechanism helped lower informational entropy thus reducing disorder and unpredictability in buyer and seller behavior and contributing to system stability. Further, by increasing penalties for dishonest behavior under the “credit on the chain” system, the platform lowered entropy in the system by promoting trust and reducing fraudulent activities. The real comment mechanism based on blockchain proposed in this paper can effectively enhance the order and transparency within the comment ecosystem. These findings contribute to theory and practice by providing strategic insights for e-commerce platforms to encourage genuine feedback, reduce informational entropy, and mitigate fake comments, ultimately fostering a more reliable online marketplace. Full article
(This article belongs to the Section Complexity)
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<p>Incentive mechanism of user real comments based on blockchain.</p>
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<p>Evolution simulation results by initialization parameter—without blockchain.</p>
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<p>Evolution simulation results by initialization parameter—with blockchain.</p>
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<p>Simulation results with different En2.</p>
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<p>Evolution simulation results when En2 = 15.</p>
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<p>Simulation results with different In.</p>
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<p>Evolution simulation results when In = 10.</p>
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24 pages, 9885 KiB  
Article
General Three-Body Problem in Conformal-Euclidean Space: New Properties of a Low-Dimensional Dynamical System
by Ashot S. Gevorkyan, Aleksander V. Bogdanov and Vladimir V. Mareev
Particles 2024, 7(4), 1038-1061; https://doi.org/10.3390/particles7040063 - 20 Nov 2024
Viewed by 361
Abstract
Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynamical systems. In addition, [...] Read more.
Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynamical systems. In addition, one often has to answer the cognitive question: is irreversibility fundamental for the description of the classical world? To answer this question, we considered a reference classical dynamical system, the general three-body problem, formulating it in conformal Euclidean space and rigorously proving its equivalence to the Newtonian three-body problem. It has been proven that a curved configuration space with a local coordinate system reveals new hidden symmetries of the internal motion of a dynamical system, which makes it possible to reduce the problem to a sixth-order system instead of the eighth order. An important consequence of the developed representation is that the chronologizing parameter of the motion of a system of bodies, which we call internal time, differs significantly from ordinary time in its properties. In particular, it more accurately describes the irreversible nature of multichannel scattering in a three-body system and other chaotic properties of a dynamical system. The paper derives an equation describing the evolution of the flow of geodesic trajectories, with the help of which the entropy of the system is constructed. New criteria for assessing the complexity of a low-dimensional dynamical system and the dimension of stochastic fractal structures arising in three-dimensional space are obtained. An effective mathematical algorithm is developed for the numerical simulation of the general three-body problem, which is traditionally a difficult-to-solve system of stiff ordinary differential equations. Full article
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<p>The problem of multichannel scattering in a classical three-body system can be represented in the most general form, as shown in the diagram, where 1, 2 and 3 denote interacting particles, brackets (<math display="inline"><semantics> <mrow> <mo>⋯</mo> </mrow> </semantics></math>) denote a coupled system of two bodies, and <math display="inline"><semantics> <msup> <mrow> <mo>(</mo> <mo>⋯</mo> <mo>)</mo> </mrow> <mo>∗</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mrow> <mo>(</mo> <mo>⋯</mo> <mo>)</mo> </mrow> <mrow> <mo>∗</mo> <mo>∗</mo> </mrow> </msup> </semantics></math> denote accordingly some short-lived coupled three-body system.</p>
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<p>In the Cartesian coordinate system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>)</mo> </mrow> </semantics></math>, the Jacobi coordinates <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> are shown, where the colored circles indicate bodies 1, 2 and 3, and the colorless circle respectively indicates the center of mass of bodies 2 and 3.</p>
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<p>The set of smooth curves <math display="inline"><semantics> <mrow> <mi mathvariant="fraktur">s</mi> <mo>=</mo> <mo>(</mo> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi mathvariant="fraktur">s</mi> <mn>3</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi mathvariant="fraktur">s</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> </semantics></math> connecting the asymptotic subspace <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>i</mi> <mi>n</mi> <mo>)</mo> </mrow> </semantics></math>, in which the three-body system <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>+</mo> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </semantics></math> is grouped, with other asymptotic subspaces <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>o</mi> <mi>u</mi> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, where the particles are grouped as follows: <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>+</mo> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> <mo>+</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> <mo>+</mo> <mn>2</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> </mrow> </semantics></math>. The distance between particles “<span class="html-italic">i</span>” and “<span class="html-italic">j</span>” in the Cartesian coordinate system is given by the expression <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>i</mi> <mo>≠</mo> <mi>j</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>0</mn> </msubsup> </semantics></math> - the average distance between particles in the corresponding pairs. During the scattering process, the three-dimensional internal time <math display="inline"><semantics> <mrow> <mi mathvariant="fraktur">s</mi> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </semantics></math>, which has an arrow, selects a specific asymptotic subspace for transition, which in some conditions may be random.</p>
