Global Topological Structures Research Articles

Global dynamics of 3D cooperative Lotka-Volterra system with the identical intrinsic growth rate

In this paper, we complete the classification on global topological structures of the three-dimensional cooperative Lotka-Volterra system with the identical intrinsic growth rate inside the Poincaré compactification of the positive octant of R3. Precisely, with the help of the replicator equations it is proved that this kind of system can have exactly 8 topologically different phase portraits. As a consequence, we obtain the necessary and sufficient conditions for the system to be bounded in the positive octant.

Being noisy in a crowd: Differential selective pressure on gene expression noise in model gene regulatory networks.

Expression noise, the variability of the amount of gene product among isogenic cells grown in identical conditions, originates from the inherent stochasticity of diffusion and binding of the molecular players involved in transcription and translation. It has been shown that expression noise is an evolvable trait and that central genes exhibit less noise than peripheral genes in gene networks. A possible explanation for this pattern is increased selective pressure on central genes since they propagate their noise to downstream targets, leading to noise amplification. To test this hypothesis, we developed a new gene regulatory network model with inheritable stochastic gene expression and simulated the evolution of gene-specific expression noise under constraint at the network level. Stabilizing selection was imposed on the expression level of all genes in the network and rounds of mutation, selection, replication and recombination were performed. We observed that local network features affect both the probability to respond to selection, and the strength of the selective pressure acting on individual genes. In particular, the reduction of gene-specific expression noise as a response to stabilizing selection on the gene expression level is higher in genes with higher centrality metrics. Furthermore, global topological structures such as network diameter, centralization and average degree affect the average expression variance and average selective pressure acting on constituent genes. Our results demonstrate that selection at the network level leads to differential selective pressure at the gene level, and local and global network characteristics are an essential component of gene-specific expression noise evolution.

Multi-scale Edge-guided Learning for 3D Reconstruction

Single-view three-dimensional (3D) object reconstruction has always been a long-term challenging task. Objects with complex topologies are hard to accurately reconstruct, which makes existing methods suffer from blurring of shape boundaries between multiple components in the object. Moreover, most of them cannot balance learning between global geometric structure information and local detail information. In this article, we propose a multi-scale edge-guided learning network (MEGLN) to utilize the global edge information guiding the network to better capture and recover local details. The goal is to exploit the multi-scale learning strategy to learn global edge information and local details, thus achieving robust 3D object reconstruction. We first design a multi-scale Gaussian difference block (MGDB) to extract global edge geometry features for input images of different scales and adopt the attention mechanism to aggregate the extracted global edge geometry features of different scales. Second, we design a multi-scale feature interaction block (MFIB) to learn local details, which utilizes the multi-scale feature interaction to capture the features of multiple objects or components at multiple scales. The MFIB can learn and capture better as much local detail information as possible under the guidance of global edge information. Finally, we dynamically fuse the predicted probabilities of the MGDB and MFIB to obtain the final predicted result, which makes our MEGLN able to recover 3D shapes with global complex topological structures and rich local details via the multi-scale learning strategy. Extensive qualitative and quantitative experimental results on the ShapeNet dataset demonstrate that our approach achieves competitive performance compared with state-of-the-art methods. Code is available at https://github.com/Ray-tju/MEGLN .

SFCM: A Fuzzy Clustering Algorithm of Extracting the Shape Information of Data

Topological data analysis is a new theoretical trend using topological techniques to mine data. This approach helps determine topological data structures. It focuses on investigating the global shape of data rather than on local information of high-dimensional data. The Mapper algorithm is considered as a sound representative approach in this area. It is used to cluster and identify concise and meaningful global topological data structures that are out of reach for many other clustering methods. In this article, we propose a new method called the Shape Fuzzy C-Means (SFCM) algorithm, which is constructed based on the Fuzzy C-Means algorithm with particular features of the Mapper algorithm. The SFCM algorithm can not only exhibit the same clustering ability as the Fuzzy C-Means but also reveal some relationships through visualizing the global shape of data supplied by the Mapper. We present a formal proof and include experiments to confirm our claims. The performance of the enhanced algorithm is demonstrated through a comparative analysis involving the original algorithm, Mapper, and the other fuzzy set based improved algorithm, F-Mapper, for synthetic and real-world data. The comparison is conducted with respect to output visualization in the topological sense and clustering stability.

Observation of Non-Abelian Nodal Links in Photonics.

