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The research groups in computer vision, graphics, and machine learning have dedicated a substantial amount of attention to the areas of 3D object reconstruction, augmentation, and registration. Deep learning is the predominant method used in artificial intelligence for addressing computer vision challenges. However, deep learning on three-dimensional data presents distinct obstacles and is now in its nascent phase. There have been significant advancements in deep learning specifically for three-dimensional data, offering a range of ways to address these issues. This study offers a comprehensive examination of the latest advancements in deep learning methodologies. We examine many benchmark models for the tasks of 3D object registration, augmentation, and reconstruction. We thoroughly analyse their architectures, advantages, and constraints. In summary, this report provides a comprehensive overview of recent advancements in three-dimensional deep learning and highlights unresolved research areas that will need to be addressed in the future.

The Gaussian wiretap channel with noncausal state interference available at the transmitter, which is also called the dirty paper wiretap channel (DP-WTC), has been extensively studied in the literature. Recently, it has been shown that taking actions on the corrupted state interference of the DP-WTC (also called the action-dependent DP-WTC) helps to increase the secrecy capacity of the DP-WTC. Subsequently, it has been shown that channel feedback further increases the secrecy capacity of the action-dependent DP-WTC (AD-DP-WTC), and a sub-optimal feedback scheme is proposed for this feedback model. In this paper, a two-step hybrid scheme and a corresponding new lower bound on the secrecy capacity of the AD-DP-WTC with noiseless feedback are proposed. The proposed new lower bound is shown to be optimal (achieving the secrecy capacity) and tighter than the existing one in the literature for some cases, and the results of this paper are further explained via numerical examples.

On behalf of the Editor-in-Chief, Prof [...]

On behalf of the Editor-in-Chief, Prof [...]

On behalf of the Editor-in-Chief, Prof [...]

Translation of the seminal 1877 paper by Ludwig Boltzmann which for the first time established the probabilistic basis of entropy. Includes a scientific commentary.

This paper presents a novel method for finding features in the analysis of variable distributions stemming from time series. We apply the methodology to the case of submitted and accepted papers in peer-reviewed journals. We provide a comparative study of editorial decisions for papers submitted to two peer-reviewed journals: the Journal of the Serbian Chemical Society (JSCS) and this MDPI Entropy journal. We cover three recent years for which the fate of submitted papers—about 600 papers to JSCS and 2500 to Entropy—is completely determined. Instead of comparing the number distributions of these papers as a function of time with respect to a uniform distribution, we analyze the relevant probabilities, from which we derive the information entropy. It is argued that such probabilities are indeed more relevant for authors than the actual number of submissions. We tie this entropy analysis to the so called diversity of the variable distributions. Furthermore, we emphasize the correspondence between the entropy and the diversity with inequality measures, like the Herfindahl-Hirschman index and the Theil index, itself being in the class of entropy measures; the Gini coefficient which also measures the diversity in ranking is calculated for further discussion. In this sample, the seasonal aspects of the peer review process are outlined. It is found that the use of such indices, non linear transformations of the data distributions, allow us to distinguish features and evolutions of the peer review process as a function of time as well as comparing the non-uniformity of distributions. Furthermore, t- and z-statistical tests are applied in order to measure the significance (p-level) of the findings, that is, whether papers are more likely to be accepted if they are submitted during a few specific months or during a particular “season”; the predictability strength depends on the journal.

The analysis of research paper collections is an interesting topic that can give insights on whether a research area is stalled in the same problems, or there is a great amount of novelty every year. Previous research has addressed similar tasks by the analysis of keywords or reference lists, with different degrees of human intervention. In this paper, we demonstrate how, with the use of Normalized Relative Compression, together with a set of automated data-processing tasks, we can successfully visually compare research articles and document collections. We also achieve very similar results with Normalized Conditional Compression that can be applied with a regular compressor. With our approach, we can group papers of different disciplines, analyze how a conference evolves throughout the different editions, or how the profile of a researcher changes through the time. We provide a set of tests that validate our technique, and show that it behaves better for these tasks than other techniques previously proposed.

On behalf of the Editor-in-Chief, Prof. Dr. Kevin H. Knuth, we are pleased to announce the Entropy Best Paper Award for 2018 [...]

We are pleased to announce the “Entropy Best Paper Award” for 2015. Nominations were selected by the Editor-in-Chief and designated Editorial Board Members from all the papers published in 2011. Reviews and research papers were evaluated separately. We gladly announce that the following three papers have won the Entropy Best Paper Award in 2015:[...]

