Local Topological Structure Research Articles

Spectral analysis and its applications for a class of scale‐free network based on the weighted m‐clique annex operation

The spectrum of network is an important tool to study the function and dynamic properties of network, and graph operation and product are an effective mechanism to construct a specific local and global topological structure. In this study, a class of weighted ‐clique annex operation controlled by scale factor and weight factor is defined, through which an iterative weighted network model with small‐world and scale‐free properties is constructed. In particular, when the number of iterations tends to infinity, the network has transfinite fractal property. Then, through the iterative features of the network structure, the iterative relationship of the eigenvalues of the normalized Laplacian matrix corresponding to the network is studied. Accordingly, some applications of the spectrum of the network, including the Kenemy constant , Multiplicative Degree‐Kirchhoff index , and the number of weighted spanning trees , are further given. In addition, we also study the effect of the two factors controlling network operation on the structure and function of the iterative weighted network , so that the network operation can better simulate the real network and have more application potential in the field of artificial network.

Optical Imaging and Analytical Design of Localized Topological Structures in Chiral Liquid Crystals

We combine numerical modeling and analytical design techniques to study several of the most common localized topological structures in frustrated chiral nematic liquid crystal cells. An energy minimization procedure is applied to the lattice model to simulate the director field distributions. These distributions are also approximated using the suitably designed analytical ansatz. We present both simulated and approximated results for optical polarizing microscopy textures and different visualizations of director field structure such as distributions of the azimuthal director angle and isolines for the normal component of the director in coordinate planes. The ansatz correctly mimicked the geometry and optical properties of the solitonic structures under consideration.

Unconventional Floquet Topological Phases from Quantum Engineering of Band-Inversion Surfaces

Floquet engineering provides a toolbox for the realization of novel quantum phases without static counterparts, while conventionally the realization may rely on the manipulation of complex temporal evolution. Here we propose a systematic and high-precision scheme to realize unconventional Floquet topological phases by engineering local band structures in particular momentum subspace called band inversion surfaces (BISs). This scheme is based on a new bulk-boundary correspondence that for a class of generic $d$-dimensional periodically driven systems, the local topological structure formed in each BIS uniquely determines the features of gapless boundary modes. By engineering the BIS configuration we demonstrate a highly efficient approach to realize, manipulate, and detect novel Floquet topological phases. In particular, we predict a two-dimensional (2D) anomalous Floquet valley-Hall phase which carries trivial global bulk topological invariants but features protected counter-propagating edge states in each quasienergy gap. The unconventional nature of this novel 2D phase is further illustrated by the examination of edge geometry dependence and its robustness to disorder scattering. Anomalous chiral topological phases with valley protection in higher dimension are also predicted and studied. Our systematic and highly feasible scheme opens a new route to realize and engineer unconventional Floquet topological phases for ultracold atoms and other quantum simulators.

Topological structures of event horizons along framed null Cartan curves in Minkowski space

In this work, we model two event horizons associated with a null Cartan curve as two lightlike hypersurfaces, respectively. We define a lightlike surface and a spacelike surface whose images coincide with the sets of critical values of two event horizons, and meanwhile we present two curves whose images coincide with the sets of critical values of these two surfaces, respectively. Using the singularity theory, we characterize the local topological structures of two event horizons, two surfaces and two curves at their singularities by means of two new invariants. Moreover, we also present a spacelike braneworld model along the particle as a spacelike surface in hyperbolic 3-space. An important fact shows that from the viewpoint of Legendrian dualities, this surface is [Formula: see text]-dual to the tangent trajectory [Formula: see text] of the null Cartan curve in Lorentz–Minkowski space-time. Meanwhile, we also consider a curve whose image is the set of critical values of this surface in hyperbolic 3-space. The third invariant of the null Cartan curve characterizes the singularities of the surface [Formula: see text] and the curve [Formula: see text] in hyperbolic 3-space. A result indicates that surface [Formula: see text] is locally diffeomorphic to the swallowtail [Formula: see text] or cuspidal edge [Formula: see text] and [Formula: see text] is locally diffeomorphic to the [Formula: see text]-cusp at certain a singular point. It is also shown that there exist deep relationships between the singularities of the surface [Formula: see text] and the curve [Formula: see text] and the order of contact between [Formula: see text] and elliptic quadric [Formula: see text] or the order of contact between [Formula: see text] and spacelike hyperplane [Formula: see text]. Finally, we present several examples to describe the main results.

