Euclidean Structure Research Articles

Systematic characterization and efficient prediction of cobalamin C deficiency clinical phenotypes using network analysis and deep learning on multi-omics data

As a monogenic disease, cobalamin C (cblC) deficiency lacks a clear correlation between gene pathogenic mutations and its spectrum of disease phenotypes, necessitating the understanding of molecular mechanisms how diverse clinical phenotypes emerge. This work aimed to disentangle the phenotypic complexity of cblC deficiency via network analysis and deep learning on multi-omics (proteomics and metabolomics) data. For this purpose, a novel computational framework was developed to systematically characterize and efficiently predict clinical phenotypes of cblC deficiency utilizing a Connect the Dots (CTD)-based Hybrid data Structural Representation of each patient and graph convolutional network (GCN)-based Multi-Omics Learning (CTDHSR-GCNMOL). CTD algorithm enabled the identification of relevant perturbed proteins or metabolites and the construction of clinical phenotype-specific co-perturbation network. GCN allowed efficient learning of subtle change patterns across clinical phenotypes not only depending on the hybrid feature description (Euclidean structure hybridized with non-Euclidean structure) of each patient but on the interaction exploration between patients offered by sample similarity network. Investigated by three clinical phenotypes (epilepsy, developmental delay and metabolic syndrome), the results showed that CTDHSR-GCNMOL identified the subsets of perturbed proteins or metabolites highly specific to each clinical phenotype and established each main disease module (network) for systematic characterization. For proteomics, epilepsy was characterized by the dysregulation of reported TAGLN2, SH3BGRL3 and LTA4H, and developmental delay was characterized by the dysregulation of reported HSP90AB1, PRDX1, GDI2, VIM, PNP and BLVRA with high confidence (selection frequencies). For untargeted metabolomics in negative ion mode, the disease status of metabolic syndrome could be well interpreted by the disturbed pathways of the top-ranked 20 perturbed metabolites all of which have been reported to be closely related with its pathogenesis in previous studies. These disturbed pathways involved butanoate metabolism, purine metabolism, alanine, aspartate and glutamate metabolism, pyrimidine metabolism, fructose and mannose metabolism, galactose metabolism, amino sugar and nucleotide sugar metabolism, and steroid hormone biosynthesis. Based on the hybridization of the abundances of perturbed proteins and metabolites with the topological structures of patient-specific perturbation network, CTDHSR-GCNMOL yielded desired prediction performance across three clinical phenotypes and outperformed the traditional block PLSDA. All these findings verified the effectiveness of CTDHSR-GCNMOL in gaining useful insights into the phenotypic complexity of cblC deficiency and guiding its targeted treatment strategies.

GCN-MHSA: A novel malicious traffic detection method based on graph convolutional neural network and multi-head self-attention mechanism

With the increasing size and complexity of network, network traffic becomes more and more correlated with each other, and the traditional manner of presenting network traffic in a Euclidean structure is difficult to effectively capture the correlation information of network traffic. In contrast, graph structured data has gained much attention in recent years due to its ability to represent the correlation between different traffic flows; In addition, models and algorithms related to Graph Convolution Neural network (GCN) have been used for malicious traffic detection. However, existing GCN-based malicious traffic detection methods still suffer from incomplete description of the flow-level features of network traffic, imperfect traffic correlation establishment mechanism and failure to distinguish the importance of features during model training. Based on this, this study proposes a malicious traffic detection method called GCN-MHSA based on Graph Convolutional Neural network and Multi-Head Self-Attention mechanism. Firstly, the flow-level features of network traffic are populated and more information close to the features are selected to describe the network traffic; And then, the link homogeneity is used to establish the correlations between network traffic; Moreover, multi-head self-attention mechanism is introduced in the GCN model to provide larger weight to important features; Finally, an improved GCN is used as a deep learning model to detect malicious traffic. Extensive experimental results on three publicly available network traffic datasets and a real network traffic dataset show that the proposed GCN-MHSA method performs better than five baselines in terms of detection effect and stability, with an improvement of about 2.4% in accuracy, recall and F1-measure as well as an improvement of about 2.1% in precision.

GCNs-Net: A Graph Convolutional Neural Network Approach for Decoding Time-Resolved EEG Motor Imagery Signals.