In 2013, Entropy instituted the “Best Paper” award to recognize outstanding papers in the area of entropy and information studies published in Entropy [1]. We are pleased to announce the “Entropy Best Paper Award” for 2014. Nominations were selected by the Editor-in-Chief and designated Editorial Board Members from all the papers published in 2010.

The accompanying papers in the first issue of Entropy, volume 5, 2003 were presented at the electronic conference on Foundations of Information Science FIS 2002 (http://www.mdpi.net/fis2002/). The running title of this FIS e-conference was THE NATURE OF INFORMATION: CONCEPTIONS, MISCONCEPTIONS, AND PARADOXES. It was held on the Internet from 6 to 10 May 2002, and was followed by a series of discussions –structured as focused sessions– which took place in the net from 10 May 2002 until 31 January 2003 (more than 400 messages were exchanged, see: http://fis.iguw.tuwien.ac.at/mailings/). This Introduction will briefly survey the problems around the concept of information, will present the central ideas of the FIS initiative, and will contrast some of the basic differences between information and mechanics (reductionism).

The journal Entropy is initiating a “Best Paper” award to recognize outstanding papers in the area of entropy and information studies published in Entropy. We are pleased to announce the first “Entropy Best Paper Award” for 2013. Nominations were selected by the Editor-in-Chief and selected Editorial Board Members from all the papers published in 2009 and evaluated by the Entropy Best Paper Award Committee. Reviews and articles were evaluated separately. A first prize is awarded to the selected review paper, and a first and second prize is awarded to the top two selected research articles.

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The diagnosis of faults in wind turbine gearboxes based on signal processing represents a significant area of research within the field of wind power generation. This paper presents an intelligent fault diagnosis method based on ensemble-refined composite multiscale fluctuation-based reverse dispersion entropy (ERCMFRDE) for a wind turbine gearbox vibration signal that is nonstationary and nonlinear and for noise problems. Firstly, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and stationary wavelet transform (SWT) are adopted for signal decomposition, noise reduction, and restructuring of gearbox signals. Secondly, we extend the single coarse-graining processing method of refined composite multiscale fluctuation-based reverse dispersion entropy (RCMFRDE) to the multiorder moment coarse-grained processing method, extracting mixed fault feature sets for denoised signals. Finally, the diagnostic results are obtained based on the least squares support vector machine (LSSVM). The dataset collected during the gearbox fault simulation on the experimental platform is employed as the research object, and the experiments are conducted using the method proposed in this paper. The experimental results demonstrate that the proposed method is an effective and reliable approach for accurately diagnosing gearbox faults, exhibiting high diagnostic accuracy and a robust performance.

Computer vision in sports analytics is gaining in popularity. Monitoring players’ performance using cameras is more flexible and does not interfere with player equipment compared to systems using sensors. This provides a wide set of opportunities for computer vision systems that help coaches, reporters, and audiences. This paper provides an introduction to the problem of measuring boxers’ performance, with a comprehensive survey of approaches in current science. The main goal of the paper is to provide a system to automatically detect punches in Olympic boxing using a single static camera. The authors use Euclidean distance to measure the distance between boxers and convolutional neural networks to classify footage frames. In order to improve classification performance, we provide and test three approaches to manipulating the images prior to fitting the classifier. The proposed solution achieves 95% balanced accuracy, 49% F1 score for frames with punches, and 97% for frames without punches. Finally, we present a working system for analyses of a boxing scene that marks boxers and labelled frames with detected clashes and punches.

With the popularity of the Internet and the increase in the level of information technology, cyber attacks have become an increasingly serious problem. They pose a great threat to the security of individuals, enterprises, and the state. This has made network intrusion detection technology critically important. In this paper, a malicious traffic detection model is constructed based on a decision tree classifier of entropy and a proximal policy optimisation algorithm (PPO) of deep reinforcement learning. Firstly, the decision tree idea in machine learning is used to make a preliminary classification judgement on the dataset based on the information entropy. The importance score of each feature in the classification work is calculated and the features with lower contributions are removed. Then, it is handed over to the PPO algorithm model for detection. An entropy regularity term is introduced in the process of the PPO algorithm update. Finally, the deep reinforcement learning algorithm is used to continuously train and update the parameters during the detection process, and finally, the detection model with higher accuracy is obtained. Experiments show that the binary classification accuracy of the malicious traffic detection model based on the deep reinforcement learning PPO algorithm can reach 99.17% under the CIC-IDS2017 dataset used in this paper.