Duality and singularities of world sheets and worldlines of geometric particles along framed base curves in world hyper-sheet

In this paper, as applications of singularity theory, we consider the singularities of a world sheet and the traveling trajectory (i.e. a worldline) of a geometric particle when they are confined in a world hyper-sheet and are generated by a Sabban framed base curve in de Sitter 3-space. Using the approach of the unfolding theory in singularity theory, we establish the relationships between the world sheet, the worldline of the geometric particle and two invariants to characterize the local topological structures of singularities of the world sheet and the worldline of the geometric particle via these two invariants, respectively. Moreover, we also describe the dual relationships between the tangent curve of framed base curve and the worldline of the geometric particle. An important fact indicates that the worldline [Formula: see text] and the tangent curve [Formula: see text] of the original curve [Formula: see text] are [Formula: see text]-dual each other. Finally, two concrete examples are presented to interpret our theoretical results.

Revealing Cu2+-localized topological structures in zeolite for effective purification of ultra-low-concentration methyl mercaptan

Purification of ultra-low-concentration malodorous gases from community and factory is a worldwide hot topic. Although adsorption is one of the most effective methods, seldom reports purified malodorous gas with a concentration lower than 1 ppm. In this work, metal (Zn, Al, Cu, Cr, Ce, Mn, and Fe) exchanged ZSM-5 are synthesized, and applied in removing 0.01 ppm of methyl mercaptan (MM), which is a typical malodorous gas. Cu-exchanged ZSM-5 shows the longest breakthrough time for MM removal among all metals. In addition, the zeolite is regenerable for MM purification. In order to make clear the most effective topological structures for Cu2+ localizations, Cu-exchanged X, Y, and ZSM-5 zeolites are compared in investigations of breakthrough time and topological structures. As a result, Cu-exchanged ZSM-5 shows the longest breakthrough time of 213 min. Moreover, removal efficiencies of various Cu2+ localizations follow the order of n-membered ring (n ≥ 8) ≪ double 6 ring ≈ 6-membered ring < 5-membered ring. A shorter-chain ring configuration creates a confinement effect, which makes the adsorption easier between Cu2+ and ultra-low-concentration MM. The main results this work help to develop and understand effective adsorbent for super clean emissions.

Analysis of Aerobics Auxiliary Training Based on Deep Learning

With the in-depth integration of information technology and subject teaching, it is also an inevitable trend to apply modern information technology to aerobics teaching. In this paper, the N-best algorithm is used in the video and real-time camera in aerobics, so that the human posture parameters in a single-frame image can be estimated. By using the relative position and motion direction of each part of the human body to describe the characteristics of aerobics, the Laplace scoring method is used to reduce the dimension of the data, and the discriminant human motion feature vector with a strong local topological structure is obtained. Finally, the iterative self-organizing data analysis technology (ISODATA algorithm) is used to dynamically determine the keyframe. In the aerobics video keyframe extraction experiments, the ST-FMP model improves the recognition accuracy of nondeterministic body parts of the flexible hybrid articulated human model (FMP) by about 15 percentage points and achieves 81% keyframe extraction accuracy, which is better than the keyframe algorithms of KFE and motion block. The proposed algorithm is sensitive to human motion features and human pose and is suitable for motion video annotation review.

Topological structures in chiral media: Effects of confined geometry.

We theoretically study orientational structures in chiral magnetics and cholesteric liquid crystal (CLC) nanosystems confined in the slab geometry. Our analysis is based on the model that, in addition to the exchange and the Dzyaloshinskii-Moriya interactions, takes into account the bulk and surface anisotropies. In CLC films, these anisotropies describe the energy of interaction with external magnetic/electric field and the anchoring energy assuming that magnetic/electric anisotropy is negative and the boundary conditions are homeotropic. We have computed the phase diagram and found that the ground state of the film is represented by various delocalized structures depending on the bulk and surface anisotropy parameters, κ^{b} and κ^{s}. These include the z helix and the z cone states, the oblique, and the x helicoids. The minimum energy paths connecting the ground state and metastable helicoids and the energy barriers separating these states are evaluated. We have shown that there is a variety of localized topological structures such as the skyrmion tube, the toron, and the bobber that can be embedded in different ground states including the z cone (conical phase) and tilted fingerprint states. We have also found the structure called the leech that can be viewed as an intermediate state between the toron and the skyrmion tube.

