# Analogies Between Analogies: The Mathematical Reports of by S. M. Ulam, A. R. Bednarek, Françoise Ulam

By S. M. Ulam, A. R. Bednarek, Françoise Ulam

Lots of the rules provided continue their value at the present time, and . . . are totally fundmental, either from a ancient and from a systematic viewpoint.--Gian-Carlo Rota, Massachusetts Institute of expertise

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**Extra info for Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and his Los Alamos Collaborators**

**Example text**

7. The basic statistical parameters, like the mean and median values, number of points in the window and standard deviation are given. The variability of data described by standard deviation EXPLORATORY SPATIAL DATA ANALYSIS. MONITORING NETWORKS. DECLUSTERING 27 is larger in the regions where the mean value is larger. I t is evident that local zones, which represent six or eight cells out of 40, illustrate the difficulty of any hypothesis for stationarities. The selection of the window size (often anisotropic) is usually a compromise: it should be large enough to have a reasonable number of data for statistics, and not too large to average the local variability that we are trying to detect.

2 I nverse distance power methods Inverse distance power (e. g. squared) method is a well-known simple linear interpolation method. The basic idea behind this approach is quite reasonable and simple: ( I ) prediction at the unsampled point is a weighted average of surrounding measurement data points, and (2) the data further from the estimated point have less influence on the prediction. y) Z(x,y) where = w1 (x,y)Z1(x1 , y1 ) L 1=1 n(x,y) is the number of points used for the current estimation, weight coefficients.

The most frequently used criteria for model comparisons are based on the analysis of validation residuals. 5) should consider and compare distributions of the residuals and their spatial structures - described by correlations. Ideally, distributions of the residuals should be symmetric around zero (no bias) and have small variance and no spatial correlations. Roughly models can be qualified usiog the criteria of accuracy and precision, which are related to the bias and variance of the residuals.