Relay channels capture the essence of several important communication scenarios such as sensor network and satellite communication. In this paper, first, we propose an efficient coding scheme for an additive white Gaussian noise (AWGN) relay channel in the presence of AWGN feedback, which generalizes the conventional scheme for the AWGN relay channel with noiseless feedback by introducing a lattice-based strategy to eliminate the impact of the feedback channel noise on the performance of the original scheme. Next, we further extend the proposed scheme to the multi-input single-output (MISO) fading relay channel (FRC) with noisy feedback. The key to this extension is to use a pre-coding strategy to transform the MISO channel into a single-input single-output (SISO) channel and applying a two-dimensional lattice coding strategy to deal with the feedback fading channel noise. Finally, we analyze the security performance of our proposed scheme in several cases, and the results of this paper are further illustrated by numerical examples.

In insecure communication environments where the communication bandwidth is limited, important image data must be compressed and encrypted for transmission. However, existing image compression and encryption algorithms suffer from poor image reconstruction quality and insufficient image encryption security. To address these problems, this paper proposes an image-compression and encryption scheme based on a newly designed hyperchaotic system and two-dimensional compressed sensing (2DCS) technique. In this paper, the chaotic performance of this hyperchaotic system is verified by bifurcation diagrams, Lyapunov diagrams, approximate entropy, and permutation entropy, which have certain advantages over the traditional 2D chaotic system. The new 2D chaotic system as a pseudo-random number generator can completely pass all the test items of NIST. Meanwhile, this paper improves on the existing 2D projected gradient (2DPG) algorithm, which improves the quality of image compression and reconstruction, and can effectively reduce the transmission pressure of image data confidential communication. In addition, a new image encryption algorithm is designed for the new 2D chaotic system, and the security of the algorithm is verified by experiments such as key space size analysis and encrypted image information entropy.

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein’s methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein’s early work clarifies his later reasoning and demonstrates its consistency and validity.

In this paper, we propose two feedback coding schemes for the action-dependent wiretap channel with noncausal state at the transmitter. The first scheme follows from the already existing secret key based feedback coding scheme for the wiretap channel. The second one follows from our recently proposed hybrid feedback scheme for the wiretap channel. We show that, for the action-dependent wiretap channel with noncausal state at the transmitter, the second feedback scheme performs better than the first one, and the capacity results of this paper are further explained via a Gaussian example, which we call the action-dependent dirty paper wiretap channel with noiseless feedback.

Accurate prediction of air quality is crucial for assessing the state of the atmospheric environment, especially considering the nonlinearity, volatility, and abrupt changes in air quality data. This paper introduces an air quality index (AQI) prediction model based on the Dung Beetle Algorithm (DBO) aimed at overcoming limitations in traditional prediction models, such as inadequate access to data features, challenges in parameter setting, and accuracy constraints. The proposed model optimizes the parameters of Variational Mode Decomposition (VMD) and integrates the Informer adaptive sequential prediction model with the Convolutional Neural Network-Long Short Term Memory (CNN-LSTM). Initially, the correlation coefficient method is utilized to identify key impact features from multivariate weather and meteorological data. Subsequently, penalty factors and the number of variational modes in the VMD are optimized using DBO. The optimized parameters are utilized to develop a variationally constrained model to decompose the air quality sequence. The data are categorized based on approximate entropy, and high-frequency data are fed into the Informer model, while low-frequency data are fed into the CNN-LSTM model. The predicted values of the subsystems are then combined and reconstructed to obtain the AQI prediction results. Evaluation using actual monitoring data from Beijing demonstrates that the proposed coupling prediction model of the air quality index in this paper is superior to other parameter optimization models. The Mean Absolute Error (MAE) decreases by 13.59%, the Root-Mean-Square Error (RMSE) decreases by 7.04%, and the R-square (R2) increases by 1.39%. This model surpasses 11 other models in terms of lower error rates and enhances prediction accuracy. Compared with the mainstream swarm intelligence optimization algorithm, DBO, as an optimization algorithm, demonstrates higher computational efficiency and is closer to the actual value. The proposed coupling model provides a new method for air quality index prediction.

This paper establishes a general framework for measuring statistical divergence. Namely, with regard to a pair of random variables that share a common range of values: quantifying the distance of the statistical distribution of one random variable from that of the other. The general framework is then applied to the topics of socioeconomic inequality and renewal processes. The general framework and its applications are shown to yield and to relate to the following: f-divergence, Hellinger divergence, Renyi divergence, and Kullback–Leibler divergence (also known as relative entropy); the Lorenz curve and socioeconomic inequality indices; the Gini index and its generalizations; the divergence of renewal processes from the Poisson process; and the divergence of anomalous relaxation from regular relaxation. Presenting a ‘fresh’ perspective on statistical divergence, this paper offers its readers a simple and transparent construction of statistical-divergence gauges, as well as novel paths that lead from statistical divergence to the aforementioned topics.

