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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&mdash, about 600 papers to JSCS and 2500 to Entropy&mdash, 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 &ldquo, season&rdquo, the predictability strength depends on the journal.

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

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

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. [...]

The following 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/).[...]

We investigate advantages and disadvantages of using Gazeau&ndash, Klauder coherent states for optical communication. In this short paper we show that using an alphabet consisting of coherent Gazeau&ndash, Klauder states related to a Kerr-type nonlinear oscillator instead of standard Perelomov coherent states results in lowering of the Helstrom bound for error probability in binary communication. We also discuss trace distance between Gazeau&ndash, Klauder coherent states and a standard coherent state as a quantifier of distinguishability of alphabets.

Recently, the concept of evaluating an unusually large learning effort of an adaptive system to detect novelties in the observed data was introduced. The present paper introduces a new measure of the learning effort of an adaptive system. The proposed method also uses adaptable parameters. Instead of a multi-scale enhanced approach, the generalized Pareto distribution is employed to estimate the probability of unusual updates, as well as for detecting novelties. This measure was successfully tested in various scenarios with (i) synthetic data, (ii) real time series datasets, and multiple adaptive filters and learning algorithms. The results of these experiments are presented.

Land speculation that occurs on the urban border can be very problematic to the healthy development of cities—critical to economic growth. Speculative land investors, concerned with profits from trading in landed property, can especially affect developing countries where regulation is often poorly controlled and overly bureaucratic. An investigation into the factors motivating land speculators operating in the urban fringe of the city of Shashemene, Ethiopia is examined. The paper, in addition to contributing to the literature, is the second-known attempt and extension of the authors’ pilot research to study the behavior of land speculators in the urban fringe of a growing Ethiopian city. A theoretical framework and conceptual breakdown are put together with historical reference to early land speculation examples. Two questionnaires were separately administered with a representative random sample of 159 members from the local land developer association (i.e., investors) and 24 senior officials from the study area. A principal component analysis categorized the most significant dynamics in controlling land speculation procurements. Results indicated motivational reasoning as the prime cause for speculative activities. Evidence indicated that land speculation is a critical dynamic for self-worth especially with business-oriented persons. Entropy, the disorder of the communicative data, suggests a possible rethinking of the way government should intervene in the urban property market. As such, developmental smart cities in Ethiopia must thoroughly consider the dynamisms of speculative activities and its effects on local housing as it moves forward−in the 2020s.

Extracting effective features from ship-radiated noise is an important way to improve the detection and recognition performance of passive sonar. Complexity features of ship-radiated noise have attracted increasing amounts of attention. However, the traditional definition of complexity based on entropy (information stored in the system) is not accurate. To this end, a new statistical complexity measure is proposed in this paper based on spectrum entropy and disequilibrium. Since the spectrum features are unique to the class of the ship, our method can distinguish different ships according to their location in the two-dimensional plane composed of complexity and spectrum entropy (CSEP). To weaken the influence of ocean ambient noise, the intrinsic time-scale decomposition (ITD) is applied to preprocess the data in this study. The effectiveness of the proposed method is validated through a classification experiment of four types of marine vessels. The recognition rate of the ITD-CSEP methodology achieved 94%, which is much higher than that of traditional feature extraction methods. Moreover, the ITD-CSEP is fast and parameter free. Hence, the method can be applied in the real time processing practical applications.

Recently, a novel concept of a non-probabilistic novelty detection measure, based on a multi-scale quantification of unusually large learning efforts of machine learning systems, was introduced as learning entropy (LE). The key finding with LE is that the learning effort of learning systems is quantifiable as a novelty measure for each individually observed data point of otherwise complex dynamic systems, while the model accuracy is not a necessary requirement for novelty detection. This brief paper extends the explanation of LE from the point of an informatics approach towards a cognitive (learning-based) information measure emphasizing the distinction from Shannon’s concept of probabilistic information. Fundamental derivations of learning entropy and of its practical estimations are recalled and further extended. The potentials, limitations, and, thus, the current challenges of LE are discussed.

