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We give global structure of spectra of periodic non-Hermitian Jacobi operators by the discriminant and its stationary points. We also give necessary and sufficient conditions for real spectra and single interval spectra. [ABSTRACT FROM AUTHOR]

In this paper we ascertain the singular point-wise behavior of the positive solutions of a semilinear elliptic boundary value problem (1) at the critical value of the parameter, λ , where it begins its metasolution regime. As the weight function m (x) changes sign in Ω, our result is a substantial extension of a previous, very recent, result of Li et al. [8] , where it was imposed the (very strong) condition that m ≥ 0 on a neighborhood of b − 1 ({ 0 }). In this paper, we are simply assuming that m (x 0) > 0 for some x 0 ∈ b − 1 ({ 0 }). • Theorem 1.1 proves that the behavior of the solutions proved by Li et al. [8] also occurs with much weaker hypotheses. • Theorem 3.1 is a substantial extension of Theorem 2.1 of López-Gómez and Sabina de Lis [12]. • Lemma 2.1 provides a useful estimate of eigenfunctions associated to an eigenvalue problem with sign changing weight. [ABSTRACT FROM AUTHOR]

In this paper, the existence of solutions, (λ , u) , of the problem - Δ u = λ u - a (x) | u | p - 1 u in Ω , u = 0 on ∂ Ω , is explored for 0 < p < 1 . When p > 1 , it is known that there is an unbounded component of such solutions bifurcating from (σ 1 , 0) , where σ 1 is the smallest eigenvalue of - Δ in Ω under Dirichlet boundary conditions on ∂ Ω . These solutions have u ∈ P , the interior of the positive cone. The continuation argument used when p > 1 to keep u ∈ P fails if 0 < p < 1 . Nevertheless when 0 < p < 1 , we are still able to show that there is a component of solutions bifurcating from (σ 1 , ∞) , unbounded outside of a neighborhood of (σ 1 , ∞) , and having u ⪈ 0 . This non-negativity for u cannot be improved as is shown via a detailed analysis of the simplest autonomous one-dimensional version of the problem: its set of non-negative solutions possesses a countable set of components, each of them consisting of positive solutions with a fixed (arbitrary) number of bumps. Finally, the structure of these components is fully described. [ABSTRACT FROM AUTHOR]

The results of a piControl experiment investigating general circulation models participating in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) were examined. The global interannual variability in the monthly surface temperature (ST) and sea level pressure (SLP) anomalies was considered. The amplitudes of the fluctuations in the anomalies of these meteorological fields between opposite phases of the El Niño–Southern Oscillation (ENSO) were calculated. It was shown that most CMIP6 models reproduced fluctuations in the ST and SLP anomalies between El Niño and La Niña not only in the equatorial Pacific, but also throughout the tropics, as well as in the middle and high latitudes. Some of the CMIP6 models reproduced the global structures of the ST and SLP anomaly oscillations quite accurately between opposite phases of ENSO, as previously determined from observational data and reanalyses. It was found that the models AS-RCEC TaiESM1, CAMS CAMS-CSM1-0, CAS FGOALS-f3-L, CMCC CMCC-ESM2, KIOST KIOST-ESM, NASA GISS-E2-1-G, NCAR CESM2-WACCM-FV2, and NCC NorCPM1 reproduced strong ENSO teleconnections in regions beyond the tropical Pacific. [ABSTRACT FROM AUTHOR]

This paper presents climatological features of the longitudinal structures WN4, WN3, and WN2 and their drivers observed in the lower thermospheric temperatures and in the ionospheric TEC. For this purpose, two long-term data sets are utilized: the satellite SABER/TIMED temperature measurements, and the global TEC maps generated with the NASA JPL for the interval of 2002–2022. As the main drivers of the longitudinal structures are mainly nonmigrating tides, this study first investigates the climatology of those nonmigrating tides, which are the main contributors of the considered longitudinal structures; these are nonmigrating diurnal DE3, DE2, and DW2, and semidiurnal SW4 and SE2 tides. The climatology of WN4, WN3, and WN2 structures in the lower thermosphere reveals that WN4 is the strongest one with a magnitude of ~20 K observed at 10° S in August, followed by WN2 with ~13.9 K at 10° S in February, and the weakest is WN3 with ~12.4 K observed over the equator in July. In the ionosphere, WN3 is the strongest structure with a magnitude of 5.9 TECU located at −30° modip latitude in October, followed by WN2 with 5.4 TECU at 30 modip in March, and the last is WN4 with 3.7 TECU at −30 modip in August. Both the climatology of the WSA and the features of its drivers are investigated as well. [ABSTRACT FROM AUTHOR]

