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• Notation of region of interest with critical contribution to failure probability is proposed. • A new active-learning function is devised based on the theory of information entropy. • Sufficient PC-Kriging accuracy in the range of the region of interest can be secured. • Computational burden can be significantly alleviated by the new active-learning function. • The proposed approach outperforms other adaptive surrogate-assisted simulation methods. A new active-learning function is developed to integrate Polynomial-Chaos Kriging with probability density evolution method. First, the relative importance of each representative point to the probability of failure is separately measured, thereby the region of interest is defined for the probability density evolution method, which covers the representative points exerting vital contributions to the probability of failure. Then, a new learning function called the probability density evolution method-oriented information entropy is readily devised based on the information theory, and the stopping condition is defined by specifying a threshold for the learning function values. Two examples are studied to show the efficacy of the adaptive Polynomial-Chaos Kriging probability density evolution method, and the recommended values of two key parameters associated with this new learning function are provided. Moreover, comprehensive comparisons are conducted against several existing reliability methods. The results highlight the advantage of the proposed active-learning function for structural reliability analysis in terms of both computational accuracy and efficiency. [ABSTRACT FROM AUTHOR]

A weighted track fusion algorithm is proposed to address the complexity of conventional sea monitoring data and the lack of effective and convenient monitoring methods. The new algorithm uses local information entropy and fuses data from the automatic identification system (AIS) and X-band radar. The new model employs ship monitoring data to detect five types of abnormal ship behavior: speed, course, position, ship spacing, and time abnormalities. The method weights various factors using a weight matrix built up from a distance difference matrix between different track points and calculations of the distance information entropy and residual degree using information entropy theory. We tested the proposed weighted track fusion algorithm the fusion accuracy using actual data for 2813 ships, AIS, and radar track points based on local information entropy. The resulting correlation accuracy was 95.54% for 2716 ship track points and a correlation accuracy of 90.72% for 97 ship tracks. The results indicate that the proposed algorithm is suitable for fusing multiple tracks and is more robust than traditional fusion methods. • A weighted track fusion algorithm is developed to address the complexity of conventional sea monitoring data and the lack of effective and convenient monitoring methods. • The new algorithm is based on local information entropy and the fusion of AIS and X-band radar data. • This paper proposes an innovative algorithm that compensates for incorrect speeds, headings, positions, and ship spacing; the accepted but time-abnormal mathematical model is also corrected. [ABSTRACT FROM AUTHOR]

In this article, the statistical properties of fermions in Rindler spacetime are studied, using Shannon's quantum information and thermodynamic properties. For this, the wave solutions and the compact expression for the energy spectrum associated with the Dirac equation in a non-inertial frame are found. It is shown that the non-inertial effect of the accelerated frame mimics an external potential in the Dirac equation and, in addition, allows the formation of bound states. Using the wave solutions, the quantum entropy of the system is analyzed in position and momentum space. Furthermore, with the energy spectrum, the thermodynamic properties of the system are analyzed. Considering the results of these statistical properties, it is possible to understand the influence of the acceleration of the non-inertial frame on quantum information. [ABSTRACT FROM AUTHOR]

[Display omitted] • Analytical expressions of the entropy index of river water quality dynamics are derived. • Spatial entropy index G x is a function of the negative half power of the Peclet number. • Expressions are independently validated by field data from tracer experiments. • Characteristics of G x under different riverine hydraulic situations are uncovered. • Expressions provide a convenient tool for theoretical analysis and engineering design. Information entropy theory has been largely applied in hydrology and water resource engineering. Recently, entropy theory has received significant attention for describing reactive solute mixing and transport processes in ground water and surface water and for its applications in water quality management. However, analytical expressions of the entropy index of riverine water quality dynamics are often not included in the literature. In this study, the analytical expressions of the spatial information entropy index (G x) in the 1D steady-state transport process under full-extent observation and tracking observations are derived after the definition of the system boundary and probability space. The expressions of G x were successfully validated by field data from two tracer experiments, and the different characteristics of G x under different riverine hydraulic situations were uncovered. The formula of G x shows a reasonable linkage with the Peclet number (Pe) in hydrodynamics. This indicates that G x is a physical quantity describing or linking to the real world more than a statistical index, and in practice, similar decision or management measurements based on entropy theory can be made for rivers with similar Pe conditions. Hydrologists will benefit in many ways from analytical expressions, such as theoretical analysis, quick calculation of the entropy index, preliminary engineering design, etc. A clearly defined example of maximum entropy time (t Gmax) and its application in water quality evaluation, monitoring optimization and pollution source identification are demonstrated. These new findings will provide a convenient tool for catchment water quality management. [ABSTRACT FROM AUTHOR]

