Entropy

18 pages, 2348 KiB

Open AccessArticle

Efficiently Characterizing the Quantum Information Flow, Loss, and Recovery in the Central Spin System

by Jiahui Chen, Mohamad Niknam and David Cory

Entropy 2024, 26(12), 1077; https://doi.org/10.3390/e26121077 - 10 Dec 2024

Understanding the flow, loss, and recovery of the information between a system and its environment is essential for advancing quantum technologies. The central spin system serves as a useful model for a single qubit, offering valuable insights into how quantum systems can be [...] Read more.

Understanding the flow, loss, and recovery of the information between a system and its environment is essential for advancing quantum technologies. The central spin system serves as a useful model for a single qubit, offering valuable insights into how quantum systems can be manipulated and protected from decoherence. This work uses the stimulated echo experiment to track the information flow between the central spin and its environment, providing a direct measure of the sensitivity of system/environment correlations to environmental dynamics. The extent of mixing and the growth of correlations are quantified through autocorrelation functions of the noise and environmental dynamics, which also enable the estimation of nested commutators between the system/environment and environmental Hamiltonians. Complementary decoupling experiments offer a straightforward measure of the strength of the system Hamiltonians. The approach is experimentally demonstrated on a spin system. Full article

(This article belongs to the Special Issue Entanglement in Quantum Spin Systems)

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16 pages, 571 KiB

Open AccessArticle

Generative Bayesian Computation for Maximum Expected Utility

by Nick Polson, Fabrizio Ruggeri and Vadim Sokolov

Entropy 2024, 26(12), 1076; https://doi.org/10.3390/e26121076 - 10 Dec 2024

Abstract

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of posterior quantiles. Our approach uses a deep [...] Read more.

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of posterior quantiles. Our approach uses a deep quantile neural estimator to directly simulate distributional utilities. Generative methods only assume the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters, data and a base distribution. Then, a supervised learning problem is solved as a non-parametric regression of generative utilities on outputs and base distribution. We propose the use of deep quantile neural networks. Our method has a number of computational advantages, primarily being density-free and an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also described. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and power utility (also known as the fractional Kelly criterion). Finally, we conclude with directions for future research. Full article

(This article belongs to the Special Issue Deep Generative Modeling: Theory and Applications)

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19 pages, 13118 KiB

Open AccessArticle

A Multi-Attribute Decision-Making Approach for Critical Node Identification in Complex Networks

by Xinyun Zhao, Yongheng Zhang, Qingying Zhai, Jinrui Zhang and Lanlan Qi

Entropy 2024, 26(12), 1075; https://doi.org/10.3390/e26121075 - 9 Dec 2024

Abstract

Correctly identifying influential nodes in a complex network and implementing targeted protection measures can significantly enhance the overall security of the network. Currently, indicators such as degree centrality, closeness centrality, betweenness centrality, H-index, and K-shell are commonly used to measure node influence. Although [...] Read more.

Correctly identifying influential nodes in a complex network and implementing targeted protection measures can significantly enhance the overall security of the network. Currently, indicators such as degree centrality, closeness centrality, betweenness centrality, H-index, and K-shell are commonly used to measure node influence. Although these indicators can identify critical nodes to some extent, they often consider node attributes from a narrow perspective and have certain limitations. Therefore, evaluating the importance of nodes using most existing indicators remains incomplete. In this paper, we propose the multi-attribute CRITIC-TOPSIS network decision indicator, or MCTNDI, which integrates closeness centrality, betweenness centrality, H-index, and network constraint coefficients to identify critical nodes in a network. This indicator combines information from multiple perspectives, including local neighborhood importance, network topological location, path centrality, and node mutual information, thereby solving the issue of the one-sided perspective of single indicators and providing a more comprehensive measure of node importance. Additionally, MCTNDI is validated through the analysis of several real-world networks, including the Contiguous USA network, Dolphins network, USAir97 network, and Tech-routers-rf network. The validation is conducted from four aspects: the results of simulated network attacks, the distribution of node importance, the monotonicity of rankings, and the similarity of indicators, illustrating MCTNDI’s effectiveness in real networks. Full article