Aiming at the issue of complex 3D shape analysis and recognition, this paper presented a novel 3D graph convolu- tion classification method. It established a joint graph convolution learning mechanism of local geometry and global structure to provide both geometrical features and global context features, which effectively improved the robustness and stability of 3D data learning. Firstly, it constructed the local graph in spatial domain by farthest point sampling and K-nearest neighbor method, and designed a dynamic spectral graph convolution operator to extract local geometric features effectively. Meanwhile, it con- structed the global feature graph based on random sampling in the feature domain, and obtained the global structure context by spectral graph convolution. Furthermore, it established a weighted graph convolution network with an attention mechanism to achieve adaptive feature fusion. Finally, under the optimization of objective function, it improved the performance of feature learning effectively. Experimental results show that the proposed joint network learning mechanism, which combined local geo- metric features with global structure features, enhances the representation ability and discrimination of deep features, and ob- tains better recognition and classification performance compared with advanced methods. This method can be used for large- scale point clouds recognition, 3D shape reconstruction and data compression. It has important research significance and broad application prospects in robot, product digital analysis, intelligent navigation, virtual reality and other fields. [ABSTRACT FROM AUTHOR]

This article deals with the existence, multiplicity, minimal complexity, and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V. Volterra its most paradigmatic example. By means of a topological approach based on techniques from global bifurcation theory, the first part of the paper ascertains their nature, multiplicity and minimal complexity, as well as their global minimal structure, in terms of the configuration of the function coefficients in the setting of the model. The second part of the paper introduces a dynamical system approach based on the theory of topological horseshoes that permits to detect, besides subharmonic solutions, “chaotic-type” solutions. As a byproduct of our analysis, the simplest predator-prey prototype models in periodic environments can provoke chaotic dynamics. This cannot occur in cooperative and quasi-cooperative dynamics, as a consequence of the ordering imposed by the maximum principle.

This paper presents climatological features of the longitudinal structures WN4, WN3, and WN2 and their drivers observed in the lower thermospheric temperatures and in the ionospheric TEC. For this purpose, two long-term data sets are utilized: the satellite SABER/TIMED temperature measurements, and the global TEC maps generated with the NASA JPL for the interval of 2002–2022. As the main drivers of the longitudinal structures are mainly nonmigrating tides, this study first investigates the climatology of those nonmigrating tides, which are the main contributors of the considered longitudinal structures; these are nonmigrating diurnal DE3, DE2, and DW2, and semidiurnal SW4 and SE2 tides. The climatology of WN4, WN3, and WN2 structures in the lower thermosphere reveals that WN4 is the strongest one with a magnitude of ~20 K observed at 10° S in August, followed by WN2 with ~13.9 K at 10° S in February, and the weakest is WN3 with ~12.4 K observed over the equator in July. In the ionosphere, WN3 is the strongest structure with a magnitude of 5.9 TECU located at −30° modip latitude in October, followed by WN2 with 5.4 TECU at 30 modip in March, and the last is WN4 with 3.7 TECU at −30 modip in August. Both the climatology of the WSA and the features of its drivers are investigated as well.

The results of a piControl experiment investigating general circulation models participating in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) were examined. The global interannual variability in the monthly surface temperature (ST) and sea level pressure (SLP) anomalies was considered. The amplitudes of the fluctuations in the anomalies of these meteorological fields between opposite phases of the El Niño–Southern Oscillation (ENSO) were calculated. It was shown that most CMIP6 models reproduced fluctuations in the ST and SLP anomalies between El Niño and La Niña not only in the equatorial Pacific, but also throughout the tropics, as well as in the middle and high latitudes. Some of the CMIP6 models reproduced the global structures of the ST and SLP anomaly oscillations quite accurately between opposite phases of ENSO, as previously determined from observational data and reanalyses. It was found that the models AS-RCEC TaiESM1, CAMS CAMS-CSM1-0, CAS FGOALS-f3-L, CMCC CMCC-ESM2, KIOST KIOST-ESM, NASA GISS-E2-1-G, NCAR CESM2-WACCM-FV2, and NCC NorCPM1 reproduced strong ENSO teleconnections in regions beyond the tropical Pacific.

Copyright of Journal of Data Acquisition & Processing / Shu Ju Cai Ji Yu Chu Li is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article introduces a framework for predicting the survival of brain tumor patients by analyzing magnetic resonance images. The prediction of brain tumor survival is challenging due to the limited size of available datasets. To overcome the issue of overfitting, we propose a self-supervised learning method that involves identifying image patches from the same or different images. By recognizing intra- and inter-image differences, the network can learn the relationships between local spatial windows in the same image and across different images. In addition to analyzing local information, we also incorporate a global structure awareness network to capture global information from the entire image. Our proposed method shows a strong correlation between local spatial relationships and survivor class prediction in FLAIR MRI brain images. We evaluate our method using the BraTS 2020 validation dataset and observe that our method outperforms others in accuracy and SpearmanR correlation metrics.