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian band topology was proposed in nodal link systems, where the nodal lines formed by consecutive pairs of bands exhibit interesting braiding structures and the underlying topological charges are described by quaternions. Here, we experimentally demonstrate non-Abelian nodal links in a biaxial hyperbolic metamaterial. The linked nodal lines threading through each other are formed by the crossings between three adjacent bands. Based on the non-Abelian charges, we further analyze various admissible nodal link configurations for the three-band system. On the interface between the metamaterial and air, surface bound states in the continuum are observed, which serves as the symmetry-enforced derivative of drumhead surface states from the linked nodal lines. Our work serves as a direct observation of the global topological structures of nodal links, and provides a platform for studying non-Abelian topological charge in the momentum space.

Global phase portraits and bifurcation diagrams for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials

<p style='text-indent:20px;'>This paper is devoted to the complete classification of global phase portraits for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials. Such system is affinely equivalent to one of five normal forms by an algebraic classification of its infinite singular points. Then, we classify the global phase portraits of these normal forms on the Poincaré disc. There are exactly <inline-formula><tex-math id="M1">\begin{document}$ 13 $\end{document}</tex-math></inline-formula> different global topological structures on the Poincaré disc. Finally we provide the bifurcation diagrams for the corresponding global phase portraits.

Using Alias Sampling Strategy Based on Network Embeddings to Detect Protein Complexes

Detecting protein complexes from available protein-protein interaction (PPI) data will help to deeply understand the mechanism of the biological activities. In recent years, various computational methods have been developed for identifying protein complexes from PPI networks. Almost all the basic computational methods mainly depend on the association of topological analysis of PPI networks. However, most of them fail to satisfactorily capture the global and local topological structures of the PPI networks, as well as the diversity of connectivity patterns between individual nodes at the same time. To solve this problem, in this work we propose a node embedding based alias sampling extension method to detect protein complexes. More specifically, for a given set of seed nodes, it first uses the alias sampling strategy based on protein node embedding similarities to select potential addable nodes. Then it makes use of a new conductance measure, which could better quantify the likelihood of a subgraph being a protein complex, to decide whether to extend the current candidate subgraph in order to find protein complexes. Evaluated on six real yeast PPI networks, our method outperforms state-of-the-art methods in detecting protein complexes. Furthermore, the experimental results demonstrate the protein complexes predicted by our method have higher biological significance.

Throughput-Optimal Broadcast in Wireless Networks with Dynamic Topology

We consider the problem of throughput-optimal broadcasting in a time-varying wireless network with an underlying Directed Acyclic (DAG) topology. Known broadcast algorithms route packets along pre-computed spanning trees. In large wireless networks with time-varying connectivities, the optimal trees are difficult to compute and maintain. In this paper, we propose a new online throughput-optimal broadcast algorithm, which takes packet-by-packet scheduling and routing decisions, obviating the need for any global topological structures, such as spanning trees. Our algorithm utilizes certain queue-like system-state information for making transmission decisions and hence, may be thought of as a generalization of the well-known back-pressure policy , which makes point-to-point unicast transmission decisions based on the local queue-length information. Technically, the back-pressure algorithm is derived by greedily stabilizing the queues. However, because of packet-duplications, the work-conservation principle is violated, and an analogous queueing process is non-trivial to define in the broadcast setting. To address this fundamental issue, we identify certain state variables whose dynamics behave like virtual queues . By stochastically stabilizing these virtual queues, we devise a throughput-optimal broadcast policy. We also derive new characterizations of the broadcast capacity of time-varying wireless DAGs and propose efficient algorithms to compute the capacity either exactly or approximately under various assumptions.

Depth-based subgraph convolutional auto-encoder for network representation learning

Network representation learning (NRL) aims to map vertices of a network into a low-dimensional space which preserves the network structure and its inherent properties. Most existing methods for network representation adopt shallow models which have relatively limited capacity to capture highly non-linear network structures, resulting in sub-optimal network representations. Therefore, it is nontrivial to explore how to effectively capture highly non-linear network structure and preserve the global and local structure in NRL. To solve this problem, in this paper we propose a new graph convolutional autoencoder architecture based on a depth-based representation of graph structure, referred to as the depth-based subgraph convolutional autoencoder (DS-CAE), which integrates both the global topological and local connectivity structures within a graph. Our idea is to first decompose a graph into a family of K-layer expansion subgraphs rooted at each vertex aimed at better capturing long-range vertex inter-dependencies. Then a set of convolution filters slide over the entire sets of subgraphs of a vertex to extract the local structural connectivity information. This is analogous to the standard convolution operation on grid data. In contrast to most existing models for unsupervised learning on graph-structured data, our model can capture highly non-linear structure by simultaneously integrating node features and network structure into network representation learning. This significantly improves the predictive performance on a number of benchmark datasets.

