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Discreteness Unravels the Black Hole Information Puzzle: Insights from a Quantum Gravity Toy Model
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Graph Partitions in Chemistry
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Parity-Time Symmetric Holographic Principle
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Dynamical Analyses Show That Professional Archers Exhibit Tighter, Finer and More Fluid Dynamical Control Than Neophytes
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Complexity Synchronization of Organ Networks
Journal Description
Entropy
Entropy
is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), MathSciNet, Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 20.4 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the first half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Entropy.
- Companion journals for Entropy include: Foundations, Thermo and MAKE.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.6 (2022)
Latest Articles
Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs
Entropy 2023, 25(12), 1615; https://doi.org/10.3390/e25121615 (registering DOI) - 02 Dec 2023
Abstract
Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven
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Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous.
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(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications II)
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Research on the Dynamical Behavior of Public Opinion Triggered by Rumor Based on a Nonlinear Oscillator Model
Entropy 2023, 25(12), 1614; https://doi.org/10.3390/e25121614 - 01 Dec 2023
Abstract
In public opinion triggered by rumors, the authenticity of the information remains uncertain, and the main topic oscillates between diverse opinions. In this paper, a nonlinear oscillator model is proposed to demonstrate the public opinion triggered by rumors. Based on the model and
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In public opinion triggered by rumors, the authenticity of the information remains uncertain, and the main topic oscillates between diverse opinions. In this paper, a nonlinear oscillator model is proposed to demonstrate the public opinion triggered by rumors. Based on the model and actual data of one case, it is found that a continuous flow of new information about rumors acts as external forces on the system, probably leading to the chaotic behavior of public opinion. Moreover, similar features are observed in three other cases, and the same model is also applicable to these cases. Based on these results, it is shown that our model possesses generality, revealing the evolutionary trends of a certain type of public opinion in real-world scenarios.
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(This article belongs to the Topic Recent Trends in Nonlinear, Chaotic and Complex Systems)
Open AccessArticle
Designing a Novel Approach Using a Greedy and Information-Theoretic Clustering-Based Algorithm for Anonymizing Microdata Sets
Entropy 2023, 25(12), 1613; https://doi.org/10.3390/e25121613 - 01 Dec 2023
Abstract
Data anonymization is a technique that safeguards individuals’ privacy by modifying attribute values in published data. However, increased modifications enhance privacy but diminish the utility of published data, necessitating a balance between privacy and utility levels. K-Anonymity is a crucial anonymization technique
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Data anonymization is a technique that safeguards individuals’ privacy by modifying attribute values in published data. However, increased modifications enhance privacy but diminish the utility of published data, necessitating a balance between privacy and utility levels. K-Anonymity is a crucial anonymization technique that generates k-anonymous clusters, where the probability of disclosing a record is . However, k-anonymity fails to protect against attribute disclosure when the diversity of sensitive values within the anonymous cluster is insufficient. Several techniques have been proposed to address this issue, among which t-closeness is considered one of the most robust privacy techniques. In this paper, we propose a novel approach employing a greedy and information-theoretic clustering-based algorithm to achieve strict privacy protection. The proposed anonymization algorithm commences by clustering the data based on both the similarity of quasi-identifier values and the diversity of sensitive attribute values. In the subsequent adjustment phase, the algorithm splits and merges the clusters to ensure that they each possess at least k members and adhere to the t-closeness requirements. Finally, the algorithm replaces the quasi-identifier values of the records in each cluster with the values of the cluster center to attain k-anonymity and t-closeness. Experimental results on three microdata sets from Facebook, Twitter, and Google+ demonstrate the proposed algorithm’s ability to preserve the utility of released data by minimizing the modifications of attribute values while satisfying the k-anonymity and t-closeness constraints.
