The expectation hypothesis of interest rates and network theory: The case of Brazil

This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity.     

Lot-sizing on a tree

For the problem of lot-sizing on a tree with constant capacities, or stochastic lot-sizing with a scenario tree, we present various reformulations based on mixing sets. We also show how earlier results for uncapacitated problems involving (Q,S_Q) inequalities can be simplified and extended. Finally some limited computational results are presented.     

Locating the two-median of a tree network with continuous link demands

Typical formulations of thep-median problem on a network assume discrete nodal demands. However, for many problems, demands are better represented by continuous functions along the links, in addition to nodal demands. For such problems, optimal server locations need not occur at nodes, so that algorithms of the kind developed for the discrete demand case can not be used. In this paper we show how the 2-median of a tree network with continuous link demands can be found using an algorithm based on sequential location and allocation. We show that the algorithm will converge to a local minimum and then present a procedure for finding the global minimum solution.     

A system of grabbing particles related to Galton‐Watson trees

We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: once a particle has been grabbed then it cannot be grabbed again, and an arm cannot grab a particle that belongs to its own cluster. We are interested in the shape of a typical polymer in the situation when the initial number of monomers is large and the numbers of arms of monomers are given by i.i.d. random variables. Our main result is a limit theorem for the empirical distribution of polymers, where limit is expressed in terms of a Galton‐Watson tree. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Topological properties of stock market networks: The case of Brazil

This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network.     

On arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ; from a result by Barth and Fournier it follows that Δ(T)?4. A necessary and a sufficient condition for being an arbitrarily vertex decomposable star-like tree have been exhibited. The conditions seem to be very close to each other.     

树映射的等度连续性

讨论了树（即：不含圈的维紧致连通的分支流形）映射的等度连续性，得到了树映射是等度连续的两个充要条件。     

网站用户登录信息挖掘特征规则

本文首先研究了基本的面向属性归纳，提出了从网站用户登录信息中挖掘用户特征规则的思路。问题从解决多属性归纳着手，特点是首先建立概念树，然后用条件属性组合与约束的方法进行挖掘。实验表明，本文设计的模型能客观地描述客户行为，为从Web信息挖掘客户特征规则提出了一条有效的途径。     

Volume growth and heat kernel estimates for the continuum random tree

In this article, we prove global and local (point-wise) volume and heat kernel bounds for the continuum random tree. We demonstrate that there are almost–surely logarithmic global fluctuations and log–logarithmic local fluctuations in the volume of balls of radius r about the leading order polynomial term as r → 0. We also show that the on-diagonal part of the heat kernel exhibits corresponding global and local fluctuations as t → 0 almost–surely. Finally, we prove that this quenched (almost–sure) behaviour contrasts with the local annealed (averaged over all realisations of the tree) volume and heat kernel behaviour, which is smooth.