Toward the development of effective and efficient brain-computer interface (BCI) systems, precise decoding of brain activity measured by an electroencephalogram (EEG) is highly demanded. Traditional works classify EEG signals without considering the topological relationship among electrodes. However, neuroscience research has increasingly emphasized network patterns of brain dynamics. Thus, the Euclidean structure of electrodes might not adequately reflect the interaction between signals. To fill the gap, a novel deep learning (DL) framework based on the graph convolutional neural networks (GCNs) is presented to enhance the decoding performance of raw EEG signals during different types of motor imagery (MI) tasks while cooperating with the functional topological relationship of electrodes. Based on the absolute Pearson's matrix of overall signals, the graph Laplacian of EEG electrodes is built up. The GCNs-Net constructed by graph convolutional layers learns the generalized features. The followed pooling layers reduce dimensionality, and the fully-connected (FC) softmax layer derives the final prediction. The introduced approach has been shown to converge for both personalized and groupwise predictions. It has achieved the highest averaged accuracy, 93.06% and 88.57% (PhysioNet dataset), 96.24% and 80.89% (high gamma dataset), at the subject and group level, respectively, compared with existing studies, which suggests adaptability and robustness to individual variability. Moreover, the performance is stably reproducible among repetitive experiments for cross-validation. The excellent performance of our method has shown that it is an important step toward better BCI approaches. To conclude, the GCNs-Net filters EEG signals based on the functional topological relationship, which manages to decode relevant features for brain MI. A DL library for EEG task classification including the code for this study is open source at https://github.com/SuperBruceJia/ EEG-DL for scientific research.

Fault prediction of unmanned aerial vehicles based on entropy weight fusion and temporal graph convolutional network with non-Euclidian structure

Predicting weak and hidden faults in unmanned aerial vehicles (UAVs) is challenging due to their variable operation conditions and complex mechanisms. Conventional neural network models process the multisensory data in the form of Euclidean structure, the intrinsic connections among the individual data points are easy to be disregarded. Additionally, multisensory data are always directly fed into the model without adequately considering the importance or contribution of each sensor. Hence, an UAV fault prediction method is proposed by combining entropy weight fusion with a temporal graph convolutional network (GCN) to address the above problems. Firstly, the importance of multisensory data of UAVs are evaluated by each entropy value, and the multisensory data fusion is further realized by multiplying corresponding signal and entropy weight. Secondly, the multisensory data combined with fusion data are transferred together into graph-structure by adjacent matrix based on the node connection between different sensor data. Finally, the graph-structure data with non-Euclidian distance properties are input into temporal GCN to both capture the spatial and temporal relationship of the data, achieving better fault prediction results of UAVs. It is demonstrated that the proposed method is both applicable and superior in characterizing and predicting fault time series information of UAVs through parameter analysis and comparison studies with various existing algorithms.

An arithmetic analysis of closed surfaces

From a computability-theoretic standpoint, we consider the following problem: Given a closed surface, as a topological space, how hard is it to recover an atlas? We prove that every computable Polish space homeomorphic to a closed surface admits an arithmetic atlas, and indeed an arithmetic triangulation. This is as simple as one could reasonably hope for; essentially, the locally Euclidean structure of a surface can be recovered from the topological structure in a first-order way, i.e., without reference to curves or homeomorphisms or other higher-order objects. It follows that given two computable presentations of the same closed surface, there is an arithmetic homeomorphism between them. Moreover, the homeomorphism problem for closed surfaces, presented as topological spaces, is arithmetic. From the algorithmic and definability-theoretic standpoint, this improves Kline’s conjecture proved by Bing in the 1940s. We also consider R 2 \mathbb {R}^2 and the closed unit ball.

Rigidity of Euclidean product structure: breakdown for low Sobolev exponents

Rigidity of Euclidean product structure: breakdown for low Sobolev exponents

The format of the cognitive map depends on the structure of the environment.