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<p>Energy surface of interaction particles for three different scattering angles. Recall that <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>3</mn> </msub> </semantics></math> in Jacobi coordinates determines the scattering angle, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>3</mn> </msub> <mo>=</mo> <mi>ϑ</mi> </mrow> </semantics></math> (see <a href="#particles-07-00063-f002" class="html-fig">Figure 2</a>).</p>
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<p>A manifold of the family <math display="inline"><semantics> <mi mathvariant="script">A</mi> </semantics></math>, which has the form <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (sphere) and two additional manifolds surrounding it from left to right <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math>. Combining these manifolds by a direct product, we obtain a complete member of the family <math display="inline"><semantics> <mi mathvariant="script">A</mi> </semantics></math>, which can be represented in the following form <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="script">R</mi> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </semantics></math>.</p>
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<p>A manifold of the family <math display="inline"><semantics> <mi mathvariant="script">B</mi> </semantics></math>, which has the form <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (two three-dimensional pyramids fastened together) and two additional manifolds surrounding it from left to right <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math>. Combining these manifolds by a direct product, we obtain a complete member of the family <math display="inline"><semantics> <mi mathvariant="script">B</mi> </semantics></math>, which can be represented in the following form <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="script">R</mi> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </semantics></math>.</p>
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<p>Internal time of three particles for three different initial data on two different complete terms of the manifolds <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math>. On the plots, blue and red colors indicate internal times that were calculated on the manifolds <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math>, respectively. Each point of internal time, if projected onto the coordinate axes, determines the configuration of three particles at a given moment.</p>
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<p>On the left are plots of two internal times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(red curve) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(blue curve), which were obtained by calculating on the <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> manifold with initial conditions differing by <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math>. On the right is a plot of the Lyapunov exponent versus time. As can be clearly seen from the plot, the Lyapunov exponent very slowly tends to zero.</p>
Full article ">Figure 9
<p>On the left are plots of two internal times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(red curve) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(blue curve), which were obtained by calculating on the <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math> manifold with initial conditions differing by <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math>. On the right is a plot of the Lyapunov exponent versus time.</p>
Full article ">Figure 10
<p>On the left in the first figure, internal times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(red curve) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(blue curve) are shown that were calculated on the manifolds’ families <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math> for the same initial data using the third line of <a href="#particles-07-00063-t002" class="html-table">Table 2</a>. The second plot from the left shows the internal time <math display="inline"><semantics> <mrow> <mi mathvariant="fraktur">s</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> depending the ordinary time “<span class="html-italic">t</span>” for the two marked families of manifolds. As can be seen from the graph, internal time can be either positive or negative. The third figure from the left shows the dimensionality of the structures formed by internal times in three-dimensional space.</p>
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29 pages, 4068 KiB  
Article
Multidimensional User Experience Analysis of Chinese Battery Electric Vehicles’ Competition: An Integrated Association Mining Framework
by Quan Gu, Jie Zhang, Shengqing Huang, Yuchao Cai, Chenlu Wang and Jiaoman Liu
Appl. Sci. 2024, 14(22), 10757; https://doi.org/10.3390/app142210757 - 20 Nov 2024
Viewed by 379
Abstract
This study introduces an integrative framework for association mining within the Chinese battery electric vehicle market, aiming to reveal key user experience (UX) factors and their interrelationships through multidimensional analysis. Utilizing latent Dirichlet allocation (LDA), the study discerned primary themes from user-generated content [...] Read more.