This paper investigates the asymptotic properties of estimators obtained from the so called CVA (canonical variate analysis) subspace algorithm proposed by Larimore (1983) in the case when the data is generated using a minimal state space system containing unit roots at the seasonal frequencies such that the yearly difference is a stationary vector autoregressive moving average (VARMA) process. The empirically most important special cases of such data generating processes are the I(1) case as well as the case of seasonally integrated quarterly or monthly data. However, increasingly also datasets with a higher sampling rate such as hourly, daily or weekly observations are available, for example for electricity consumption. In these cases the vector error correction representation (VECM) of the vector autoregressive (VAR) model is not very helpful as it demands the parameterization of one matrix per seasonal unit root. Even for weekly series this amounts to 52 matrices using yearly periodicity, for hourly data this is prohibitive. For such processes estimation using quasi-maximum likelihood maximization is extremely hard since the Gaussian likelihood typically has many local maxima while the parameter space often is high-dimensional. Additionally estimating a large number of models to test hypotheses on the cointegrating rank at the various unit roots becomes practically impossible for weekly data, for example. This paper shows that in this setting CVA provides consistent estimators of the transfer function generating the data, making it a valuable initial estimator for subsequent quasi-likelihood maximization. Furthermore, the paper proposes new tests for the cointegrating rank at the seasonal frequencies, which are easy to compute and numerically robust, making the method suitable for automatic modeling. A simulation study demonstrates by example that for processes of moderate to large dimension the new tests may outperform traditional tests based on long VAR approximations in sample sizes typically found in quarterly macroeconomic data. Further simulations show that the unit root tests are robust with respect to different distributions for the innovations as well as with respect to GARCH-type conditional heteroskedasticity. Moreover, an application to Kaggle data on hourly electricity consumption by different American providers demonstrates the usefulness of the method for applications. Therefore the CVA algorithm provides a very useful initial guess for subsequent quasi maximum likelihood estimation and also delivers relevant information on the cointegrating ranks at the different unit root frequencies. It is thus a useful tool for example in (but not limited to) automatic modeling applications where a large number of time series involving a substantial number of variables need to be modelled in parallel.

In this paper, we present a novel blind signal detector based on the entropy of the power spectrum subband energy ratio (PSER), the detection performance of which is significantly better than that of the classical energy detector. This detector is a full power spectrum detection method, and does not require the noise variance or prior information about the signal to be detected. According to the analysis of the statistical characteristics of the power spectrum subband energy ratio, this paper proposes concepts such as interval probability, interval entropy, sample entropy, joint interval entropy, PSER entropy, and sample entropy variance. Based on the multinomial distribution, in this paper the formulas for calculating the PSER entropy and the variance of sample entropy in the case of pure noise are derived. Based on the mixture multinomial distribution, the formulas for calculating the PSER entropy and the variance of sample entropy in the case of the signals mixed with noise are also derived. Under the constant false alarm strategy, the detector based on the entropy of the power spectrum subband energy ratio is derived. The experimental results for the primary signal detection are consistent with the theoretical calculation results, which proves that the detection method is correct.

The construction sector plays an important role in a country’s economic development. The financial performance of a company is a good indicator of its financial health and status. In Malaysia, the government encourages the construction industry to develop an advanced infrastructure related to health, transport, education and housing. In view of the COVID-19 pandemic, the operations and financial performance of construction sector companies have been affected recently. Additionally, uncertainty plays a vital role in the multi-criteria decision-making (MCDM) process. Based on previous studies, there has been no comprehensive study conducted on the evaluation of the financial performance of construction companies by integrating entropy and fuzzy VIKOR models. Therefore, this paper aims to propose an MCDM model to evaluate and compare the financial performance of construction companies with an integrated entropy–fuzzy VIKOR model. A case study is carried out by evaluating the listed construction companies in Malaysia with the proposed model. The findings of this paper indicate that the company ECONBHD achieves the best financial performance over the study period. The significance of this paper is to determine the priority of the financial ratios and ranking of the construction companies with the proposed entropy–fuzzy VIKOR model.

Dempster-Shafer (DS) evidence theory is widely used in various fields of uncertain information processing, but it may produce counterintuitive results when dealing with conflicting data. Therefore, this paper proposes a new data fusion method which combines the Deng entropy and the negation of basic probability assignment (BPA). In this method, the uncertain degree in the original BPA and the negation of BPA are considered simultaneously. The degree of uncertainty of BPA and negation of BPA is measured by the Deng entropy, and the two uncertain measurement results are integrated as the final uncertainty degree of the evidence. This new method can not only deal with the data fusion of conflicting evidence, but it can also obtain more uncertain information through the negation of BPA, which is of great help to improve the accuracy of information processing and to reduce the loss of information. We apply it to numerical examples and fault diagnosis experiments to verify the effectiveness and superiority of the method. In addition, some open issues existing in current work, such as the limitations of the Dempster-Shafer theory (DST) under the open world assumption and the necessary properties of uncertainty measurement methods, are also discussed in this paper.