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(This article belongs to the Special Issue Information Security and Data Privacy)
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Spatiotemporal Variations of the Frequency–Magnitude Distribution in the 2019 Mw 7.1 Ridgecrest, California, Earthquake Sequence
Entropy 2023, 25(12), 1612; https://doi.org/10.3390/e25121612 - 01 Dec 2023
Abstract
Significant seismic activity has been witnessed in the area of Ridgecrest (Southern California) over the past 40 years, with the largest being the Mw 5.8 event on 20 September 1995. In July 2019, a strong earthquake of Mw 7.1, preceded by
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Significant seismic activity has been witnessed in the area of Ridgecrest (Southern California) over the past 40 years, with the largest being the Mw 5.8 event on 20 September 1995. In July 2019, a strong earthquake of Mw 7.1, preceded by a Mw 6.4 foreshock, impacted Ridgecrest. The mainshock triggered thousands of aftershocks that were thoroughly documented along the activated faults. In this study, we analyzed the spatiotemporal variations of the frequency–magnitude distribution in the area of Ridgecrest using the fragment–asperity model derived within the framework of non-extensive statistical physics (NESP), which is well-suited for investigating complex dynamic systems with scale-invariant properties, multi-fractality, and long-range interactions. Analysis was performed for the entire duration, as well as within various time windows during 1981–2022, in order to estimate the qM parameter and to investigate how these variations are related to the dynamic evolution of seismic activity. In addition, we analyzed the spatiotemporal qM value distributions along the activated fault zone during 1981–2019 and during each month after the occurrence of the Mw 7.1 Ridgecrest earthquake. The results indicate a significant increase in the qM parameter when large-magnitude earthquakes occur, suggesting the system’s transition in an out-of-equilibrium phase and its preparation for seismic energy release.
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(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)
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DyLFG: A Dynamic Network Learning Framework Based on Geometry
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and
Entropy 2023, 25(12), 1611; https://doi.org/10.3390/e25121611 - 30 Nov 2023
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Dynamic network representation learning has recently attracted increasing attention because real-world networks evolve over time, that is nodes and edges join or leave the networks over time. Different from static networks, the representation learning of dynamic networks should not only consider how to
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Dynamic network representation learning has recently attracted increasing attention because real-world networks evolve over time, that is nodes and edges join or leave the networks over time. Different from static networks, the representation learning of dynamic networks should not only consider how to capture the structural information of network snapshots, but also consider how to capture the temporal dynamic information of network structure evolution from the network snapshot sequence. From the existing work on dynamic network representation, there are two main problems: (1) A significant number of methods target dynamic networks, which only allow nodes to increase over time, not decrease, which reduces the applicability of such methods to real-world networks. (2) At present, most network-embedding methods, especially dynamic network representation learning approaches, use Euclidean embedding space. However, the network itself is geometrically non-Euclidean, which leads to geometric inconsistencies between the embedded space and the underlying space of the network, which can affect the performance of the model. In order to solve the above two problems, we propose a geometry-based dynamic network learning framework, namely DyLFG. Our proposed framework targets dynamic networks, which allow nodes and edges to join or exit the network over time. In order to extract the structural information of network snapshots, we designed a new hyperbolic geometry processing layer, which is different from the previous literature. In order to deal with the temporal dynamics of the network snapshot sequence, we propose a gated recurrent unit (GRU) module based on Ricci curvature, that is the RGRU. In the proposed framework, we used a temporal attention layer and the RGRU to evolve the neural network weight matrix to capture temporal dynamics in the network snapshot sequence. The experimental results showed that our model outperformed the baseline approaches on the baseline datasets.
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Open AccessFeature PaperArticle
Discrete-Time Quantum Walk on Multilayer Networks
Entropy 2023, 25(12), 1610; https://doi.org/10.3390/e25121610 - 30 Nov 2023
Abstract
A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a
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A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.