This study introduces an integrative framework for association mining within the Chinese battery electric vehicle market, aiming to reveal key user experience (UX) factors and their interrelationships through multidimensional analysis. Utilizing latent Dirichlet allocation (LDA), the study discerned primary themes from user-generated content (UGC). The entropy weight method categorized level 2 factors, while domain-adaptive sentiment analysis quantified emotional responses to BEV user experience dimensions, highlighting significant sentiment disparities among competitors. Co-occurrence network analysis deepened insights into the emotional fabric of UX by exploring tertiary factor associations. Theoretically, this study advances a novel framework informed by Norman’s UX theory, integrating analytical techniques to capture the complexity of UX. Practically, it delivers strategic guidance for BEV manufacturers by analyzing emotional polarities and attribute associations, guiding product innovation and responding to market dynamics. The empirical evidence corroborates the framework’s efficacy in revealing the emotional associations within BEVUX factors, offering valuable implications for both theoretical development and practical application. Full article
(This article belongs to the Special Issue Advanced Technologies for User-Centered Design and User Experience)
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<p>Research technical framework.</p>
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<p>Sentiment score histogram for the “subjective perception” theme in target competitors.</p>
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<p>Sentiment score comparison for the “interior” keyword in subjective perception.</p>
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<p>Co-occurrence network of keyword eigenvector centrality for the extremely negative “interior” label.</p>
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<p>Co-occurrence network of keyword eigenvector centrality for the strongly positive “interior” label.</p>
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<p>Co-occurrence network of keyword eigenvector centrality for the strongly positive “interior” label.</p>
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16 pages, 971 KiB  
Article
Derangetropy in Probability Distributions and Information Dynamics
by Masoud Ataei and Xiaogang Wang
Entropy 2024, 26(11), 996; https://doi.org/10.3390/e26110996 - 18 Nov 2024
Viewed by 291
Abstract
We introduce derangetropy, which is a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a [...] Read more.
We introduce derangetropy, which is a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory. Full article
(This article belongs to the Special Issue Mathematics in Information Theory and Modern Applications)
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<p>Plots of probability density functions <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </semantics></math> (<b>left</b>) and derangetropy functionals <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (<b>right</b>) for <math display="inline"><semantics> <mrow> <mo>uniform</mo> <mspace width="0.166667em"/> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>normal</mo> <mspace width="0.166667em"/> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>exponential</mo> <mspace width="0.166667em"/> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>semicircle</mo> <mspace width="0.166667em"/> <mo>(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>arcsin</mo> <mspace width="0.166667em"/> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> distributions.</p>
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<p>Plots of total (solid line), structural (dashed line) and modulation (dotted line) informational energies for uniform (0, 1) distribution.</p>
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<p>Plots of <math display="inline"><semantics> <msubsup> <mi>ρ</mi> <mi>f</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (solid line) and <math display="inline"><semantics> <msubsup> <mi>ρ</mi> <mi>f</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (dashed line) for <math display="inline"><semantics> <mrow> <mo>uniform</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> distribution.</p>
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<p>Plots of <math display="inline"><semantics> <msubsup> <mi>ρ</mi> <mi>f</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (solid line), <math display="inline"><semantics> <msubsup> <mi>ρ</mi> <mi>f</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (dashed line) and <math display="inline"><semantics> <msubsup> <mi>ρ</mi> <mi>f</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (dotted line) for <math display="inline"><semantics> <mrow> <mo>Arcsin</mo> <mspace width="0.166667em"/> <mo>(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> distribution.</p>
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<p>Schematics of electrode placement and derangetropy functionals for control and MDD subjects. (<b>a</b>) Electrode placement and mesh matrix representing the 10–20 international system; (<b>b</b>) plots of derangetropy functional for a healthy subject when eyes closed; (<b>c</b>) plots of derangetropy functional for a subject with MDD when eyes closed.</p>
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<p>Schematic of the rectangular clockwise integration path.</p>
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19 pages, 323 KiB  
Article
State-Space Solution to Spectral Entropy Analysis and Optimal State-Feedback Control for Continuous-Time Linear Systems
by Victor A. Boichenko, Alexey A. Belov and Olga G. Andrianova
Mathematics 2024, 12(22), 3604; https://doi.org/10.3390/math12223604 - 18 Nov 2024
Viewed by 396
Abstract
In this paper, a problem of random disturbance attenuation capabilities for linear time-invariant continuous systems, affected by random disturbances with bounded σ-entropy, is studied. The σ-entropy norm defines a performance index of the system on the set of the aforementioned input [...] Read more.