Investigating the significant “roles” within financial complex networks and their stability is of great importance for preventing financial risks. On one hand, this paper initially constructs a complex network model of the stock market based on mutual information theory and threshold methods, combined with the closing price returns of stocks. It then analyzes the basic topological characteristics of this network and examines its stability under random and targeted attacks by varying the threshold values. On the other hand, using systemic risk entropy as a metric to quantify the stability of the stock market, this paper validates the impact of the COVID-19 pandemic as a widespread, unexpected event on network stability. The research results indicate that this complex network exhibits small-world characteristics but cannot be strictly classified as a scale-free network. In this network, key roles are played by the industrial sector, media and information services, pharmaceuticals and healthcare, transportation, and utilities. Upon reducing the threshold, the network’s resilience to random attacks is correspondingly strengthened. Dynamically, from 2000 to 2022, systemic risk in significant industrial share markets significantly increased. From a static perspective, the period around 2019, affected by the COVID-19 pandemic, experienced the most drastic fluctuations. Compared to the year 2000, systemic risk entropy in 2022 increased nearly sixtyfold, further indicating an increasing instability within this complex network.

Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach based on modified hierarchical fluctuation dispersion entropy of tan-sigmoid mapping (MHFDE_TANSIG) and northern goshawk optimization–support vector machine (NGO–SVM) for wind turbine gearboxes. The tan-sigmoid (TANSIG) mapping function replaces the normal cumulative distribution function (NCDF) of the hierarchical fluctuation dispersion entropy (HFDE) method. Additionally, the hierarchical decomposition of the HFDE method is improved, resulting in the proposed MHFDE_TANSIG method. The vibration signals of wind turbine gearboxes are analyzed using the MHFDE_TANSIG method to extract fault features. The constructed fault feature set is used to intelligently recognize and classify the fault type of the gearboxes with the NGO–SVM classifier. The fault diagnosis methods based on MHFDE_TANSIG and NGO–SVM are applied to the experimental data analysis of gearboxes with different operating conditions. The results show that the fault diagnosis model proposed in this paper has the best performance with an average accuracy rate of 97.25%.

Autonomous search is an ongoing cycle of sensing, statistical estimation, and motion control with the objective to find and localise targets in a designated search area. Traditionally, the theoretical framework for autonomous search combines sequential Bayesian estimation with information theoretic motion control. This paper formulates autonomous search in the framework of possibility theory. Although the possibilistic formulation is slightly more involved than the traditional method, it provides a means for quantitative modelling and reasoning in the presence of epistemic uncertainty. This feature is demonstrated in the paper in the context of partially known probability of detection, expressed as an interval value. The paper presents an elegant Bayes-like solution to sequential estimation, with the reward function for motion control defined to take into account the epistemic uncertainty. The advantages of the proposed search algorithm are demonstrated by numerical simulations.

Medical image diagnosis using deep learning has shown significant promise in clinical medicine. However, it often encounters two major difficulties in real-world applications: (1) domain shift, which invalidates the trained model on new datasets, and (2) class imbalance problems leading to model biases towards majority classes. To address these challenges, this paper proposes a transfer learning solution, named Dynamic Weighting Translation Transfer Learning (DTTL), for imbalanced medical image classification. The approach is grounded in information and entropy theory and comprises three modules: Cross-domain Discriminability Adaptation (CDA), Dynamic Domain Translation (DDT), and Balanced Target Learning (BTL). CDA connects discriminative feature learning between source and target domains using a synthetic discriminability loss and a domain-invariant feature learning loss. The DDT unit develops a dynamic translation process for imbalanced classes between two domains, utilizing a confidence-based selection approach to select the most useful synthesized images to create a pseudo-labeled balanced target domain. Finally, the BTL unit performs supervised learning on the reassembled target set to obtain the final diagnostic model. This paper delves into maximizing the entropy of class distributions, while simultaneously minimizing the cross-entropy between the source and target domains to reduce domain discrepancies. By incorporating entropy concepts into our framework, our method not only significantly enhances medical image classification in practical settings but also innovates the application of entropy and information theory within deep learning and medical image processing realms. Extensive experiments demonstrate that DTTL achieves the best performance compared to existing state-of-the-art methods for imbalanced medical image classification tasks.