(This article belongs to the Special Issue Computational and Statistical Physics Approaches for Complex Systems and Social Phenomena, 3rd Edition)

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10 pages, 335 KiB

Open AccessArticle

Frustrated Synchronization of the Kuramoto Model on Complex Networks

by Géza Ódor, Shengfeng Deng and Jeffrey Kelling

Entropy 2024, 26(12), 1074; https://doi.org/10.3390/e26121074 - 9 Dec 2024

Abstract

We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular

40^{5}

and

100^{4}

lattice results with those of

12, 000^{2}

lattice substrates with power-law decaying long links (ll). The latter [...] Read more.

We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular

40^{5}

and

100^{4}

lattice results with those of

12, 000^{2}

lattice substrates with power-law decaying long links (ll). The latter heterogeneous network exhibits

d_{s} > 4

spectral dimensions. We show strong corrections to scaling and mean-field type of criticality at

d = 5

, with logarithmic corrections at

d = 4

Euclidean dimensions. Contrarily, the ll model exhibits a non-mean-field smeared transition, with oscillating corrections at similarly high spectral dimensions. This suggests that the network heterogeneity is relevant, causing frustrated synchronization akin to Griffiths effects. Full article

(This article belongs to the Special Issue Universality Classes of Synchronization Phase Transitions)

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33 pages, 8127 KiB

Open AccessArticle

Complexity Analysis and Control of Output Competition in a Closed-Loop Supply Chain of Cross-Border E-Commerce Under Different Logistics Modes Considering Chain-to-Chain Information Asymmetry

by Feng-Jie Xie, Lu-Ying Wen, Wen-Tian Cui and Xiao-Yang Shen

Entropy 2024, 26(12), 1073; https://doi.org/10.3390/e26121073 - 9 Dec 2024

Abstract

To investigate the dynamic complexity of chain-to-chain output decisions in a closed-loop supply chain system of cross-border e-commerce (CBEC), this study decomposes the system into four product–market (PM) chains, based on the e-commerce platform’s information-sharing strategy and the manufacturer’s selected logistics mode (direct [...] Read more.

To investigate the dynamic complexity of chain-to-chain output decisions in a closed-loop supply chain system of cross-border e-commerce (CBEC), this study decomposes the system into four product–market (PM) chains, based on the e-commerce platform’s information-sharing strategy and the manufacturer’s selected logistics mode (direct mail or bonded warehouse). By combining game theory with complex systems theory, discrete dynamic models for output competition among PM chains under four scenarios are constructed. The Nash equilibrium solution and stability conditions of the models are derived according to the principles of nonlinear dynamics. The stability of the model under the four scenarios, as well as the impacts of the initial output level and comprehensive tax rates on the stability and stability control of the system, are analyzed using numerical simulation methods. Our findings suggest that maintaining system stability requires controlling the initial output levels, the output adjustment speeds, and tariff rates to remain within specific thresholds. When these thresholds are exceeded, the entropy value of the model increases, and the system outputs decisions to enter a chaotic or uncontrollable state via period-doubling bifurcations. When the output adjustment speed of the four PM chains is high, the direct-mail logistics mode exhibits greater stability. Furthermore, under increased tariff rates for CBEC, the bonded warehouse mode has a stronger ability to maintain stability in system output decisions. Conversely, when the general import tax rate increases, the direct-mail mode demonstrates better stability. Regardless of the logistics mode, the information-sharing strategy can enhance the stability of system output decisions, while increased e-commerce platform commission rates tend to reduce stability. Interestingly, the use of a non-information-sharing strategy and the direct-mail logistics mode may be more conducive to increasing the profit levels of overseas manufacturers. Finally, the delayed feedback control method can effectively reduce the entropy value, suppress chaotic phenomena in the system, and restore stability to output decisions from a fluctuating state. Full article

(This article belongs to the Section Multidisciplinary Applications)

