Whole Perfect Vectors and Fermat’s Last Theorem

A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.

Research on Node Classification Based on Joint Weighted Node Vectors

Node of network has lots of information, such as topology, text and label information. Therefore, node classification is an open issue. Recently, one vector of node is directly connected at the end of another vector. However, this method actually obtains the performance by extending dimensions and considering that the text and structural information are one-to-one, which is obviously unreasonable. Regarding this issue, a method by weighting vectors is proposed in this paper. Three methods, negative logarithm, modulus and sigmoid function are used to weight-trained vectors, then recombine the weighted vectors and put them into the SVM classifier for evaluation output. By comparing three different weighting methods, the results showed that using negative logarithm weighting achieved better results than the other two using modulus and sigmoid function weighting, and was superior to directly concatenating vectors in the same dimension.

Photovoltaic Models Parameters Estimation Based on Weighted Mean of Vectors

Renewable energy sources are gaining popularity,particularly photovoltaic energy as a clean energy source.This is evident in the advancement of scientific research aimed at improving solar cell performance.Due to the non-linear nature of the photovoltaic cell,modeling solar cells and extracting their parameters is one of the most important challenges in this discipline.As a result,the use of optimization algorithms to solve this problem is expanding and evolving at a rapid rate.In this paper,a weIghted meaN oF vectOrs algorithm(INFO)that calculates the weighted mean for a set of vectors in the search space has been applied to estimate the parameters of solar cells in an efficient and precise way.In each generation,the INFO utilizes three operations to update the vectors’locations:updating rules,vector merging,and local search.The INFO is applied to estimate the parameters of static models such as single and double diodes,as well as dynamic models such as integral and fractional models.The outcomes of all applications are examined and compared to several recent algorithms.As well as the results are evaluated through statistical analysis.The results analyzed supported the proposed algorithm’s efficiency,accuracy,and durability when compared to recent optimization algorithms.

Some Results for Exact Support Recovery of Block Joint Sparse Matrix via Block Multiple Measurement Vectors Algorithm

Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.

Norms of Dual Complex Vectors and Dual Complex Matrices

In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.

On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors

This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.

A HEVC Video Steganalysis Method Using the Optimality of Motion Vector Prediction

Among steganalysis techniques,detection against MV(motion vector)domain-based video steganography in the HEVC(High Efficiency Video Coding)standard remains a challenging issue.For the purpose of improving the detection performance,this paper proposes a steganalysis method that can perfectly detectMV-based steganography in HEVC.Firstly,we define the local optimality of MVP(Motion Vector Prediction)based on the technology of AMVP(Advanced Motion Vector Prediction).Secondly,we analyze that in HEVC video,message embedding either usingMVP index orMVD(Motion Vector Difference)may destroy the above optimality of MVP.And then,we define the optimal rate of MVP as a steganalysis feature.Finally,we conduct steganalysis detection experiments on two general datasets for three popular steganographymethods and compare the performance with four state-ofthe-art steganalysis methods.The experimental results demonstrate the effectiveness of the proposed feature set.Furthermore,our method stands out for its practical applicability,requiring no model training and exhibiting low computational complexity,making it a viable solution for real-world scenarios.

A semantic vector map-based approach for aircraft positioning in GNSS/GPS denied large-scale environment

Accurate positioning is one of the essential requirements for numerous applications of remote sensing data,especially in the event of a noisy or unreliable satellite signal.Toward this end,we present a novel framework for aircraft geo-localization in a large range that only requires a downward-facing monocular camera,an altimeter,a compass,and an open-source Vector Map(VMAP).The algorithm combines the matching and particle filter methods.Shape vector and correlation between two building contour vectors are defined,and a coarse-to-fine building vector matching(CFBVM)method is proposed in the matching stage,for which the original matching results are described by the Gaussian mixture model(GMM).Subsequently,an improved resampling strategy is designed to reduce computing expenses with a huge number of initial particles,and a credibility indicator is designed to avoid location mistakes in the particle filter stage.An experimental evaluation of the approach based on flight data is provided.On a flight at a height of 0.2 km over a flight distance of 2 km,the aircraft is geo-localized in a reference map of 11,025 km~2using 0.09 km~2aerial images without any prior information.The absolute localization error is less than 10 m.

