Global Topology Research Articles

Rethinking Rotation Invariance with Point Cloud Registration

Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks for invariance have seldom been looked into. In this work, we review rotation invariance (RI) in terms of point cloud registration (PCR) and propose an effective framework for rotation invariance learning via three sequential stages, namely rotation-invariant shape encoding, aligned feature integration, and deep feature registration. We first encode shape descriptors constructed with respect to reference frames defined over different scales, e.g., local patches and global topology, to generate rotation-invariant latent shape codes. Within the integration stage, we propose an Aligned Integration Transformer (AIT) to produce a discriminative feature representation by integrating point-wise self- and cross-relations established within the shape codes. Meanwhile, we adopt rigid transformations between reference frames to align the shape codes for feature consistency across different scales. Finally, the deep integrated feature is registered to both rotation-invariant shape codes to maximize their feature similarities, such that rotation invariance of the integrated feature is preserved and shared semantic information is implicitly extracted from shape codes. Experimental results on 3D shape classification, part segmentation, and retrieval tasks prove the feasibility of our framework. Our project page is released at: https://rotation3d.github.io/.

Disrupted topological organization of white matter structural networks in high myopia patients revealed by diffusion kurtosis imaging and tractography.

High myopia (HM) is a public health issue that can lead to severe visual impairment. Previous studies have exhibited widespread white matter (WM) integrity damage in HM patients. However, how these WM damages are topologically related, and the network-level structural disruptions underlying HM has not been fully defined. We aimed to assess the alterations of brain WM structural networks in HM patients using diffusion kurtosis imaging (DKI) and tractography in the present study. Individual whole-brain and ROI-level WM networks were constructed using DKI tractography in 30 HM patients and 33 healthy controls. Graph theory analysis was then applied to explore the altered global and regional network topological properties. Pearson correlations between regional properties and disease duration in the HM group were also assessed. For global topology, although both groups showed a small-world network organization, HM patients exhibited significant decreased local efficiency and clustering coefficient compared with controls. For regional topology, HM patients and controls showed highly similar hub distributions, except for three additional hub regions in HM patients including left insula, anterior cingulate and paracingulate gyri (ACG), and median cingulate and paracingulate gyri (DCG). In addition, HM patients showed significantly altered nodal betweenness centrality (BC) mainly in the bilateral inferior occipital gyrus (IOG), left superior occipital gyrus (SOG), caudate nucleus, rolandic operculum and right putamen, pallidum, and gyrus rectus compared with controls. Intriguingly, the nodal BC of left IOG was negatively correlated with disease duration in HM patients. Our findings suggest that HM exhibited alterations in WM structural networks as indicated by decreased local specialization. This study may advance the current understanding of the pathophysiological mechanisms underlying HM.

Parallel and anti-parallel helical surface states for topological semimetals

Weyl points, carrying a Z-type monopole charge C, have bulk-surface correspondence (BSC) associated with helical surface states (HSSs). When |C| >1, multi-HSSs can appear in a parallel manner. However, when a pair of Weyl points carrying C=pm 1 meet, a Dirac point carrying C = 0 can be obtained and the BSC vanishes. Nonetheless, a recent study in Zhang et al. (Phys Rev Res 4:033170, 2022) shows that a new BSC can survive for Dirac points when the system has time-reversal ({T})-glide ({G}) symmetry ({tilde{Theta }}=TG), i.e., anti-parallel double/quad-HSSs associated with a new Z_{2}-type monopole charge {Q} appear. In this paper, we systematically review and discuss both the parallel and anti-parallel multi-HSSs for Weyl and Dirac points, carrying two different kinds of monopole charges. Two material examples are offered to understand the whole configuration of multi-HSSs. One carries the Z-type monopole charge C, showing both local and global topology for three kinds of Weyl points, and it leads to parallel multi-HSSs. The other carries the Z_{2}-type monopole charge {Q}, only showing the global topology for {tilde{Theta }}-invariant Dirac points, and it is accompanied by anti-parallel multi-HSSs.