The sampling method is widely used for the quantification of reactor physics analysis uncertainty, while the traditional statistical sampling methods often require a huge number of samples to ensure the stability of uncertainty quantification results. For this reason, a new two-step sampling scheme based on the combination of information entropy theory and moment matching technique is proposed for the quantification of the reactor physics uncertainty. We construct a convex programming model to optimize initial samples by simultaneously maximizing information entropy and minimizing moment deviations. The optimized samples can not only characterize the statistics of the real distribution better, but also control the information entropy with a smaller sample size. Moreover, a quantitative criterion for sample selection induced by the maximum entropy and moment matching is proposed. Finally, a series of empirical studies are carried out to show the capability and efficiency of the introduced two-step sampling method. • A quantitative criterion for selecting samples is introduced. • A convex optimization model is constructed to optimize the initial sample set. • A new two-step sampling method is proposed for uncertainty quantification. • The proposed method can reduce the sample size significantly. • The stability of the uncertain quantitative results is enhanced by the MEMM method. [ABSTRACT FROM AUTHOR]

Social collaborative design rooted in online platforms has emerged as a new paradigm for product innovation, with open and dynamic design elements bringing about external design resources and internal fluctuations. To guarantee sustainable operation of the design system, assessing the impact of the uncertainty of the external environment and randomness of the internal organization on the efficiency and stability of the system's operation is essential. To that end, this paper proposes a quantitative evolutionary analysis model based on information entropy theory to assess the benefits and drawbacks of system evolution by measuring the degree of development and harmony of the system, as well as to anticipate future evolutionary trajectories using a classical time-series prediction model. The accuracy and validity of the model were verified using 794,509 design data points accumulated over 10 years on the Zhubajie platform, the largest social collaborative design platform in China. In summary, our study provides a method for stakeholders to evaluate the evolutionary trend of the design ecosystem. Platform managers can utilize this model for controlling the operating state of the system to ensure safe and effective operation. [ABSTRACT FROM AUTHOR]

Information theory turns out to be an interesting tool for studying the consequences of Higgs observations to various new physics candidate theories by means of the information measure as the entropy of Higgs-Boson through its various detection modes at the Large Hadron Collider. The present article investigates the parameter space of a supersymmetric scenario where sfermions and one of the Higgs superfields are decoupled, while the gauginos, Higgsinos, and the remaining Higgs doublet are still allowed to be lighter. Our analysis reveals that this is quite a viable choice in the light of LHC discovery of a Higgs which resembles the SM Higgs-Boson and nothing else so far. While the supersymmetry breaking scale M S could be as high as 1011 GeV or so, the most preferred values of the M S and tan ⁡ β are found to be around 3.6 × 10 7 GeV and 41 respectively, which is also consistent with the relic abundance of the neutralino dark matter. The corresponding value of neutralino (m χ ˜ 1 0 ) LSP is estimated to be around 1.01 TeV. The preferred values of other parameters, namely, the Higgsino mass (μ) and gaugino mass parameters (M 1 and M 2) are found to be about 1.05 TeV, 1.74 TeV, and 2.57 TeV, respectively. [ABSTRACT FROM AUTHOR]