A solution method for decomposing vector fields in Hamilton energy

Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems.

An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction

Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.

Improved Twin Support Vector Machine Algorithm and Applications in Classification Problems

The distribution of data has a significant impact on the results of classification.When the distribution of one class is insignificant compared to the distribution of another class,data imbalance occurs.This will result in rising outlier values and noise.Therefore,the speed and performance of classification could be greatly affected.Given the above problems,this paper starts with the motivation and mathematical representing of classification,puts forward a new classification method based on the relationship between different classification formulations.Combined with the vector characteristics of the actual problem and the choice of matrix characteristics,we firstly analyze the orderly regression to introduce slack variables to solve the constraint problem of the lone point.Then we introduce the fuzzy factors to solve the problem of the gap between the isolated points on the basis of the support vector machine.We introduce the cost control to solve the problem of sample skew.Finally,based on the bi-boundary support vector machine,a twostep weight setting twin classifier is constructed.This can help to identify multitasks with feature-selected patterns without the need for additional optimizers,which solves the problem of large-scale classification that can’t deal effectively with the very low category distribution gap.

Differentially Private Support Vector Machines with Knowledge Aggregation

With the widespread data collection and processing,privacy-preserving machine learning has become increasingly important in addressing privacy risks related to individuals.Support vector machine(SVM)is one of the most elementary learning models of machine learning.Privacy issues surrounding SVM classifier training have attracted increasing attention.In this paper,we investigate Differential Privacy-compliant Federated Machine Learning with Dimensionality Reduction,called FedDPDR-DPML,which greatly improves data utility while providing strong privacy guarantees.Considering in distributed learning scenarios,multiple participants usually hold unbalanced or small amounts of data.Therefore,FedDPDR-DPML enables multiple participants to collaboratively learn a global model based on weighted model averaging and knowledge aggregation and then the server distributes the global model to each participant to improve local data utility.Aiming at high-dimensional data,we adopt differential privacy in both the principal component analysis(PCA)-based dimensionality reduction phase and SVM classifiers training phase,which improves model accuracy while achieving strict differential privacy protection.Besides,we train Differential privacy(DP)-compliant SVM classifiers by adding noise to the objective function itself,thus leading to better data utility.Extensive experiments on three high-dimensional datasets demonstrate that FedDPDR-DPML can achieve high accuracy while ensuring strong privacy protection.

Diffraction deep neural network-based classification for vector vortex beams

The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably affected by atmospheric turbulence(AT)when it propagates through the free-space optical communication environment,which results in detection errors at the receiver.In this paper,we propose a VVB classification scheme to detect VVBs with continuously changing polarization states under AT,where a diffractive deep neural network(DDNN)is designed and trained to classify the intensity distribution of the input distorted VVBs,and the horizontal direction of polarization of the input distorted beam is adopted as the feature for the classification through the DDNN.The numerical simulations and experimental results demonstrate that the proposed scheme has high accuracy in classification tasks.The energy distribution percentage remains above 95%from weak to medium AT,and the classification accuracy can remain above 95%for various strengths of turbulence.It has a faster convergence and better accuracy than that based on a convolutional neural network.

Performance Analysis of Support Vector Machine (SVM) on Challenging Datasets for Forest Fire Detection