IsoGloVe: A New Count-based Graph Embedding Method based on Geodesic Distance

Graph embedding techniques have gained increasing attention for their ability to encode the complex structural information of networks into low-dimensional vectors. Existing graph embedding methods have achieved considerable success in various applications. However, these methods have limitations in capturing global graph topology information and fail to provide insights into the underlying mechanisms of network function. In this paper, we propose IsoGloVe, a count-based method that encodes graph topology into vectors using the co-occurrence statistics of fixed-size routes in random walks. IsoGloVe calculates the final embeddings based on the geodesic distances of the node’s neighbors on a manifold. This representation in geodesic space allows for the analysis of node interactions and contributes to a better understanding of complex network structure and function. The performance of IsoGloVe is evaluated on various protein-protein interactions (PPI) using graph reconstruction, node classification, and visualization. The findings reveal that IsoGloVe surpasses other comparable methods with a 30% increase in MAP for graph reconstruction and a 25% increase in model scores for node classification in the Yeast PPI network. In addition, IsoGloVe demonstrated a 6.9% increase in MAP for graph reconstruction on the Human PPI network.

Local Assortativity Affects the Synchronizability of Scale-Free Network

Synchronization is critical for system-level behavior in physical, chemical, biological, and social systems. Empirical evidence has shown that the network topology strongly impacts the synchronizability of the system, and the analysis of their relationship remains an open challenge. We know that the eigenvalue distribution determines a network's synchronizability, but analytical expressions that connect network topology and all relevant eigenvalues (e.g., the extreme values) remain elusive. Here, we accurately determine its synchronizability by proposing an analytical method to estimate the extreme eigenvalues using perturbation theory. Our analytical method exposes the role that global and local topology combine to influence synchronizability. We show that the smallest nonzero eigenvalue <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda ^{(2)}$</tex-math></inline-formula> , which determines synchronizability, is estimated by the smallest degree augmented by the inverse degree difference in the least connected nodes. From this, we can conclude that there exists a clear negative relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda ^{(2)}$</tex-math></inline-formula> and the local assortativity of nodes with the smallest degree value. We validate the accuracy of our framework within the setting of a scale-free network and can be driven by commonly used ordinary differential equations (e.g., 3-D Rosler dynamics or Hindmarsh–Rose neuronal circuit). From the results, we demonstrate that the synchronizability of the network can be tuned by rewiring the connections of these particular nodes while maintaining the general degree profile of the network.

Similarity measures-based graph co-contrastive learning for drug-disease association prediction.

An imperative step in drug discovery is the prediction of drug-disease associations (DDAs), which tries to uncover potential therapeutic possibilities for already validated drugs. It is costly and time-consuming to predict DDAs using wet experiments. Graph Neural Networks as an emerging technique have shown superior capacity of dealing with DDA prediction. However, existing Graph Neural Networks-based DDA prediction methods suffer from sparse supervised signals. As graph contrastive learning has shined in mitigating sparse supervised signals, we seek to leverage graph contrastive learning to enhance the prediction of DDAs. Unfortunately, most conventional graph contrastive learning-based models corrupt the raw data graph to augment data, which are unsuitable for DDA prediction. Meanwhile, these methods could not model the interactions between nodes effectively, thereby reducing the accuracy of association predictions. A model is proposed to tap potential drug candidates for diseases, which is called Similarity Measures-based Graph Co-contrastive Learning (SMGCL). For learning embeddings from complicated network topologies, SMGCL includes three essential processes: (i) constructs three views based on similarities between drugs and diseases and DDA information; (ii) two graph encoders are performed over the three views, so as to model both local and global topologies simultaneously; and (iii) a graph co-contrastive learning method is introduced, which co-trains the representations of nodes to maximize the agreement between them, thus generating high-quality prediction results. Contrastive learning serves as an auxiliary task for improving DDA predictions. Evaluated by cross-validations, SMGCL achieves pleasing comprehensive performances. Further proof of the SMGCL's practicality is provided by case study of Alzheimer's disease. https://github.com/Jcmorz/SMGCL.

Contagion in social networks: On contagion thresholds

Consider a story initiated by a set S of nodes belonging to a network. We assume that all the remaining nodes in the network have the same adoption threshold q such that each of them will accept the story if and only if the story has been accepted by at least a fraction q of its neighbors. Consequently, there is a maximum threshold q at and below which a full contagion (i.e. acceptance of the story by all nodes in the network) can occur from S, called the contagion threshold of S. We study how it is influenced by the neighborhood of S or by the global topology of the network. Firstly, we establish two algorithms to compute the contagion threshold of any given set of nodes in a network. Secondly, we show that the contagion threshold of a connected set in a tree is completely determined by the maximum degree of the nodes not in the set. Next, we derive bounds for the contagion threshold, while indicating when it preserves the neighborhood-inclusion pre-order and when the preservation may fail. Finally, we look at the structural characterization of the sets of nodes with high contagion thresholds.

