Stanislaw M. Ulam

Bio: Stanislaw M. Ulam is an academic researcher from Los Alamos National Laboratory. The author has contributed to research in topics: Von Neumann architecture & Projective linear group. The author has an hindex of 24, co-authored 68 publications receiving 10818 citations. Previous affiliations of Stanislaw M. Ulam include University of Florida & University of Wisconsin-Madison.

The Monte Carlo method.

Abstract: We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.

Adventures of a Mathematician

Abstract: This autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the 'Super,' in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. It includes an epilogue by Francoise Ulam and Jan Mycielski that sheds new light on Ulam's character and mathematical originality.

The Fractal Geometry of Nature

Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

Inference from Iterative Simulation Using Multiple Sequences

Abstract: The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.

Thermal Radiation Heat Transfer

Abstract: A comprehensive discussion of heat transfer by thermal radiation is presented, including the radiative behavior of materials, radiation between surfaces, and gas radiation. Among the topics considered are property prediction by electromagnetic theory, the observed properties of solid materials, radiation in the presence of other modes of energy transfer, the equations of transfer for an absorbing-emitting gas, and radiative transfer in scattering and absorbing media. Also considered are radiation exchange between black isothermal surfaces, radiation exchange in enclosures composed of diffuse gray surfaces and in enclosures having some specularly reflecting surfaces, and radiation exchange between nondiffuse nongray surfaces. The use of the Monte Carlo technique in solving radiant-exchange problems and problems of radiative transfer through absorbing-emitting media is explained.

The Kolmogorov-Smirnov Test for Goodness of Fit

Abstract: The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted. Confidence limits for a cumulative distribution are described. Examples are given. Indications that the test is superior to the chi-square test are cited.