Local Affine Preservation With Motion Consistency for Feature Matching of Remote Sensing Images

As a fundamental and essential task in the field of remote sensing and photogrammetry, feature matching endeavors to establish reliable correspondences between two sets of feature points extracted from an image pair of the same scene. In this article, we propose an efficient and general algorithm, which is called local affine preservation (LAP) matching, for robust feature matching of remote sensing images. We start by constructing the putative point correspondences according to the similarity of well-designed feature descriptors and then focus on removing false matches from the putative set. The key idea of LAP is to search motion-consistent neighborhoods and maintain the local neighborhood topological structures of the true putative matches. To this end, we present a local geometric constraint, which exploits the property of affine invariance to measure the preservation degree of neighborhood topology, since the property is still held under both rigid and complex nonrigid transformations for a minimum topological unit. Moreover, in order to avoid the random distribution of outliers to destroy the neighborhood structure preservation of inliers, a neighbor mining strategy is introduced to search motion-consistent neighbors for each correspondence. We formulate the problem into an optimization model and derive a closed-form solution with linearithmic time complexity. Extensive experimental results on remote sensing images demonstrate that our LAP is able to achieve better performance over the current state-of-the-art approaches.

Understanding topological defects in fluidized dry active nematics.

Dense assemblies of self-propelling rods (SPRs) may exhibit fascinating collective behaviors and anomalous physical properties that are far away from equilibrium. Using large-scale Brownian dynamics simulations, we investigate the dynamics of disclination defects in 2D fluidized swarming motions of dense dry SPRs (i.e., without hydrodynamic effects) that form notable local positional topological structures that are reminiscent of smectic order. We find the deformations of smectic-like rod layers can create unique polar structures that lead to slow translations and rotations of ±1/2-order defects, which are fundamentally different from the fast streaming defect motions observed in wet active matter. We measure and characterize the statistical properties of topological defects and reveal their connections with the coherent structures. Furthermore, we construct a bottom-up active-liquid-crystal model to analyze the instability of polar lanes, which effectively leads to defect formation between interlocked polar lanes and serves as the origin of the large-scale swarming motions.

Density-Guided Locality Consensus for Fast Feature Matching

Establishing correct feature correspondences from two images of the same scene or target is a critical prerequisite in various applications. This letter proposes a simple but novel method to efficiently remove outliers from a putative match set, which is performed on searching potential inliers that can well preserve local topology structure. To this end, we provide a mathematical formulation and its closed-form solution for fast optimization. To construct local structure more accurately, we introduce a density-guided strategy, which enables our method to distinguish inliers and outliers more easily, thus largely enhancing the matching performance. Extensive experiments on both rigid and nonrigid datasets demonstrate the superiority of our method against the state of the art in both accuracy and efficiency.

Visual Analysis and Interactive Comparison for Heterogeneous Information Network Embedding Model

<p indent="0mm">To understand the differences between various heterogeneous information networks (HINs) embedding models, and to solve intricate and hidden problems in model evaluation, the comparative analysis method should include the following steps. First, the evaluation indicators and tasks are made consistent for all models. Then the parameters and structural features are extracted from the model training process and the complete and non-averaged evaluation results are retained for visualization. Based on the model parameters and characteristics data, we design and implement a visual analysis tool named HINCompare, which includes an overview of the distribution of basic evaluation indicators, a comparison view of recommended results, and a feature view of the local topology structure for model embedding. The tool allows developers to explore the common patterns of different feature aggregation methods of different models and the differences in their architectures. In addition, HINCompare shows user’s preferences for movie types and years with heat maps, which are combined with the contextual information of the recommended results for further analysis and evaluation. The system provides insights into black-box problems of models and increases interpretability by supplying information about the sources of the results. We conduct the preliminary evaluation study with Douban movie data to verify the effectiveness of the system.