Edge-event-triggered encryption-decryption observer-based control of multiagent systems for privacy protection under multiple cyber attacks

This study investigates the secure and privacy-preserving consensus problem for a class of Lipschitz nonlinear multiagent systems (MASs) under undirected topology and multiple cyber attacks. An observer-based dynamic cryptography-based encryption-decryption (CED) pairing algorithm is proposed to achieve privacy preservation and defend against replay attacks simultaneously. To reduce the computation and communication resources and facilitate paired password design, a Zeno-free edge-event-triggered mechanism (EETM) based on edge (rather than neighbor) information is developed in a completely distributed manner, using only local observation information without any knowledge about the global topology. The designed EETM can accommodate multiple event-triggered functions, which simplifies the EETM design procedure. Interestingly, the CED pairing algorithm makes the effect of replay attacks equivalent to that of denial-of-service (DoS) attacks. Thus, DoS and replay attacks can be handled as the same types of attacks. In addition, a resilient EETM-based control strategy against DoS and replay attacks is proposed to make the MAS reach consensus faster, within the attack sleep time. Furthermore, sufficient conditions for the frequency and duration of replay and DoS attacks are established to achieve secure consensus of the MAS. Finally, a numerical example is provided to demonstrate the validity and superiority of the proposed method.

Velocity-free distributed coordinated optimal control for second-order multi-agent systems

This paper solves the coordinated optimal consensus problem for second-order multi-agent systems without velocity information from the distributed perspective. Particularly, all the agents are driven towards a consensus at an optimal solution inside the intersection of multiple feasible sets that minimizes a global target function aggregated by a group of convex local ones. Each local target function is exclusively assigned to a respective agent. Also, each feasible set constructed by inequality and set constraints privately belongs to a respective agent. Resorting to a novel auxiliary dynamics, a velocity-free distributed coordinated optimal control strategy is proposed without relying on global topology information. Using convex theory under the Lyapunov framework, it is demonstrated that the concerned coordinated optimal control objective is fulfilled by implementing the proposed distributed control strategy despite no velocity information. Examples are finally given to confirm the control effectiveness.

IMPROVING CONTROL STRATEGIES OF INFECTIONS BY RESISTANT PATHOGENS IN A HOSPITAL NETWORK

The efficacy of infection prevention and control on several hospital networks is assessed. We tested two kinds of strategy, a network-topology-based allocation and a [Formula: see text]-based allocation, where [Formula: see text] is the basic reproduction number of the infection. For this, a multi-patch deterministic model simulates the spread of carbapenemase-producing Enterobacteriaceae in several theoretical hospital networks parametrized by data from Brazil. Our results show that: (i) the allocation methods based on the [Formula: see text] of the hospitals may work better than the network-topology-based allocations; (ii) results from control efficacy for a specific hospital network cannot be generalized to other types of networks. Putting together the global network topology with local factors that drive pathogens transmission, the [Formula: see text]-based allocation method seems to be enough to control of healthcare-associated infections. Overall, the obtained results emphasize the importance of data collection on infection transmission and patient transfers.

Network Topology Optimization via Deep Reinforcement Learning

Topology impacts important network performance metrics, including link utilization, throughput and latency, and is of central importance to network operators. However, due to the combinatorial nature of network topology, it is extremely difficult to obtain an optimal solution, especially since topology planning in networks also often comes with management-specific constraints. As a result, local optimization with hand-tuned heuristic methods from human experts is often adopted in practice. Yet, heuristic methods cannot cover the global topology design space while taking into account constraints, and cannot guarantee to find good solutions. In this paper, we propose a novel deep reinforcement learning (DRL) algorithm for graph searching, called DRL-GS, for network topology optimization. DRL-GS consists of three novel components, including a verifier to validate the correctness of a generated network topology, a graph neural network (GNN) to efficiently approximate topology rating, and a DRL agent to conduct a topology search. DRL-GS can efficiently search over relatively large topology space and output topology with satisfactory performance. We conduct a case study based on a real-world network scenario, and our experimental results demonstrate the superior performance of DRL-GS in terms of both efficiency and performance.