Principal component analysis network (PCANet) is a feature learning algorithm that is widely used in face recognition and object classification. However, original PCANet still has some shortages. One is that the principal component analysis (PCA) algorithm only extracts features by considering the global structure. The other lies in that the original PCANet only employs one particular single layer convolutional results, which loses the information of other convolutional layers. In this paper, we propose a new simple and efficient convolutional neural network called global and local structure network (GLSNet) to address the problems. The network extracts the features both from the global structure and the local structure of the original data space. Specifically, a principal component analysis (PCA) convolutional layer which learns the filters by PCA algorithm is used to remove the noises and redundant information at the first stage. Then at the second stage, another PCA convolution is added to extract features by considering the global structure. As for the local structure, we use the neighborhood preserving embedding (NPE) algorithm to learn the convolutional filters. At the output stage, the global structure feature extracted by PCA convolution and the local structure feature extracted by NPE convolution is concatenated as a united feature. Furthermore, the first layer convolutional feature is also taken into consideration to obtain shallow-level information. Finally, these features are concatenated as a united feature, and a spatial pyramid pooling layer is followed to pool above the united features. To test the effectiveness of the proposed algorithm, the experiments on some image datasets, including three types: human face dataset, object dataset, and handprinted dataset, proceeded. And it performs better than the original PCANet and some improvement algorithms of PCANet, such as PLDANet, and MMPCANet.

As an important technology in 3D vision, point-cloud registration has broad development prospects in the fields of space-based remote sensing, photogrammetry, robotics, and so on. Of the available algorithms, the Iterative Closest Point (ICP) algorithm has been used as the classic algorithm for solving point cloud registration. However, with the point cloud data being under the influence of noise, outliers, overlapping values, and other issues, the performance of the ICP algorithm will be affected to varying degrees. This paper proposes a global structure and adaptive weight aware ICP algorithm (GSAW-ICP) for image registration. Specifically, we first proposed a global structure mathematical model based on the reconstruction of local surfaces using both the rotation of normal vectors and the change in curvature, so as to better describe the deformation of the object. The model was optimized for the convergence strategy, so that it had a wider convergence domain and a better convergence effect than either of the original point-to-point or point-to-point constrained models. Secondly, for outliers and overlapping values, the GSAW-ICP algorithm was able to assign appropriate weights, so as to optimize both the noise and outlier interference of the overall system. Our proposed algorithm was extensively tested on noisy, anomalous, and real datasets, and the proposed method was proven to have a better performance than other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

As a critical part of desision tree (DT） growth, its nodes can be split to grow by either axis- or nonaxis-aligned way based on such splitting criteria as purity and misclassification error. However, these have nothing to do with the geometric structure of data, e. g. multicentric data or single-center data. In order to compensate for this, two splitting criteria are proposed by combining the between-class margin in the same inner node (BCM） and the between-node margin within the same class (BNM） respectively with the purity measure in weighting and the two-step method. Unlike traditional greedy growth of DT which only finds the current locally optimal splitting point, the proposed method first selects the top-k purity splitting nodes, then determines the optimal one by maximizing BCM and minimizing BNM. Since not only alleviating purity-based local optimality but also considering global structures of the data, our method greatly improves the division of descendant nodes and generalization of the formed trees, while enhancing the interpretability. In addition, two aforementioned splitting criteria can be combined to further boost the performance. The comparison results on 21 benchmark datasets show an improvement in predictive performance of new trees with reduction in complexity, while also are competitive with many other DTs using hybrid splitting criteria. [ABSTRACT FROM AUTHOR]

In order to solve the issue mismatching and structure disconnecting in exemplar-based image inpainting, an image completion algorithm based on improved total variation minimization method had been proposed in the paper, refer as ETVM. The structure of image had been extracted using improved total variation minimization method, and the known information of image is sufficiently used by existing methods. The robust filling mechanism can be achieved according to the direction of image structure and it has less noise than original image. The priority term had been redefined to eliminate the product effect and ensure data term had always effective. The priority of repairing patch and the best matching patch are determined by the similarity of the known information and the consistency of the unknown information in the repairing patch. The comparisons with cognitive computing image algorithms had been shown that the proposed method can ensure better selection of candidate image pixel to fill with, and it is achieved better global coherence of image completion than others. The inpainting results of noisy images show that the proposed method has good robustness and can also get good inpainting results for noisy images. [ABSTRACT FROM AUTHOR]