Graph Embedding Based Novel Gene Discovery Associated With Diabetes Mellitus.

Diabetes mellitus is a group of complex metabolic disorders which has affected hundreds of millions of patients world-widely. The underlying pathogenesis of various types of diabetes is still unclear, which hinders the way of developing more efficient therapies. Although many genes have been found associated with diabetes mellitus, more novel genes are still needed to be discovered towards a complete picture of the underlying mechanism. With the development of complex molecular networks, network-based disease-gene prediction methods have been widely proposed. However, most existing methods are based on the hypothesis of guilt-by-association and often handcraft node features based on local topological structures. Advances in graph embedding techniques have enabled automatically global feature extraction from molecular networks. Inspired by the successful applications of cutting-edge graph embedding methods on complex diseases, we proposed a computational framework to investigate novel genes associated with diabetes mellitus. There are three main steps in the framework: network feature extraction based on graph embedding methods; feature denoising and regeneration using stacked autoencoder; and disease-gene prediction based on machine learning classifiers. We compared the performance by using different graph embedding methods and machine learning classifiers and designed the best workflow for predicting genes associated with diabetes mellitus. Functional enrichment analysis based on Human Phenotype Ontology (HPO), KEGG, and GO biological process and publication search further evaluated the predicted novel genes.

Recognition of singularities of rectifying worldsheets generated by framed worldlines

In this paper, we consider the local topological structures of a class of new worldsheets, call it the rectifying worldsheets, which are generated by a class of singular worldlines. Using the classification approaches of the finite type on the tangent developables and defining the extended striction curve, this paper gives the detailed classification of the rectifying worldsheets of singular worldlines. It is demonstrated that the rectifying worldsheets of singular worldlines will appear not only in cuspidal edge and swallowtail, but cuspidal beaks under suitable conditions. Especially the singularities of rectifying worldsheets of singular worldlines are associated with curvature functions such that the singularities can be characterized by these functions. Two examples are provided to put the theoretical results into the practice of computation and classification.

Loop-Closure Detection Using Local Relative Orientation Matching

Loop-closure detection (LCD), which aims to recognize a previously visited location, is a crucial component of the simultaneous localization and mapping system. In this paper, a novel appearance-based LCD method is presented. In particular, we propose a simple yet surprisingly useful feature matching algorithm for real-time geometrical verification of candidate loop-closures, termed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local relative orientation</i> matching (LRO). It aims to efficiently establish reliable feature correspondences based on preserving local topological structures between the query image and candidate frame. To effectively retrieve candidate loop closures, we introduce the aggregated selective match kernel framework into the LCD task, which can effectively represent images and reduce the quantization noise of the traditional bag-of-words framework. In addition, the SuperPoint neural network is employed to extract reliable interest points and feature descriptors. Extensive experimental results demonstrate that our LRO can significantly improve the LCD performance, and the proposed overall LCD method can achieve much better performance over the current state-of-the-art on six publicly available datasets.

Assessing the derivation of time parameters from branched polymer coarse-grain model.

The parameterization of rheological models for polymers is often obtained from experiments via the top-down approach. This procedure allows us to determine good fitting parameters for homogeneous materials but is less effective for polymer mixtures. From a molecular simulation point of view, the timescales needed to derive those parameters are often accessed through the use of coarse-grain potentials. However, these potentials are often derived from linear model systems and the transferability to a more complex structure is not straightforward. Here, we verify the transferability of a potential computed from linear polymer simulations to more complex molecular shapes and present a type of analysis, which was recently formulated in the framework of a tube theory, to a coarse-grain molecular approach in order to derive the input parameters for a rheological model. We describe the different behaviors arising from the local topological structure of molecular sub-units. Coarse-grain models and mean-field based tube theory for polymers form a powerful combination with potentially important applications.

