nonlinear structure
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Semantic Web ◽  
2022 ◽  
pp. 1-16
Author(s):  
Hu Zhang ◽  
Jingjing Zhou ◽  
Ru Li ◽  
Yue Fan

With the rapid development of neural networks, much attention has been focused on network embedding for complex network data, which aims to learn low-dimensional embedding of nodes in the network and how to effectively apply learned network representations to various graph-based analytical tasks. Two typical models exist namely the shallow random walk network representation method and deep learning models such as graph convolution networks (GCNs). The former one can be used to capture the linear structure of the network using depth-first search (DFS) and width-first search (BFS), whereas Hierarchical GCN (HGCN) is an unsupervised graph embedding that can be used to describe the global nonlinear structure of the network via aggregating node information. However, the two existing kinds of models cannot simultaneously capture the nonlinear and linear structure information of nodes. Thus, the nodal characteristics of nonlinear and linear structures are explored in this paper, and an unsupervised representation method based on HGCN that joins learning of shallow and deep models is proposed. Experiments on node classification and dimension reduction visualization are carried out on citation, language, and traffic networks. The results show that, compared with the existing shallow network representation model and deep network model, the proposed model achieves better performances in terms of micro-F1, macro-F1 and accuracy scores.


Author(s):  
Jing Wang ◽  
Jinglin Zhou ◽  
Xiaolu Chen

AbstractThis chapter proposes another nonlinear PLS method, named as locality-preserving partial least squares (LPPLS), which embeds the nonlinear degenerative and structure-preserving properties of LPP into the PLS model. The core of LPPLS is to replace the role of PCA in PLS with LPP. When extracting the principal components of $$\boldsymbol{t}_i$$ t i and $$\boldsymbol{u}_i$$ u i , two conditions must satisfy: (1) $$\boldsymbol{t}_i$$ t i and $$\boldsymbol{u}_i$$ u i retain the most information about the local nonlinear structure of their respective data sets. (2) The correlation between $$\boldsymbol{t}_i$$ t i and $$\boldsymbol{u}_i$$ u i is the largest. Finally, a quality-related monitoring strategy is established based on LPPLS.


2021 ◽  
Vol 3 (4) ◽  
pp. 966-989
Author(s):  
Vanessa Buhrmester ◽  
David Münch ◽  
Michael Arens

Deep Learning is a state-of-the-art technique to make inference on extensive or complex data. As a black box model due to their multilayer nonlinear structure, Deep Neural Networks are often criticized as being non-transparent and their predictions not traceable by humans. Furthermore, the models learn from artificially generated datasets, which often do not reflect reality. By basing decision-making algorithms on Deep Neural Networks, prejudice and unfairness may be promoted unknowingly due to a lack of transparency. Hence, several so-called explanators, or explainers, have been developed. Explainers try to give insight into the inner structure of machine learning black boxes by analyzing the connection between the input and output. In this survey, we present the mechanisms and properties of explaining systems for Deep Neural Networks for Computer Vision tasks. We give a comprehensive overview about the taxonomy of related studies and compare several survey papers that deal with explainability in general. We work out the drawbacks and gaps and summarize further research ideas.


Author(s):  
C. R. Argüelles ◽  
E. A. Becerra-Vergara ◽  
A. Krut ◽  
R. Yunis ◽  
J. A. Rueda ◽  
...  

We study the nonlinear structure formation in cosmology accounting for the quantum nature of the dark matter (DM) particles in the initial conditions at decoupling, as well as in the relaxation and stability of the DM halos. Different from cosmological N-body simulations, we use a thermodynamic approach for collisionless systems of self-gravitating fermions in general relativity, in which the halos reach the steady state by maximizing a coarse-grained entropy. We show the ability of this approach to provide answers to crucial open problems in cosmology, among others: the mass and nature of the DM particle, the formation and nature of supermassive black holes in the early Universe, the nature of the intermediate mass black holes in small halos, and the core-cusp problem.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Euihun Joung ◽  
Min-gi Kim ◽  
Yujin Kim

Abstract Conformal geometry is studied using the unfolded formulation à la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of $$ \mathfrak{so}\left(2,d\right) $$ so 2 d . We sketch the nonlinear structure of the equations and explain how Weyl invariant densities, which Type-B Weyl anomaly consist of, could be systematically computed within the unfolded formulation. The unfolded equation for conformal geometry is also shown to be reduced to various on-shell gravitational systems by requiring additional algebraic constraints.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yongbin Liu ◽  
Jingjie Wang ◽  
Wei Bai