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24 pages, 74482 KiB

Open AccessArticle

Bayesian Regression Analysis for Dependent Data with an Elliptical Shape

by Yian Yu, Long Tang, Kang Ren, Zhonglue Chen, Shengdi Chen and Jianqing Shi

Entropy 2024, 26(12), 1072; https://doi.org/10.3390/e26121072 - 9 Dec 2024

Abstract

This paper proposes a parametric hierarchical model for functional data with an elliptical shape, using a Gaussian process prior to capturing the data dependencies that reflect systematic errors while modeling the underlying curved shape through a von Mises–Fisher distribution. The model definition, Bayesian [...] Read more.

This paper proposes a parametric hierarchical model for functional data with an elliptical shape, using a Gaussian process prior to capturing the data dependencies that reflect systematic errors while modeling the underlying curved shape through a von Mises–Fisher distribution. The model definition, Bayesian inference, and MCMC algorithm are discussed. The effectiveness of the model is demonstrated through the reconstruction of curved trajectories using both simulated and real-world examples. The discussion in this paper focuses on two-dimensional problems, but the framework can be extended to higher-dimensional spaces, making it adaptable to a wide range of applications. Full article

(This article belongs to the Special Issue Statistical Methods for Modeling High-Dimensional and Complex Data: Second Edition)

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16 pages, 13233 KiB

Open AccessArticle

Tethered Balloon Cluster Deployments and Optimization for Emergency Communication Networks

by Mingyu Guan, Zhongxiao Feng, Shengming Jiang and Weiming Zhou

Entropy 2024, 26(12), 1071; https://doi.org/10.3390/e26121071 - 9 Dec 2024

Abstract

Natural disasters can severely disrupt conventional communication systems, hampering relief efforts. High-altitude tethered balloon base stations (HATBBSs) are a promising solution to communication disruptions, providing wide communication coverage in disaster-stricken areas. However, a single HATBBS is insufficient for large disaster zones, and limited [...] Read more.

Natural disasters can severely disrupt conventional communication systems, hampering relief efforts. High-altitude tethered balloon base stations (HATBBSs) are a promising solution to communication disruptions, providing wide communication coverage in disaster-stricken areas. However, a single HATBBS is insufficient for large disaster zones, and limited resources may restrict the number and energy capacity of available base stations. To address these challenges, this study proposes a cluster deployment of tethered balloons to form flying ad hoc networks (FANETs) as a backbone for post-disaster communications. A meta-heuristic-based multi-objective particle swarm optimization (MOPSO) algorithm is employed to optimize the placement of balloons and power control to maximize target coverage and system energy efficiency. Comparative analysis with a stochastic algorithm (SA) demonstrates that MOPSO converges faster, with significant advantages in determining optimal balloon placement. The simulation results show that MOPSO effectively improves network throughput while reducing average delay and packet loss rate. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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18 pages, 570 KiB

Open AccessArticle

Infinite-Dimensional Quantum Entropy: The Unified Entropy Case

by Roman Gielerak, Joanna Wiśniewska and Marek Sawerwain

Entropy 2024, 26(12), 1070; https://doi.org/10.3390/e26121070 - 9 Dec 2024

Abstract

Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states [...] Read more.

Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies were extended to this case study. Certain numerical examples for computing the proposed finite- and infinite-dimensional entropies are outlined as well, which allowed us to calculate the entropy values for infinite Hilbert spaces. Full article

(This article belongs to the Section Statistical Physics)

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22 pages, 1347 KiB

Open AccessArticle

Semi-Empirical Approach to Evaluating Model Fit for Sea Clutter Returns: Focusing on Future Measurements in the Adriatic Sea

by Bojan Vondra

Entropy 2024, 26(12), 1069; https://doi.org/10.3390/e26121069 - 9 Dec 2024

Abstract

A method for evaluating Kullback–Leibler (KL) divergence and Squared Hellinger (SH) distance between empirical data and a model distribution is proposed. This method exclusively utilises the empirical Cumulative Distribution Function (CDF) of the data and the CDF of the model, avoiding data processing [...] Read more.

