For positive real numbers a,b,a+b≤max{a+b1/2 a1/2,b+a1/2b1/2}.In this note,we generalize this fact to matrices by proving that for positive semidefinite matrices A and B of order n,for any c∈[-1,1]and j=1,2,…,n,sj(...For positive real numbers a,b,a+b≤max{a+b1/2 a1/2,b+a1/2b1/2}.In this note,we generalize this fact to matrices by proving that for positive semidefinite matrices A and B of order n,for any c∈[-1,1]and j=1,2,…,n,sj(A+B)≤sj((A⊕B)+φc(A,B))≤sj(A+|B1/2A1/2|)⊕(B+|A1/2B1/2|),where sj(X)denotes the j-th largest singular value of X andφc(A,B):=1/2((1+c)|B1/2A1/2|(1-c)A1/2B1/2(1-c)B1/2A1/2(1+c)|A1/2B1/2|).This result sharpens some known result.Meanwhile,some related results are established.展开更多
@1 Definition 1 Let A=(α<sub>ij</sub>)∈C<sup>n×n</sup>,B=(b<sub>ij</sub>)∈C<sup>n×n</sup>,is nonsingular.The generalizedsingular values of A（relative to B...@1 Definition 1 Let A=(α<sub>ij</sub>)∈C<sup>n×n</sup>,B=(b<sub>ij</sub>)∈C<sup>n×n</sup>,is nonsingular.The generalizedsingular values of A（relative to B）are following determinate nonnegative real numberswhen ||·||<sub>2</sub> denotes the Euclid vector norm,〈n〉={1,2,…,n}.Definition 2 Let A,B∈C<sup>n×n</sup>,if there exist λ∈C and x∈C<sup>n</sup>\{0}。展开更多
The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the ...The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the function fλ（z） has infinitely many singular values for all b 〉 0 except b = 1. It is also shown that, for 0 〈 b 〈 1, all the critical values of fλ（z） lie in the left half plane while, for b 〉 1, lie in the right half plane. Further, it is seen that all these critical values are outside the open disk centered at origin and having radius ｜λ/lnb｜for all b 〉 0 except b = 1. Moreover, the real fixed points of fλ （z） and their nature are investigated.展开更多
The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication ...The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication medium where it could be intercepted by unauthorized entities.This study provides an approach to color image encryption that could find practical use in various contexts.The proposed method,which combines four chaotic systems,employs singular value decomposition and a chaotic sequence,making it both secure and compression-friendly.The unified average change intensity,the number of pixels’change rate,information entropy analysis,correlation coefficient analysis,compression friendliness,and security against brute force,statistical analysis and differential attacks are all used to evaluate the algorithm’s performance.Following a thorough investigation of the experimental data,it is concluded that the proposed image encryption approach is secure against a wide range of attacks and provides superior compression friendliness when compared to chaos-based alternatives.展开更多
The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identi...The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identify the dynamic parameter of spacecraftrapidly and accurately, an accelerated ERA with a partial singularvalues decomposition (PSVD) algorithm is presented. In the PSVD, theHankel matrix is reduced to dual diagonal form first, and thentransformed into a tridiagonal matrix.展开更多
In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ?dimtortion function ? K ...Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ?dimtortion function ? K (r) and the Agard η-distortion function η K (t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true.展开更多
In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, some results of the Rayleigh quotient （matrix） of Hermitian matrices are extended to those for arbitrary matrix on one hand. On th...In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, some results of the Rayleigh quotient （matrix） of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.展开更多
We first provide a simple estimate for || A-1||∞and||A-1||1 of a strictly diagonally dominant matrix A. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scaling wit...We first provide a simple estimate for || A-1||∞and||A-1||1 of a strictly diagonally dominant matrix A. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scaling with a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness of the new bounds.展开更多
A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type i...A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.展开更多
We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We ob...We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.展开更多
In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be r...In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.展开更多
A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and...A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.展开更多
By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation...By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.展开更多
