Every property is testable on a natural class of scale-free multigraphs

In this paper, we introduce a natural class of multigraphs called hierarchical-scale-free (HSF) multigraphs, and consider constant-time testability on the class. We show that a very wide subclass, specifically, that in which the power-law exponent is greater than two, of HSF is hyperfinite. Based on this result, an algorithm for a deterministic partitioning oracle can be constructed. We conclude by showing that every property is constant-time testable on the above subclass of HSF. This algorithm utilizes findings by Newman and Sohler of STOC'11. However, their algorithm is based on the bounded-degree model, while it is known that actual scale-free networks usually include hubs, which have a very large degree. HSF is based on scale-free properties and includes such hubs. This is the first universal result of constant-time testability on the general graph model, and it has the potential to be applicable on a very wide range of scale-free networks.Comment: 13 pages, one figure. Difference from ver. 1: Definitions of HSF and SF become more general. Typos were fixe

A Comprehensive Analysis of Time Series Segmentation on the Japanese Stock Prices

This study conducts a comprehensive analysis of time series segmentation on the Japanese stock prices listed on the first section of the Tokyo Stock Exchange during the period from 4 January 2000 to 30 January 2012. A recursive segmentation procedure is used under the assumption of a Gaussian mixture. The daily number of each quintile of volatilities for all the segments is investigated empirically. It is found that from June 2004 to June 2007, a large majority of stocks are stable and that from 2008 several stocks showed instability. On March 2011, the daily number of instable securities steeply increased due to societal turmoil influenced by the East Japan Great Earthquake. It is concluded that the number of stocks included in each quintile of volatilities provides useful information on macroeconomic situations.Comment: 10 pages, 5 figures, submitted to the 4th World Congress on Social Simulation (WCSS2012

Patterns of Regional Travel Behavior: An Analysis of Japanese Hotel Reservation Data

This study considers the availability of room opportunities collected from a Japanese hotel booking site. We empirically analyze the daily number of room opportunities for four areas. To determine the migration trends of travelers, we discuss a finite mixture of Poisson distributions and the EM-algorithm as its parameter estimation method. We further propose a method to infer the probability of opportunities existing for each observation. We characterize demand-supply situations by means of relationship between the averaged room prices and the probability of opportunity existing.Comment: 22 pages, 16 figures; International Review of Financial Analysis (2011