Atsuyuki Okabe

Bio: Atsuyuki Okabe is an academic researcher from Aoyama Gakuin University. The author has contributed to research in topics: Voronoi diagram & Weighted Voronoi diagram. The author has an hindex of 28, co-authored 127 publications receiving 7551 citations. Previous affiliations of Atsuyuki Okabe include University of Tsukuba & University of Tokyo.

Spatial Tessellations: Concepts and Applications of Voronoi Diagrams

Abstract: Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.

A kernel density estimation method for networks, its computational method and a GIS-based tool

Abstract: We develop a kernel density estimation method for estimating the density of points on a network and implement the method in the GIS environment. This method could be applied to, for instance, finding 'hot spots' of traffic accidents, street crimes or leakages in gas and oil pipe lines. We first show that the application of the ordinary two-dimensional kernel method to density estimation on a network produces biased estimates. Second, we formulate a 'natural' extension of the univariate kernel method to density estimation on a network, and prove that its estimator is biased; in particular, it overestimates the densities around nodes. Third, we formulate an unbiased discontinuous kernel function on a network. Fourth, we formulate an unbiased continuous kernel function on a network. Fifth, we develop computational methods for these kernels and derive their computational complexity; and we also develop a plug-in tool for operating these methods in the GIS environment. Sixth, an application of the proposed methods to the density estimation of traffic accidents on streets is illustrated. Lastly, we summarize the major results and describe some suggestions for the practical use of the proposed methods.

Point pattern analysis

Abstract: Introduction Measures of Dispersion Quadrat Analysis Measures of Dispersion Distance Methods Measures of Arrangements Summary

The K-Function Method on a Network and Its Computational Implementation

Abstract: This paper proposes two statistical methods, called the network K-function method and the network cross K-function method, for analyzing the distribution of points on a network. First, by extending the ordinary K-function method defined on a homogeneous infinite plane with the Euclidean distance, the paper formulates the K-function method and the cross K-function method on a finite irregular network with the shortest-path distance. Second, the paper shows advantages of the network K-function methods, such as that the network K-function methods can deal with spatial point processes on a street network in a small district, and that they can exactly take the boundary effect into account. Third, the paper develops the computational implementation of the network K-functions, and shows that the computational order of the K-function method is O(n2Q log nQ) and that of the network cross K-function is O(nQ log U3Q), where nQ is the number of nodes of a network.

The capacity of wireless networks

Abstract: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is /spl Theta/(W/spl radic/An) bit-meters per second. Thus even under optimal circumstances, the throughput is only /spl Theta/(W//spl radic/n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.

Voronoi diagrams—a survey of a fundamental geometric data structure

Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Coverage control for mobile sensing networks

Abstract: This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

Large Sample Properties of Matching Estimators for Average Treatment Effects

Abstract: Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data. In this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results. We focus on matching with replacement with a fixed number of matches. First, we show that matching estimators are not N 1/2 -consistent in general and describe conditions under which matching estimators do attain N 1/2 -consistency. Second, we show that even in settings where matching estimators are N 1/2 -consistent, simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound. Third, we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions. Software for implementing these methods is available in Matlab, Stata, and R.