A method for evaluating Kullback–Leibler (KL) divergence and Squared Hellinger (SH) distance between empirical data and a model distribution is proposed. This method exclusively utilises the empirical Cumulative Distribution Function (CDF) of the data and the CDF of the model, avoiding data processing such as histogram binning. The proposed method converges almost surely, with the proof based on the use of exponentially distributed waiting times. An example demonstrates convergence of the KL divergence and SH distance to their true values when utilising the Generalised Pareto (GP) distribution as empirical data and the K distribution as the model. Another example illustrates the goodness of fit of these (GP and K-distribution) models to real sea clutter data from the widely used Intelligent PIxel processing X-band (IPIX) measurements. The proposed method can be applied to assess the goodness of fit of various models (not limited to GP or K distribution) to clutter measurement data such as those from the Adriatic Sea. Distinctive features of this small and immature sea, like the presence of over 1300 islands that affect local wind and wave patterns, are likely to result in an amplitude distribution of sea clutter returns that differs from predictions of models designed for oceans or open seas. However, to the author’s knowledge, no data on this specific topic are currently available in the open literature, and such measurements have yet to be conducted. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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21 pages, 325 KiB

Open AccessArticle

Quantum Collapse and Computation in an Everett Multiverse

by Fabrizio Tamburini and Ignazio Licata

Entropy 2024, 26(12), 1068; https://doi.org/10.3390/e26121068 - 9 Dec 2024

Abstract

The mathematical representation of the universe consists of sequences of symbols, rules and operators containing Gödel’s undecidable propositions: information and its manipulation, also with Turing Machines. Classical information theory and mathematics, ideally independent from the medium used, can be interpreted realistically and objectively [...] Read more.

The mathematical representation of the universe consists of sequences of symbols, rules and operators containing Gödel’s undecidable propositions: information and its manipulation, also with Turing Machines. Classical information theory and mathematics, ideally independent from the medium used, can be interpreted realistically and objectively from their correspondence with quantum information, which is physical. Each representation of the universe and its evolution are, in any case, physical subsets of the universe, structured sets of observers and their complements in the universe made with spacetime events generated by local quantum measurements. Their description becomes a semantically closed structure without a global object-environment loss of decoherence as a von Neumann’s universal constructor with a semantical abstract whose structure cannot be decided deterministically a priori from an internal observer. In a semantically closed structure, the realization of a specific event that writes the semantical abstract of the constructor is a problem of finding “which way” for the evolution of the universe as a choice of the constructor’s state in a metastructure, like the many-world Everett scenario, from a specific result of any quantum measurement, corresponding to a Gödel undecidable proposition for an internal observer. Full article

(This article belongs to the Section Complexity)

14 pages, 269 KiB

Open AccessArticle

Boson–Fermion Algebraic Mapping in Second Quantization

by Fabio Lingua, Diego Molina Peñafiel, Lucrezia Ravera and Sebastián Salgado

Entropy 2024, 26(12), 1067; https://doi.org/10.3390/e26121067 - 8 Dec 2024

Abstract

We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained [...] Read more.

We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed. This discussion includes the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians. Full article

(This article belongs to the Special Issue Foundational Aspects of Gauge Field Theory)

32 pages, 1510 KiB

Open AccessArticle

Carnot and the Archetype of Waterfalls

by Hans U. Fuchs, Elisabeth Dumont and Federico Corni

Entropy 2024, 26(12), 1066; https://doi.org/10.3390/e26121066 - 7 Dec 2024

Abstract

Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of [...] Read more.

Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of waterfalls to causative thermal processes: heat powers motion in a heat engine just as falling water does when activating rotation in a water wheel. We understand Carnot’s waterfall imagery as an archetype of human reasoning—as an embodiment of how we experience and understand causative (agentive) phenomena. We project it onto the macroscopic phenomena identified in physical science and so unlock the power of analogical structure mapping between theories of fluids, electricity and magnetism, heat, substances, gravity, and linear and rotational motion. In particular, the notion of (motive) power of a waterfall lets us create imaginative explanations of the interactions of Forces of Nature and helps us construct a generalized energy principle. Two-hundred years after Carnot made us aware of it, his Waterfall Analogy is a powerful example of theory construction with roots deep in how we experience phenomena as caused by natural agents. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

18 pages, 517 KiB

Open AccessArticle

Predictive Complexity of Quantum Subsystems

by Curtis T. Asplund and Elisa Panciu

Entropy 2024, 26(12), 1065; https://doi.org/10.3390/e26121065 - 7 Dec 2024

Abstract

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is [...] Read more.

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement. Full article

(This article belongs to the Section Quantum Information)

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11 pages, 286 KiB

Open AccessArticle

Entropic Order Parameters for Categorical Symmetries in 2D-CFT

by Javier Molina-Vilaplana, Pablo Saura-Bastida and Germán Sierra

Entropy 2024, 26(12), 1064; https://doi.org/10.3390/e26121064 - 6 Dec 2024

Abstract

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in

(1 + 1)

-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states [...] Read more.

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in

(1 + 1)

-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of

(1 + 1)

-d theories with categorical symmetries. Full article

(This article belongs to the Special Issue Entanglement Entropy in Quantum Field Theory)

22 pages, 3678 KiB

Open AccessArticle

Robust Model-Free Identification of the Causal Networks Underlying Complex Nonlinear Systems

by Guanxue Yang, Shimin Lei and Guanxiao Yang

Entropy 2024, 26(12), 1063; https://doi.org/10.3390/e26121063 - 6 Dec 2024

Abstract

Inferring causal networks from noisy observations is of vital importance in various fields. Due to the complexity of system modeling, the way in which universal and feasible inference algorithms are studied is a key challenge for network reconstruction. In this study, without any [...] Read more.

Inferring causal networks from noisy observations is of vital importance in various fields. Due to the complexity of system modeling, the way in which universal and feasible inference algorithms are studied is a key challenge for network reconstruction. In this study, without any assumptions, we develop a novel model-free framework to uncover only the direct relationships in networked systems from observations of their nonlinear dynamics. Our proposed methods are termed multiple-order Polynomial Conditional Granger Causality (PCGC) and sparse PCGC (SPCGC). PCGC mainly adopts polynomial functions to approximate the whole system model, which can be used to judge the interactions among nodes through subsequent nonlinear Granger causality analysis. For SPCGC, Lasso optimization is first used for dimension reduction, and then PCGC is executed to obtain the final network. Specifically, the conditional variables are fused in this general, model-free framework regardless of their formulations in the system model, which could effectively reconcile the inference of direct interactions with an indirect influence. Based on many classical dynamical systems, the performances of PCGC and SPCGC are analyzed and verified. Generally, the proposed framework could be quite promising for the provision of certain guidance for data-driven modeling with an unknown model. Full article

(This article belongs to the Special Issue Causality and Complex Systems)

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20 pages, 4184 KiB

Open AccessArticle

Air Quality Prediction Based on Singular Spectrum Analysis and Artificial Neural Networks

by Javier Linkolk López-Gonzales, Rodrigo Salas, Daira Velandia and Paulo Canas Rodrigues

Entropy 2024, 26(12), 1062; https://doi.org/10.3390/e26121062 - 6 Dec 2024

Abstract

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating [...] Read more.

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating highly nonlinear functions. This study proposes to improve the precision in the prediction of air quality. For this purpose, a hybrid adaptation is considered. It is based on an integration of the singular spectrum analysis and the recurrent neural network long short-term memory; the SSA is applied to the original time series to split signal and noise, which are then predicted separately and added together to obtain the final forecasts. This hybrid method provided better performance when compared with other methods. Full article

(This article belongs to the Special Issue Big Data Analytics and Information Science for Business and Biomedical Applications: Third Edition)

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27 pages, 428 KiB

Open AccessArticle

Identifying Causal Effects Under Functional Dependencies

by Yizuo Chen and Adnan Darwiche

Entropy 2024, 26(12), 1061; https://doi.org/10.3390/e26121061 - 6 Dec 2024

Abstract

We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable [...] Read more.