This article focuses on the adaptive Kriging metamodel-based reliability analysis for reducing a sequential number of calls of the complex original functions. To avoid the repetitive and tedious deterministic response analysis with stochastic simulation method (including Monte Carlo Simulation and its various improvement, such as importance sampling, subset simulation) in reliability analysis, herein a novel sequential sampling strategy related to Kriging metamodel is proposed, which is implemented based on information entropy theory. In addition, the generalized F-discrepancy method is simultaneously quoted to further optimize the candidate pool to improve the effectiveness of the training metamodel. Finally, a new structural reliability analysis method is proposed, which continuously reduces the number of deterministic analysis of structures without sacrificing accuracy. To highlight the applicability of the method and verify its accuracy and effectiveness, a series of typical examples are tested and compared, including highly nonlinear limit state functions, high-dimension performance function with analytic expressions and dynamic reliability analysis of nonlinear engineering structures subject to seismic excitation with implicit performance function. Numerical results show that significant computational savings and desired accuracy can be achieved when dealing with different reliability analysis cases. • The GF discrepancy is quoted to obtain the uniform representative points. • A learning function called IE-AK is proposed for structural reliability analysis. • A new reliability analysis method is constructed based on GF-discrepancy and IE-AK. [ABSTRACT FROM AUTHOR]

• We provide a new graph entropy design to measure the smoothness of graph feature manifold and conclude that motif-based information structures determine this graph entropy. • We propose a novel graph data augmentation strategy that protects not only the integrity of topological structure but also the integrity of motif-based information structures. Our strategy shows advantages in maintaining more graph entropy compared with other methods. • We demonstrate our model on different datasets, and experiments show that our work is superior in real-world node classification tasks. • Our approach significantly enhances the robustness of GCN and could alleviate the over-smoothing phenomenon to a certain extend. The Graph Convolutional Networks (GCN) proposed by Kipf and Welling is an effective model to improve semi-supervised learning of pattern recognition, but faces the obstacle of over-smoothing, which will weaken the representation ability of GCN. Recently some works are proposed to tackle above limitation by randomly perturbing graph topology or feature matrix to generate data augmentations as input for training. However, these operations inevitably do damage to the integrity of information structures and have to sacrifice the smoothness of feature manifold. In this paper, we first introduce a novel graph entropy definition as a measure to quantitatively evaluate the smoothness of a data manifold and then point out that this graph entropy is controlled by triangle motif-based information structures. Considering the preservation of graph entropy, we propose an effective strategy to generate randomly perturbed training data but maintain both graph topology and graph entropy. Extensive experiments have been conducted on real-world datasets and the results verify the effectiveness of our proposed method in improving semi-supervised node classification accuracy compared with a surge of baselines. Beyond that, our proposed approach could significantly enhance the robustness of training process for GCN. [ABSTRACT FROM AUTHOR]

Flavour-violating interactions of the stop-quarks are expected to provide an additional few GeV contributions to the Higgs-Boson mass, particularly when mix with scharm-quarks, thereby allowing reduced supersymmetry (SUSY) breaking scale compared to flavour-conserving constrained minimal supersymmetric Standard Model (CMSSM). Inspired by this, we analyse the interactions mentioned above in the context of CMSSM using the information entropy of the Higgs-Boson for a wider region of flavour-violating CMSSM parameter space (m 0 , m 1 / 2 , A 0 , tan ⁡ β , s g n (μ) , δ c t i j) , where δ c t i j represents the flavour-violating coupling of the top-quark with the charm-quark and i , j defining left and right chiralities of squarks. Our information-theoretic analysis of the model mentioned above reveals the most favourable values of (m 0 , m 1 / 2 , A 0 , tan ⁡ β , δ c t i j) as (4.30 TeV , 2.32 TeV , − 4.96 TeV , 22.8 , 0.037) and (4.16 TeV , 3.89 TeV , − 4.10 TeV , 19.4 , 0.039) for (i , j) = (L , R) and (R , L) , respectively, corresponding to the maximum entropy which suggest the SUSY breaking scale to be about 5 TeV, thereby allowing considerable low values of sparticles masses than the flavour-conserving CMSSM. [ABSTRACT FROM AUTHOR]