Categorical data analysis of 2 × 2 contingency tables is extremely common, not least because they provide risk difference, risk ratio, odds ratio, and log odds statistics in medical research. A χ2 test analysis is most often used, although some researchers use likelihood ratio test (LRT) analysis. Does it matter which test is used? A review of the literature, examination of the theoretical foundations, and analyses of simulations and empirical data are used by this paper to argue that only the LRT should be used when we are interested in testing whether the binomial proportions are equal. This so-called test of independence is by far the most popular, meaning the χ2 test is widely misused. By contrast, the χ2 test should be reserved for where the data appear to match too closely a particular hypothesis (e.g., the null hypothesis), where the variance is of interest, and is less than expected. Low variance can be of interest in various scenarios, particularly in investigations of data integrity. Finally, it is argued that the evidential approach provides a consistent and coherent method that avoids the difficulties posed by significance testing. The approach facilitates the calculation of appropriate log likelihood ratios to suit our research aims, whether this is to test the proportions or to test the variance. The conclusions from this paper apply to larger contingency tables, including multi-way tables.

New insights into intractable industrial challenges can be revealed by framing them in terms of natural science. One intractable industrial challenge is that creative production can be much more financially expensive and time consuming than standardized production. Creative products include a wide range of goods that have one or more original characteristics. The scaling up of creative production is hindered by high financial production costs and long production durations. In this paper, creative production is framed in terms of interactions between entropy and complexity during progressions from emergent pragmatics to action semantics. An analysis of interactions between entropy and complexity is provided that relates established practice in creative production to organizational survival in changing environments. The analysis in this paper is related to assembly theory, which is a recent theoretical development in natural science that addresses how open-ended generation of complex physical objects can emerge from selection in biology. Parallels between assembly practice in industrial production and assembly theory in natural science are explained through constructs that are common to both, such as assembly index. Overall, analyses reported in the paper reveal that interactions between entropy and complexity underlie intractable challenges in creative production, from the production of individual products to the survival of companies.

Linear complementary dual (LCD) codes, which are a class of linear codes introduced by Massey, have been extensively studied in the literature recently. It has been shown that LCD codes play a role in measures to counter passive and active side-channel analyses on embedded cryptosystems. In this paper, tables are presented of good quaternary Hermitian LCD codes and they are used in the construction of puncturing, shortening and combination codes. The results of this, including three tables of the best-known quaternary Hermitian LCD codes of any length n≤25 with corresponding dimension k, are presented. In addition, many of these quaternary Hermitian LCD codes given in this paper are optimal and saturate the lower or upper bound of Grassl’s code table, and some of them are nearly optimal.

Domestic and international risk shocks have greatly increased the demand for systemic risk management in China. This paper estimates China’s multi-layer financial network based on multiple financial relationships among banks, assets, and firms, using China’s banking system data in 2021. An improved PageRank algorithm is proposed to identify systemically important banks and other economic sectors, and a stress test is conducted. This study finds that China’s multi-layer financial network is sparse, and the distribution of transactions across financial markets is uneven. Regulatory authorities should support economic recovery and adjust the money supply, while banks should differentiate competition and manage risks better. Based on the PageRank index, this paper assesses the systemic importance of large commercial banks from the perspective of network structure, emphasizing the role of banks’ transaction behavior and market participation. Different industries and asset classes are also assessed, suggesting that increased attention should be paid to industry risks and regulatory oversight of bank investments. Finally, stress tests confirm that the improved PageRank algorithm is applicable within the multi-layer financial network, reinforcing the need for prudential supervision of the banking system and revealing that the degree of transaction concentration will affect the systemic importance of financial institutions.

Underwriters play a pivotal role in the IPO process. Information entropy, a tool for measuring the uncertainty and complexity of information, has been widely applied to various issues in complex networks. Information entropy can quantify the uncertainty and complexity of nodes in the network, providing a unique analytical perspective and methodological support for this study. This paper employs a bipartite network analysis method to construct the relationship network between underwriters and accounting firms, using the centrality of underwriters in the network as a measure of their influence to explore the impact of underwriters’ influence on the distribution of interests and audit outcomes. The findings indicate that a more pronounced influence of underwriters significantly increases the ratio of underwriting fees to audit fees. Higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals that companies underwritten by more influential underwriters experience a decline in audit quality. Finally, the study reveals that a well-structured audit committee governance and the rationalization of market sentiments can mitigate the negative impacts of underwriters’ influence. The innovation of this paper is that it enriches the content related to underwriters by constructing the relationship network between underwriters and accounting firms for the first time using a bipartite network through the lens of information entropy. This conclusion provides new directions for thinking about the motives and possibilities behind financial institutions’ cooperation, offering insights for market regulation and policy formulation.