We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Secondly, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure that removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects. Our treatment of functional dependencies in this context mandates a formal, systematic, and general treatment of positivity assumptions, which are prevalent in the literature on causal effect identifiability and which interact with functional dependencies, leading to another contribution of the presented work. Full article

(This article belongs to the Special Issue Causal Graphical Models and Their Applications)

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11 pages, 1800 KiB

Open AccessArticle

Interplay of Spin Nernst Effect and Entanglement Negativity in Layered Ferrimagnets: A Study via Exact Diagonalization

by Leonardo S. Lima

Entropy 2024, 26(12), 1060; https://doi.org/10.3390/e26121060 - 6 Dec 2024

Abstract

In this paper, we analyzed the influence of the spin Nernst effect on quantum correlation in a layered ferrimagnetic model. In the study of three-dimensional ferrimagnets, the focus is on materials with a specific arrangement of spins, where the neighboring spins are parallel [...] Read more.

In this paper, we analyzed the influence of the spin Nernst effect on quantum correlation in a layered ferrimagnetic model. In the study of three-dimensional ferrimagnets, the focus is on materials with a specific arrangement of spins, where the neighboring spins are parallel and the others are antiparallel. The anisotropic nature of these materials means that the interactions between spins depend on their relative orientations in different directions. We analyzed the effect of magnon bands induced by the coupling parameters on entanglement negativity. The influence of the coupling parameters of the topologic phase transition on quantum entanglement is investigated as well. Numerical simulations using the Lanczos algorithm and exact diagonalization for different lattice sizes are compared with the results of spin wave theory. Full article

(This article belongs to the Special Issue Entanglement in Quantum Spin Systems)

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19 pages, 7347 KiB

Open AccessArticle

Adapting SAM2 Model from Natural Images for Tooth Segmentation in Dental Panoramic X-Ray Images

by Zifeng Li, Wenzhong Tang, Shijun Gao, Yanyang Wang and Shuai Wang

Entropy 2024, 26(12), 1059; https://doi.org/10.3390/e26121059 - 6 Dec 2024

Abstract

Dental panoramic X-ray imaging, due to its high cost-effectiveness and low radiation dose, has become a widely used diagnostic tool in dentistry. Accurate tooth segmentation is crucial for lesion analysis and treatment planning, helping dentists to quickly and precisely assess the condition of [...] Read more.

Dental panoramic X-ray imaging, due to its high cost-effectiveness and low radiation dose, has become a widely used diagnostic tool in dentistry. Accurate tooth segmentation is crucial for lesion analysis and treatment planning, helping dentists to quickly and precisely assess the condition of teeth. However, dental X-ray images often suffer from noise, low contrast, and overlapping anatomical structures, coupled with limited available datasets, leading traditional deep learning models to experience overfitting, which affects generalization ability. In addition, high-precision deep models typically require significant computational resources for inference, making deployment in real-world applications challenging. To address these challenges, this paper proposes a tooth segmentation method based on the pre-trained SAM2 model. We employ adapter modules to fine-tune the SAM2 model and introduce ScConv modules and gated attention mechanisms to enhance the model’s semantic understanding and multi-scale feature extraction capabilities for medical images. In terms of efficiency, we utilize knowledge distillation, using the fine-tuned SAM2 model as the teacher model for distilling knowledge to a smaller model named LightUNet. Experimental results on the UFBA-UESC dataset show that, in terms of performance, our model significantly outperforms the traditional UNet model in multiple metrics such as IoU, effectively improving segmentation accuracy and model robustness, particularly with limited sample datasets. In terms of efficiency, LightUNet achieves comparable performance to UNet, but with only 1.6% of its parameters and 24.0% of the inference time, demonstrating its feasibility for deployment on edge devices. Full article

(This article belongs to the Section Multidisciplinary Applications)

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