Humans and animals form cognitive maps that allow them to navigate through large-scale environments. Here we address a central unresolved question about these maps: whether they exhibit similar characteristics across all environments, or-alternatively-whether different environments yield different types of maps. To investigate this question, we examined spatial learning in three virtual environments: an open courtyard with patios connected by paths (open maze), a set of rooms connected by corridors (closed maze), and a set of isolated rooms connected only by teleporters (teleport maze). All three environments shared the same underlying topological graph structure. Postlearning tests showed that participants formed representations of the three environments that varied in accuracy, format, and individual variability. The open maze was most accurately remembered, followed by the closed maze, and then the teleport maze. In the open maze, most participants developed representations that reflected the Euclidean structure of the space, whereas in the teleport maze, most participants constructed representations that aligned more closely with a mental model of an interconnected graph. In the closed maze, substantial individual variability emerged, with some participants forming Euclidean representations and others forming graph-like representations. These results indicate that an environment's features shape the quality and nature of the spatial representations formed within it, determining whether spatial knowledge takes a Euclidean or graph-like format. Consequently, experimental findings obtained in any single environment may not generalize to others with different features. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Euclidean volumes of hyperbolic knots

The hyperbolic structure on a 3 3 –dimensional cone–manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an algebraic number, which is reminiscent of Sabitov’s theorem (the Bellows Conjecture). This fact also stands in contrast to hyperbolic volumes whose number–theoretic nature is usually quite complicated.

GAC-SleepNet: A dual-structured sleep staging method based on graph structure and Euclidean structure

Sleep staging is a precondition for the diagnosis and treatment of sleep disorders. However, how to fully exploit the relationship between spatial features of the brain and sleep stages is an important task. Many current classical algorithms only extract the characteristic information of the brain in the Euclidean space without considering other spatial structures. In this study, a sleep staging network named GAC-SleepNet is designed. GAC-SleepNet uses the characteristic information in the dual structure of the graph structure and the Euclidean structure for the classification of sleep stages. In the graph structure, this study uses a graph convolutional neural network to learn the deep features of each sleep stage and converts the features in the topological structure into feature vectors by a multilayer perceptron. In the Euclidean structure, this study uses convolutional neural networks to learn the temporal features of sleep information and combine attention mechanism to portray the connection between different sleep periods and EEG signals, while enhancing the description of global features to avoid local optima. In this study, the performance of the proposed network is evaluated on two public datasets. The experimental results show that the dual spatial structure captures more adequate and comprehensive information about sleep features and shows advancement in terms of different evaluation metrics.

Bringing nature indoors: characterizing the unique contribution of fractal structure and the effects of Euclidean context on perception of fractal patterns.

Imbuing the benefits of natural design into humanmade spaces, installations of fractal patterns have been employed to shape occupant experience. Previous work has demonstrated consistent trends for fractal judgments in the presence of design elements. The current study identifies the extent to which underlying pattern structure and perceptions of pattern complexity drive viewer judgments, and how response trends are altered with the incorporation of Euclidean context reminiscent of indoor spaces. This series of studies first establishes that pattern appeal, interest, naturalness, and relaxation have a fundamentally inverse relationship with perceptions of pattern complexity and that the presence of fractal structure contributes uniquely and positively to pattern perception. Subsequently, the addition of Euclidean structure establishes a discrete pattern boundary that alters fractal perceptions of interest and excitement but not the remaining judgments. The presence of consistent subpopulations, particularly those that contradict overarching perceptual trends is supported across studies, and further emphasizes the importance of adjusting pattern selection to consider the greatest number of possible viewers. Through informed pattern selection, designs can be installed to maximize desired experience of a space while minimizing negative impressions bound to arise in a minority of occupants. This set of studies demonstrates that through control of perceived pattern complexity and whether an emphasis is placed on pattern boundaries, fractal patterns can serve to establish predictable experiences of humanmade spaces in order to inject the benefits of nature into manufactured environments.

Traffic Speed Prediction Based on Time Classification in Combination With Spatial Graph Convolutional Network

With the advancement of automatic driving and smart city, it is critical to predict traffic information for traffic management, traffic planning, and traffic safety. When predicting traffic information, the spatial structure of the roads will also affect the traffic flow information, such as speed, occupancy rate, etc. The common method either merely focusing on the temporal feature without the considering the spatial structure, or the method of spatial feature extraction is only applicable to Euclidean structure, which does not apply to Non-Euclidean structure. This paper proposes a traffic speed prediction method based on time classification in combination with spatial Graph Convolutional Network. This method employs Gated Recurrent Unit to extract the temporal correlation and Graph Convolutional Network to extract the traffic network’s spatial structure. In consideration of the varying features of traffic speed on weekdays and weekends in the time dimension, time is divided into two types: weekdays and weekends. Since the structure of the road network will not change in the short term in actual process, the same network structure of spatial graph convolution can reasonably be shared in the spatial dimension after which the two sections are fused for training and prediction. Finally, this proposed method is compared to some baseline models to prove the performance. Generally speaking, this strategy produces more accurate prediction results on the PEMS_BAY and METR_LA data sets than the baseline models.