Active inference is a physics of life process theory of perception, action and learning that is applicable to natural and artificial agents. In this paper, active inference theory is related to different types of practice in social organization. Here, the term social organization is used to clarify that this paper does not encompass organization in biological systems. Rather, the paper addresses active inference in social organization that utilizes industrial engineering, quality management, and artificial intelligence alongside human intelligence. Social organization referred to in this paper can be in private companies, public institutions, other for-profit or not-for-profit organizations, and any combination of them. The relevance of active inference theory is explained in terms of variational free energy, prediction errors, generative models, and Markov blankets. Active inference theory is most relevant to the social organization of work that is highly repetitive. By contrast, there are more challenges involved in applying active inference theory for social organization of less repetitive endeavors such as one-of-a-kind projects. These challenges need to be addressed in order for active inference to provide a unifying framework for different types of social organization employing human and artificial intelligence.

The paper presents the generalization of the almost forty years of experience in the field of setting and solving the multiple criteria decision-making (MCDM) problems in various branches of a human activity under different types of uncertainties that inevitably accompany such problems. Based only on the pragmatic intentions, the authors avoid the detailed descriptions of the known methods for the decision-making, while instead focusing on the most frequently used mathematical tools and methodologies in the decision-making practice. Therefore, the paper may be classified as a special kind of illustrative review of the mathematical tools that are focused on applications and are the most used in the solutions of MCDM problems. As an illustrative example, a complete user-friendly computer implementation of such tools and methodology is presented with application to the simple “buying a cat” problem, which, however, possesses all the attributes of the hierarchical fuzzy MCDM task.

With the promotion of intelligent substations, more and more robots have been used in industrial sites. However, most of the meter reading methods are interfered with by the complex background environment, which makes it difficult to extract the meter area and pointer centerline, which is difficult to meet the actual needs of the substation. To solve the current problems of pointer meter reading for industrial use, this paper studies the automatic reading method of pointer instruments by putting forward the Faster Region-based Convolutional Network (Faster-RCNN) based object detection integrating with traditional computer vision. Firstly, the Faster-RCNN is used to detect the target instrument panel region. At the same time, the Poisson fusion method is proposed to expand the data set. The K-fold verification algorithm is used to optimize the quality of the data set, which solves the lack of quantity and low quality of the data set, and the accuracy of target detection is improved. Then, through some image processing methods, the image is preprocessed. Finally, the position of the centerline of the pointer is detected by the Hough transform, and the reading can be obtained. The evaluation of the algorithm performance shows that the method proposed in this paper is suitable for automatic reading of pointer meters in the substation environment, and provides a feasible idea for the target detection and reading of pointer meters.

About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy’s strengths and of limitations is essential to ensure the proper improvement of this research field.

Fractional-order chaos has complex dynamic behavior characteristics, so its application in secure communication has attracted much attention. Compared with the design of fractional-order chaos-based cipher, there are fewer researches on security analysis. This paper conducts a comprehensive security analysis of a color image encryption algorithm using a fractional-order hyperchaotic system (CIEA-FOHS). Experimental simulation based on excellent numerical statistical results supported that CIEA-FOHS is cryptographically secure. Yet, from the perspective of cryptanalysis, this paper found that CIEA-FOHS can be broken by a chosen-plaintext attack method owing to its some inherent security defects. Firstly, the diffusion part can be eliminated by choosing some special images with all the same pixel values. Secondly, the permutation-only part can be deciphered by some chosen plain images and the corresponding cipher images. Finally, using the equivalent diffusion and permutation keys obtained in the previous two steps, the original plain image can be recovered from a target cipher image. Theoretical analysis and experimental simulations show that the attack method is both effective and efficient. To enhance the security, some suggestions for improvement are given. The reported results would help the designers of chaotic cryptography pay more attention to the gap of complex chaotic system and secure cryptosystem.

Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code, without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.

Transportation of perishable foodstuff is an engineering and commercial activity ruled by an international Agreement (the ATP) that needs an updated regulation. Before addressing such updating, some analyses are required about the physics of the problem, in order to identify the optimum use of the available technologies and the advantages represented by new methodologies that could be enabled soon. It is worth pointing out that manufacturers of ATP equipment follow quite closely the prescriptions given by this Agreement. So, optimizing those prescriptions will generate a general optimization trend in this sector. In this paper, a coherent analysis on these subjects is presented, and a new coefficient is proposed for qualifying ATP units, and some new tests are also proposed for measuring that coefficient in an efficient and inexpensive way. These goals are justified in this paper as a contribution from basic physics to a particular domain of Thermal Engineering. The paper is intended to be a bridge from Science to Technology, which is a must to get optimum results in exploiting technical knowledge.