We consider the problem of channel coding over multiterminal state-dependent channels in which neither transmitters nor receivers but only a helper node has a non-causal knowledge of the state. Such channel models arise in many emerging communication schemes. We start by investigating the parallel state-dependent channel with the same but differently scaled state corrupting the receivers. A cognitive helper knows the state in a non-causal manner and wishes to mitigate the interference that impacts the transmission between two transmit–receive pairs. Outer and inner bounds are derived. In our analysis, the channel parameters are partitioned into various cases, and segments on the capacity region boundary are characterized for each case. Furthermore, we show that for a particular set of channel parameters, the capacity region is entirely characterized. In the second part of this work, we address a similar scenario, but now each channel is corrupted by an independent state. We derive an inner bound using a coding scheme that integrates single-bin Gel’fand–Pinsker coding and Marton’s coding for the broadcast channel. We also derive an outer bound and further partition the channel parameters into several cases for which parts of the capacity region boundary are characterized.

This paper shows that the empirical distribution of cross-sectional analyst coverage in China’s stock markets follows an exponential law in a given month from 2011 to 2020. The findings hold in both the emerging (Shanghai) and the developed market (Hong Kong). Moreover, the unique distribution parameter (i.e., mean) is directly related to the amount of market-wide information. Average analyst coverage exhibits a significant negative predictive power for stock-market uncertainty, highlighting the role of security analysts in diminishing the total uncertainty. The exponential law can be derived from the maximum entropy principle (MEP). When analysts, who are constrained by average ability in generating information (i.e., the first-order moment), strive to maximize the amount of market-wide information, this objective yields the exponential distribution. Contrary to the conventional wisdom that security analysts specialize in the generation of firm-specific information, empirical findings suggest that analysts primarily produce market-wide information for 25 countries. Nevertheless, it remains unclear why cross-sectional analyst coverage reflects market-wide information, this paper provides an entropy-based explanation.

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

Since financial assets on stock exchanges were created, investors have sought to predict their future values. Currently, cryptocurrencies are also seen as assets. Machine learning is increasingly adopted to assist and automate investments. The main objective of this paper is to make daily predictions about the movement direction of financial time series through classification models, financial time series preprocessing methods, and feature selection with genetic algorithms. The target time series are Bitcoin, Ibovespa, and Vale. The methodology of this paper includes the following steps: collecting time series of financial assets; data preprocessing; feature selection with genetic algorithms; and the training and testing of machine learning models. The results were obtained by evaluating the models with the area under the ROC curve metric. For the best prediction models for Bitcoin, Ibovespa, and Vale, values of 0.61, 0.62, and 0.58 were obtained, respectively. In conclusion, the feature selection allowed the improvement of performance in most models, and the input series in the form of percentage variation obtained a good performance, although it was composed of fewer attributes in relation to the other sets tested.

A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie–Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie–Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov–Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models.

Federated learning (FL) is a distributed machine learning framework that enables scattered participants to collaboratively train machine learning models without revealing information to other participants. Due to its distributed nature, FL is susceptible to being manipulated by malicious clients. These malicious clients can launch backdoor attacks by contaminating local data or tampering with local model gradients, thereby damaging the global model. However, existing backdoor attacks in distributed scenarios have several vulnerabilities. For example, (1) the triggers in distributed backdoor attacks are mostly visible and easily perceivable by humans; (2) these triggers are mostly applied in the spatial domain, inevitably corrupting the semantic information of the contaminated pixels. To address these issues, this paper introduces a frequency-domain injection-based backdoor attack in FL. Specifically, by performing a Fourier transform, the trigger and the clean image are linearly mixed in the frequency domain, injecting the low-frequency information of the trigger into the clean image while preserving its semantic information. Experiments on multiple image classification datasets demonstrate that the attack method proposed in this paper is stealthier and more effective in FL scenarios compared to existing attack methods.

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is obtained through two approaches: one involves tracing out the environment from a bosonic eigenstate of the combined environment and system of interest (the empirical approach), while the other involves tracing out the environment from the mixed state of the combined environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism of information theory and empiricism of statistical mechanics are integrated into a common “infomechanical” framework.

Slope Entropy (SlpEn) is a novel method recently proposed in the field of time series entropy estimation. In addition to the well-known embedded dimension parameter, m, used in other methods, it applies two additional thresholds, denoted as δ and γ, to derive a symbolic representation of a data subsequence. The original paper introducing SlpEn provided some guidelines for recommended specific values of these two parameters, which have been successfully followed in subsequent studies. However, a deeper understanding of the role of these thresholds is necessary to explore the potential for further SlpEn optimisations. Some works have already addressed the role of δ, but in this paper, we extend this investigation to include the role of γ and explore the impact of using an asymmetric scheme to select threshold values. We conduct a comparative analysis between the standard SlpEn method as initially proposed and an optimised version obtained through a grid search to maximise signal classification performance based on SlpEn. The results confirm that the optimised version achieves higher time series classification accuracy, albeit at the cost of significantly increased computational complexity.

