Entropy

Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a widely used algorithm for exploratory clustering applications. Despite the DBSCAN algorithm being considered an unsupervised pattern recognition method, it has two parameters that must be tuned prior to the clustering process in order to reduce uncertainties, the minimum number of points in a clustering segmentation MinPts, and the radii around selected points from a specific dataset Eps. This article presents the performance of a clustering hybrid algorithm for automatically grouping datasets into a two-dimensional space using the well-known algorithm DBSCAN. Here, the function nearest neighbor and a genetic algorithm were used for the automation of parameters MinPts and Eps. Furthermore, the Factor Analysis (FA) method was defined for pre-processing through a dimensionality reduction of high-dimensional datasets with dimensions greater than two. Finally, the performance of the clustering algorithm called FA+GA-DBSCAN was evaluated using artificial datasets. In addition, the precision and Entropy of the clustering hybrid algorithm were measured, which showed there was less probability of error in clustering the most condensed datasets. Full article

Financial economic research has extensively documented the fact that the impact of the arrival of negative news on stock prices is more intense than that of the arrival of positive news. The authors of the present study followed an innovative approach based on the utilization of two artificial intelligence algorithms to test that asymmetric response effect. Methods: The first algorithm was used to web-scrape the social network Twitter to download the top tweets of the 24 largest market-capitalized publicly traded companies in the world during the last decade. A second algorithm was then used to analyze the contents of the tweets, converting that information into social sentiment indexes and building a time series for each considered company. After comparing the social sentiment indexes’ movements with the daily closing stock price of individual companies using transfer entropy, our estimations confirmed that the intensity of the impact of negative and positive news on the daily stock prices is statistically different, as well as that the intensity with which negative news affects stock prices is greater than that of positive news. The results support the idea of the asymmetric effect that negative sentiment has a greater effect than positive sentiment, and these results were confirmed with the EGARCH model. Full article

Feature selection (FS) is a vital step in data mining and machine learning, especially for analyzing the data in high-dimensional feature space. Gene expression data usually consist of a few samples characterized by high-dimensional feature space. As a result, they are not suitable to be processed by simple methods, such as the filter-based method. In this study, we propose a novel feature selection algorithm based on the Explosion Gravitation Field Algorithm, called EGFAFS. To reduce the dimensions of the feature space to acceptable dimensions, we constructed a recommended feature pool by a series of Random Forests based on the Gini index. Furthermore, by paying more attention to the features in the recommended feature pool, we can find the best subset more efficiently. To verify the performance of EGFAFS for FS, we tested EGFAFS on eight gene expression datasets compared with four heuristic-based FS methods (GA, PSO, SA, and DE) and four other FS methods (Boruta, HSICLasso, DNN-FS, and EGSG). The results show that EGFAFS has better performance for FS on gene expression data in terms of evaluation metrics, having more than the other eight FS algorithms. The genes selected by EGFAGS play an essential role in the differential co-expression network and some biological functions further demonstrate the success of EGFAFS for solving FS problems on gene expression data. Full article

To promote the application of entropy concepts in uncertainty analysis of water resources complex system, a quantitative evaluation and obstacle factor diagnosis model of agricultural drought disaster risk was proposed using connection number and information entropy. The results applied to Suzhou City showed that the agricultural drought disaster risks in Suzhou during 2007–2017 were all in middle-risk status, while it presented a decreasing trend from 2010. The information entropy values of the difference degree item bI were markedly lower than those of the difference degree b, indicating that bI provided more information in the evaluation process. Furthermore, the status of drought damage sensitivity and drought hazard were improved significantly. Nevertheless, high exposure to drought and weak drought resistance capacity seriously impeded the reduction of risk. Thus, the key to decreasing risk was to maintain the level of damage sensitivity, while the difficulties were to reduce exposure and enhance resistance. In addition, the percentage of the agricultural population, population density, and percentage of effective irrigation area were the main obstacle factors of risk and also the key points of risk control in Suzhou. In short, the results suggest that the evaluation and diagnosis method is effective and conducive to regional drought disaster risk management. Full article

One of the biggest challenges for the fault diagnosis research of industrial robots is that the normal data is far more than the fault data; that is, the data is imbalanced. The traditional diagnosis approaches of industrial robots are more biased toward the majority categories, which makes the diagnosis accuracy of the minority categories decrease. To solve the imbalanced problem, the traditional algorithm is improved by using cost-sensitive learning, single-class learning and other approaches. However, these algorithms also have a series of problems. For instance, it is difficult to estimate the true misclassification cost, overfitting, and long computation time. Therefore, a fault diagnosis approach for industrial robots, based on the Multiclass Mahalanobis-Taguchi system (MMTS), is proposed in this article. It can be classified the categories by measuring the deviation degree from the sample to the reference space, which is more suitable for classifying imbalanced data. The accuracy, G-mean and F-measure are used to verify the effectiveness of the proposed approach on an industrial robot platform. The experimental results show that the proposed approach’s accuracy, F-measure and G-mean improves by an average of 20.74%, 12.85% and 21.68%, compared with the other five traditional approaches when the imbalance ratio is 9. With the increase in the imbalance ratio, the proposed approach has better stability than the traditional algorithms. Full article

Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of thermodynamic quantities in nonequilibrium systems to their quantum origins, namely, to the quantum uncertainty principles. Our results enable us to make this categorical statement: For Gaussian systems, thermodynamic functions are functionals of the Robertson-Schrödinger uncertainty function, which is always non-negative for quantum systems, but not necessarily so for classical systems. Here, quantum refers to noncommutativity of the canonical operator pairs. From the nonequilibrium free energy, we succeeded in deriving several inequalities between certain thermodynamic quantities. They assume the same forms as those in conventional thermodynamics, but these are nonequilibrium in nature and they hold for all times and at strong coupling. In addition we show that a fluctuation-dissipation inequality exists at all times in the nonequilibrium dynamics of the system. For nonequilibrium systems which relax to an equilibrium state at late times, this fluctuation-dissipation inequality leads to the Robertson-Schrödinger uncertainty principle with the help of the Cauchy-Schwarz inequality. This work provides the microscopic quantum basis to certain important thermodynamic properties of macroscopic nonequilibrium systems. Full article

Magnetic resonance imaging (MRI) plays an important role in disease diagnosis. The noise that appears in MRI images is commonly governed by a Rician distribution. The bendlets system is a second-order shearlet transform with bent elements. Thus, the bendlets system is a powerful tool with which to represent images with curve contours, such as the brain MRI images, sparsely. By means of the characteristic of bendlets, an adaptive denoising method for microsection images with Rician noise is proposed. In this method, the curve contour and texture can be identified as low-frequency components, which is not the case with other methods, such as the wavelet, shearlet, and so on. It is well known that the Rician noise belongs to a high-frequency channel, so it can be easily removed without blurring the clarity of the contour. Compared with other algorithms, such as the shearlet transform, block matching 3D, bilateral filtering, and Wiener filtering, the values of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) obtained by the proposed method are better than those of other methods. Full article

In order to automatically perceive the user’s dietary nutritional information in the smart home environment, this paper proposes a dietary nutritional information autonomous perception method based on machine vision in smart homes. Firstly, we proposed a food-recognition algorithm based on YOLOv5 to monitor the user’s dietary intake using the social robot. Secondly, in order to obtain the nutritional composition of the user’s dietary intake, we calibrated the weight of food ingredients and designed the method for the calculation of food nutritional composition; then, we proposed a dietary nutritional information autonomous perception method based on machine vision (DNPM) that supports the quantitative analysis of nutritional composition. Finally, the proposed algorithm was tested on the self-expanded dataset CFNet-34 based on the Chinese food dataset ChineseFoodNet. The test results show that the average recognition accuracy of the food-recognition algorithm based on YOLOv5 is 89.7%, showing good accuracy and robustness. According to the performance test results of the dietary nutritional information autonomous perception system in smart homes, the average nutritional composition perception accuracy of the system was 90.1%, the response time was less than 6 ms, and the speed was higher than 18 fps, showing excellent robustness and nutritional composition perception performance. Full article

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-$\phi$-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices. Full article

Owing to the loss of effective information and incomplete feature extraction caused by the convolution and pooling operations in a convolution subsampling network, the accuracy and speed of current speech processing architectures based on the conformer model are influenced because the shallow features of speech signals are not completely extracted. To solve these problems, in this study, we researched a method that used a capsule network to improve the accuracy of feature extraction in a conformer-based model, and then, we proposed a new end-to-end model architecture for speech recognition. First, to improve the accuracy of speech feature extraction, a capsule network with a dynamic routing mechanism was introduced into the conformer model; thus, the structural information in speech was preserved, and it was input to the conformer blocks via sequestered vectors; the learning ability of the conformed-based model was significantly enhanced using dynamic weight updating. Second, a residual network was added to the capsule blocks, thus, the mapping ability of our model was improved and the training difficulty was reduced. Furthermore, the bi-transformer model was adopted in the decoding network to promote the consistency of the hypotheses in different directions through bidirectional modeling. Finally, the effectiveness and robustness of the proposed model were verified against different types of recognition models by performing multiple sets of experiments. The experimental results demonstrated that our speech recognition model achieved a lower word error rate without a language model because of the higher accuracy of speech feature extraction and learning using our model architecture with a capsule network. Furthermore, our model architecture benefited from the advantage of the capsule network and the conformer encoder, and also has potential for other speech-related applications. Full article