Anomaly detection refers to detecting data points, events, or behaviour that do not comply with expected or normal behaviour. For example, a typical problem related to anomaly detection on an industrial level is having little labelled data and a few run-to-failure examples, making it challenging to develop reliable and accurate prognostics and health management systems for fault detection and identification. Certain machine learning approaches for anomaly detection require normal data to train, which reduces the need for historical data with fault labels, where the main task is to differentiate between normal and anomalous behaviour. Several reconstruction-based deep learning approaches are explored in this work and compared towards detecting anomalies in air compressors. Anomalies in such systems are not point-anomalies, but instead, an increasing deviation from the normal condition as the system components start to degrade. In this paper, a descriptive range of the deviation based on the reconstruction-based techniques is proposed. Most anomaly detection approaches are considered black box models, predicting whether an event should be considered an anomaly or not. This paper proposes a method for increasing the transparency and explainability of reconstruction-based anomaly detection to indicate which parts of a system contribute to the deviation from expected behaviour. The results show that the proposed methods detect abnormal behaviour in air compressors accurately and reliably and indicate why it deviates. The proposed approach is capable of detecting faults without the need for historical examples of similar faults. The proposed method for explainable anomaly detection is crucial to any prognostics and health management (PHM) system due to its purpose of detecting deviations and identifying causes. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

As a fundamental infrastructure of energy supply for future society, energy Internet (EI) can achieve clean energy generation, conversion, storage and consumption in a more economic and safer way. This paper demonstrates the technology principle of advanced adiabatic compressed air energy storage system (AA-CAES), as well as analysis of the technical characteristics of AA-CAES. Furthermore, we propose an overall architectural scheme of a clean energy router (CER) based on AA-CAES. The storage and mutual conversion mechanism of wind and solar power, heating, and other clean energy were designed to provide a key technological solution for the coordination and comprehensive utilization of various clean energies for the EI. Therefore, the design of the CER scheme and its efficiency were analyzed based on a thermodynamic simulation model of AA-CAES. Meanwhile, we explored the energy conversion mechanism of the CER and improved its overall efficiency. The CER based on AA-CAES proposed in this paper can provide a reference for efficient comprehensive energy utilization (CEU) (93.6%) in regions with abundant wind and solar energy sources.

In the present paper, we study a diauxic growth that can be generated by a class of model at the mesoscopic scale. Although the diauxic growth can be related to the macroscopic scale, similarly to the logistic scale, one may ask whether models on mesoscopic or microscopic scales may lead to such a behavior. The present paper is the first step towards the developing of the mesoscopic models that lead to a diauxic growth at the macroscopic scale. We propose various nonlinear mesoscopic models conservative or not that lead directly to some diauxic growths.

Conventional biomechanical analyses of human movement have been generally derived from linear mathematics. While these methods can be useful in many situations, they fail to describe the behavior of the human body systems that are predominately nonlinear. For this reason, nonlinear analyses have become more prevalent in recent literature. These analytical techniques are typically investigated using concepts related to variability, stability, complexity, and adaptability. This review aims to investigate the application of nonlinear metrics to assess postural stability. A systematic review was conducted of papers published from 2009 to 2019. Databases searched were PubMed, Google Scholar, Science-Direct and EBSCO. The main inclusion consisted of: Sample entropy, fractal dimension, Lyapunov exponent used as nonlinear measures, and assessment of the variability of the center of pressure during standing using force plate. Following screening, 43 articles out of the initial 1100 were reviewed including 33 articles on sample entropy, 10 articles on fractal dimension, and 4 papers on the Lyapunov exponent. This systematic study shows the reductions in postural regularity related to aging and the disease or injures in the adaptive capabilities of the movement system and how the predictability changes with different task constraints.

Many single-particle tracking data related to the motion in crowded environments exhibit anomalous diffusion behavior. This phenomenon can be described by different theoretical models. In this paper, fractional Brownian motion (FBM) was examined as the exemplary Gaussian process with fractional dynamics. The autocovariance function (ACVF) is a function that determines completely the Gaussian process. In the case of experimental data with anomalous dynamics, the main problem is first to recognize the type of anomaly and then to reconstruct properly the physical rules governing such a phenomenon. The challenge is to identify the process from short trajectory inputs. Various approaches to address this problem can be found in the literature, e.g., theoretical properties of the sample ACVF for a given process. This method is effective, however, it does not utilize all of the information contained in the sample ACVF for a given trajectory, i.e., only values of statistics for selected lags are used for identification. An evolution of this approach is proposed in this paper, where the process is determined based on the knowledge extracted from the ACVF. The designed method is intuitive and it uses information directly available in a new fashion. Moreover, the knowledge retrieval from the sample ACVF vector is enhanced with a learning-based scheme operating on the most informative subset of available lags, which is proven to be an effective encoder of the properties inherited in complex data. Finally, the robustness of the proposed algorithm for FBM is demonstrated with the use of Monte Carlo simulations.

