Two-dimensional cross entropy multi-threshold image segmentation based on improved BBO algorithm

In order to improve the global search ability of biogeography-based optimization(BBO)algorithm in multi-threshold image segmentation,a multi-threshold image segmentation based on improved BBO algorithm is proposed.When using BBO algorithm to optimize threshold,firstly,the elitist selection operator is used to retain the optimal set of solutions.Secondly,a migration strategy based on fusion of good solution and pending solution is introduced to reduce premature convergence and invalid migration of traditional migration operations.Thirdly,to reduce the blindness of traditional mutation operations,a mutation operation through binary computation is created.Then,it is applied to the multi-threshold image segmentation of two-dimensional cross entropy.Finally,this method is used to segment the typical image and compared with two-dimensional multi-threshold segmentation based on particle swarm optimization algorithm and the two-dimensional multi-threshold image segmentation based on standard BBO algorithm.The experimental results show that the method has good convergence stability,it can effectively shorten the time of iteration,and the optimization performance is better than the standard BBO algorithm.

Using Cross Entropy as a Performance Metric for Quantifying Uncertainty in DNN Image Classifiers: An Application to Classification of Lung Cancer on CT Images

Cross entropy is a measure in machine learning and deep learning that assesses the difference between predicted and actual probability distributions. In this study, we propose cross entropy as a performance evaluation metric for image classifier models and apply it to the CT image classification of lung cancer. A convolutional neural network is employed as the deep neural network (DNN) image classifier, with the residual network (ResNet) 50 chosen as the DNN archi-tecture. The image data used comprise a lung CT image set. Two classification models are built from datasets with varying amounts of data, and lung cancer is categorized into four classes using 10-fold cross-validation. Furthermore, we employ t-distributed stochastic neighbor embedding to visually explain the data distribution after classification. Experimental results demonstrate that cross en-tropy is a highly useful metric for evaluating the reliability of image classifier models. It is noted that for a more comprehensive evaluation of model perfor-mance, combining with other evaluation metrics is considered essential. .

Performance Comparison of Vision Transformer- and CNN-Based Image Classification Using Cross Entropy: A Preliminary Application to Lung Cancer Discrimination from CT Images

This study evaluates the performance and reliability of a vision transformer (ViT) compared to convolutional neural networks (CNNs) using the ResNet50 model in classifying lung cancer from CT images into four categories: lung adenocarcinoma (LUAD), lung squamous cell carcinoma (LUSC), large cell carcinoma (LULC), and normal. Although CNNs have made significant advancements in medical imaging, their limited capacity to capture long-range dependencies has led to the exploration of ViTs, which leverage self-attention mechanisms for a more comprehensive global understanding of images. The study utilized a dataset of 748 lung CT images to train both models with standardized input sizes, assessing their performance through conventional metrics—accuracy, precision, recall, F1 score, specificity, and AUC—as well as cross entropy, a novel metric for evaluating prediction uncertainty. Both models achieved similar accuracy rates (95%), with ViT demonstrating a slight edge over ResNet50 in precision and F1 scores for specific classes. However, ResNet50 exhibited higher recall for LULC, indicating fewer missed cases. Cross entropy analysis showed that the ViT model had lower average uncertainty, particularly in the LUAD, Normal, and LUSC classes, compared to ResNet50. This finding suggests that ViT predictions are generally more reliable, though ResNet50 performed better for LULC. The study underscores that accuracy alone is insufficient for model comparison, as cross entropy offers deeper insights into the reliability and confidence of model predictions. The results highlight the importance of incorporating cross entropy alongside traditional metrics for a more comprehensive evaluation of deep learning models in medical image classification, providing a nuanced understanding of their performance and reliability. While the ViT outperformed the CNN-based ResNet50 in lung cancer classification based on cross-entropy values, the performance differences were minor and may not hold clinical significance. Therefore, it may be premature to consider replacing CNNs with ViTs in this specific application.

Image Thresholding Using Two-Dimensional Tsallis Cross Entropy Based on Either Chaotic Particle Swarm Optimization or Decomposition

The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.

Two-dimensional horizontal visibility graph analysis of human brain aging on gray matter

Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

An improved cross entropy algorithm for steelmaking-continuous casting production scheduling with complicated technological routes

In order to increase productivity and reduce energy consumption of steelmaking-continuous casting(SCC) production process, especially with complicated technological routes, the cross entropy(CE) method was adopted to optimize the SCC production scheduling(SCCPS) problem. Based on the CE method, a matrix encoding scheme was proposed and a backward decoding method was used to generate a reasonable schedule. To describe the distribution of the solution space, a probability distribution model was built and used to generate individuals. In addition, the probability updating mechanism of the probability distribution model was proposed which helps to find the optimal individual gradually. Because of the poor stability and premature convergence of the standard cross entropy(SCE) algorithm, the improved cross entropy(ICE) algorithm was proposed with the following improvements: individual generation mechanism combined with heuristic rules, retention mechanism of the optimal individual, local search mechanism and dynamic parameters of the algorithm. Simulation experiments validate that the CE method is effective in solving the SCCPS problem with complicated technological routes and the ICE algorithm proposed has superior performance to the SCE algorithm and the genetic algorithm(GA).