Distributed Output-Feedback Bipartite Consensus for Stochastic Nonlinear Multiagent Systems Under Directed Switching Networks

This article investigates the distributed dynamic output-feedback bipartite consensus for a class of stochastic nonlinear multiagent systems (MASs) with time delays and actuators faults under directed switching graphs. First, a distributed extended state compensator is constructed for each agent to compensate for the consensus errors and actuators’ faults only using the output information of neighbors. Then, based on the compensator, a linear memoryless output-feedback controller is designed. Using a technical lemma and the stochastic Lyapunov stability theory, it is proved that combined with the given constraint conditions on graphs switching the 2nd-moment asymptotic bipartite consensus for the MASs can be achieved. Different from existing results, the proposed compensator can not only save the network bandwidth but also compensate for the actuators’ faults. The proposed scheme also significantly relaxes the conditions on the communication network to directed switching graphs and even allows the graph to be disconnected over some time intervals. The common design parameters under any graphs can avoid the detection of graph switching, which will need global topology information. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.

Disrupted longitudinal restoration of brain connectivity during weight normalization in severe anorexia nervosa

Altered intrinsic brain connectivity of patients with anorexia nervosa has been observed in the acute phase of the disorder, but it remains unclear to what extent these alterations recover during weight normalization. In this study, we used functional imaging data from three time points to probe longitudinal changes in intrinsic connectivity patterns in patients with severe anorexia nervosa (BMI ≤ 15.5 kg/m2) over the course of weight normalization. At three distinct stages of inpatient treatment, we examined resting-state functional connectivity in 27 women with severe anorexia nervosa and 40 closely matched healthy controls. Using network-based statistics and graph-theoretic measures, we examined differences in global network strength, subnetworks with altered intrinsic connectivity, and global network topology. Patients with severe anorexia nervosa showed weakened intrinsic connectivity and altered network topology which did not recover during treatment. The persistent disruption of brain networks suggests sustained alterations of information processing in weight-recovered severe anorexia nervosa.

The Origin of the Difference between Space and Time

All differences between the role of space and time in nature are explained by proposing principles in which none of the spacetime coordinates has an a priori special role. Spacetime is treated as a non-dynamical manifold, with a fixed global RD topology. The dynamical theory of gravity determines only the metric tensor on a fixed manifold. All dynamics is treated as a Cauchy problem, so it follows that one coordinate takes a special role. It is proposed that any boundary condition that is finite everywhere leads to a solution which is also finite everywhere. This explains the (1,D−1) signature of the metric, the boundedness of energy from below, the absence of tachyons, and other related properties of nature. The time arrow is explained by proposing that the boundary condition should be ordered. The quantization is considered as a boundary condition for field operators. Only the physical degrees of freedom are quantized.

NSRGRN: a network structure refinement method for gene regulatory network inference.

The elucidation of gene regulatory networks (GRNs) is one of the central challenges of systems biology, which is crucial for understanding pathogenesis and curing diseases. Various computational methods have been developed for GRN inference, but identifying redundant regulation remains a fundamental problem. Although considering topological properties and edge importance measures simultaneously can identify and reduce redundant regulations, how to address their respective weaknesses whilst leveraging their strengths is a critical problem faced by researchers. Here, we propose a network structure refinement method for GRN (NSRGRN) that effectively combines the topological properties and edge importance measures during GRN inference. NSRGRN has two major parts. The first part constructs a preliminary ranking list of gene regulations to avoid starting the GRN inference from a directed complete graph. The second part develops a novel network structure refinement (NSR) algorithm to refine the network structure from local and global topology perspectives. Specifically, the Conditional Mutual Information with Directionality and network motifs are applied to optimise the local topology, and the lower and upper networks are used to balance the bilateral relationship between the local topology's optimisation and the global topology's maintenance. NSRGRN is compared with six state-of-the-art methods on three datasets (26 networks in total), and it shows the best all-round performance. Furthermore, when acting as a post-processing step, the NSR algorithm can improve the results of other methods in most datasets.

Distorted-toroidal Flux Rope Model

The 3D characterization of magnetic flux ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitations on inferring the 3D global topology and physical properties from the 1D time series from any spacecraft. To advance our understanding of magnetic flux ropes whose configuration departs from the typical stiff geometries, here we present an analytical solution for a 3D flux rope model with an arbitrary cross section and a toroidal global shape. This constitutes the next level of complexity following the elliptic-cylindrical (EC) geometry. The mathematical framework was established by Nieves-Chinchilla et al. with the EC flux rope model, which describes a magnetic topology with an elliptical cross section as a first approach to changes in the cross section. In the distorted-toroidal flux rope model, the cross section is described by a general function. The model is completely described by a nonorthogonal geometry and the Maxwell equations can be consistently solved to obtain the magnetic field and relevant physical quantities. As a proof of concept, this model is generalized in terms of the radial dependence of current density components. The last part of this paper is dedicated to a specific function, , to illustrate possibilities of the model. This model paves the way toward the investigation of complex distortions of magnetic structures in the solar wind. Future investigations will explore these distortions in depth by analyzing specific events; studying implications for physical quantities, such as magnetic fluxes, helicity, or energy; and evaluating the force balance with the ambient solar wind that allows such distortions.

