Variable Resolution Bivariate Plots

Abstract

Scatterplots are the method of choice for displaying the distribution of points in two dimensions. They are used to discover patterns such as holes, outliers, modes, and association between the two variables. A common problem is overstriking—the overlap on the plotting surface of glyphs representing individual observations. Overstriking can create a misleading impression of the data distribution. The variable resolution bivariate plots (Varebi plots) proposed in this article deal with the problem of overstriking by mixing display of a density estimate and display of individual observations. The idea is to determine the display format by analyzing the actual amount of overstriking on the screen. Thus, the display format will depend on the sample size, the distribution of the observations, the size and shape of individual icons, and the size of the window. It may change automatically when the window is resized. Varebi plots reveal detail wherever possible, and show the overall trend when displaying detail is not feasible.     

Determinimg abelian p-groups from their n-Socles

A necessary condition is given for a very wide separable p-group to be derermined by its n-socle (the set of elements of order at most p ⁿ). A group G is very wide if it has a direct summand of final rank ‖G‖ which itself is a direct sum of cyclic groups. In the case, n=1 (as Shelat has shown)this condition is sufficient but for n>1 examples are given to show that this condition is not sufficient.     

A numerical study of energy consumption and time efficiency of sensor networks with different structural topologies and routing methods

This paper reports a numerical study of energy consumption and time efficiency of sensor networks with five different structural topologies and four different routing methods, regarding their performances and costs, which might provide some references and guidelines for designing sensor networks under various conditions for possible applications.     

Visual Revelations

Abstract

Berger Statistical Superhero: A Review Reviewed by Albert Madansky

A Mathematician Reads the Newspaper by John Allen Paulos, New York: Anchor Books (Doubleday), 1996: xi + 212 pp. Reviewed by Thomas L. Moore     

The linear noise approximation for reaction-diffusion systems on networks

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays travelling waves in its deterministic limit. The role of stochastic fluctuations is investigated and shown to drive the emergence of stochastic waves beyond the region of the instability predicted from the deterministic theory. Simulations are performed to test the theoretical results and are analyzed via a generalized Fourier transform algorithm. This transform is defined using the eigenvectors of the discrete Laplacian defined on the network. A peak in the numerical power spectrum of the fluctuations is observed in quantitative agreement with the theoretical predictions.     

Study of Strangeness Photoproduction on the Neutron in the Threshold Region

Photoproduction of the neutral kaon on the deuteron has been investigated at the Research Center for Electron Photon Science, Tohoku University. We constructed the Neutral Kaon Spectrometer-2 for the detection of charged particles from the decay of the neutral kaon and the hyperon. We obtained a momentum distribution of K ⁰ with the inclusive measurement. It was consistent with the previous measurement. The total cross section of γ + d → K ⁰ + Λ + p was estimated from the measured integral cross section of γ + d → Λ + X. The total cross section with respect to the photon energy was compared with the theoretical calculations. It favored the Saclay-Lyon A model calculation with the ratio of the neutral to charged coupling constants of the axial-vector meson, K ₁, as ~ ?1.5. The energy dependence and the magnitude of the total cross section were similar to the total cross section of γ + p → K ⁺ Λ.     

Fiber Optics: Physics and Technology,by Fedor Mitschke

This Conference, under the auspices of OEEC and the International Union of Pure and Applied Physics, was attended by more than a hundred delegates, representing some twenty-six nations. The Conference Chairman was Professor Sanborn C. Brown (U.S.A.), and the Conference Secretary Mr. Norman Clarke. The forty papers to be discused had been circulated to delegates well before the Conference, and the actual sessions were devoted to general discussions based on groups of papers which formed a unifying theme. Immediately after the close of the Conference, Prof. Brown and Mr. Clarke began the preparation of a full report of the proceedings, which will make a substantial volume. Among the general topics discussed were the place of physics in general education (opened by Mr. Clarke); the selection of university entrants for physics courses (Prof. G. K. T. Conn); examinations in physics (Dr. H. F. Boulind); the use of films and television in physics teaching (Dr. Harvey White, U.S.A.); and the Physical Science Study Committee's syllabus and programme (Prof. J. R. Zacharias, U.S.A.).