A Cross Entropy-Genetic Algorithm for m-Machines No-Wait Job-ShopScheduling Problem

No-wait job-shop scheduling (NWJSS) problem is one of the classical scheduling problems that exist on many kinds of industry with no-wait constraint, such as metal working, plastic, chemical, and food industries. Several methods have been proposed to solve this problem, both exact (i.e. integer programming) and metaheuristic methods. Cross entropy (CE), as a new metaheuristic, can be an alternative method to solve NWJSS problem. This method has been used in combinatorial optimization, as well as multi-external optimization and rare-event simulation. On these problems, CE implementation results an optimal value with less computational time in average. However, using original CE to solve large scale NWJSS requires high computational time. Considering this shortcoming, this paper proposed a hybrid of cross entropy with genetic algorithm (GA), called CEGA, on m-machines NWJSS. The results are compared with other metaheuritics: Genetic Algorithm-Simulated Annealing (GASA) and hybrid tabu search. The results showed that CEGA providing better or at least equal makespans in comparison with the other two methods.

Introduce a Novel PCA Method for Intuitionistic Fuzzy Sets Based on Cross Entropy

In this paper, a new method for Principal Component Analysis in intuitionistic fuzzy situations has been proposed. This approach is based on cross entropy as an information index. This new method is a useful method for data reduction for situations in which data are not exact. The inexactness in the situations assumed here is due to fuzziness and missing data information, so that we have two functions (membership and non-membership). Thus, method proposed here is suitable for Atanasov’s Intuitionistic Fuzzy Sets (A-IFSs) in which we have an uncertainty due to a mixture of fuzziness and missing data information. For the demonstration of the application of the method, we have used an example and have presented a conclusion.

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon＇s information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.

Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises

It is shown how the cross-correlation time and strength of coloured cross-correlated white noises can set an upper bound for the time derivative of entropy in a nonequilibrium system. The value of upper bound can be calculated directly based on the Schwartz inequality principle and the Fokker-Planck equation of the dynamical system driven by coloured cross-correlated white noises. The present calculations can be used to interpret the interplay of the dissipative constant and cross-correlation time and strength of coloured cross-correlated white noises on the upper bound.

Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems

In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx（F）EntM and MaxMinx（F）EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx（F）Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as （MinMinx（F）Ent）m and （MaxMinx（F）Ent）m distributions.

Improved Cross Entropy Algorithm for Steelmaking Continuous Casting Production Scheduling with Minimum Power Consumption

A matrix encoding scheme for the steelmaking continuous casting( SCC) production scheduling( SCCPS) problem and the corresponding decoding method are proposed. Based on it,a cross entropy( CE) method is adopted and an improved cross entropy( ICE) algorithm is proposed to solve the SCCPS problem to minimize total power consumption. To describe the distribution of the solution space of the CE method,a probability model is built and used to generate individuals by sampling and a probability updating mechanism is introduced to trace the promising samples. For the ICE algorithm,some samples are generated by the heuristic rules for the shortest makespan due to the relation between the makespan and the total power consumption,which can reduce the search space greatly. The optimal sample in each iteration is retained through a retention mechanism to ensure that the historical optimal sample is not lost so as to improve the efficiency and global convergence. A local search procedure is carried out on a part of better samples so as to improve the local exploitation capability of the ICE algorithm and get a better result. The parameter setting is investigated by the Taguchi method of design-of-experiment. A number of simulation experiments are implemented to validate the effectiveness of the ICE algorithm in solving the SCCPS problem and also the superiority of the ICE algorithm is verified through the comparison with the standard cross entropy( SCE) algorithm.

Cross Entropy Based Sparse Logistic Regression to Identify Phenotype-Related Mutations in Methicillin-Resistant <i>Staphylococcus aureus</i>

Emergence of drug resistant bacteria is one of the serious problems in today’s public health. However, the relationship between genomic mutation of bacteria and the phenotypic difference of them is still unclear. In this paper, based on the mutation information in whole genome sequences of 96 MRSA strains, two kinds of phenotypes (pathogenicity and drug resistance) were learnt and predicted by machine learning algorithms. As a result of effective feature selection by cross entropy based sparse logistic regression, these phenotypes could be predicted in sufficiently high accuracy (100% and 97.87%, respectively) with less than 10 features. It means that we could develop a novel rapid test method in the future for checking MRSA phenotypes.