This article delves into the analysis of performance and utilization of Support Vector Machines (SVMs) for the critical task of forest fire detection using image datasets. With the increasing threat of forest fires to ecosystems and human settlements, the need for rapid and accurate detection systems is of utmost importance. SVMs, renowned for their strong classification capabilities, exhibit proficiency in recognizing patterns associated with fire within images. By training on labeled data, SVMs acquire the ability to identify distinctive attributes associated with fire, such as flames, smoke, or alterations in the visual characteristics of the forest area. The document thoroughly examines the use of SVMs, covering crucial elements like data preprocessing, feature extraction, and model training. It rigorously evaluates parameters such as accuracy, efficiency, and practical applicability. The knowledge gained from this study aids in the development of efficient forest fire detection systems, enabling prompt responses and improving disaster management. Moreover, the correlation between SVM accuracy and the difficulties presented by high-dimensional datasets is carefully investigated, demonstrated through a revealing case study. The relationship between accuracy scores and the different resolutions used for resizing the training datasets has also been discussed in this article. These comprehensive studies result in a definitive overview of the difficulties faced and the potential sectors requiring further improvement and focus.

Enhanced Steganalysis for Color Images Using Curvelet Features and Support Vector Machine

Algorithms for steganography are methods of hiding data transfers in media files.Several machine learning architectures have been presented recently to improve stego image identification performance by using spatial information,and these methods have made it feasible to handle a wide range of problems associated with image analysis.Images with little information or low payload are used by information embedding methods,but the goal of all contemporary research is to employ high-payload images for classification.To address the need for both low-and high-payload images,this work provides a machine-learning approach to steganography image classification that uses Curvelet transformation to efficiently extract characteristics from both type of images.Support Vector Machine(SVM),a commonplace classification technique,has been employed to determine whether the image is a stego or cover.The Wavelet Obtained Weights(WOW),Spatial Universal Wavelet Relative Distortion(S-UNIWARD),Highly Undetectable Steganography(HUGO),and Minimizing the Power of Optimal Detector(MiPOD)steganography techniques are used in a variety of experimental scenarios to evaluate the performance of the proposedmethod.Using WOW at several payloads,the proposed approach proves its classification accuracy of 98.60%.It exhibits its superiority over SOTA methods.

Predicting Turbidite Channel in Deep-Water Canyon Based on Grey Relational Analysis-Support Vector Machine Model:A Case Study of the Lingshui Depression in Qiongdongnan Basin,South China Sea

The turbidite channel of South China Sea has been highly concerned.Influenced by the complex fault and the rapid phase change of lithofacies,predicting the channel through conventional seismic attributes is not accurate enough.In response to this disadvantage,this study used a method combining grey relational analysis(GRA)and support vectormachine(SVM)and established a set of prediction technical procedures suitable for reservoirs with complex geological conditions.In the case study of the Huangliu Formation in Qiongdongnan Basin,South China Sea,this study first dimensionalized the conventional seismic attributes of Gas Layer Group I and then used the GRA method to obtain the main relational factors.A higher relational degree indicates a higher probability of responding to the attributes of the turbidite channel.This study then accumulated the optimized attributes with the highest relational factors to obtain a first-order accumulated sequence,which was used as the input training sample of the SVM model,thus successfully constructing the SVM turbidite channel model.Drilling results prove that the GRA-SVMmethod has a high drilling coincidence rate.Utilizing the core and logging data and taking full use of the advantages of seismic inversion in predicting the sand boundary of water channels,this study divides the sedimentary microfacies of the Huangliu Formation in the Lingshui 17-2 Gas Field.This comprehensive study has shown that the GRA-SVM method has high accuracy for predicting turbidite channels and can be used as a superior turbidite channel prediction method under complex geological conditions.

Spatial quantum coherent modulation with perfect hybrid vector vortex beam based on atomic medium

The perfect hybrid vector vortex beam(PHVVB)with helical phase wavefront structure has aroused significant concern in recent years,as its beam waist does not expand with the topological charge(TC).In this work,we investigate the spatial quantum coherent modulation effect with PHVVB based on the atomic medium,and we observe the absorption characteristic of the PHVVB with different TCs under variant magnetic fields.We find that the transmission spectrum linewidth of PHVVB can be effectively maintained regardless of the TC.Still,the width of transmission peaks increases slightly as the beam size expands in hot atomic vapor.This distinctive quantum coherence phenomenon,demonstrated by the interaction of an atomic medium with a hybrid vector-structured beam,might be anticipated to open up new opportunities for quantum coherence modulation and accurate magnetic field measurement.