In this paper, a problem of random disturbance attenuation capabilities for linear time-invariant continuous systems, affected by random disturbances with bounded σ-entropy, is studied. The σ-entropy norm defines a performance index of the system on the set of the aforementioned input signals. Two problems are considered. The first is a state-space σ-entropy analysis of linear systems, and the second is an optimal control design using the σ-entropy norm as an optimization objective. The state-space solution to the σ-entropy analysis problem is derived from the representation of the σ-entropy norm in the frequency domain. The formulae of the σ-entropy norm computation in the state space are presented in the form of coupled matrix equations: one algebraic Riccati equation, one nonlinear equation over log determinant function, and two Lyapunov equations. Optimal control law is obtained using game theory and a saddle-point condition of optimality. The optimal state-feedback control, which minimizes the σ-entropy norm of the closed-loop system, is found from the solution of two algebraic Riccati equations, one Lyapunov equation, and the log determinant equation. Full article
(This article belongs to the Section Dynamical Systems)
17 pages, 2195 KiB  
Article
A Comprehensive Evaluation Method for Assessing the Seismic Resilience of Building Sites Based on the TOPSIS Model and the Entropy Method
by Yuting Wang, Da Peng, Tao Bo, Xinlong Zhao and Jingshan Bo
Buildings 2024, 14(11), 3667; https://doi.org/10.3390/buildings14113667 - 18 Nov 2024
Viewed by 371
Abstract
The seismic design philosophy based on resilience represents the latest development in structural seismic design theory and is currently the most advanced concept in the field of seismic design research. A building site serves as the foundation and environment for structures, and evaluating [...] Read more.
The seismic design philosophy based on resilience represents the latest development in structural seismic design theory and is currently the most advanced concept in the field of seismic design research. A building site serves as the foundation and environment for structures, and evaluating its seismic resilience is a crucial aspect of designing and assessing buildings’ seismic resilience. To meet the needs of evaluating building seismic resilience, the concept of seismic resilience for building sites is introduced in this paper. This evaluation is approached from three dimensions: seismic action, site seismic capacity, and site recovery capability. An indicator system for evaluating the seismic resilience of building sites is constructed using 23 key indicators that reflect the site’s seismic resilience. A seismic resilience evaluation model for building sites is established based on the TOPSIS model and the entropy method. The feasibility and rationality of the proposed evaluation method are demonstrated through application examples. The research findings in this paper provide a valuable reference for advancing the evaluation of both building seismic resilience and site seismic resilience. Full article
(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)
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<p>Building site seismic resilience indicator system.</p>
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<p>Maps of 60 building sites.</p>
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<p>Category distribution map of 60 building sites in Beijing (The numbers in parentheses represent the number of building sites).</p>
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<p>Resilience distribution map of 60 building sites in Beijing (The numbers in parentheses represent the number of building sites).</p>
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12 pages, 5537 KiB  
Article
Accompanying Hemoglobin Polymerization in Red Blood Cells in Patients with Sickle Cell Disease Using Fluorescence Lifetime Imaging
by Fernanda Aparecida Borges da Silva, João Batista Florindo, Amilcar Castro de Mattos, Fernando Ferreira Costa, Irene Lorand-Metze and Konradin Metze
Int. J. Mol. Sci. 2024, 25(22), 12290; https://doi.org/10.3390/ijms252212290 - 15 Nov 2024
Viewed by 547
Abstract
In recent studies, it has been shown that fluorescence lifetime imaging (FLIM) may reveal intracellular structural details in unstained cytological preparations that are not revealed by standard staining procedures. The aim of our investigation was to examine whether FLIM images could reveal areas [...] Read more.