Nonnegative Matrix Factorization (NMF) has become a popular technique for dimensionality reduction, and been widely used in machine learning, computer vision, and data mining. Existing unsupervised NMF methods impose the intrinsic geometric constraint on the encoding matrix, which only indirectly affects the base matrix. Moreover, they ignore the global structure of the data space. To address these issues, in this paper we propose a novel unsupervised NMF learning framework, called Robust Graph regularized Nonnegative Matrix Factorization (RGNMF). RGNMF constructs a sparse graph imposed on the basis matrix to catch the global structure and preserve the discriminative information. And it models the local structure by building a k-NN graph constrained on the encoding matrix, which gains the compact representation. Consequently, RGNMF not only respects the global structure, but also depicts the local structure. In addition, it employs such a $\text{L}_{2,1}$ -norm cost function to decompose the basis matrix and encoding matrix that its robustness can be improved. Further, it imposes the $\text{L}_{2,1}$ -norm constraint on the basis matrix to choose the discriminative feature. Hence, RGNMF can gain the robust discriminative representation by combining structure learning and $\text{L}_{2,1}$ -norm constraints imposed on the basis matrix and encoding matrix. Extensive experiments on real-world problems demonstrate that RGNMF achieves better clustering results than the state-of-the-art approaches.

The paper reports the results of observations of the interplanetary scintillation of a compact radio source 3С 48 at the descending phase 24 solar cycle. The observations were conducted using a BSA LPI radiotelescope at frequency of 111 MHz. A comparison was made between an index (level) of the scintillation and solar wind speed, which was computed by a width of the scintillation temporal spectra. Complete series of observations from 2015 to 2019 displays a weak declining dependence of the scintillation level on the solar wind speed; the correlation, however, is rather low (averages about –0.15) due to a significant scatter in the data. With averaging over one-year intervals, the correlation coefficient module increases almost up to 1 with scintillation index in the mean approximately inversely proportional to solar wind speed. The paper further elaborates on a possible relationship between a spatial-temporal structure of the scintillation level and mean plasma density of the solar wind. [ABSTRACT FROM AUTHOR]

We previously generated diverse mathematical functions that are difficult for optimization algorithms. Represented as 2D contour plots, each image depicts a 'blue river' running through an intricate landscape. This paper describes the challenge of constructing an aesthetic montage of these images. A survey revealed a spectrum of tastes, divergent in preference from order to disorder, considering the structure created by connecting these 'blue rivers'. A new artwork, Negentropy Triptych, was created to depict this spectrum by manually swapping images from a random arrangement, guided by human eye to enhance or destroy the structure. An optimization algorithm automates the process, with the results of its efforts to emulate the artistic vision presented and discussed. The challenges faced by the algorithm, despite exploring several objective functions, highlight the difficulties of capturing the goals that a human decision-maker can easily achieve. Therefore, machine learning of these goals is a promising future direction. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Multidimensional scaling is a process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to have high computational complexities, making them inapplicable on large data sets. This work introduces a stochastic, force directed approach to multidimensional scaling with a time and space complexity of O (N) , with N data points. The method can be combined with force directed layouts of the family of neighbour embedding such as t -SNE, to produce embeddings that preserve both the global and the local structures of the data. Experiments assess the quality of the embeddings produced by the standalone version and its hybrid extension both quantitatively and qualitatively, showing competitive results outperforming state-of-the-art approaches. Codes are available at https://github.com/PierreLambert3/SQuaD-MDS-and-FItSNE-hybrid. [ABSTRACT FROM AUTHOR]

Unsupervised cell clustering on the basis of meaningful biological variation in single-cell RNA sequencing (scRNA seq) data has received significant attention, as it assists with ontological subpopulation identification among the data. A key step in the clustering process is to compute distances between the cells under a specified distance measure. Although particular distance measures may successfully separate cells into biologically relevant clusters, they may fail to retain global structure of the data, such as relative similarity between the cell clusters. In this article, we modify a biologically motivated distance measure, SIDEseq, for use of aggregate comparisons of cell types in large single-cell assays, and demonstrate that, across simulated and real scRNA seq data, the distance matrix more consistently retains global cell type relationships than commonly used distance measures for scRNA seq clustering. We call the modified distance measure "SIDEREF." We explore spectral dimension reduction of the SIDEREF distance matrix as a means of noise filtering, similar to principal components analysis applied directly to expression data. We utilize a summary measure of relative cell type distances to better display the cell group relationships. SIDEREF visualizations more consistently reflect global structures in the data than other commonly considered distance measures. We utilize relative cell type distances and the SIDEREF distance measure to uncover compositional differences between annotated leukocyte cell groups in a compendium of Mus musculus scRNA seq assays comprising 12 tissues. SIDEREF and associated analysis is openly available on GitHub. [ABSTRACT FROM AUTHOR]

