相关论文: Integrable cluster dynamics of directed networks a…

We generalize to vector bundles the techniques introduced for line bundles in prior work of the author with Liu, Osserman and Zhang. We then use this method to prove the injectivity of the Petri map for vector bundles and the surjectivity…

Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…

The neighborhood complex of a graph was introduced by Lov\'asz to provide topological lower bounds on chromatic number. More general homomorphism complexes of graphs were further studied by Babson and Kozlov. Such `Hom complexes' are also…

We find there is relationship between the associated bigraph and the cluster (or community) detecting on network. By imbedding the associated bigraph of some network (suppose it has cluster structures) into some space, we can identify the…

Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…

Dynamic Complexity was introduced by Immerman and Patnaik \cite{PatnaikImmerman97} (see also \cite{DongST95}). It has seen a resurgence of interest in the recent past, see…

Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by…

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…

This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…

We enlarge the spectral problem of a generalized D-Kaup-Newell (D-KN) spectral problem. Solving the enlarged zero-curvature equations, we produce integrable couplings. A reduction of the spectral matrix leads to a second integrable coupling…

This paper studies a dynamical system, which contains two contours. There is a cluster on each contour. The cluster contains particles, located in adjacent cells. The clusters move under prescribed rules. The delays of clusters are due to…

We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…

A discrete analog of the holomorphic map $z^{\gamma}$ is studied. It is given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding circle patterns are embedded and described by special…

A number of examples of Hamiltonian systems that are integrable by classical means are cast within the framework of isospectral flows in loop algebras. These include: the Neumann oscillator, the cubically nonlinear Schr\"odinger systems and…

Integrable deformations of a class of Rikitake dynamical systems are constructed by deforming their underlying Lie-Poisson Hamiltonian structures, which are considered linearizations of Poisson--Lie structures on certain (dual) Lie groups.…

The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…

The proliferation of high-dimensional data from sources such as social media, sensor networks, and online platforms has created new challenges for clustering algorithms. Multi-view clustering, which integrates complementary information from…

The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…