Throughput-Optimal Multi-Hop Broadcast Algorithms

We design throughput-optimal dynamic broadcast algorithms for multi-hop networks with arbitrary topologies. Most of the previous broadcast algorithms route packets along spanning trees. For large time-varying networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper, we design a class of dynamic algorithms, which make simple packet-by-packet scheduling and routing decisions, and hence obviate the need for maintaining any global topological structures, such as spanning trees. Our algorithms may be conveniently understood as a non-trivial generalization of the familiar back-pressure algorithm for unicast traffic, which performs packet routing and scheduling based on queue lengths. However, in the broadcast setting, due to packet duplications, it is difficult to define appropriate queuing structures. We design and prove the optimality of a virtual queue-based algorithm, where virtual queues are defined for subsets of nodes. We then propose a multi-class broadcast policy, which combines the above scheduling algorithm with in-class-in-order packet forwarding, resulting in significant reduction in complexity. Finally, we evaluate the performance of the proposed algorithms via extensive numerical simulations.

Classification of Global Phase Portrait of Planar Quintic Quasi-Homogeneous Coprime Polynomial Systems

This paper is devoted to the complete classification of global phase portraits (short for GPP) of quasi-homogeneous but non-homogeneous coprime planar quintic polynomial differential systems (short for QCQS). We firstly study the canonical forms of QCQS. It is shown that these canonical forms can have 0, 1, 2, 4 parameters. Then, we investigate the global topological structures of all canonical forms, by using the quasi-homogeneous blow-up technique for the finite singularities and the Poincare–Lyapunov compactification for the infinite singularities. We finally perform a topological classification for the set of GPP.

Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems

This paper is devoted to the complete classification of global phase portraits of quasi-homogeneous but non-homogeneous coprime planar polynomial differential systems of degree $$4$$ . To prove our result, we firstly study the canonical forms for these systems. Then, the global topological structures of the systems having canonical forms are studied by using the quasi-homogeneous blow-up technique for the finite singularities and the Poincare-Lyapunov compactification for the infinite singularities. Finally we perform a topological classification for the set of global phase portraits.

Integrating local and global topological structures for semi-supervised dimensionality reduction

Dimensionality reduction plays an important role in many machine learning tasks. This paper studies semi-supervised dimensionality reduction using pairwise constraints. In this setting, domain knowledge is given in the form of pairwise constraint, which specifies whether a pair of instances belongs to the same class (must-link constraint) or different classes (cannot-link constraint). In this paper, a novel semi-supervised dimensionality reduction method called LGS3DR is proposed, which can integrate both local and global topological structures of the data as well as pairwise constraints. The LGS3DR method is effective and has a closed form solution. Experiments on data visualization and face recognition show that LGS3DR is superior to many existing dimensionality reduction methods.

Towards the global GIS

This paper outlines the concept of a “global GIS,” and defines various aspects of its development, as well as various options and decisions that must be made. The emphasis is on the advantages and disadvantages of maintaining a global topological structure, and whether topology should be generated “on the fly” in response to a specific query. We first define what we mean by “space” in this context, followed by a description of topological structures and how we may use them in the context of graph traversal problems. We then describe some appropriate data structures. After mentioning some of the real-world problems associated with polygon construction problems, we touch on how graphs may represent change over time. A global topological structure is then proposed which resolves some of the problems mentioned. This is based on incremental graph updating methods. Some unresolved problems associated with using global topological structures are then discussed, especially those associated with queries, such as polygon overlay, that generate a new local topological structure. We conclude with some preliminary rules, and suggest further work.

Global topological approach to highly excited vibration: a case study of H 2O, CH 2Br 2 and CD 2Br 2

A global topological approach based on the algebraic coset representation to study highly excited molecular vibration is proposed. The algorithm allows us to elucidate ample highly excited vibrational dynamics from a global viewpoint. Topics for highly excited states studied include (1) global topological structures, (2) global symmetric and antisymmetric characters, (3) resonance overlaps and chaotic motion, (4) action transfer coefficients and (5) survival probabilities denoting the decaying of the action stored in a mode, with sample calculations for H 2O, CH 2Br 2 and CD 2Br 2.

Decorrelating the topology in full QCD

We investigate the performance of the hybrid Monte Carlo algorithm in updating non-trivial global topological structures. We find that the hybrid Monte Carlo algorithm has serious problems decorrelating the global topological charge. This represents a warning which must be seriously considered when simulating full QCD, regardless of the number and type of fermions, with this or any similar algorithm. Simulated tempering is examined as a means of accelerating the decorrelation.

Hybrid Monte Carlo and topological modes of full QCD

We investigate the performance of the hybrid Monte Carlo algorithm, the standard algorithm used for lattice QCD simulations involving fermions, in updating non-trivial global topological structures. We find that the hybrid Monte Carlo algorithm has serious problems decorrelating the global topological charge. This represents a warning which must be seriously considered when simulating full QCD by hybrid Monte Carlo.