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(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes
Entropy 2023, 25(12), 1609; https://doi.org/10.3390/e25121609 - 30 Nov 2023
Abstract
How to improve the computational efficiency of flow field simulations around irregular objects in near-continuum and continuum flow regimes has always been a challenge in the aerospace re-entry process. The discrete velocity method (DVM) is a commonly used algorithm for the discretized solutions
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How to improve the computational efficiency of flow field simulations around irregular objects in near-continuum and continuum flow regimes has always been a challenge in the aerospace re-entry process. The discrete velocity method (DVM) is a commonly used algorithm for the discretized solutions of the Boltzmann-BGK model equation. However, the discretization of both physical and molecular velocity spaces in DVM can result in significant computational costs. This paper focuses on unlocking the key to accelerate the convergence in DVM calculations, thereby reducing the computational burden. Three versions of DVM are investigated: the semi-implicit DVM (DVM-I), fully implicit DVM (DVM-II), and fully implicit DVM with an inner iteration of the macroscopic governing equation (DVM-III). In order to achieve full implicit discretization of the collision term in the Boltzmann-BGK equation, it is necessary to solve the corresponding macroscopic governing equation in DVM-II and DVM-III. In DVM-III, an inner iterative process of the macroscopic governing equation is employed between two adjacent DVM steps, enabling a more accurate prediction of the equilibrium state for the full implicit discretization of the collision term. Fortunately, the computational cost of solving the macroscopic governing equation is significantly lower than that of the Boltzmann-BGK equation. This is primarily due to the smaller number of conservative variables in the macroscopic governing equation compared to the discrete velocity distribution functions in the Boltzmann-BGK equation. Our findings demonstrate that the fully implicit discretization of the collision term in the Boltzmann-BGK equation can accelerate DVM calculations by one order of magnitude in continuum and near-continuum flow regimes. Furthermore, the introduction of the inner iteration of the macroscopic governing equation provides an additional 1–2 orders of magnitude acceleration. Such advancements hold promise in providing a computational approach for simulating flows around irregular objects in near-space environments.
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(This article belongs to the Special Issue Kinetic Theory-based Methods in Fluid Dynamics II)
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Inferred Rate of Default as a Credit Risk Indicator in the Bulgarian Bank System
Entropy 2023, 25(12), 1608; https://doi.org/10.3390/e25121608 - 30 Nov 2023
Abstract
The inferred rate of default (IRD) was first introduced as an indicator of default risk computable from information publicly reported by the Bulgarian National Bank. We have provided a more detailed justification for the suggested methodology for forecasting the IRD on the bank-group-
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The inferred rate of default (IRD) was first introduced as an indicator of default risk computable from information publicly reported by the Bulgarian National Bank. We have provided a more detailed justification for the suggested methodology for forecasting the IRD on the bank-group- and bank-system-level based on macroeconomic factors. Furthermore, we supply additional empirical evidence in the time-series analysis. Additionally, we demonstrate that IRD provides a new perspective for comparing credit risk across bank groups. The estimation methods and model assumptions agree with current Bulgarian regulations and the IFRS 9 accounting standard. The suggested models could be used by practitioners in monthly forecasting the point-in-time probability of default in the context of accounting reporting and in monitoring and managing credit risk.
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(This article belongs to the Special Issue Differential Equations and Networks for Description of Natural and Social Systems: Methodology and Applications)
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Stable and Fast Deep Mutual Information Maximization Based on Wasserstein Distance
Entropy 2023, 25(12), 1607; https://doi.org/10.3390/e25121607 - 30 Nov 2023
Abstract
Deep learning is one of the most exciting and promising techniques in the field of artificial intelligence (AI), which drives AI applications to be more intelligent and comprehensive. However, existing deep learning techniques usually require a large amount of expensive labeled data, which
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Deep learning is one of the most exciting and promising techniques in the field of artificial intelligence (AI), which drives AI applications to be more intelligent and comprehensive. However, existing deep learning techniques usually require a large amount of expensive labeled data, which limit the application and development of deep learning techniques, and thus it is imperative to study unsupervised machine learning. The learning of deep representations by mutual information estimation and maximization (Deep InfoMax or DIM) method has achieved unprecedented results in the field of unsupervised learning. However, in the DIM method, to restrict the encoder to learn more normalized feature representations, an adversarial network learning method is used to make the encoder output consistent with a priori positively distributed data. As we know, the model training of the adversarial network learning method is difficult to converge, because there is a logarithmic function in the loss function of the cross-entropy measure, and the gradient of the model parameters is susceptible to the “gradient explosion” or “gradient disappearance” phenomena, which makes the training of the DIM method extremely unstable. In this regard, we propose a Wasserstein distance-based DIM method to solve the stability problem of model training, and our method is called the WDIM. Subsequently, the training stability of the WDIM method and the classification ability of unsupervised learning are verified on the CIFAR10, CIFAR100, and STL10 datasets. The experiments show that our proposed WDIM method is more stable to parameter updates, has faster model convergence, and at the same time, has almost the same accuracy as the DIM method on the classification task of unsupervised learning. Finally, we also propose a reflection of future research for the WDIM method, aiming to provide a research idea and direction for solving the image classification task with unsupervised learning.