The paper makes a case that the current discussions on replicability and the abuse of significance testing have overlooked a more general contributor to the untrustworthiness of published empirical evidence, which is the uninformed and recipe-like implementation of statistical modeling and inference. It is argued that this contributes to the untrustworthiness problem in several different ways, including [a] statistical misspecification, [b] unwarranted evidential interpretations of frequentist inference results, and [c] questionable modeling strategies that rely on curve-fitting. What is more, the alternative proposals to replace or modify frequentist testing, including [i] replacing p-values with observed confidence intervals and effects sizes, and [ii] redefining statistical significance, will not address the untrustworthiness of evidence problem since they are equally vulnerable to [a]–[c]. The paper calls for distinguishing between unduly data-dependant ‘statistical results’, such as a point estimate, a p-value, and accept/reject H0, from ‘evidence for or against inferential claims’. The post-data severity (SEV) evaluation of the accept/reject H0 results, converts them into evidence for or against germane inferential claims. These claims can be used to address/elucidate several foundational issues, including (i) statistical vs. substantive significance, (ii) the large n problem, and (iii) the replicability of evidence. Also, the SEV perspective sheds light on the impertinence of the proposed alternatives [i]–[iii], and oppugns [iii] the alleged arbitrariness of framing H0 and H1 which is often exploited to undermine the credibility of frequentist testing.

To address the problem that traditional spectral clustering algorithms cannot obtain the complete structural information of networks, this paper proposes a spectral clustering community detection algorithm, PMIK-SC, based on the point-wise mutual information (PMI) graph kernel. The kernel is constructed according to the point-wise mutual information between nodes, which is then used as a proximity matrix to reconstruct the network and obtain the symmetric normalized Laplacian matrix. Finally, the network is partitioned by the eigendecomposition and eigenvector clustering of the Laplacian matrix. In addition, to determine the number of clusters during spectral clustering, this paper proposes a fast algorithm, BI-CNE, for estimating the number of communities. For a specific network, the algorithm first reconstructs the original network and then runs Monte Carlo sampling to estimate the number of communities by Bayesian inference. Experimental results show that the detection speed and accuracy of the algorithm are superior to other existing algorithms for estimating the number of communities. On this basis, the spectral clustering community detection algorithm PMIK-SC also has high accuracy and stability compared with other community detection algorithms and spectral clustering algorithms.

This paper studies the performance of location-based beamforming with the presence of artificial noise (AN). Secure transmission can be achieved using the location information of the user. However, the shape of the beam depends on the number of antennas used. When the scale of the antenna array is not sufficiently large, it becomes difficult to differentiate the performance between the legitimate user and eavesdroppers nearby. In this paper, we leverage AN to minimize the area near the user with eavesdropping risk. The impact of AN is considered for both the legitimate user and the eavesdropper. Closed-form expressions are derived for the expectations of the signal to interference plus noise ratios (SINRs) and the bit error rates. Then, a secure beamforming scheme is proposed to ensure a minimum SINR requirement for the legitimate user and minimize the SINR of the eavesdropper. Numerical results show that, even with a small number of antennas, the proposed beamforming scheme can effectively degrade the performance of eavesdroppers near the legitimate user.

This paper investigates the mathematical model of the quantum wavelength-division-multiplexing (WDM) network based on the entanglement distribution with the least required wavelengths and passive devices. By adequately utilizing wavelength multiplexers, demultiplexers, and star couplers, N wavelengths are enough to distribute the entanglement among each pair of N users. Moreover, the number of devices employed is reduced by substituting a waveguide grating router for multiplexers and demultiplexers. Furthermore, this study examines implementing the BBM92 quantum key distribution in an entangled-based quantum WDM network. The proposed scheme in this paper may be applied to potential applications such as teleportation in entangled-based quantum WDM networks.

