The Effect of Photographic Reducers in Autoradiographic Intensification Method for Image Recovery of Incorrectly Exposed Radiographs

Autoradiographic image intensification methods for recovering the images of underexposed step wedges, resolution targets and radiographs were investigated. The fog level of the intensified image was decreased by treating the film in a subproportional photographic reducer (mixture of potassium ferricyanide and sodium thiosulfate) prior to activation with S-35 thiourea. The fog level of intensified images of a step wedge decreased from a density of 1.32 to .12, the maximum contrast increased from 2.08 to 5.52, the relative speed increase calculated at 0.6 above fog level increased from 3.05 to 4.06 while resolution remained the same at 5.0 lines per millimeter.Radiographs of underexposed images were recovered by using this autoradiographic image intensification method. The underexposed radiograph was developed in the conventional manner using the Kodak X-Omat processor and treated in the subproportional photographic reducer to lower the fog density. The silver image of the underexposed radiograph was made radioactive with a solution of sulfur-35 thiourea, air-dried and exposed to another emulsion. The intensified image was also developed in the conventional manner. Its diagnostic usefulness was judged by experienced radiologists as optimal, adequate, poor but diagnostic, or totally unacceptable in comparison to optimally exposed radiographs. Of the six underexposed radiographs involving various body regions studied following intensification, five were consistently rated adequate. This technique, when fully developed and applied will result in reduced radiation dose to patients undergoing radiologic examinations. A significant difference exists between the intensified image of a double-coated and single-coated emulsion. When both emulsions are treated in a subproportional reducer prior to activation with S-35 thiourea, the intensified image obtained from a single-coated emulsion has less base plus fog density, higher gamma, and is more contrasty than that of a double-coated emulsion. These results indicate that to make deliberate underexposures, it is better to use a singlecoated than a double-coated emulsion

Mathematical aspects of degressive proportionality

We analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of apportionment functions are specified and the corresponding partitions of the seats in the European Parliament among the Member States of the European Union are presented. Although the choice of the allocation functions is theoretically unlimited, we show that the constraints are so strong that the acceptable functions lead to rather similar solutions.Comment: several minor corrections, revised version 10 pages in two column style, one figure and two tables include

Local limit theorems for subgraph counts

We introduce a general framework for studying anticoncentration and local limit theorems for random variables, including graph statistics. Our methods involve an interplay between Fourier analysis, decoupling, hypercontractivity of Boolean functions, and transference between ``fixed-size'' and ``independent'' models. We also adapt a notion of ``graph factors'' due to Janson. As a consequence, we derive a local central limit theorem for connected subgraph counts in the Erd\H{o}s-Renyi random graph $G(n,p)$, building on work of Gilmer and Kopparty and of Berkowitz. These results improve an anticoncentration result of Fox, Kwan, and Sauermann and partially answers a question of Fox, Kwan, and Sauermann. We also derive a local limit central limit theorem for induced subgraph counts, as long as $p$ is bounded away from a set of ``problematic'' densities, partially answering a question of Fox, Kwan, and Sauermann. We then prove these restrictions are necessary by exhibiting a disconnected graph for which anticoncentration for subgraph counts at the optimal scale fails for all constant $p$, and finding a graph $H$ for which anticoncentration for induced subgraph counts fails in $G(n,1/2)$. These counterexamples resolve anticoncentration conjectures of Fox, Kwan, and Sauermann in the negative. Finally, we also examine the behavior of counts of $k$-term arithmetic progressions in subsets of $\mathbb{Z}/n\mathbb{Z}$ and deduce a local limit theorem wherein the behavior is Gaussian at a global scale but has nontrivial local oscillations (according to a Ramanujan theta function). These results improve on results of and answer questions of the authors and Berkowitz, and answer a question of Fox, Kwan, and Sauermann

A study of the persistence characteristics of various cathode ray tube phosphors

"January 16, 1948." Based on a thesis submitted to M.I.T. Dept. of Physics, 1948.Bibliography: p. 102-104.Army Signal Corps Contract No. W-36-039 sc-32037.W.T. Dyall

Earth resources technology satellite operations control center and data processing facility. Book 2 - Systems studies Final report

Systems analysis for ERTS NASA Data Processing Facility system and subsystem