This paper presents an extensive and practical study of the estimation of stable channel bank shape and dimensions using the maximum entropy principle. The transverse slope (St) distribution of threshold channel bank cross-sections satisfies the properties of the probability space. The entropy of St is subject to two constraint conditions, and the principle of maximum entropy must be applied to find the least biased probability distribution. Accordingly, the Lagrange multiplier (&lambda, ) as a critical parameter in the entropy equation is calculated numerically based on the maximum entropy principle. The main goal of the present paper is the investigation of the hydraulic parameters influence governing the mean transverse slope [...]

Selective assembly is the method of obtaining high precision assemblies from relatively low precision components. For precision instruments, the geometric error on mating surface is an important factor affecting assembly accuracy. Different from the traditional selective assembly method, this paper proposes an optimization method of selective assembly for shafts and holes based on relative entropy and dynamic programming. In this method, relative entropy is applied to evaluate the clearance uniformity between shafts and holes, and dynamic programming is used to optimize selective assembly of batches of shafts and holes. In this paper, the case studied has 8 shafts and 20 holes, which need to be assembled into 8 products. The results show that optimal combinations are selected, which provide new insights into selective assembly optimization and lay the foundation for selective assembly of multi-batch precision parts.

In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state. Only employing such an assumption, the thermodynamic driving force of crystallization and the surface tension can be determined in the way it is commonly performed. The present paper is devoted to the theoretical treatment of a different situation, when nucleation proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for such cases, we need adequate expressions for the thermodynamic driving force and the surface tension accounting for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. In the present paper, such relations are derived. They are expressed via deviations of structural order parameters from their equilibrium values. Relaxation processes result in changes of the structural order parameters with time. As a consequence, the thermodynamic driving force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, also become time-dependent. We show that this scenario may be realized in the vicinity and below the glass transition temperature, and it may occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process) in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations for a model system. The theory is successfully applied to the interpretation of experimental data. Several further consequences of this newly developed theoretical treatment are discussed in detail. In line with our previous investigations, we reconfirm that only when the characteristic times of structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal nucleation, elastic stresses evolving in nucleation may significantly affect this process. Advancing the methods of theoretical analysis of elastic stress effects on nucleation, for the first time expressions are derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation on nucleation, is now available. As one of its applications, this theoretical treatment provides a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer glasses (the so-called &ldquo, breakdown&rdquo, of CNT at temperatures below the temperature of the maximum steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes of the thermodynamic driving force, the surface tension, and the work of critical cluster formation, in the necessity to account of structural relaxation and stress effects) than assumed so far. If these effects are properly accounted for, then CNT appropriately describes both the initial, the intermediate, and the final states of crystal nucleation.

This paper presents a dynamic deoxyribonucleic acid (DNA) image encryption based on Secure Hash Algorithm-512 (SHA-512), having the structure of two rounds of permutation&ndash, diffusion, by employing two chaotic systems, dynamic DNA coding, DNA sequencing operations, and conditional shifting. We employed the SHA-512 algorithm to generate a 512-bit hash value and later utilized this value with the natural DNA sequence to calculate the initial values for the chaotic systems and the eight intermittent parameters. We implemented a two-dimensional rectangular transform (2D-RT) on the permutation. We used four-wing chaotic systems and Lorentz systems to generate chaotic sequences and recombined three channel matrices and chaotic matrices with intermittent parameters. We calculated hamming distances of DNA matrices, updated the initial values of two chaotic systems, and generated the corresponding chaotic matrices to complete the diffusion operation. After diffusion, we decoded and decomposed the DNA matrices, and then scrambled and merged these matrices into an encrypted image. According to experiments, the encryption method in this paper not only was able to withstand statistical attacks, plaintext attacks, brute-force attacks, and a host of other attacks, but also could reduce the complexity of the algorithm because it adopted DNA sequencing operations that were different from traditional DNA sequencing operations.

The paper introduces a new concept of social entropy and a new concept of social order, both based on the normative framework of society. From these two concepts, typologies (logical and historical) of societies are inferred and examined in their basic features. To these ends, some well-known concepts such as entropy, order, system, network, synergy, norm, autopoieticity, fetality, and complexity are revisited and placed into an integrated framework. The core body of this paper addresses the structure and the mechanism of social entropy, understood as an institutionally working counterpart of social order. Finally, this paper concludes that social entropy is an artefact, like society itself, and acts through people&rsquo, s behavior.