A damaged stator vane can disrupt the circumferential symmetry of the design flow for turbine assemblies, which can lead to a low-engine-order (LEO) forced response of rotor blades. To help engineers be able to better address sudden vane damage failures, this paper conducts a mechanism analysis of the LEO forced response of rotor blades induced by a single damaged vane using an in-house computational fluid dynamic code (Hybrid Grid Aeroelasticity Environment). Firstly, it is found that the damaged vane introduces a family of LEO aerodynamic excitations with high amplitudes by full-annulus unsteady aeroelastic simulations of a single-stage turbine. In particular, the LEO forced response of the rotor blades excited by 3EO is 2.01 times higher than the resonance response excited by vane passing frequency, and the LEO resonance risk of the rotor blades is greatly increased. Then, by analyzing the flow characteristics of the wake and potential field of the stator row with a damaged vane, the localized high transient pressure in the notch cavity and the radial redistribution of the secondary vortex at the stator exit are the main sources of the low-order harmonic components in the flow field. Importantly, the interaction mechanisms in two regions with high LEO excitation amplitude on the rotor blade surface are revealed separately. Finally, an evaluation and comparison of a single damaged vane in terms of aerodynamic performance and LEO forced response was carried out. The results of this paper provide a good theoretical basis for engineers to effectively control the resonance response of rotor blades caused by a damaged stator vane in turbine design.

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.

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.

Quantum obfuscation is one of the important primitives in quantum cryptography that can be used to enhance the security of various quantum cryptographic schemes. The research on quantum obfuscation focuses mainly on the obfuscatability of quantum functions. As a primary quantum function, the quantum power function has led to the development of quantum obfuscation because it is applicable to construct new obfuscation applications such as quantum encryption schemes. However, the previous definition of quantum power functions is constrained and cannot be beneficial to the further construction of other quantum functions. Thus, it is essential to extend the definition of the basic quantum power function in a more general manner. In this paper, we provide a formal definition of two quantum power functions called generalized quantum power functions with coefficients, each of which is characterized by a leading coefficient and an exponent that corresponds to either a quantum or classical state, indicating the generality. The first is the quantum power function with a leading coefficient, and the second is the quantum n-th power function, which are both fundamental components of quantum polynomial functions. In addition, obfuscation schemes for the functions are constructed by quantum teleportation and quantum superdense coding, and demonstrations of their obfuscatability are also provided in this paper. This work establishes the fundamental basis for constructing more quantum functions that can be utilized for quantum obfuscation, therefore contributing to the theory of quantum obfuscation.

Federated learning, as one of the three main technical routes for privacy computing, has been widely studied and applied in both academia and industry. However, malicious nodes may tamper with the algorithm execution process or submit false learning results, which directly affects the performance of federated learning. In addition, learning nodes can easily obtain the global model. In practical applications, we would like to obtain the federated learning results only by the demand side. Unfortunately, no discussion on protecting the privacy of the global model is found in the existing research. As emerging cryptographic tools, the zero-knowledge virtual machine (ZKVM) and homomorphic encryption provide new ideas for the design of federated learning frameworks. We have introduced ZKVM for the first time, creating learning nodes as local computing provers. This provides execution integrity proofs for multi-class machine learning algorithms. Meanwhile, we discuss how to generate verifiable proofs for large-scale machine learning tasks under resource constraints. In addition, we implement the fully homomorphic encryption (FHE) scheme in ZKVM. We encrypt the model weights so that the federated learning nodes always collaborate in the ciphertext space. The real results can be obtained only after the demand side decrypts them using the private key. The innovativeness of this paper is demonstrated in the following aspects: 1. We introduce the ZKVM for the first time, which achieves zero-knowledge proofs (ZKP) for machine learning tasks with multiple classes and arbitrary scales. 2. We encrypt the global model, which protects the model privacy during local computation and transmission. 3. We propose and implement a new federated learning framework. We measure the verification costs under different federated learning rounds on the IRIS dataset. Despite the impact of homomorphic encryption on computational accuracy, the framework proposed in this paper achieves a satisfactory 90% model accuracy. Our framework is highly secure and is expected to further improve the overall efficiency as cryptographic tools continue to evolve.

Based on authorized patents of China’s artificial intelligence industry from 2013 to 2022, this paper constructs an Industry–University–Research institution (IUR) collaboration network and an Inter-Firm (IF) collaboration network and used the entropy weight method to take both the quantity and quality of patents into account to calculate the innovation performance of firms. Through the hierarchical clustering algorithm and classification and regression trees (CART) algorithm, in-depth analysis has been conducted on the intricate non-linear influence mechanisms between multiple variables and a firm’s innovation performance. The findings indicate the following: (1) Based on the network centrality (NC), structural hole (SH), collaboration breadth (CB), and collaboration depth (CD) of both IUR and IF collaboration networks, two types of focal firms are identified. (2) For different types of focal firms, the combinations of network characteristics affecting their innovation performance are various. (3) In the IUR collaboration network, focal firms with a wide range of heterogeneous collaborative partners can obtain high innovation performance. However, focal firms in the IF collaboration network can achieve the same aim by maintaining deep collaboration with other focal firms. This paper not only helps firms make scientific decisions for development but also provides valuable suggestions for government policymakers.