Single image super resolution(SISR)techniques produce images of high resolution(HR)as output from input images of low resolution(LR).Motivated by the effectiveness of deep learning methods,we provide a framework based...Single image super resolution(SISR)techniques produce images of high resolution(HR)as output from input images of low resolution(LR).Motivated by the effectiveness of deep learning methods,we provide a framework based on deep learning to achieve super resolution(SR)by utilizing deep singular-residual neural network(DSRNN)in training phase.Residuals are obtained from the difference between HR and LR images to generate LR-residual example pairs.Singular value decomposition(SVD)is applied to each LR-residual image pair to decompose into subbands of low and high frequency components.Later,DSRNN is trained on these subbands through input and output channels by optimizing the weights and biases of the network.With fewer layers in DSRNN,the influence of exploding gradients is reduced.This speeds up the learning process and also improves accuracy by using skip connections.The trained DSRNN parameters yield residuals to recover the HR subbands in the testing phase.Experimental analysis shows that the proposed method results in superior performance to existingmethods in terms of subjective quality.Extensive testing results on popular benchmark datasets such as set5,set14,and urban100 for a scaling factor of 4 show the effectiveness of the proposed method across different qualitative evaluation metrics.展开更多
Sonic Hedgehog Medulloblastoma(SHH-MB)is one of the four primary molecular subgroups of Medulloblastoma.It is estimated to be responsible for nearly one-third of allMB cases.Using transcriptomic and DNA methylation pr...Sonic Hedgehog Medulloblastoma(SHH-MB)is one of the four primary molecular subgroups of Medulloblastoma.It is estimated to be responsible for nearly one-third of allMB cases.Using transcriptomic and DNA methylation profiling techniques,new developments in this field determined four molecular subtypes for SHH-MB.SHH-MB subtypes show distinct DNAmethylation patterns that allow their discrimination fromoverlapping subtypes and predict clinical outcomes.Class overlapping occurs when two or more classes share common features,making it difficult to distinguish them as separate.Using the DNA methylation dataset,a novel classification technique is presented to address the issue of overlapping SHH-MBsubtypes.Penalizedmultinomial regression(PMR),Tomek links(TL),and singular value decomposition(SVD)were all smoothly integrated into a single framework.SVD and group lasso improve computational efficiency,address the problem of high-dimensional datasets,and clarify class distinctions by removing redundant or irrelevant features that might lead to class overlap.As a method to eliminate the issues of decision boundary overlap and class imbalance in the classification task,TL enhances dataset balance and increases the clarity of decision boundaries through the elimination of overlapping samples.Using fivefold cross-validation,our proposed method(TL-SVDPMR)achieved a remarkable overall accuracy of almost 95%in the classification of SHH-MB molecular subtypes.The results demonstrate the strong performance of the proposed classification model among the various SHH-MB subtypes given a high average of the area under the curve(AUC)values.Additionally,the statistical significance test indicates that TL-SVDPMR is more accurate than both SVM and random forest algorithms in classifying the overlapping SHH-MB subtypes,highlighting its importance for precision medicine applications.Our findings emphasized the success of combining SVD,TL,and PMRtechniques to improve the classification performance for biomedical applications with many features and overlapping subtypes.展开更多
This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis.The...This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis.These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content(VTEC)values collected across varied ionospheric conditions and measured over the region of interest.The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors.The reconstruction accuracy of the algorithm was found to be better than 4 TECU(TECU=1016electrons/m2)for more than 99.9%of the time when tested over the complete year of 2016 with only eight basis vectors.The containment factor,defined here,indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high,aiding in improved algorithm performance.The performance,however,was found to be sensitive to the seasons and geomagnetic conditions.Deteriorated performance was observed when tested for the St.Patrick's Day storm data.The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm.The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables,which may find utility in navigation,radar,and various other applications.展开更多