Incomplete data are unavoidable for survival analysis as well as life testing, so more and more researchers are beginning to study censoring data. This paper discusses and considers the estimation of unknown parameters featured by the Kumaraswamy distribution on the condition of generalized progressive hybrid censoring scheme. Estimation of reliability is also considered in this paper. To begin with, the maximum likelihood estimators are derived. In addition, Bayesian estimators under not only symmetric but also asymmetric loss functions, like general entropy, squared error as well as linex loss function, are also offered. Since the Bayesian estimates fail to be of explicit computation, Lindley approximation, as well as the Tierney and Kadane method, is employed to obtain the Bayesian estimates. A simulation research is conducted for the comparison of the effectiveness of the proposed estimators. A real-life example is employed for illustration.

A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few examples have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear examples of reaction–subdiffusion systems, based on, equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These examples illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.

This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in earlier publications. As objects of analysis we use impossible figures of the kind created by the Penroses and Escher. We make no assumptions as to how an impossible figure is perceived, taking it instead as a fixed physical object allowing one of several deterministic descriptions. Systems of epistemic random variables are obtained by probabilistically mixing these deterministic systems. This probabilistic mixture reflects our uncertainty or lack of knowledge rather than random variability in the frequentist sense., Entropy 2020, 22(9), 981; format of the published paper differs from this preprint

Approximate Entropy and especially Sample Entropy are recently frequently used algorithms for calculating the measure of complexity of a time series. A lesser known fact is that there are also accelerated modifications of these two algorithms, namely Fast Approximate Entropy and Fast Sample Entropy. All these algorithms are effectively implemented in the R software package TSEntropies. This paper contains not only an explanation of all these algorithms, but also the principle of their acceleration. Furthermore, the paper contains a description of the functions of this software package and their parameters, as well as simple examples of using this software package to calculate these measures of complexity of an artificial time series and the time series of a complex real-world system represented by the course of supercomputer infrastructure power consumption. These time series were also used to test the speed of this package and to compare its speed with another R package pracma. The results show that TSEntropies is up to 100 times faster than pracma and another important result is that the computational times of the new Fast Approximate Entropy and Fast Sample Entropy algorithms are up to 500 times lower than the computational times of their original versions. At the very end of this paper, the possible use of this software package TSEntropies is proposed. Web of Science 22 8 art. no. 863

This paper presents theory and simulation of viscous dissipation in evolving interfaces and membranes under kinematic conditions, known as astigmatic flow, ubiquitous during growth processes in nature. The essential aim is to characterize and explain the underlying connections between curvedness and shape evolution and the rate of entropy production due to viscous bending and torsion rates. The membrane dissipation model used here is known as the Boussinesq-Scriven fluid model. Since the standard approaches in morphological evolution are based on the average, Gaussian and deviatoric curvatures, which comingle shape with curvedness, this paper introduces a novel decoupled approach whereby shape is independent of curvedness. In this curvedness-shape landscape, the entropy production surface under constant homogeneous normal velocity decays with growth but oscillates with shape changes. Saddles and spheres are minima while cylindrical patches are maxima. The astigmatic flow trajectories on the entropy production surface, show that only cylinders and spheres grow under the constant shape. Small deviations from cylindrical shapes evolve towards spheres or saddles depending on the initial condition, where dissipation rates decrease. Taken together the results and analysis provide novel and significant relations between shape evolution and viscous dissipation in deforming viscous membrane and surfaces.

The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics.

In 1980, Ruff and Kanamori (RK) published an article on seismicity and the subduction zones where they reported that the largest characteristic earthquake (Mw) of a subduction zone is correlated with two geophysical quantities: the rate of convergence between the oceanic and continental plates (V) and the age of the corresponding subducting oceanic lithosphere (T). This proposal was synthetized by using an empirical graph (RK-diagram) that includes the variables Mw, V and T. We have recently published an article that reports that there are some common characteristics between real seismicity, sandpaper experiments and a critically self-organized spring-block model. In that paper, among several results we qualitatively recovered a RK-diagram type constructed with equivalent synthetic quantities corresponding to Mw, V and T. In the present paper, we improve that synthetic RK-diagram by means of a simple model relating the elastic ratio &gamma, of a critically self-organized spring-block model with the age of a lithospheric downgoing plate. In addition, we extend the RK-diagram by including some large subduction earthquakes occurred after 1980. Similar behavior to the former RK-diagram is observed and its SOC synthetic counterpart is obtained.

The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from normal working conditions during the identification task is minimized. In this paper, the adaptive filtering (AF) scheme for plant model parameter estimation is proposed. The experimental results are obtained using the nonlinear interacting water tanks system. The adaptive filtering is expressed by minimizing the error between the system and the plant model outputs subject to the white noise signal affecting system output. This measurement error is quantified by the comparison of Minimum Error Entropy Renyi (MEER), Least Entropy Like (LEL), Least Squares (LS), and Least Absolute Deviation (LAD) estimators, respectively. The plant model parameters were obtained using sequential quadratic programming (SQP) algorithm. The robustness tests for the double-tank water system parameter estimators are performed using the ellipsoidal confidence regions. The effectiveness analysis for the above-mentioned estimators relies on the total number of iterations and the number of function evaluation comparisons. The main contribution of this paper is the evaluation of different estimation methods for the nonlinear system identification using various excitation signals. The proposed empirical study is illustrated by the numerical examples, and the simulation results are discussed.