Few-shot fine-grained image classification aims to recognize sub-categories of the same super-category given only a few labeled samples. To deal with the low inter-class variation and the high intra-class discordance, both the supervised guidance from the global view and the detail information hidden in the local structure are necessary. However, such global structure and local detail are usually applied separately by existing methods, as a result, the features are not discriminative enough. To address this issue, we propose a novel few-shot fine-grained image classification framework which enhances the Discriminative ability of Local structures utilizing class-aware Global structures (DLG). Firstly, the DLG model calculates the global structures utilizing prototype representations of each class, and then constructs class-aware attention maps for query images to enhance their discriminative local structures with the aid of global structures. Finally, a classification module based on local structures is performed to make predictions. Results of case studies demonstrate that the class-aware attention maps can focus on class discriminative regions. Extensive experiments on fine-grained datasets demonstrate that DLG outperforms the state-of-the-art methods. Taking Stanford Dogs as an example, the proposed DLG outperforms the baselines. More specifically, DLG obtains at least 13.4% and 17.9% average gain on accuracy for 1-shot and 5-shot classification problem respectively. Code can be found at https://gitee.com/csy213/few-shot-dlg. [ABSTRACT FROM AUTHOR]

Feature matching is a fundamental problem in many computer vision tasks. This paper proposes a novel effective framework for mismatch removal, named LOcality-guided Global-preserving Optimization (LOGO). To identify inliers from a putative matching set generated by feature descriptor similarity, we introduce a fixed-point progressive approach to optimize a graph-based objective, which represents a two-class assignment problem regarding an affinity matrix containing global structures. We introduce a strategy that a small initial set with a high inlier ratio exploits the topology of the affinity matrix to elicit other inliers based on their reliable geometry, which enhances the robustness to outliers. Geometrically, we provide a locality-guided matching strategy, i.e., using local topology consensus as a criterion to determine the initial set, thus expanding to yield the final feature matching set. In addition, we apply local affine transformations based on reference points to determine the local consensus and similarity scores of nodes and edges, ensuring the validity and generality for various scenarios including complex nonrigid transformations. Extensive experiments demonstrate the effectiveness and robustness of the proposed LOGO, which is competitive with the current state-of-the-art methods. It also exhibits favorable potential for high-level vision tasks, such as essential and fundamental matrix estimation, image registration and loop closure detection. [ABSTRACT FROM AUTHOR]

Graph embedding is one of the most efficient dimensionality reduction methods in machine learning and pattern recognition. Many local or global graph embedding methods have been proposed and impressive results have been achieved. However, little attention has been paid to the methods that integrate both local and global structural information without constructing complex graphs. In this paper, we propose a simple and effective global structure guided neighborhood preserving embedding method for dimensionality reduction called GSGNPE. Specifically, instead of constructing global graph, principal component analysis (PCA) projection matrix is first introduced to extract the global structural information of the original data, and then the induced global information is integrated with local neighborhood preserving structure to generate a discriminant projection. Moreover, the L 2 , 1 -norm regularization is employed in our method to enhance the robustness to occlusion. Finally, we propose an iterative optimization algorithm to solve the proposed problem, and its convergence is also theoretically analyzed. Extensive experiments on four face and six non-face benchmark data sets demonstrate the competitive performance of our proposed method in comparison with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

As an important technology in 3D vision, point-cloud registration has broad development prospects in the fields of space-based remote sensing, photogrammetry, robotics, and so on. Of the available algorithms, the Iterative Closest Point (ICP) algorithm has been used as the classic algorithm for solving point cloud registration. However, with the point cloud data being under the influence of noise, outliers, overlapping values, and other issues, the performance of the ICP algorithm will be affected to varying degrees. This paper proposes a global structure and adaptive weight aware ICP algorithm (GSAW-ICP) for image registration. Specifically, we first proposed a global structure mathematical model based on the reconstruction of local surfaces using both the rotation of normal vectors and the change in curvature, so as to better describe the deformation of the object. The model was optimized for the convergence strategy, so that it had a wider convergence domain and a better convergence effect than either of the original point-to-point or point-to-point constrained models. Secondly, for outliers and overlapping values, the GSAW-ICP algorithm was able to assign appropriate weights, so as to optimize both the noise and outlier interference of the overall system. Our proposed algorithm was extensively tested on noisy, anomalous, and real datasets, and the proposed method was proven to have a better performance than other state-of-the-art algorithms.

Given the discontinuous structure of vibro-impact system, Newton iteration was used to establish an effective numerical integration strategy, and this numerical integration strategy was applied to the cell mapping algorithm. The effectiveness of this method was verified by an application example of a typical duffing vibro-impact system, and the global coexistence attractor and global catastrophe of the system were further discussed. The research shows that Newton iterative integration method is suitable for vibro-impact system, and the study of periodic motion and chaotic motion of the system is not only effective, but also efficient, The algorithm can quickly locate the collision time and improve the calculation speed. With the change of parameters, there are abundant catastrophe phenomena in the vibro-impact system, including the rout from period directly to chaos, the crisis of multi-periodic solution and chaotic solution.