Low-field nuclear magnetic resonance(NMR)has broad application prospects in the explo-ration and development of unconventional oil and gas reservoirs.However,NMR instruments tend to acquire echo signals with relativel...Low-field nuclear magnetic resonance(NMR)has broad application prospects in the explo-ration and development of unconventional oil and gas reservoirs.However,NMR instruments tend to acquire echo signals with relatively low signal-to-noise ratio(SNR),resulting in poor accuracy of T2 spectrum inversion.It is crucial to preprocess the low SNR data with denoising methods before inversion.In this paper,a hybrid NMR data denoising method combining empirical mode decomposition-singular value decomposition(EMD-SVD)was proposed.Firstly,the echo data were decomposed with the EMD method to low-and high-frequency intrinsic mode function(IMF)components as well as a residual.Next,the SVD method was employed for the high-frequency IMF components denoising.Finally,the low-frequency IMF components,the denoised high-frequency IMF components,and the residual are summed to form the denoised signal.To validate the effectiveness and feasibility of the EMD-SVDmethod,numerical simulations,experimental data,and NMR log data processingwere conducted.The results indicate that the inverted NMR spectra with the EMD-SVD denoising method exhibit higher quality compared to the EMD method and the SVD method.展开更多
Iterative Learning Control is an effective way of controlling the errors which act directly on the repetitive system. The stability of the system is the main objective in designing. The Small Gain Theorem is used in t...Iterative Learning Control is an effective way of controlling the errors which act directly on the repetitive system. The stability of the system is the main objective in designing. The Small Gain Theorem is used in the design process of State Feedback ILC. The feedback controller along with the Iterative Learning Control adds an advantage in producing a system with minimal error. The past error and current error feedback Iterative control system are studied with reference to the region of disturbance at the output. This paper mainly focuses on comparing the region of disturbance at the output end. The past error feed forward and current error feedback systems are developed on the singular values. Hence, we use the singular values to set an output disturbance limit for the past error and current error feedback ILC system. Thus, we obtain a result of past error feed forward performing better than the current error feedback system. This implies greater region of disturbance suppression to past error feed forward than the other.展开更多
Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, ...Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, there may exist a corresponding local fault in themachine, and if further extracting the periodic impulse components from the vibration signals, theseverity of the local fault can be estimated and tracked. However, the signal-to-noise ratios (SNRs)of the vibration acceleration signals are often so small that the periodic impulse components aresubmersed in much background noises and other components, and it is difficult or inconvenient for usto detect and extract the periodic impulse components with the current common analyzing methods forvibration signals. Therefore, another technique, called singular value decomposition (SVD), istried to be introduced to solve the problem. First, the principle of detecting and extracting thesignal periodic components using singular value decomposition is summarized and discussed. Second,the infeasibility of the direct use of the existing SVD based detecting and extracting approach ispointed out. Third, the approach to construct the matrix for SVD from the signal series is improvedlargely, which is the key program to improve the SVD technique; Other associated improvement is alsoproposed. Finally, a simulating application example and a real-life application example ondetecting and extracting the periodic impulse components are given, which showed that the introducedand improved SVD technique is feasible.展开更多
基金Supported by the Natural Science Foundation of Anhui Province(1708085QA05)the Natural Science Foundation of Anhui Higher Education Institutions of China(KJ2019A0588,KJ2020ZD008)。
文摘For positive real numbers a,b,a+b≤max{a+b1/2 a1/2,b+a1/2b1/2}.In this note,we generalize this fact to matrices by proving that for positive semidefinite matrices A and B of order n,for any c∈[-1,1]and j=1,2,…,n,sj(A+B)≤sj((A⊕B)+φc(A,B))≤sj(A+|B1/2A1/2|)⊕(B+|A1/2B1/2|),where sj(X)denotes the j-th largest singular value of X andφc(A,B):=1/2((1+c)|B1/2A1/2|(1-c)A1/2B1/2(1-c)B1/2A1/2(1+c)|A1/2B1/2|).This result sharpens some known result.Meanwhile,some related results are established.
文摘@1 Definition 1 Let A=(α<sub>ij</sub>)∈C<sup>n×n</sup>,B=(b<sub>ij</sub>)∈C<sup>n×n</sup>,is nonsingular.The generalizedsingular values of A（relative to B）are following determinate nonnegative real numberswhen ||·||<sub>2</sub> denotes the Euclid vector norm,〈n〉={1,2,…,n}.Definition 2 Let A,B∈C<sup>n×n</sup>,if there exist λ∈C and x∈C<sup>n</sup>\{0}。
文摘The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the function fλ（z） has infinitely many singular values for all b 〉 0 except b = 1. It is also shown that, for 0 〈 b 〈 1, all the critical values of fλ（z） lie in the left half plane while, for b 〉 1, lie in the right half plane. Further, it is seen that all these critical values are outside the open disk centered at origin and having radius ｜λ/lnb｜for all b 〉 0 except b = 1. Moreover, the real fixed points of fλ （z） and their nature are investigated.
基金funded by Deanship of Scientific Research at King Khalid University under Grant Number R.G.P.2/86/43.