A spatial designer's search goal is sequentially updated during the spatial design exploration process. The design exploration process requires a proactive process that supports better-informed design decisions and refreshes the search direction to avoid being fixed; however, no study has been conducted to date. This paper describes a framework called CreativeSearch, which provides three types of guidance feedback by analyzing a spatial designer's design process. Particularly, by integrating the Bayesian Information Gain (BIG) framework and information entropy theory, CreativeSearch provides three types of guidance feedback. A user study conducted with 20 spatial designers confirmed that CreativeSearch supported them in exploring creative design ideas by lowering their mental load. Furthermore, CreativeSearch made designers proactive and supported their design decisions. The guidance feedback framework described in this paper is expected to extend the research on proactive and creative design exploration processes. • A new web-based spatial design exploration support system with the guidance feedback is proposed. • Three types of guidance feedback based on information theories are created. • The feedback is provided for suggesting a search direction and novel design ideas and lowering the user's mental load. • It helps spatial designers proactively explore creative design ideas and make better-informed decisions. [ABSTRACT FROM AUTHOR]

Codon usage bias is a well recognized phenomenon but the relative influence of its major causes: G+C content, mutational biases, and selection, are often difficult to disentangle. This paper presents methods to calculate modified effective codon numbers that allow the investigation of the sources of codon bias and how genes or organisms have their codon biases shaped. In particular, it demonstrates that variation in codon usage bias across organisms is likely driven more by likely mutational forces while the variation in codon usage bias within genomes is likely driven by codon selectional forces. [ABSTRACT FROM AUTHOR]

• For each line outage k there is a potential for cascading failure occurrence PCFO(k). • There is a functionality between pre-outage steady state operating data and PCFO(k). • For each line outage there are dominant operating variables affecting PCFO(k). • Using SVM a predictor denoted PPCFO(k) is design to evaluate PCFO(k). • Using PPCFO(k), the operator will be able to take preventive remedial actions. The process of cascading failures is one of the most important threats to the security of the power system, which can lead to a number of blackouts. Therefore, predicting the potential of cascading failure occurrence (PCFO) using pre-outages information is very essential. In this study, PCFO, associated to each line outage which is an important factor for causing blackout, is predicted before line outage using pre-outage steady state operating data (PSSOD). In the proposed scheme, support vector machine (SVM) is used as an intelligent predicting tool with information of dominant operating variables (DOV) as its input vector. DOV is a subset of PSSOD which have rich information about line criticalness and associated PCFO of the line outage. DOV can be identified using the joint mutual information (JMI) mathematical method based on the theory of mutual information and entropy between operating variables. In a real-time environment, the DOV associated to each line outage are collected by wide area measurement system (WAMS) in the power system control center (PSCC) and given to the SVM as an input vector for PCFO prediction. Therefore, the proposed scheme can be used as an alarming system for evaluating the PCFO of lines. By predicting PCFO, there is a chance for changing operating point of the power system from insecure mode to secure one by preventive actions. The proposed scheme has been implemented on IEEE 39-bus test system and its performance is validated with the desired results. [ABSTRACT FROM AUTHOR]

The utilization of shoreline resources is time-varying, establishing an evaluation mechanism of it is beneficial to the port development and management. An evaluation index system was forged in this paper from three perspectives of shoreline utilization, development of economic and traffic location. The synthetic weight was adopted based on the widely-used method of analytic hierarchy process (AHP) and information entropy theory combining the subjectivity and objectivity. The score of each index can be derived according to the mathematical relationships established by the quantification method instead of experts scoring. The evaluation index system was validated by the application of Lianyungang port in 2015. Lianyungang port in 2005 was then carried out to compare the variation with 2015. The numerical scores showed the shoreline resources utilization had improved from 5.30 to 5.98 with slight progress. Rizhao port was finally conducted with the score of 6.29 and the differences between two ports were analyzed. The evaluation method can be applied extensively into different ports of different times with generalizability and operability. It will contribute to the sustainability of shoreline resources and provide a scientific basis for the shoreline management and planning. [Display omitted] • The weights of the indexes are derived from the combination of AHP and information entropy which takes the advantages of subjectivity and objectivity • The indexes in the system are quantified, the relationships between the indexes' value and score are established by piecewise functions and probability distribution fitting • The evaluation method can be applied into different ports or different times without the process of experts scoring [ABSTRACT FROM AUTHOR]