PN-GCN: Positive-negative graph convolution neural network in information system to classification

Graph convolution neural network (GCN) shows strong performance in non-Euclidean structure data. In recent years, many researchers have applied GCN to Euclidean structure data, such as images and languages, and obtained excellent results, which expanded the application range of GCN. Despite a large number of related methods, few studies deal with information systems from the perspective of graphs. In fact, the information system is also a non-Euclidean data structure, and there is serious information loss when using classical measurement methods to construct its data structure. Thus, the promotion of GCN is hindered in information systems. This paper applies GCN to the classification of information systems. Firstly, an intuitionistic fuzzy relation, called positive-negative relation, is established in the information system, and the physical meaning of this relationship is explained. Secondly, based on the positive-negative relation, a positive-negative relation graph convolution neural network model is constructed called PN-GCN. Finally, the effectiveness and robustness of PN-GCN are validated through experiments.

Fluctuation-based outlier detection

Outlier detection is an important topic in machine learning and has been used in a wide range of applications. Outliers are objects that are few in number and deviate from the majority of objects. As a result of these two properties, we show that outliers are susceptible to a mechanism called fluctuation. This article proposes a method called fluctuation-based outlier detection (FBOD) that achieves a low linear time complexity and detects outliers purely based on the concept of fluctuation without employing any distance, density or isolation measure. Fundamentally different from all existing methods. FBOD first converts the Euclidean structure datasets into graphs by using random links, then propagates the feature value according to the connection of the graph. Finally, by comparing the difference between the fluctuation of an object and its neighbors, FBOD determines the object with a larger difference as an outlier. The results of experiments comparing FBOD with eight state-of-the-art algorithms on eight real-worlds tabular datasets and three video datasets show that FBOD outperforms its competitors in the majority of cases and that FBOD has only 5% of the execution time of the fastest algorithm. The experiment codes are available at: https://github.com/FluctuationOD/Fluctuation-based-Outlier-Detection.

4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data.

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered. Also, different deforming objects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus they need to be temporally aligned. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemannian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the [Formula: see text] metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates; (2) the computation of geodesics between 4D surfaces; (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces; and (4) the synthesis of random 4D surfaces. We demonstrate the performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

Geometric Deep Neural Network Using Rigid and Non-Rigid Transformations for Landmark-Based Human Behavior Analysis.

Deep learning architectures, albeit successful in most computer vision tasks, were designed for data with an underlying Euclidean structure, which is not usually fulfilled since pre-processed data may lie on a non-linear space. In this article, we propose a geometric deep learning approach using rigid and non-rigid transformations, named KShapenet, for 2D and 3D landmark-based human motion analysis. Landmark configuration sequences are first modeled as trajectories on Kendall's shape space and then mapped to a linear tangent space. The resulting structured data are then input to a deep learning architecture, which includes a layer that optimizes over rigid and non-rigid transformations of landmark configurations, followed by a CNN-LSTM network. We apply KShapenet to 3D human landmark sequences for action and gait recognition, and 2D facial landmark sequences for expression recognition, and demonstrate the competitiveness of the proposed approach with respect to state-of-the-art.

A methodology for shape matching of non-rigid structures based on integrated graphical information

Shape matching is a long-studied problem and lies at the core of many applications in statistical shape analysis, virtual reality and human–computer interaction. This paper presents an automatic dense correspondence method to match the mesh vertices of two 3D shapes under near-isometric and non-rigid deformations. The goal is achieved by combining three types of graphic structure information. The method includes three major steps: first, we describe the vertices based on three types of graphical information, Euclidean structure information, Riemannian structure information, and conformal structure information; second, the match between two shapes is formulated as an optimization problem and a novel objective function is proposed; third, we resolve the optimal solution by using the projected descent optimization procedure to solve the objective function. The method is tested on various shape pairs with different poses, surface details, and topological noises. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several challenging 3D shape matching datasets where we achieve superior performance to existing methods.