As two main steelmaking materials, iron ore and scrap steel have different price lead-lag relationships (PLRs) on midstream and downstream steel products in China. The relationships also differ as the time scale varies. In this study, we compare the price influences of two important steel materials on midstream and downstream steel products at different time scales. First, we utilize the maximal overlap discrete wavelet transform (MODWT) method to decompose the original steel materials and products price series into short-term, midterm, and long-term time scale series. Then, we introduce the cross-correlation and Podobnik test method to calculate and test the price lead-lag relationships (PLRs) between two steel materials and 16 steel products. Finally, we construct 12 price lead-lag relationship networks and choose network indicators to present the price influence of the two materials at different time scales. We find that first, most scrap steel and steel products prices fluctuate at the same time lag order, while iron ore leads most steel products price for one day. Second, products that exist in the downstream industry chain usually lead to iron ore. Third, as the time scale becomes longer, the lead relationships from steel materials to steel products become closer. Full article

The physical implementation of the continuous-time memristor makes it widely used in chaotic circuits, whereas the discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize the $Ti{O}_2$ memristor model, and the discretized model also meets the three fingerprints characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling of the proposed $Ti{O}_2$ memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete $Ti{O}_2$ memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication. Full article

Recent work has shown that people use temporal information including order, delay, and variability to infer causality between events. In this study, we build on this work by investigating the role of time in dynamic systems, where causes take continuous values and also continually influence their effects. Recent studies of learning in these systems explored short interactions in a setting with rapidly evolving dynamics and modeled people as relying on simpler, resource-limited strategies to grapple with the stream of information. A natural question that arises from such an account is whether interacting with systems that unfold more slowly might reduce the systematic errors that result from these strategies. Paradoxically, we find that slowing the task indeed reduced the frequency of one type of error, albeit at the cost of increasing the overall error rate. To explain these results we posit that human learners analyze continuous dynamics into discrete events and use the observed relationships between events to draw conclusions about causal structure. We formalize this intuition in terms of a novel Causal Event Abstraction model and show that this model indeed captures the observed pattern of errors. We comment on the implications these results have for causal cognition. Full article

Describing the permanence of cultural objects is an important step in understanding societal trends. A relatively novel cultural object is the video game, which is an interactive media, that is, the player is an active contributor to the overall experience. This article aims to investigate video game permanence in collective memory using their popularity as a proxy, employing data based on the Steam platform from July 2012 to December 2020. The objectives include characterizing the database; studying the growth of players, games, and game categories; providing a model for the relative popularity distribution; and applying this model in three strata, global, major categories, and among categories. We detected linear growth trends in the number of players and the number of categories, and an exponential trend in the number of games released. Furthermore, we verified that lognormal distributions, emerging from multiplicative processes, provide a first approximation for the popularity in all strata. In addition, we proposed an improvement via Box–Cox transformations with similar parameters (from $-0.12$ ($95\%$ CI: $-0.18$, $-0.07$) to $-0.04$ ($95\%$ CI: $-0.08$, 0)). We were able to justify this improved model by interpreting the magnitude of each Box–Cox parameter as a measure of memory effects. Full article

Estimating sentence-like units and sentence boundaries in human language is an important task in the context of natural language understanding. While this topic has been considered using a range of techniques, including rule-based approaches and supervised and unsupervised algorithms, a common aspect of these methods is that they inherently rely on a priori knowledge of human language in one form or another. Recently we have been exploring synthetic languages based on the concept of modeling behaviors using emergent languages. These synthetic languages are characterized by a small alphabet and limited vocabulary and grammatical structure. A particular challenge for synthetic languages is that there is generally no a priori language model available, which limits the use of many natural language processing methods. In this paper, we are interested in exploring how it may be possible to discover natural `chunks’ in synthetic language sequences in terms of sentence-like units. The problem is how to do this with no linguistic or semantic language model. Our approach is to consider the problem from the perspective of information theory. We extend the basis of information geometry and propose a new concept, which we term information topology, to model the incremental flow of information in natural sequences. We introduce an information topology view of the incremental information and incremental tangent angle of the Wasserstein-1 distance of the probabilistic symbolic language input. It is not suggested as a fully viable alternative for sentence boundary detection per se but provides a new conceptual method for estimating the structure and natural limits of information flow in language sequences but without any semantic knowledge. We consider relevant existing performance metrics such as the F-measure and indicate limitations, leading to the introduction of a new information-theoretic global performance based on modeled distributions. Although the methodology is not proposed for human language sentence detection, we provide some examples using human language corpora where potentially useful results are shown. The proposed model shows potential advantages for overcoming difficulties due to the disambiguation of complex language and potential improvements for human language methods. Full article

It has been clarified that words in written texts are classified into two groups called Type-I and Type-II words. The Type-I words are words that exhibit long-range dynamic correlations in written texts while the Type-II words do not show any type of dynamic correlations. Although the stochastic process of yielding Type-II words has been clarified to be a superposition of Poisson point processes with various intensities, there is no definitive model for Type-I words. In this study, we introduce a Hawkes process, which is known as a kind of self-exciting point process, as a candidate for the stochastic process that governs yielding Type-I words; i.e., the purpose of this study is to establish that the Hawkes process is useful to model occurrence patterns of Type-I words in real written texts. The relation between the Hawkes process and an existing model for Type-I words, in which hierarchical structures of written texts are considered to play a central role in yielding dynamic correlations, will also be discussed. Full article

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs. Full article