相关论文: Spanning Trees and bootstrap reliability estimatio…
A branch vertex in a tree is a vertex of degree at least three. We prove that, for all $s\geq 1$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch…
We study the minimum spanning tree distribution on the space of spanning trees of the $n$-by-$n$ grid for large $n$. We establish bounds on the decay rates of the probability of the most and the least probable spanning trees as…
The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an $n$-node input graph to be read sequentially in $p$ passes using $\tilde{O}(n)$ space. In this…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
The recent financial crisis has stressed the need to understand financial systems as networks of interdependent countries, where cross-border financial linkages play the fundamental role. It has also been emphasized that the relevance of…
Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within…
Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna's seminal paper, the linear Pearson's correlation coefficient between…
Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching the…
A spring-block chain placed on a running conveyor belt is considered for modeling stylized facts observed in the dynamics of stock indexes. Individual stocks are modeled by the blocks, while the stock-stock correlations are introduced via…
The properties of q-dependent cross-correlation matrices of stock market have been analyzed by using the random matrix theory and complex network. The correlation structures of the fluctuations at different magnitudes have unique…
Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,1986]. This paper studies the problem of finding an optimal approximating tree. The star decomposition scheme for sets of three binary…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We introduce a multiscale measure of network instability based on the joint use of Detrended Cross-Correlation Analysis (DCCA) and Minimum Spanning Tree (MST) filtering. The proposed metric, the Elastic Detrended Cross-Correlation Ratio…
Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable…
We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments…
In many domains, data measurements can naturally be associated with the leaves of a tree, expressing the relationships among these measurements. For example, companies belong to industries, which in turn belong to ever coarser divisions…
Flow network models can capture the underlying physics and operational constraints of many networked systems including the power grid and transportation and water networks. However, analyzing reliability of systems using computationally…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
We present a linear programming based algorithm for computing a spanning tree $T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is $O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any spanning…
According to the leading models in modern finance, the presence of intraday lead-lag relationships between financial assets is negligible in efficient markets. With the advance of technology, however, markets have become more sophisticated.…