Distributed Model-Free Adaptive Control for MIMO Nonlinear Multiagent Systems Under Deception Attacks

The consensus tracking and containment control problems of multiple-input and multiple-output (MIMO) nonaffine nonlinear multiagent systems (MASs) are studied in this article under deception attacks using the distributed model-free adaptive control (DMFAC) method. An equivalent dynamic linearized data model of MIMO MASs’s distributed output vector containing deception signals is established using dynamic linearization technology. Then, a fully data-driven DMFAC strategy is designed just using I/O information instead of the knowledge of mathematical model. Furthermore, the boundedness of distributed output vector of MIMO-MASs under deception attacks is proved through the contraction mapping principle without employing global topology graph information. Finally, the validity of the proposed DMFAC scheme is verified through detailed simulations.

Similar image matching via global topology consensus

Recovering three-dimensional structure from images is one of the important researches in computer vision. The quality of feature matching is one of the keys to obtaining more accurate results. However, as different objects or different surfaces of objects have similar images with the same elements and different typography, the camera pose estimation will be wrong and the task will fail. This paper proposes a new mismatch elimination algorithm based on global topology consistency. We first formulate the matching task as a mathematical model based on the global constraints, then convert the feature matching into grid matching, calculate the confidence of the grids according to the changes in the angle and displacement between correspondence grid vectors, and remove the mismatches with low confidence. The experiments have demonstrated that our proposed method performs better than the state-of-the-art feature matching methods to accomplish outlier match rejection in the task of similar image matching and could be helped to obtain the correct camera pose to reconstruct more complete and more accurate object models.

Brain diffusion tensor imaging reveals altered connections and networks in epilepsy patients.

Accumulating evidence shows that epilepsy is a disease caused by brain network dysfunction. This study explored changes in brain network structure in epilepsy patients based on graph analysis of diffusion tensor imaging data. The brain structure networks of 42 healthy control individuals and 26 epilepsy patients were constructed. Using graph theory analysis, global and local network topology parameters of the brain structure network were calculated, and changes in global and local characteristics of the brain network in epilepsy patients were quantitatively analyzed. Compared with the healthy control group, the epilepsy patient group showed lower global efficiency, local efficiency, clustering coefficient, and a longer shortest path length. Both healthy control individuals and epilepsy patients showed small-world attributes, with no significant difference between groups. The epilepsy patient group showed lower nodal local efficiency and nodal clustering coefficient in the right olfactory cortex and right rectus and lower nodal degree centrality in the right olfactory cortex and the left paracentral lobular compared with the healthy control group. In addition, the epilepsy patient group showed a smaller fiber number of edges in specific regions of the frontal lobe, temporal lobe, and default mode network, indicating reduced connection strength. Epilepsy patients exhibited lower global and local brain network properties as well as reduced white matter fiber connectivity in key brain regions. These findings further support the idea that epilepsy is a brain network disorder.

Global spatio-temporal synergistic topology learning for skeleton-based action recognition

Compared to RGB video-based action recognition, skeleton-based action recognition algorithm has attracted much more attention due to being more lightweight, better generalization and robustness. The extraction of temporal and spatial features is a crucial factor for skeleton-based action recognition. However, existing feature extraction methods suffer from two limitations: (1) the isolated extraction of temporal and spatial feature cannot capture temporal feature connections among non-adjacent joints and (2) convolution-limited perceptual fields cannot capture global temporal features of joints effectively. In this work, we propose a global spatio-temporal synergistic feature learning module (GSTL), which generates global spatio-temporal synergistic topology of joints by spatio-temporal feature fusion. By further combining the GSTL with a temporal modeling unit, we develop a powerful global spatio-temporal synergistic topology learning network (GSTLN), and it achieves competitive performance with fewer parameters on three challenge datasets: NTU RGB + D, NTU RGB + D 120, and NW-UCLA.