Learning Vector Quantization-Based Fuzzy Rules Oversampling Method

Imbalanced datasets are common in practical applications,and oversampling methods using fuzzy rules have been shown to enhance the classification performance of imbalanced data by taking into account the relationship between data attributes.However,the creation of fuzzy rules typically depends on expert knowledge,which may not fully leverage the label information in training data and may be subjective.To address this issue,a novel fuzzy rule oversampling approach is developed based on the learning vector quantization(LVQ)algorithm.In this method,the label information of the training data is utilized to determine the antecedent part of If-Then fuzzy rules by dynamically dividing attribute intervals using LVQ.Subsequently,fuzzy rules are generated and adjusted to calculate rule weights.The number of new samples to be synthesized for each rule is then computed,and samples from the minority class are synthesized based on the newly generated fuzzy rules.This results in the establishment of a fuzzy rule oversampling method based on LVQ.To evaluate the effectiveness of this method,comparative experiments are conducted on 12 publicly available imbalance datasets with five other sampling techniques in combination with the support function machine.The experimental results demonstrate that the proposed method can significantly enhance the classification algorithm across seven performance indicators,including a boost of 2.15%to 12.34%in Accuracy,6.11%to 27.06%in G-mean,and 4.69%to 18.78%in AUC.These show that the proposed method is capable of more efficiently improving the classification performance of imbalanced data.

Active Fault Tolerant Nonsingular Terminal Sliding Mode Control for Electromechanical System Based on Support Vector Machine

Effective fault diagnosis and fault-tolerant control method for aeronautics electromechanical actuator is concerned in this paper.By borrowing the advantages of model-driven and data-driven methods,a fault tolerant nonsingular terminal sliding mode control method based on support vector machine(SVM)is proposed.A SVM is designed to estimate the fault by off-line learning from small sample data with solving convex quadratic programming method and is introduced into a high-gain observer,so as to improve the state estimation and fault detection accuracy when the fault occurs.The state estimation value of the observer is used for state reconfiguration.A novel nonsingular terminal sliding mode surface is designed,and Lyapunov theorem is used to derive a parameter adaptation law and a control law.It is guaranteed that the proposed controller can achieve asymptotical stability which is superior to many advanced fault-tolerant controllers.In addition,the parameter estimation also can help to diagnose the system faults because the faults can be reflected by the parameters variation.Extensive comparative simulation and experimental results illustrate the effectiveness and advancement of the proposed controller compared with several other main-stream controllers.

Underwater Image Classification Based on EfficientnetB0 and Two-Hidden-Layer Random Vector Functional Link

The ocean plays an important role in maintaining the equilibrium of Earth’s ecology and providing humans access to a wealth of resources.To obtain a high-precision underwater image classification model,we propose a classification model that combines an EfficientnetB0 neural network and a two-hidden-layer random vector functional link network(EfficientnetB0-TRVFL).The features of underwater images were extracted using the EfficientnetB0 neural network pretrained via ImageNet,and a new fully connected layer was trained on the underwater image dataset using the transfer learning method.Transfer learning ensures the initial performance of the network and helps in the development of a high-precision classification model.Subsequently,a TRVFL was proposed to improve the classification property of the model.Net construction of the two hidden layers exhibited a high accuracy when the same hidden layer nodes were used.The parameters of the second hidden layer were obtained using a novel calculation method,which reduced the outcome error to improve the performance instability caused by the random generation of parameters of RVFL.Finally,the TRVFL classifier was used to classify features and obtain classification results.The proposed EfficientnetB0-TRVFL classification model achieved 87.28%,74.06%,and 99.59%accuracy on the MLC2008,MLC2009,and Fish-gres datasets,respectively.The best convolutional neural networks and existing methods were stacked up through box plots and Kolmogorov-Smirnov tests,respectively.The increases imply improved systematization properties in underwater image classification tasks.The image classification model offers important performance advantages and better stability compared with existing methods.