Nonnegative Matrix Factorization (NMF) is a popular technique for machine learning. Its power is that it can decompose a nonnegative matrix into two nonnegative factors whose product well approximates the nonnegative matrix. However, the nonnegative constraint of the data matrix limits its application. Additionally, the representations learned by NMF fail to respect the intrinsic geometric structure of the data. In this paper, we propose a novel unsupervised matrix factorization method, called Robust Structured Convex Nonnegative Matrix Factorization (RSCNMF). RSCNMF not only achieves meaningful factorizations of the mixed-sign data, but also learns a discriminative representation by leveraging local and global structures of the data. Moreover, it introduces the L2,1-norm loss function to deal with noise and outliers, and exploits the L2,1-norm feature regularizer to select discriminative features across all the samples. We develop an alternate iterative scheme to solve such a new model. The convergence of RSCNMF is proven theoretically and verified empirically. The experimental results on eight real-world data sets show that our RSCNMF algorithm matches or outperforms the state-of-the-art methods.

The results of the long-term (2015–2019) series of interplanetary scintillation observations carried out with the LPA LPI radio telescope at the frequency 111 MHz are presented. We analyzed the radial dependences of the relative level (index) of interplanetary scintillations of the radio source 3C 48, the line of sight to which during the year shifts from low to medium and high heliolatitudes. For all annual series, we showed that the radial dependence of the scintillation index turns out to be flatter than expected for the model of a spherically symmetric medium. The difference is explained by the latitudinal effect, considering the influence of the near-equatorial layer with an increased plasma density. Modeling the low-latitude layer shows that the layer thickness at the phase of the decline in solar activity is, on average, two times greater than near the activity minimum. [ABSTRACT FROM AUTHOR]

A comparison is made of the data from the annual series of interplanetary scintillation monitoring performed at the maximum (2015) and minimum (2019) of solar activity. The observations were carried out with the LPA LPI radio telescope at the frequency 111 MHz. We showed that the time-of-day dependences of the scintillation level averaged over monthly intervals for the summer months at the minimum and maximum are approximately the same. For the winter months, at the decay phase and at the minimum of activity, an annual periodicity in the scintillation level is observed; at the maximum of activity, there is no periodicity. The results obtained can be explained by a combination of the cyclic dynamics of the global structure of the solar wind and the change in the location of the solar wind regions probed in the experiment during the year. [ABSTRACT FROM AUTHOR]

The earth's crust is under various stresses including compressive stress, tensile stress and torsional stress, resulting in uplift, subsidence, depression and strike-slip. The tectonic movement caused uplifts and depressions in the crust, leading to changes in the land and sea. During the geological evolution history, the crust uplifted into orogenic belts or uplift areas, while depressions changed to various types of basins. Global basins can be divided into five major types, namely rift-craton, intracratonic depression, foreland, fault and depression ones. There are eight major deformation styles in the global structure, namely, east-west, north-south, north-east, north-north-east, north-west, epsilon-shaped, S- or reversed-S shaped, and twisted ones. Oil and gas in the Paleozoic cratonic basins of China are mainly distributed in paleo-uplifts, paleo-slopes, regional unconformities, and fault zones. In Mesozoic and Cenozoic faulted basins, oil and gas are mainly distributed in steep slopes, gentle slopes, and central structural belts. In Mesozoic and Cenozoic foreland basins, oil and gas are distributed in fault fold belts, slope belts and overthrust belts. Various twisted structures, such as broom-shaped, echelon, knob-shaped, reversed S-shaped, and λ-shaped ones, control oil and gas distribution.

Quantitative identification of key nodes in complex networks is of great significance for studying the robustness and vulnerability of complex networks. Although various centralities have been proposed to solve this issue, each approach has its limitations for its own perspective of determining an actor to be “key”. In this paper, we propose a novel method to identify key nodes in complex networks based on global structure. Three aspects including the shortest path length, the number of shortest paths and the number of non-shortest paths are considered, and we establish three corresponding influence matrices. Node efficiency, which can reflect the contribution of one node to the information transmission of the entire network, is selected as the initial value of node's influence on other nodes, and then the comprehensive influence matrix is constructed to reflect the influence among nodes. The proposed method provides a new measure to identify key nodes in complex networks from the perspective of global network structure, and can obtain more accurate identification results. Four experiments are conducted to evaluate the performance of our proposed method based on Susceptible-Infected (SI) model, and the results demonstrate the superiority of our method.

This paper considers unsupervised dimensionality reduction of multi-view data, where locality preserving canonical correlation analysis and a new locality-preserving canonical correlation analysis are two typical effective methods. However, they ignore the global structure while considering the local structure of data, and are sensitive to noises because of the relationship of neighbors based on the Euclidean distance. In this paper, we propose a novel multi-view dimensionality reduction method: multiset canonical correlations analysis based on low-rank representation. Our model introduces the cross-view similarity matrix to consider the correlation of all different points in cross views, which makes it not only preserve the local structure but also the global structure of data. And the cross-view similarity matrix is constructed by using low-rank representation, which can make the model more robust. In addition, a parameter ß is introduced to adjust the importance of the correlation of different sample points, enhancing the generalization ability for different datasets. Experiments on four multi-view datasets show our proposed method has better performance than the related methods.