文摘The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication medium where it could be intercepted by unauthorized entities.This study provides an approach to color image encryption that could find practical use in various contexts.The proposed method,which combines four chaotic systems,employs singular value decomposition and a chaotic sequence,making it both secure and compression-friendly.The unified average change intensity,the number of pixels’change rate,information entropy analysis,correlation coefficient analysis,compression friendliness,and security against brute force,statistical analysis and differential attacks are all used to evaluate the algorithm’s performance.Following a thorough investigation of the experimental data,it is concluded that the proposed image encryption approach is secure against a wide range of attacks and provides superior compression friendliness when compared to chaos-based alternatives.
文摘The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identify the dynamic parameter of spacecraftrapidly and accurately, an accelerated ERA with a partial singularvalues decomposition (PSVD) algorithm is presented. In the PSVD, theHankel matrix is reduced to dual diagonal form first, and thentransformed into a tridiagonal matrix.
文摘In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
文摘Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ?dimtortion function ? K (r) and the Agard η-distortion function η K (t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true.
文摘In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, some results of the Rayleigh quotient （matrix） of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.
基金Supported by Natural Science Foundation of Shanxi Province (No.20011041).
文摘We first provide a simple estimate for || A-1||∞and||A-1||1 of a strictly diagonally dominant matrix A. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scaling with a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness of the new bounds.
基金the National Natural Science Foundation of China (No.19971086)the Doctoral Program Foundation of National Education Department of China.
文摘A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.
基金supported by Shandong Provincial NSF(ZR2022MA020).
文摘We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.
基金supported by the National Natural Science Foundation of China (No.12172154)the 111 Project (No.B14044)+1 种基金the Natural Science Foundation of Gansu Province (No.23JRRA1035)the Natural Science Foundation of Anhui University of Finance and Economics (No.ACKYC20043).
文摘In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.
基金The National Natural Science Foundation of China( No. 69092008)
文摘A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.
基金Supported by The Special Foundation of Chinese Meteorological Bureau Climate Changes Program(200920)The Special Foundation of Hunan Major Scientific and Technological Research Program(2008FJ1006)~~
文摘By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.
文摘Single image super resolution(SISR)techniques produce images of high resolution(HR)as output from input images of low resolution(LR).Motivated by the effectiveness of deep learning methods,we provide a framework based on deep learning to achieve super resolution(SR)by utilizing deep singular-residual neural network(DSRNN)in training phase.Residuals are obtained from the difference between HR and LR images to generate LR-residual example pairs.Singular value decomposition(SVD)is applied to each LR-residual image pair to decompose into subbands of low and high frequency components.Later,DSRNN is trained on these subbands through input and output channels by optimizing the weights and biases of the network.With fewer layers in DSRNN,the influence of exploding gradients is reduced.This speeds up the learning process and also improves accuracy by using skip connections.The trained DSRNN parameters yield residuals to recover the HR subbands in the testing phase.Experimental analysis shows that the proposed method results in superior performance to existingmethods in terms of subjective quality.Extensive testing results on popular benchmark datasets such as set5,set14,and urban100 for a scaling factor of 4 show the effectiveness of the proposed method across different qualitative evaluation metrics.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2024-02-01137).
文摘Sonic Hedgehog Medulloblastoma(SHH-MB)is one of the four primary molecular subgroups of Medulloblastoma.It is estimated to be responsible for nearly one-third of allMB cases.Using transcriptomic and DNA methylation profiling techniques,new developments in this field determined four molecular subtypes for SHH-MB.SHH-MB subtypes show distinct DNAmethylation patterns that allow their discrimination fromoverlapping subtypes and predict clinical outcomes.Class overlapping occurs when two or more classes share common features,making it difficult to distinguish them as separate.Using the DNA methylation dataset,a novel classification technique is presented to address the issue of overlapping SHH-MBsubtypes.Penalizedmultinomial regression(PMR),Tomek links(TL),and singular value decomposition(SVD)were all smoothly integrated into a single framework.SVD and group lasso improve computational efficiency,address the problem of high-dimensional datasets,and clarify class distinctions by removing redundant or irrelevant features that might lead to class overlap.As a method to eliminate the issues of decision boundary overlap and class imbalance in the classification task,TL enhances dataset balance and increases the clarity of decision boundaries through the elimination of overlapping samples.Using fivefold cross-validation,our proposed method(TL-SVDPMR)achieved a remarkable overall accuracy of almost 95%in the classification of SHH-MB molecular subtypes.The results demonstrate the strong performance of the proposed classification model among the various SHH-MB subtypes given a high average of the area under the curve(AUC)values.Additionally,the statistical significance test indicates that TL-SVDPMR is more accurate than both SVM and random forest algorithms in classifying the overlapping SHH-MB subtypes,highlighting its importance for precision medicine applications.Our findings emphasized the success of combining SVD,TL,and PMRtechniques to improve the classification performance for biomedical applications with many features and overlapping subtypes.