In recent studies, it has been shown that fluorescence lifetime imaging (FLIM) may reveal intracellular structural details in unstained cytological preparations that are not revealed by standard staining procedures. The aim of our investigation was to examine whether FLIM images could reveal areas suggestive of polymerization in red blood cells (RBCs) of sickle cell disease (SCD) patients. We examined label-free blood films using auto-fluorescence FLIM images of 45 SCD patients and compared the results with those of 27 control persons without hematological disease. All control RBCs revealed homogeneous cytoplasm without any foci. Rounded non-sickled RBCs in SCD showed between zero and three small intensively fluorescent dots with higher lifetime values. In sickled RBCs, we found additionally larger irregularly shaped intensively fluorescent areas with increased FLIM values. These areas were interpreted as equivalent to polymerized hemoglobin. The rounded, non-sickled RBCs of SCD patients with homogeneous cytoplasm were not different from those of the erythrocytes of control patients in light microscopy. Yet, variables from the local binary pattern-transformed matrix of the FLIM values per pixel showed significant differences between non-sickled RBCs and those of control cells. In a linear discriminant analysis, using local binary pattern-transformed texture features (mean and entropy) of the erythrocyte cytoplasm of normal appearing cells, the final model could distinguish between SCD patients and control persons with an accuracy of 84.7% of the patients. When the classification was based on the examination of a single rounded erythrocyte, an accuracy of 68.5% was achieved. Employing the Linear Discriminant Analysis classifier method for machine learning, the accuracy was 68.1%. We believe that our study shows that FLIM is able to disclose the topography of the intracellular polymerization process of hemoglobin in sickle cell disease and that the images are compatible with the theory of the two-step nucleation. Furthermore, we think that the presented technique may be an interesting tool for the investigation of therapeutic inhibition of polymerization. Full article
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<p>Image of a peripheral blood film of a control case with several normal RBCs. Upper left: auto-fluorescence picture. Upper middle: fluorescence lifetime image: the blue color corresponds to the lifetime of hemoglobin. Surrounding plasma in green/yellow color corresponding to a higher lifetime. A cursor is placed on a RBC (right inferior corner). Upper right: histogram of the lifetime distribution of the image (pseudo-colors according to the rainbow spectrum). Blue represents the shortest lifetime and red is the longest. The histogram shows that hemoglobin has a short lifetime. Below is the fluorescence lifetime decay curve of the selected spot in the image. Every dot represents a single photon.</p>
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<p>Upper left: autofluorescence and FLIM images of a patient with homozygous SS hemoglobinopathy. Two normal-shaped and one sickled RBC. Each of the normal looking ones shows one highly fluorescent dot. The sickled RBC has areas with a higher fluorescence suggestive of polymerization. The histogram on the right side represents the lifetime of the region where the cursor is placed. Lower right is the decay curve of the selected region of interest.</p>
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<p>RBCs from a blood smear of a patient with SC hemoglobinopathy. Left: auto-fluorescence and right FLIM image. In the center, a sickled cell with an irregular heterogeneous area of enhanced fluorescence revealing a higher lifetime value in the FLIM compared to the surrounding cytoplasm. Some of the non-sickled RBCs show highly fluorescent dots.</p>
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<p>RBCs from a blood smear of S beta-thalassemia hemoglobinopathy. Three entire sickled cells with irregular, sometimes heterogeneous areas with enhanced fluorescence revealing higher lifetime values compared to the surrounding cytoplasm. Some of the non-sickled RBCs show highly fluorescent dots.</p>
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<p>Distribution of non-sickled cells in patients with SCD according to the sub-types: SS in black, SC in green, and S thalassemia in orange. There were no significant differences among the different sub-types of SCD.</p>