In recent years, the huge expansion of digital technologies has vastly increased the volume of data to be explored, such that reducing the dimensionality of data is an essential step in data exploration. The integrity of a dimensionality reduction technique relates to the goodness of maintaining the data structure. Dimensionality reduction techniques such as Principal Component Analyses (PCA) and Multidimensional Scaling (MDS) globally preserve the distance ranking at the expense of neglecting small-distance preservation. Conversely, the structure capturing of some other methods such as Isomap, Locally Linear Embedding (LLE), Laplacian Eigenmaps t-Stochastic Neighbour Embedding (t-SNE), Uniform Manifold Approximation and Projection (UMAP), and TriMap rely on the number of neighbours considered. This paper presents a dimensionality reduction technique, Same Degree Distribution (SDD) that does not rely on the number of neighbours, thanks to using degree-distributions in both high and low dimensional spaces. Degree-distribution is similar to Student-t distribution and is less expensive than Gaussian distribution. As such, it enables better global data preservation in less processing time. Moreover, to improve the data structure capturing, SDD has been extended to Multi-SDDs (MSDD), which employs various degree-distributions on top of SDD. The proposed approach and its extension demonstrated a greater performance compared with eight other benchmark methods, tested in several popular synthetics and real datasets such as Iris, Breast Cancer, Swiss Roll, MNIST, and Make Blob evaluated by the co-ranking matrix and Kendall's Tau coefficient. For further work, we aim to approximate the number of distributions and their degrees in relation to the given dataset. Reducing the computational complexity is another objective for further work.

In this paper we first study the asymptotic oscillations of a connected component of the positive solution set of some non-positone operator equations using global bifurcation theories. Then by using these results, we study the asymptotic oscillations of a connected component of the positive solution set of some differential boundary value problems. This paper extends some previous results on asymptotic oscillations of a connected component of the positive solution set of differential boundary value problems to the operator equations in real Banach spaces and includes a more general boundary condition. The existence of infinitely many solutions can also be obtained by using our main results. [ABSTRACT FROM AUTHOR]

A planar ODE system which models the industrialization of a small open economy is considered. Because fractional powers are involved, its interior equilibria are hardly found by solving a transcendental equation and the routine qualitative analysis is not applicable. We qualitatively discuss the transcendental equation, eliminating the transcendental term to polynomialize the expression of extreme value, so that we can compute polynomials to obtain the number of interior equilibria in all cases and complete their qualitative analysis. Orbits near the origin, at which the system cannot be extended differentiably, are investigated by using the GNS method. Then we display all bifurcations of equilibria such as saddle-node bifurcation, transcritical bifurcation and a codimension 2 bifurcation on a one-dimensional center manifold. Furthermore, we prove nonexistence of closed orbits, homoclinic loops and heteroclinic loops, exhibit global orbital structure of the system and analyze the tendency of the industrialization development. [ABSTRACT FROM AUTHOR]

Manifold alignment is very prevalent in machine learning for extracting common latent space from multiple datasets. These algorithms generally aim to achieve higher alignment accuracies by preserving the original structure while ensuring closeness between manifolds. This paper proposes a novel semi-supervised manifold alignment method that combines, in each manifold, both global and local linear reconstructions. We preserve a local structure through multiple manifold embedding methods. Moreover, we view manifold embedding methods as special forms of principal component analysis (PCA) and, thus, present a new penalty weight PCA approach to preserving a noise-free global structure. Finally, a closed-form solution is presented in the manifold alignment. This method can concurrently match the pair-wise correspondence and preserve both the global and local structures of each dataset to obtain a latent low-dimensional space. The extensive experiments on manifold alignment prove that the proposed method achieves significantly better alignment results than the comparative methods.