文摘This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis.These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content(VTEC)values collected across varied ionospheric conditions and measured over the region of interest.The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors.The reconstruction accuracy of the algorithm was found to be better than 4 TECU(TECU=1016electrons/m2)for more than 99.9%of the time when tested over the complete year of 2016 with only eight basis vectors.The containment factor,defined here,indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high,aiding in improved algorithm performance.The performance,however,was found to be sensitive to the seasons and geomagnetic conditions.Deteriorated performance was observed when tested for the St.Patrick's Day storm data.The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm.The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables,which may find utility in navigation,radar,and various other applications.
基金supported by the National Natural Science Foundation of China(grant no.42304118)the Young Elite Scientist Sponsorship Program by BAST(grant no.BYESS2023027)the Science Foundation of China University of Petroleum,Beijing(grant no.2462022QNXZ001).
文摘Low-field nuclear magnetic resonance(NMR)has broad application prospects in the explo-ration and development of unconventional oil and gas reservoirs.However,NMR instruments tend to acquire echo signals with relatively low signal-to-noise ratio(SNR),resulting in poor accuracy of T2 spectrum inversion.It is crucial to preprocess the low SNR data with denoising methods before inversion.In this paper,a hybrid NMR data denoising method combining empirical mode decomposition-singular value decomposition(EMD-SVD)was proposed.Firstly,the echo data were decomposed with the EMD method to low-and high-frequency intrinsic mode function(IMF)components as well as a residual.Next,the SVD method was employed for the high-frequency IMF components denoising.Finally,the low-frequency IMF components,the denoised high-frequency IMF components,and the residual are summed to form the denoised signal.To validate the effectiveness and feasibility of the EMD-SVDmethod,numerical simulations,experimental data,and NMR log data processingwere conducted.The results indicate that the inverted NMR spectra with the EMD-SVD denoising method exhibit higher quality compared to the EMD method and the SVD method.
文摘Iterative Learning Control is an effective way of controlling the errors which act directly on the repetitive system. The stability of the system is the main objective in designing. The Small Gain Theorem is used in the design process of State Feedback ILC. The feedback controller along with the Iterative Learning Control adds an advantage in producing a system with minimal error. The past error and current error feedback Iterative control system are studied with reference to the region of disturbance at the output. This paper mainly focuses on comparing the region of disturbance at the output end. The past error feed forward and current error feedback systems are developed on the singular values. Hence, we use the singular values to set an output disturbance limit for the past error and current error feedback ILC system. Thus, we obtain a result of past error feed forward performing better than the current error feedback system. This implies greater region of disturbance suppression to past error feed forward than the other.
基金This project is supported by National Natural Science Foundation of China (No.59905011, 60275041).
文摘Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, there may exist a corresponding local fault in themachine, and if further extracting the periodic impulse components from the vibration signals, theseverity of the local fault can be estimated and tracked. However, the signal-to-noise ratios (SNRs)of the vibration acceleration signals are often so small that the periodic impulse components aresubmersed in much background noises and other components, and it is difficult or inconvenient for usto detect and extract the periodic impulse components with the current common analyzing methods forvibration signals. Therefore, another technique, called singular value decomposition (SVD), istried to be introduced to solve the problem. First, the principle of detecting and extracting thesignal periodic components using singular value decomposition is summarized and discussed. Second,the infeasibility of the direct use of the existing SVD based detecting and extracting approach ispointed out. Third, the approach to construct the matrix for SVD from the signal series is improvedlargely, which is the key program to improve the SVD technique; Other associated improvement is alsoproposed. Finally, a simulating application example and a real-life application example ondetecting and extracting the periodic impulse components are given, which showed that the introducedand improved SVD technique is feasible.