Euclidean spacetime functionalism

We explore the significance of physical theories set in Euclidean spacetimes (i.e., theories with Riemannian rather than pseudo-Riemannian metrical structure). In particular, we explore (a) the use of these theories in contemporary physics at large, and (b) the sense in which there can be a notion of temporal evolution in these theories. Having achieved these tasks, we proceed to reflect on the lessons that one can take from such theories for Knox’s ‘inertial frame’ version of spacetime functionalism, which seems (on the face of it) to issue incorrect verdicts in the case of theories with Euclidean metrical structure.

Grid adaptive reduced-order model of fluid flow based on graph convolutional neural network

In the interdisciplinary field of data-driven models and computational fluid mechanics, the reduced-order model for flow field prediction is mainly constructed by a convolutional neural network (CNN) in recent years. However, the standard CNN is only applicable to data with Euclidean spatial structure, while data with non-Euclidean properties can only be convolved after pixelization, which usually leads to decreased data accuracy. In this work, a novel data-driven framework based on graph convolution network (GCN) is proposed to allow the convolution operator to predict fluid dynamics on non-uniform structured or unstructured mesh data. This is achieved by the fact that the graph data inherit the spatial characteristics of the mesh and by the message passing mechanism of GCN. The conversion method from the form of mesh data to graph data and the operation mechanism of GCN are clarified. Moreover, additional relevance features and weight loss function of the dataset are also investigated to improve the model performance. The model learns an end-to-end mapping between the mesh spatial features and the physical flow field. Through our studies of various cases of internal flow, it is shown that the proposed GCN-based model offers excellent adaptability to non-uniformly distributed mesh data, while also achieving a high accuracy and three-order speedup compared with numerical simulation. Our framework generalizes the graph convolution network to flow field prediction and opens the door to further extending GCN to most existing data-driven architectures of fluid dynamics in the future.

SCIR-Net: Structured Color Image Representation Based 3D Object Detection Network from Point Clouds

3D object detection from point clouds data has become an indispensable part in autonomous driving. Previous works for processing point clouds lie in either projection or voxelization. However, projection-based methods suffer from information loss while voxelization-based methods bring huge computation. In this paper, we propose to encode point clouds into structured color image representation (SCIR) and utilize 2D CNN to fulfill the 3D detection task. Specifically, we use the structured color image encoding module to convert the irregular 3D point clouds into a squared 2D tensor image, where each point corresponds to a spatial point in the 3D space. Furthermore, in order to fit for the Euclidean structure, we apply feature normalization to parameterize the 2D tensor image onto a regular dense color image. Then, we conduct repeated multi-scale fusion with different levels so as to augment the initial features and learn scale-aware feature representations for box prediction. Extensive experiments on KITTI benchmark, Waymo Open Dataset and more challenging nuScenes dataset show that our proposed method yields decent results and demonstrate the effectiveness of such representations for point clouds.

Affinity-Point Graph Convolutional Network for 3D Point Cloud Analysis

Efficient learning of 3D shape representation from point cloud is one of the biggest requirements in 3D computer vision. In recent years, convolutional neural networks have achieved great success in 2D image representation learning. However, unlike images that have a Euclidean structure, 3D point clouds are irregular since the neighbors of each node are inconsistent. Many studies have tried to develop various convolutional graph neural networks to overcome this problem and to achieve great results. Nevertheless, these studies simply took the centroid point and its corresponding neighbors as the graph structure, thus ignoring the structural information. In this paper, an Affinity-Point Graph Convolutional Network (AP-GCN) is proposed to learn the graph structure for each reference point. In this method, the affinity between points is first defined using the feature of each point feature. Then, a graph with affinity information is built. After that, the edge-conditioned convolution is performed between the graph vertices and edges to obtain stronger neighborhood information. Finally, the learned information is used for recognition and segmentation tasks. Comprehensive experiments demonstrate that AP-GCN learned much more reasonable features and achieved significant improvements in 3D computer vision tasks such as object classification and segmentation.