Application of Weighted Cross-Entropy Loss Function in Intrusion Detection

The deep learning model is overfitted and the accuracy of the test set is reduced when the deep learning model is trained in the network intrusion detection parameters, due to the traditional loss function convergence problem. Firstly, we utilize a network model architecture combining Gelu activation function and deep neural network;Secondly, the cross-entropy loss function is improved to a weighted cross entropy loss function, and at last it is applied to intrusion detection to improve the accuracy of intrusion detection. In order to compare the effect of the experiment, the KDDcup99 data set, which is commonly used in intrusion detection, is selected as the experimental data and use accuracy, precision, recall and F1-score as evaluation parameters. The experimental results show that the model using the weighted cross-entropy loss function combined with the Gelu activation function under the deep neural network architecture improves the evaluation parameters by about 2% compared with the ordinary cross-entropy loss function model. Experiments prove that the weighted cross-entropy loss function can enhance the model’s ability to discriminate samples.

On the Thermodynamics of a Two-Dimensional Electron Gas with Non-Parabolic Dispersion

A thermodynamic density of states, electron density in the subband and the entropy of the gas as function of the temperature and the total two-dimensional electron density are studied. Semiconductor conduction band dispersion is described by the simplified Kane model. Numerical simulation shows that with an increase in the total electron concentration, thermodynamic density of states at low temperatures changes abruptly and smoothes jumps at high temperatures. This change manifests itself in the peculiar thermodynamic characteristics. The results are used to interpret existing experimental data.

Variance Reduction Technique for Estimating Value-at-Risk based on the Cross - Entropy

Value-at-Risk （VaR） estimation via Monte Carlo （MC） simulation is studied here. The variance reduction technique is proposed in order to speed up MC algorithm. The algorithm for estimating the probability of high portfolio losses （more general risk measure） based on the Cross - Entropy importance sampling is developed. This algorithm can easily be applied in any light- or heavy-tailed case without an extra adaptation. Besides, it does not loose in the performance in comparison to other known methods. A numerical study in both cases is performed and the variance reduction rate is compared with other known methods. The problem of VaR estimation using procedures for estimating the probability of high portfolio losses is also discussed.

Incremental clustering algorithm via crossentropy

A new incremental clustering method is presented, which partitions dynamic data sets by mapping data points in high dimension space into low dimension space based on （fuzzy） cross-entropy（CE）. This algorithm is divided into two parts： initial clustering process and incremental clustering process. The former calculates fuzzy cross-entropy or cross-entropy of one point relafive to others and a hierachical method based on cross-entropy is used for clustering static data sets. Moreover, it has the lower time complexity. The latter assigns new points to the suitable cluster by calculating membership of data point to existed centers based on the cross-entropy measure. Experimental compafisons show the proposed methood has lower time complexity than common methods in the large-scale data situations cr dynamic work environments.

基于模糊交叉熵与TOPSIS的碳审计风险评估

审计在促进“双碳”目标实现的过程中发挥着重要的监督与评价作用,有效规范了企业的碳排放行为,推动了企业生产方式的绿色转型。当前,我国的碳审计发展尚处起步阶段,存在着诸如制度不健全、碳数据核算困难、碳审计人才缺乏等一系列问题,多种因素的叠加使得碳审计工作面临着极大的风险与挑战。在文献梳理的基础上,本文依托传统风险导向审计理论,首先从环境风险、固有风险、控制风险、检查风险四个层面建立碳审计风险评估指标体系;其次,借助模糊交叉熵和TOPSIS算法构架新型的碳审计风险评估模型,探索碳审计风险评估模型的运行步骤,明晰风险评估模型中的决策方案排序策略;再次,通过对特定案例的深入分析,阐释模糊交叉熵和TOPSIS风险评估模型在碳审计风险评估中的具体应用流程,全方位探究风险评估模型中各类运算结果的分析方法;最后,针对碳审计所面临的各种风险,相应地从碳审计模式设计、双碳大数据中心构建、人才队伍建设三个方面提出管理碳审计检查风险的措施与建议。有关研究思路和结论能够为审计组织如何发现碳审计存在的关键风险因素、衡量碳审计风险水平、评价和控制碳审计风险提供理论支持。

基于组合赋权-DEA的跨境铁路外部环境风险评价

研究目的:跨境铁路大多穿越不同国家,铁路沿线的自然、社会环境条件复杂多变,给跨境铁路外部环境安全带来巨大威胁。为保障跨境铁路平稳运行,采用组合赋权-DEA方法在全面识别跨境铁路沿线风险的基础上进行风险评价,旨在为跨境铁路风险管理工作提供借鉴。研究结论:(1)全面识别跨境铁路沿线外部环境风险,从自然环境与社会环境方面共选取30个风险指标构建跨境铁路外部环境风险评价指标体系,结合AHP-熵权法对各风险指标组合赋权;(2)应用基于DEA的风险评价方法,以各风险指标发生的概率和后果为变量,对跨境铁路外部环境风险进行评价和排序;(3)研究结果显示,跨境铁路侵限风险应予以重点关注,安保区内违法生产经营次之;(4)本文研究可为跨境铁路沿线外部环境安全管理工作提供新的思路,保障跨境铁路运输更加平稳高效运行。