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<p>Dot plot showing the distribution of LBP mean (Y axis) and LBP entropy (X axis) to show the distribution of each cell in the control group (blue), and SCD: non-sickled cells are in green and sickled cells are in orange. Both parameters were able to discriminate between normal and SCD in 84.7% of the cases.</p>
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13 pages, 464 KiB  
Review
Entropy of Neuronal Spike Patterns
by Artur Luczak
Entropy 2024, 26(11), 967; https://doi.org/10.3390/e26110967 - 11 Nov 2024
Viewed by 463
Abstract
Neuronal spike patterns are the fundamental units of neural communication in the brain, which is still not fully understood. Entropy measures offer a quantitative framework to assess the variability and information content of these spike patterns. By quantifying the uncertainty and informational content [...] Read more.
Neuronal spike patterns are the fundamental units of neural communication in the brain, which is still not fully understood. Entropy measures offer a quantitative framework to assess the variability and information content of these spike patterns. By quantifying the uncertainty and informational content of neuronal patterns, entropy measures provide insights into neural coding strategies, synaptic plasticity, network dynamics, and cognitive processes. Here, we review basic entropy metrics and then we provide examples of recent advancements in using entropy as a tool to improve our understanding of neuronal processing. It focuses especially on studies on critical dynamics in neural networks and the relation of entropy to predictive coding and cortical communication. We highlight the necessity of expanding entropy measures from single neurons to encompass multi-neuronal activity patterns, as cortical circuits communicate through coordinated spatiotemporal activity patterns, called neuronal packets. We discuss how the sequential and partially stereotypical nature of neuronal packets influences the entropy of cortical communication. Stereotypy reduces entropy by enhancing reliability and predictability in neural signaling, while variability within packets increases entropy, allowing for greater information capacity. This balance between stereotypy and variability supports both robustness and flexibility in cortical information processing. We also review challenges in applying entropy to analyze such spatiotemporal neuronal spike patterns, notably, the “curse of dimensionality” in estimating entropy for high-dimensional neuronal data. Finally, we discuss strategies to overcome these challenges, including dimensionality reduction techniques, advanced entropy estimators, sparse coding schemes, and the integration of machine learning approaches. Thus, this work summarizes the most recent developments on how entropy measures contribute to our understanding of principles underlying neural coding. Full article
(This article belongs to the Section Multidisciplinary Applications)
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Figure 1

Figure 1
<p>Cartoon illustration of neuronal activity packets. (<b>A</b>) Sequential activity patterns (called packets) during deep sleep where activity occurs sporadically. Within each packet, neurons fire with a stereotyped sequential pattern (each neuron marked with different color). (<b>B</b>) In an awake state, when more information is transmitted, packets occur right after each other, without long periods of silence, but temporal relationships between neurons are similar to those in the sleep state. (<b>C</b>) Consistency and variability in neuronal packets (geometrical interpretation). The gray area illustrates the space of all spiking patterns theoretically possible for a packet. The left-side panels show a cartoon of sample packets, each corresponding to a single point in gray space. The white area inside represents the space of packets experimentally observed in the brain. Packets evoked by different sensory stimuli occupy smaller subspaces (colored blobs). The right-side panels illustrate stimulus-evoked packets. The overall structure of evoked packets is similar, with differences in the firing rate and in the spike timing of neurons encoding information about different stimuli (figure modified from [<a href="#B18-entropy-26-00967" class="html-bibr">18</a>]).</p>
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