Semi-supervised classification by graph p-Laplacian convolutional networks

The graph convolutional networks (GCN) generalizes convolution neural networks into the graph with an arbitrary topology structure. Since the geodesic function in the null space of the graph Laplacian matrix is constant, graph Laplacian fails to preserve the local topology structure information between samples properly. GCN thus cannot learn better representative sample features by the convolution operation of the graph Laplacian based structure information and input sample information. To address this issue, this paper exploits the manifold structure information of data by the graph p-Laplacian matrix and proposes the graph p-Laplacian convolutional networks (GpLCN). As the graph p-Laplacian matrix is a generalization of the graph Laplacian matrix, GpLCN can extract more abundant sample features and improves the classification performance utilizing graph p-Laplacian to preserve the rich intrinsic data manifold structure information. Moreover, after simplifying and deducing the formula of the one-order spectral graph p-Laplacian convolution, we introduce a new layer-wise propagation rule based on the one-order approximation. Extensive experiment results on the Citeseer, Cora and Pubmed database demonstrate that our GpLCN outperforms GCN.

Multi-Task Particle Swarm Optimization With Dynamic Neighbor and Level-Based Inter-Task Learning

Existing multifactorial particle swarm optimization algorithms treat all particles equally with a consistent inter-task exemplar selection and generation strategy. This may lead to poor performance when the algorithm searches partial optimal areas belonging to different tasks at the later stage. In pedagogy, teachers teach students in different levels distinctively under their cognitive and learning abilities. Inspired by this idea, in this work, we devise a novel level-based inter-task learning strategy upon a dynamic local topology of inter-task particles. The proposed method separates particles into several levels and assigns particles to different levels with distinct inter-task learning methods. Specifically, we propose a level-based inter-task learning strategy to transfer sharing information among the cross-task neighborhood. By assigning the particles with diverse search preferences, the algorithm is able to explore the search space by using the cross-task knowledge, while reserving an ability to refine the search area. In addition, to address the issue of inter-task neighbor selection, we reform dynamically the local topology structure across the inter-task particles by methodical sampling, evaluating and selecting processes. Experimental results on the benchmark problems demonstrate that the proposed method enables the efficient cross-domain information transfer via the level-based inter-task learning.

Generative network models of altered structural brain connectivity in schizophrenia

Alterations in the structural connectome of schizophrenia patients have been widely characterized, but the mechanisms remain largely unknown. Generative network models have recently been introduced as a tool to test the biological underpinnings of altered brain network formation. We evaluated different generative network models in healthy controls (n=152), schizophrenia patients (n=66), and their unaffected first-degree relatives (n=32), and we identified spatial and topological factors contributing to network formation. We further investigated how these factors relate to cognition and to polygenic risk for schizophrenia. Our data show that among the four tested classes of generative network models, structural brain networks were optimally accounted for by a two-factor model combining spatial constraints and topological neighborhood structure. The same wiring model explained brain network formation across study groups. However, relatives and schizophrenia patients exhibited significantly lower spatial constraints and lower topological facilitation compared to healthy controls. Further exploratory analyses point to potential associations of the model parameter reflecting spatial constraints with the polygenic risk for schizophrenia and cognitive performance. Our results identify spatial constraints and local topological structure as two interrelated mechanisms contributing to regular brain network formation as well as altered connectomes in schizophrenia and healthy individuals at familial risk for schizophrenia. On an exploratory level, our data further point to the potential relevance of spatial constraints for the genetic risk for schizophrenia and general cognitive functioning, thereby encouraging future studies in following up on these observations to gain further insights into the biological basis and behavioral relevance of model parameters.

Regularized Matrix Factorization for Multilabel Learning With Missing Labels

This article tackles the problem of multilabel learning with missing labels. For this problem, it is widely accepted that label correlations can be used to recover the ground-truth label matrix. Most of the existing approaches impose the low-rank assumption on the observed label matrix to exploit label correlations by decomposing it into two matrices, which describe the latent factors of instances and labels, respectively. The quality of these latent factors highly influences the recovery of ground-truth labels and the construction of the multilabel classification model. In this article, we propose recovering the ground-truth label matrix by regularized matrix factorization. Specifically, the latent factors of instances are regularized by the local topological structure derived from the feature space, which can be further used to induce an effective multilabel model. Moreover, the latent factors of labels and the label correlations are mutually adapted via label manifold regularization. In this way, the recovery of the ground-truth label matrix and the construction of the multilabel classification model are optimized jointly and can benefit from the regularized matrix factorization. Extensive experimental studies show that the proposed approach significantly outperforms the state-of-the-art algorithms on both full-label and missing-label data.