• Data entropy has a functional data component and a data uncertainty component. • Functional entropy quantifies the effectiveness of a physical process. • The effectiveness of different processes can be compared because they can be quantified in the fundamental units of information. Information entropy is a fundamental property of measurement data and can be decomposed into functional and relative uncertainty components. The purpose of this paper is to mathematically isolate functional entropy and to demonstrate its application to model data. The equation for functional entropy is developed and its utility is demonstrated using hypothetical data that describes different processes that contribute to the same effect. Functional entropy assigns an effectiveness value to these processes in the fundamental units of information, which makes it a useful tool for comparing different data sets and their associated processes. [ABSTRACT FROM AUTHOR]

We report a non-clinical, mathematical method of studying genetic sequences based on the information theory. Our method involves calculating the information entropy spectrum of genomes by splitting them into "windows" containing a fixed number of nucleotides. The information entropy value of each window is computed using the m-block information entropy formula. We show that the information entropy spectrum of genomes contains sufficient information to allow detection of genetic mutations, as well as possibly predicting future ones. Our study indicates that the best m-block size is 2 and the optimal window size should contain more than 9, and less than 33 nucleotides. In order to implement the proposed technique, we created specialized software, which is freely available. Here we report the successful test of this method on the reference RNA sequence of the SARS-CoV-2 virus collected in Wuhan, Dec. 2019 (MN908947) and one of its randomly selected variants from Taiwan, Feb. 2020 (MT370518), displaying 7 mutations. • Information Entropy Spectra of genetic sequences. • Comparison of genomes using Information Entropy Spectra. • Detection of genetic mutations from Information Entropy Spectra. • New method to study mutations in DNA/RNA sequences. [ABSTRACT FROM AUTHOR]

The data of dissolved gas in oil analysis (DGA) is uncertain affected by the influence of transformer capacity and fault location, which makes transformer fault diagnosis model based on DGA has low accuracy. Therefore, we propose a hybrid feature selection method based on fuzzy information entropy, whereby optimizing the reasonable DGA feature parameter according to the feature information between the parameter and fault type, to reduce the influence of DGA data uncertainty on the fault diagnosis accuracy. Firstly, the characteristic relevance and redundancy functions are constructed based on fuzzy information entropy theory. Secondly, these functions are taken as the optimization objectives of binary-chaotic multi-objective particle swarm optimization algorithm(B-CMOPSO), to search for the feature subsets in the feature space composed of 46 DGA feature parameters. Then, the optimal feature subset is selected based on the simulation accuracy of ELM, SVM, Adaboost.M1 and BPNN on the feature subsets. Finally, 30 simulation experiments are carried out to compare with several multi-objective optimization algorithms, common Filter methods and common DGA feature combinations, and the rationality of the proposed method is verified by the t -test method. The results show that the 4 classifiers accuracy means is maximatily improved by 18.95%, 20.77%, 19.85% and 21.27% respectively compared with common DGA feature combinations, indicating that the optimal feature subset preserves more feature information and can effectively reduce the influence of DGA data uncertainty on diagnostic accuracy. [ABSTRACT FROM AUTHOR]

An information entropy based approach for the discharge measurements is evaluated for the gaging of the Isère river at the Grenoble university campus. Over a four month period, six discharge measurements were made using a vessel-mounted aDcp. Simultaneously, particle tracking velocimetry (PTV) from video images was used to estimate surface velocities. The surface velocities are projected along the regularly surveyed river section of the Isère-Campus gaging station. The vertical velocity profile at each stream-wise location is approximated by a 1D entropy profile. Information entropy 1D velocity vertical profile depends on two parameters which are fitted using aDcp and surface velocity measurements. The inclusion of the surface velocities reduces the dispersion of the estimated entropy parameters. The measurements show that the two parameters are linearly related with a slope that is stage dependent and thus, surface velocity dependent. From there, the information entropy theory for 1D velocity distribution offers a protocol by which surface velocities only are used to compute the discharges. The protocol is calibrated with both aDcp and surface velocity measurements. It is finally validated with several events during which only surface velocities are measured. For the high water flood event the estimated discharge falls within 2% of the one estimated with the rating curve of the gaging station. • river discharge evaluation with video surface velocities measurements alone. • velocity profile fitting with information entropy, aDcp and surface velocities. • the 2 entropy parameters linearly related and function of maximum surface velocity. • accuracy of the video-based discharge estimation as small as 2%. [ABSTRACT FROM AUTHOR]