Dimensionality reduction of images with high-dimensional nonlinear structure is the key to improving the recognition rate. Although some traditional algorithms have achieved some results in the process of dimensionality reduction, they also expose their respective defects. In order to achieve the ideal effect of high-dimensional nonlinear image recognition, based on the analysis of the traditional dimensionality reduction algorithm and refining its advantages, an image recognition technology based on the nonlinear dimensionality reduction method is proposed. As an effective nonlinear feature extraction method, the nonlinear dimensionality reduction method can find the nonlinear structure of datasets and maintain the intrinsic structure of data. Applying the nonlinear dimensionality reduction method to image recognition is to divide the input image into blocks, take it as a dataset in high-dimensional space, reduce the dimension of its structure, and obtain the low-dimensional expression vector of its eigenstructure so that the problem of image recognition can be carried out in a lower dimension. Thus, the computational complexity can be reduced, the recognition accuracy can be improved, and it is convenient for further processing such as image recognition and search. The defects of traditional algorithms are solved, and the commodity price recognition and simulation experiments are carried out, which verifies the feasibility of image recognition technology based on the nonlinear dimensionality reduction method in commodity price recognition.


Aerospace ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 344
Author(s):  
Chao An ◽  
Yang Meng ◽  
Changchuan Xie ◽  
Chao Yang

Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM.


Author(s):  
Nir Ben Shaya ◽  
Izhak Bucher ◽  
Amit Dolev

AbstractDescribed is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between the spatially filtered response and the excitation, the open-loop unstable solution branches are stabilized under a 2:1 parametric excitation of a chosen mode of vibration. For a given phase, the closed-loop automatically locks on a limit cycle, through an Autoresonance scheme, at any desired point on the solution branches. Axially driven slender beams and nanowires develop large transverse vibration under suitable amplitudes and frequency base-excitation that are sensitive to small potential coupled field. To utilize such a structure as a sensor, stable and robust operation are made possible by the control scheme. In addition, an optimal operating point with large sensitivity to the sensed potential field can be set using phase as a tunable parameter. Detailed analysis of the dynamical behavior, experimental verifications, and demonstrations sheds light on some features of the system dynamics.


Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2065
Author(s):  
Lucía Inglada-Pérez ◽  
Pablo Coto-Millán

Finding low-dimensional chaos is a relevant issue as it could allow short-term reliable forecasting. However, the existence of chaos in shipping freight rates remains an open and outstanding matter as previous research used methodology that can produce misleading results. Using daily data, this paper aims to unveil the nonlinear dynamics of the Baltic Dry Index that has been proposed as a measure of the shipping rates for certain raw materials. We tested for the existence of nonlinearity and low-dimensional chaos. We have also examined the chaotic dynamics throughout three sub-sampling periods, which have been determined by the volatility pattern of the series. For this purpose, from a comprehensive view we apply several metric and topological techniques, including the most suitable methods for noisy time series analysis. The proposed methodology considers the characteristics of chaotic time series, such as nonlinearity, determinism, sensitivity to initial conditions, fractal dimension and recurrence. Although there is strong evidence of a nonlinear structure, a chaotic and, therefore, deterministic behavior cannot be assumed during the whole or the three periods considered. Our findings indicate that the generalized autoregressive conditional heteroscedastic (GARCH) model and exponential GARCH (EGARCH) model explain a significant part of the nonlinear structure that is found in the dry bulk shipping freight market.


Author(s):  
Jie Liu ◽  
Tianqi Ding ◽  
Shanhui Liu ◽  
Bingbing Hu

Dynamic force is the key indicator for monitoring the condition of a mechanical product. These mechanical structures always encompass some nonlinear factors. Most previous studies focused on obtaining the dynamic force of linear structures. Consequently, this study focuses on the nonlinear mechanical structure, and a novel identification strategy is proposed to indirectly identify the excitation force. For the identification strategy, based on a nonlinear state-space model, a force identification equation for the nonlinear structure is built, wherein the transfer matrix consists of coefficient matrices of the nonlinear state-space model, and these coefficient matrices are calculated by a nonlinear subspace identification algorithm. Then, under the generalized cross-validation criterion, the truncated total least squares method is introduced to solve the ill-posed equation to eventually obtain the excitation force of the nonlinear structure. The identification results from two numerical simulation cases and one experimental case illustrate that the proposed identification strategy can stably and accurately identify the excitation force of nonlinear structures.


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