The comprehensive utilization technology of combined cooling, heating and power (CCHP) systems is the leading edge of renewable and sustainable energy research. In this paper, we propose a novel CCHP system based on a hybrid trigenerative compressed air energy storage system (HT-CAES), which can meet various forms of energy demand. A comprehensive thermodynamic model of the HT-CAES has been carried out, and a thermodynamic performance analysis with energy and exergy methods has been done. Furthermore, a sensitivity analysis and assessment capacity for CHP is investigated by the critical parameters effected on the performance of the HT-CAES. The results indicate that round-trip efficiency, electricity storage efficiency, and exergy efficiency can reach 73%, 53.6%, and 50.6%, respectively. Therefore, the system proposed in this paper has high efficiency and flexibility to jointly supply multiple energy to meet demands, so it has broad prospects in regions with abundant solar energy resource.

Due to telecommunications market saturation, it is very important for telco operators to always have fresh insights into their customer&rsquo, s dynamics. In that regard, social network analytics and its application with graph theory can be very useful. In this paper we analyze a social network that is represented by a large telco network graph and perform clustering of its nodes by studying a broad set of metrics, e.g., node in/out degree, first and second order influence, eigenvector, authority and hub values. This paper demonstrates that it is possible to identify some important nodes in our social network (graph) that are vital regarding churn prediction. We show that if such a node leaves a monitored telco operator, customers that frequently interact with that specific node will be more prone to leave the monitored telco operator network as well, thus, by analyzing existing churn and previous call patterns, we proactively predict new customers that will probably churn. The churn prediction results are quantified by using top decile lift metrics. The proposed method is general enough to be readily adopted in any field where homophilic or friendship connections can be assumed as a potential churn driver.

This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet, is a generalization of an orthonormal basis. A lot of applications are modeled by non-negative functions, taking this into account in this paper, we consider framelet systems generated using some refinable non-negative functions, namely, B-splines. The FVIEs we considered were reduced to a set of linear system of equations and were solved numerically based on a collocation discretization technique. We present many important examples of FVIEs for which accurate and efficient numerical solutions have been accomplished and the numerical results converge very rapidly to the exact ones.

Intuitionistic fuzzy distance measurement is an effective method to study multi-attribute emergency decision-making (MAEDM) problems. Unfortunately, the traditional intuitionistic fuzzy distance measurement method cannot accurately reflect the difference between membership and non-membership data, where it is easy to cause information confusion. Therefore, from the intuitionistic fuzzy number (IFN), this paper constructs a decision-making model based on intuitionistic fuzzy cross-entropy and a comprehensive grey correlation analysis algorithm. For the MAEDM problems of completely unknown and partially known attribute weights, this method establishes a grey correlation analysis algorithm based on the objective evaluation value and subjective preference value of decision makers (DMs), which makes up for the shortcomings of traditional model information loss and greatly improves the accuracy of MAEDM. Finally, taking the Wenchuan Earthquake on May 12th 2008 as a case study, this paper constructs and solves the ranking problem of shelters. Through the sensitivity comparison analysis, when the grey resolution coefficient increases from 0.4 to 1.0, the ranking result of building shelters remains stable. Compared to the traditional intuitionistic fuzzy distance, this method is shown to be more reliable.

Due to the existence of marine environmental noise, coupled with the instability of underwater acoustic channel, ship-radiated noise (SRN) signals detected by sensors tend to suffer noise pollution as well as distortion caused by the transmission medium, making the denoising of the raw detected signals the new focus in the field of underwater acoustic target recognition. In view of this, this paper presents a novel hybrid feature extraction scheme integrating improved variational mode decomposition (IVMD), normalized maximal information coefficient (norMIC) and permutation entropy (PE) for SRN signals. Firstly, the IVMD method is employed to decompose the SRN signals into a number of finite intrinsic mode functions (IMFs). The noise IMFs are then filtered out by a denoising method before PE extraction. Next, the MIC between each retained IMF and the raw SRN signal and PE of retained IMFs are calculated, respectively. After this, the norMICs are used to weigh the PE values of the retained IMFs and the sum of the weighted PE results is regarded as the classification parameter. Finally, the feature vectors are fed into the particle swarm optimization-based support vector machine multi-class classifier (PSO-SVM) to identify different types of SRN samples. The experimental results have indicated that the classification accuracy of the proposed method is as high as 99.1667%, which is much higher than that of other currently existing methods. Hence, the method proposed in this paper is more suitable for feature extraction of SRN signals in practical application.