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(This article belongs to the Section Information Theory, Probability and Statistics)
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Multiview Data Clustering with Similarity Graph Learning Guided Unsupervised Feature Selection
Entropy 2023, 25(12), 1606; https://doi.org/10.3390/e25121606 - 30 Nov 2023
Abstract
In multiview data clustering, consistent or complementary information in the multiview data can achieve better clustering results. However, the high dimensions, lack of labeling, and redundancy of multiview data certainly affect the clustering effect, posing a challenge to multiview clustering. A clustering algorithm
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In multiview data clustering, consistent or complementary information in the multiview data can achieve better clustering results. However, the high dimensions, lack of labeling, and redundancy of multiview data certainly affect the clustering effect, posing a challenge to multiview clustering. A clustering algorithm based on multiview feature selection clustering (MFSC), which combines similarity graph learning and unsupervised feature selection, is designed in this study. During the MFSC implementation, local manifold regularization is integrated into similarity graph learning, with the clustering label of similarity graph learning as the standard for unsupervised feature selection. MFSC can retain the characteristics of the clustering label on the premise of maintaining the manifold structure of multiview data. The algorithm is systematically evaluated using benchmark multiview and simulated data. The clustering experiment results prove that the MFSC algorithm is more effective than the traditional algorithm.
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(This article belongs to the Special Issue Pattern Recognition and Data Clustering in Information Theory)
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Cohesion: A Measure of Organisation and Epistemic Uncertainty of Incoherent Ensembles
Entropy 2023, 25(12), 1605; https://doi.org/10.3390/e25121605 - 30 Nov 2023
Abstract
This paper offers a measure of how organised a system is, as defined by self-consistency. Complex dynamics such as tipping points and feedback loops can cause systems with identical initial parameters to vary greatly by their final state. These systems can be called
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This paper offers a measure of how organised a system is, as defined by self-consistency. Complex dynamics such as tipping points and feedback loops can cause systems with identical initial parameters to vary greatly by their final state. These systems can be called non-ergodic or incoherent. This lack of consistency (or replicability) of a system can be seen to drive an additional form of uncertainty, beyond the variance that is typically considered. However, certain self-organising systems can be shown to have some self-consistency around these tipping points, when compared with systems that find no consistent final states. Here, we propose a measure of this self-consistency that is used to quantify our confidence in the outcomes of agent-based models, simulations or experiments of dynamical systems, which may or may not contain multiple attractors.
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(This article belongs to the Special Issue Information and Self-Organization III)
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Phase-Specific Damage Tolerance of a Eutectic High Entropy Alloy
Entropy 2023, 25(12), 1604; https://doi.org/10.3390/e25121604 - 30 Nov 2023
Abstract
Phase-specific damage tolerance was investigated for the AlCoCrFeNi2.1 high entropy alloy with a lamellar microstructure of L12 and B2 phases. A microcantilever bending technique was utilized with notches milled in each of the two phases as well as at the phase
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Phase-specific damage tolerance was investigated for the AlCoCrFeNi2.1 high entropy alloy with a lamellar microstructure of L12 and B2 phases. A microcantilever bending technique was utilized with notches milled in each of the two phases as well as at the phase boundary. The L12 phase exhibited superior bending strength, strain hardening, and plastic deformation, while the B2 phase showed limited damage tolerance during bending due to micro-crack formation. The dimensionalized stiffness (DS) of the L12 phase cantilevers were relatively constant, indicating strain hardening followed by increase in stiffness at the later stages and, therefore, indicating plastic failure. In contrast, the B2 phase cantilevers showed a continuous drop in stiffness, indicating crack propagation. Distinct differences in micro-scale deformation mechanisms were reflected in post-compression fractography, with L12-phase cantilevers showing typical characteristics of ductile failure, including the activation of multiple slip planes, shear lips at the notch edge, and tearing inside the notch versus quasi-cleavage fracture with cleavage facets and a river pattern on the fracture surface for the B2-phase cantilevers.