We consider the multidimensional Hamilton–Jacobi (HJ) equation u t + γ − 1 | D u | γ = 0 with 1 < γ < 2 being a constant and for bounded C 2 initial data. When γ = 2 , this is the typical case of interest with a uniformly convex Hamiltonian. When γ = 1 , this is the famous Eikonal equation from geometric optics, the Hamiltonian being Lipschitz continuous with homogeneity 1. We intend to fill the gap in between these two cases. When 1 < γ < 2 , the Hamiltonian H (p) = γ − 1 | p | γ is not uniformly convex and is only C 1 in any neighborhood of 0 , which causes new difficulties. In particular, points on characteristics emanating from points with vanishing gradient of the initial data could be "bad" points, so the singular set is more complicated than what is observed in the case γ = 2. We establish here the regularity of solutions and the global structure of the singular set from a topological standpoint: the solution inherits the regularity of the initial data in the complement of the singular set and there is a one-to-one correspondence between the connected components of the singular set and the path-connected components of the set { y 0 | g (y 0) > inf y ∈ ℝ n g (y) }. [ABSTRACT FROM AUTHOR]

Given the discontinuous structure of vibro-impact system. Newton iteration was used to establish an effective numerical integration strategy. and this numerical integration strategy was applied to the cell mapping algorithm. The effectiveness of this method was verified by an application example of a typical duffing vibro-impact system. and the global coexistence attractor and global catastrophe of the system were further discussed. The research shows that Newton iterative integration method is suitable for vibro-impact system, and the study of periodic motion and chaotic motion of the system is not only effective, but also efficient. The algorithm can quickly lo- cate the collision time and improve the calculation speed. With the change of parameters. there are abundant catastrophe phenomena in the vibro-impact system. including the rout from period directly to chaos. the crisis of multi-periodic solution and chaotic solution. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we obtain the global structure of positive solutions for nonlinear discrete simply supported beam equation Δ4u(t−2)=λf(t,u(t)),t∈T,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, $$\begin{aligned}& \Delta ^{4}u(t-2)= \lambda f\bigl(t,u(t)\bigr),\quad t\in \mathbb{T}, \\& u(1)=u(T+1)=\Delta ^{2}u(0)=\Delta ^{2}u(T)=0, \end{aligned}$$ with f∈C(T×[0,∞),[0,∞)) $f\in C(\mathbb{T}\times [0,\infty ),[0,\infty ))$ satisfying local linear growth condition and f(t,0)=0 $f(t,0)=0$ uniformly for t∈T $t\in \mathbb{T}$, where T={2,…,T} $\mathbb{T}=\{2,\ldots,T\}$, λ>0 $\lambda >0$ is a parameter. The main results are based on the global bifurcation theorem.

Multiple kernel clustering (MKC) based on global structure alignment (GSA) has unified many existing MKC algorithms, and shown outstanding clustering performance. However, we observe that most of existing GSA-based MKC algorithms only maximally align global structure of data with an ideal similarity matrix, while ignoring the local geometrical structure hidden in data, which is regarded to be important in improving the clustering performance. To address this issue, we propose a global and local structure alignment framework for MKC (GLSAMKC) which well considers both the alignment between the global structure and local structure of data with the same ideal similarity matrix. To illustrate the effectiveness of the proposed framework, we instantiate two specific GLSAMKC-based algorithms by exploiting the local structure with local linear embedding and locality preserving projection, respectively. A two-step alternate iterative and convergent optimization algorithm is developed to implement the resultant optimization problem. Extensive experimental results on five benchmark data sets demonstrate the superiority of proposed algorithms compared with the many state-of-the-art MKC algorithms, indicating the effectiveness of the proposed framework.

Nonnegative matrix factorization (NMF) has attracted more and more attention due to its wide applications in computer vision, information retrieval, and machine learning. In contrast to the original NMF and its variants, this paper proposes a novel unsupervised learning framework, called robust structured nonnegative matrix factorization (RSNMF) which respects both global and local structures of the data space. Specifically, to learn a discriminative representation, RSNMF explores both the global structure via considering the data variance and the local structure via exploiting the data neighborhood. To well address the problem of noise and outliers, it imposes joint L 2,1 -norm minimization on both the loss function of NMF and the regularization of the basis matrix. The geometric structure and the joint L 2,1 -norm are formulated as an optimization model, which is solved by the proposed iterative algorithm. Finally, the convergence of RSNMF is analyzed theoretically and empirically. The experimental results on real-world data sets show the effectiveness of our proposed algorithm in comparison to state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

State-of-the-art neural style transfer methods have demonstrated amazing results by training feed-forward convolutional neural networks or using an iterative optimization strategy. The image representation used in these methods, which contains two components: style representation and content representation, is typically based on high-level features extracted from pre-trained classification networks. Because the classification networks are originally designed for object recognition, the extracted features often focus on the central object and neglect other details. As a result, the style textures tend to scatter over the stylized outputs and disrupt the content structures. To address this issue, we present a novel image stylization method that involves an additional structure representation. Our structure representation, which considers two factors: i) the global structure represented by the depth map and ii) the local structure details represented by the image edges, effectively reflects the spatial distribution of all the components in an image as well as the structure of dominant objects respectively. Experimental results demonstrate that our method achieves an impressive visual effectiveness, which is particularly significant when processing images sensitive to structure distortion, e.g. images containing multiple objects potentially at different depths, or dominant objects with clear structures. [ABSTRACT FROM AUTHOR]

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