Dempster&ndash, Shafer theory has been widely used in many applications, especially in the measurement of information uncertainty. However, under the D-S theory, how to use the belief entropy to measure the uncertainty is still an open issue. In this paper, we list some significant properties. The main contribution of this paper is to propose a new entropy, for which some properties are discussed. Our new model has two components. The first is Nguyen entropy. The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. In addition, under certain conditions, the new belief entropy can be transformed into Shannon entropy. Compared with the others, the new entropy considers the impact of FOD. Through some numerical examples and simulation, the proposed belief entropy is proven to be able to measure uncertainty accurately.

This paper mainly focuses on the problem of lossy compression storage based on the data value that represents the subjective assessment of users when the storage size is still not enough after the conventional lossless data compression. To this end, we transform this problem to an optimization, which pursues the least importance-weighted reconstruction error in data reconstruction within limited total storage size, where the importance is adopted to characterize the data value from the viewpoint of users. Based on it, this paper puts forward an optimal allocation strategy in the storage of digital data by the exponential distortion measurement, which can make rational use of all the storage space. In fact, the theoretical results show that it is a kind of restrictive water-filling. It also characterizes the trade-off between the relative weighted reconstruction error and the available storage size. Consequently, if a relatively small part of total data value is allowed to lose, this strategy will improve the performance of data compression. Furthermore, this paper also presents that both the users&rsquo, preferences and the special characteristics of data distribution can trigger the small-probability event scenarios where only a fraction of data can cover the vast majority of users&rsquo, interests. Whether it is for one of the reasons above, the data with highly clustered message importance is beneficial to compression storage. In contrast, from the perspective of optimal storage space allocation based on data value, the data with a uniform information distribution is incompressible, which is consistent with that in the information theory.

The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of $f$-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong~data-processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains., Comment: Published in the Entropy journal, May 18, 2020. Journal version (open access) is available at https://www.mdpi.com/1099-4300/22/5/563

During recent years our society has often been exposed to coherent information waves of high amplitudes. These are waves of huge social energy. Often they are of destructive character, a kind of information tsunami. However, they can also carry positive improvements in human society, as waves of decision-making matching rational recommendations of societal institutes. The main distinguishing features of these waves are their high amplitude, coherence (homogeneous character of social actions generated by them), and short time needed for their generation and relaxation. Such waves can be treated as large-scale exhibitions of the bandwagon effect. We show that this socio-psychic phenomenon can be modeled based on the recently developed social laser theory. This theory can be used to model stimulated amplification of coherent social actions. &ldquo, Actions&rdquo, are treated very generally, from mass protests to votes and other collective decisions, such as, e.g., acceptance (often unconscious) of some societal recommendations. In this paper, we concentrate on the theory of laser resonators, physical vs. social. For the latter, we analyze in detail the functioning of Internet-based echo chambers. Their main purpose is increasing of the power of the quantum information field as well as its coherence. Of course, the bandwagon effect is well known and well studied in social psychology. However, social laser theory gives the possibility to model it by using general formalism of quantum field theory. The paper contains the minimum of mathematics and it can be read by researchers working in psychological, cognitive, social, and political sciences, it might also be interesting for experts in information theory and artificial intelligence.

In practice, to build a machine learning model of big data, one needs to tune model parameters. The process of parameter tuning involves extremely time-consuming and computationally expensive grid search. However, the theory of statistical physics provides techniques allowing us to optimize this process. The paper shows that a function of the output of topic modeling demonstrates self-similar behavior under variation of the number of clusters. Such behavior allows using a renormalization technique. A combination of renormalization procedure with the Renyi entropy approach allows for quick searching of the optimal number of topics. In this paper, the renormalization procedure is developed for the probabilistic Latent Semantic Analysis (pLSA), and the Latent Dirichlet Allocation model with variational Expectation&ndash, Maximization algorithm (VLDA) and the Latent Dirichlet Allocation model with granulated Gibbs sampling procedure (GLDA). The experiments were conducted on two test datasets with a known number of topics in two different languages and on one unlabeled test dataset with an unknown number of topics. The paper shows that the renormalization procedure allows for finding an approximation of the optimal number of topics at least 30 times faster than the grid search without significant loss of quality.

Soft-matter systems when driven out of equilibrium often give rise to structures that usually lie in between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh&ndash, B&eacute, nard convection system which when driven out of equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out of equilibrium. This study, thus acts as a foundation for modeling a complex system as a two-state system, where the states: order and disorder can coexist as the system is driven away from equilibrium.