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(This article belongs to the Special Issue Advances in High-Entropy Alloys)
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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes
by
, , , , , , and
Entropy 2023, 25(12), 1603; https://doi.org/10.3390/e25121603 - 30 Nov 2023
Abstract
Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of
[...] Read more.
Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of literature has investigated the construction of asymmetric QEC codes. However, the asymmetry of most QEC codes identified in the literature is limited by the dual-containing condition within the Calderbank-Shor-Steane (CSS) framework. This limitation restricts the exploration of their full potential in terms of asymmetry. In order to enhance the asymmetry of asymmetric QEC codes, we utilize entanglement-assisted technology and exploit the algebraic structure of cyclotomic cosets of constacyclic codes to achieve this goal. In this paper, we generalize the decomposition method of the defining set for constacyclic codes and apply it to count the number of pre-shared entangled states in order to construct four new classes of asymmetric entanglement-assisted quantum maximal-distance separable (EAQMDS) codes that satisfy the asymmetric entanglement-assisted quantum Singleton bound. Compared with the codes existing in the literature, the lengths of the constructed EAQMDS codes and the number of pre-shared entangled states are more general, and the codes constructed in this paper have greater asymmetry.
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(This article belongs to the Special Issue Quantum Shannon Theory and Its Applications)
Open AccessArticle
Market Impact Analysis of Financial Literacy among A-Share Market Investors: An Agent-Based Model
Entropy 2023, 25(12), 1602; https://doi.org/10.3390/e25121602 - 29 Nov 2023
Abstract
Financial literacy has become increasingly crucial in today’s complex financial markets. This paper explores the impact of financial literacy on the stock market by establishing an artificial financial market that aligns with the characteristics of the Chinese A-share market using agent-based modeling. The
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Financial literacy has become increasingly crucial in today’s complex financial markets. This paper explores the impact of financial literacy on the stock market by establishing an artificial financial market that aligns with the characteristics of the Chinese A-share market using agent-based modeling. The study incorporates financial literacy into investors’ mixed beliefs and simulates their behavior in the market. The results show that improving individual investors’ financial literacy can improve market quality and investor performance, as well as reduce the unequal distribution of wealth to some extent. However, the phenomenon of speculative trading and irrational behavior in the market can pose potential risks that require regulatory measures. Thus, policy recommendations to improve individual investors’ financial literacy and establish corresponding regulatory measures are proposed.
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(This article belongs to the Special Issue Complexity in Economics and Finance: New Directions and Challenges)
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Random Lasers as Social Processes Simulators
by
, , , , , and
Entropy 2023, 25(12), 1601; https://doi.org/10.3390/e25121601 - 29 Nov 2023
Abstract
In this work, we suggest a quantum-like simulator concept to study social processes related to the solution of NP-hard problems. The simulator is based on the solaser model recently proposed by us in the framework of information cascade growth and echo chamber formation
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In this work, we suggest a quantum-like simulator concept to study social processes related to the solution of NP-hard problems. The simulator is based on the solaser model recently proposed by us in the framework of information cascade growth and echo chamber formation in social network communities. The simulator is connected with the random laser approach that we examine in the A and D-class (superradiant) laser limits. Novel network-enforced cooperativity parameters of decision-making agents, which may be measured as a result of the solaser simulation, are introduced and justified for social systems. The innovation diffusion in complex networks is discussed as one of the possible impacts of our proposal.
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(This article belongs to the Special Issue Quantum Models of Cognition and Decision-Making II)
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Postulating the Unicity of the Macroscopic Physical World
Entropy 2023, 25(12), 1600; https://doi.org/10.3390/e25121600 - 29 Nov 2023
Abstract
We argue that a clear view of quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows for a framework
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We argue that a clear view of quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows for a framework in which quantum mechanics can be constructed in a complete mathematically consistent way. This is made possible by using general operator algebras to extend the mathematical description of the physical world toward macroscopic systems. Such an approach goes beyond the usual type-I operator algebras used in standard textbook quantum mechanics. This avoids a major pitfall, which is the temptation to make the usual type-I formalism ’universal’. This may also provide a meta-framework for both classical and quantum physics, shedding new light on ancient conceptual antagonisms and clarifying the status of quantum objects. Beyond exploring remote corners of quantum physics, we expect these ideas to be helpful to better understand and develop quantum technologies.
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(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)
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What Is in a Simplicial Complex? A Metaplex-Based Approach to Its Structure and Dynamics
Entropy 2023, 25(12), 1599; https://doi.org/10.3390/e25121599 - 29 Nov 2023
Abstract
Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this
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Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this work, we provide some examples of complex systems in which this representation would be a more appropriate model of real-world phenomena. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which also includes the definition of dynamical systems on them. A metaplex is formed by regions of a continuous space of any dimension interconnected by sinks and sources that works controlled by discrete (graph) operators. The definition of simplicial metaplexes given here allows the description of the diffusion dynamics of this system in a way that solves the existing problems with previous models. We make a detailed analysis of the generalities and possible extensions of this model beyond simplicial complexes, e.g., from polytopal and cell complexes to manifold complexes, and apply it to a real-world simplicial complex representing the visual cortex of a macaque.
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(This article belongs to the Special Issue Models, Topology and Inference of Multilayer and Higher-Order Networks)
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Bridging Extremes: The Invertible Bimodal Gumbel Distribution
Entropy 2023, 25(12), 1598; https://doi.org/10.3390/e25121598 - 29 Nov 2023
Abstract
This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in
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This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously.
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(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)
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Open AccessFeature PaperArticle
Kernel-Based Independence Tests for Causal Structure Learning on Functional Data
Entropy 2023, 25(12), 1597; https://doi.org/10.3390/e25121597 - 28 Nov 2023
Abstract
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over
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Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert–Schmidt independence criterion (hsic) and its d-variate version (d-hsic), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (cpt) based on the Hilbert–Schmidt conditional independence criterion (hscic), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socioeconomic data.
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(This article belongs to the Special Issue Causality and Complex Systems)
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Self-Organisation of Prediction Models
Entropy 2023, 25(12), 1596; https://doi.org/10.3390/e25121596 - 28 Nov 2023
Abstract
Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining a
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Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining a selective advantage from the beneficial use of activity requires a consistent combination of sensual perception, memorised experience, statistical or causal prediction models, and the resulting favourable decisions on actions. This information processing chain originated from mere physical interaction processes prior to life, here denoted as structural information exchange. From there, the self-organised transition to symbolic information processing marks the beginning of life, evolving through the novel purposivity of trial-and-error feedback and the accumulation of symbolic information. The emergence of symbols and prediction models can be described as a ritualisation transition, a symmetry-breaking kinetic phase transition of the second kind previously known from behavioural biology. The related new symmetry is the neutrally stable arbitrariness, conventionality, or code invariance of symbols with respect to their meaning. The meaning of such symbols is given by the structural effect they ultimately unleash, directly or indirectly, by deciding on which actions to take. The early genetic code represents the first symbols. The genetically inherited symbolic information is the first prediction model for activities sufficient for survival under the condition of environmental continuity, sometimes understood as the “final causality” property of the model.
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(This article belongs to the Special Issue Information and Self-Organization III)
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