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ESTIMATION of microquantities of purines by paper chromatography was first suggested by Hotchkiss1. Later, detection by photographing with an ultra-violet source has amplified the method2. Tennent et al. 3 and others have designed adaptors for the Beckman spectrophotometer to enable direct estimation of the purines from paper chromatograms. This method requires costly instrumentation, and is time-consuming unless an automatic recorder is provided.

THE analysis of the protein composition of blood serum or plasma by means of zone electrophoresis on filter paper has stimulated interest in clinical laboratories throughout the world. In addition to numerous publications dealing with the applications of the technique in various pathological conditions, critical assessments of its validity and accuracy have appeared1–4, in which attention is properly directed to the limitations of the method from the point of view of the numerical evaluation of the separated protein fractions. It has seemed desirable to undertake a study of the accuracy and reproducibility of this method of protein analysis, using two of the most commonly employed protein-dyeing techniques.

A practical system for translation of information coded on punched paper tape to a matrix on a photograph is presented. The information here consisted of stereo random brightness fields; however, the system should be applicable to any three-dimensional information. The matrix is developed by slow digital scan of an intensity (ten levels) modulated oscilloscope and is photographed by a camera on time exposure. The system requires 166 seconds to produce each 10 000 element matrix and hence cannot be used for on-line work. However, for the researcher who can tolerate this limitation, the system's low cost, simplicity, and good resolution (better than 100 elements per inch) should prove attractive.

Some of the major results of future goals of an automatic program synthesis project are described in the two papers that comprise this document. The first paper gives a detailed algorithm for synthesizing a computer program from a trace of its behavior. Since the algorithm involves a search, the length of time required to do the synthesis of nontrivial programs can be quite large. Techniques are given for preprocessing the trace information to reduce enumeration, for pruning the search using a failure memory technique, and for utilizing multiple traces to the best advantage. The results of numerous tests are given to demonstrate the value of the techniques. The other paper gives a brief overview of the automatic programming system within which the above algorithm is being used. This system is still under development. (Author/CH)

The primary aim of these five technical papers is to indicate aspects of proof theory which may be of use in the study of non-numerical computing. The three main papers are entitled: "Checking of Computer Programs;""Consistency Proofs and Programs for Translators;" and "Experiments with Computers on the Complexity of Non-numerical computations." The author shows that many theorems on computability in traditional metamathematics are of little use to the computer scientist because they do not lead to feasible algorithms. He also suggests alternative approaches to proof theory which would be of greater applicability. (MM)

In H. K. Weiss' letter to the Editor (“The Fiske Model of Warfare”, Opns Res. 10, 569–571 (1962).), Weiss pointed out that Rear Admiral Fiske, USN, seemed to have foreshadowed by 11 years the developments that have come to be known as Lanchester's Square Law. Weiss stated that Fiske appears to have been the first to observe publicly that, when the damage each of two forces can inflict on the other is proportional to its own size, the change of size of each force was geometric rather than arithmetic.

THE recent communication on this subject by R. Robinson1 has prompted me to record some observations made about two years ago on this subject.

The report is a collection of Working Papers in Speech Recognition on the following topics: Organization of the HEARSAY II speech understanding system; The DRAGON system -- an overview; Parameter-independent machine segmentation and labeling; A new time-domain analysis of fricatives and stop consonants; Sub-lexical levels in the HEARSAY II speech understanding system; Inference and use of simple predictive grammars; Real-time linear predictive coding of speech on the SPS-41 microprogrammed triple-processor system; A 16-bit A-D-A conversion system for high-fidelity audio research.

In a recent paper 1 I stated that von Neumann had originated the suggestion for the use of Schur's canonical form for arbitrary matrices. I have since learned that the suggestion actually is due in the first instance to John Greenstadt, who brought it to von Neumann's attention. The history of this is rather interesting and was communicated to me in a letter from John Greenstadt, which I quote below. “The full story is, that the triangularization occurred to me early in 1953, after trying in vain to find a general iterative diagonalization procedure, even where one knew that it was possible to diagonalize (defective degeneracy being the impossible case). It seemed to me that one thing that made for the stability of the Jacobi method was the fact that all the elements in the transformation matrix were less than 1. A natural generalization embodying this requirement was to consider unitary transformations. Then, a quick check of Murnaghan's book showed that one could hope only to triangularize, but that this was always possible. “I did some hand calculations on this, and lo and behold! it converged in the few cases I tried. I then programmed it for the CPC and tried many other cases. For several months thereafter, Kogbetliantz, John Sheldon, and I tried to prove convergence, when the algorithm involved the sequential annihilation of off-diagonal elements. We (particularly Sheldon) tried many approaches, but with no hint of success. Finally, in the latter part of 1953, we decided to ask von Neumann, who was then a consultant for IBM, when he was in New York at our offices. “I had prepared a writeup describing the procedure, but von Neumann (rightly) didn't want to bother reading it, so I explained it to him in about two minutes. He spent the next 15 minutes thinking up all the approaches we had thought of in three or four months, plus a few ones—all, however, without promise. “At this point he decided that it was a nontrivial problem, and perhaps not worth it anyway, and immediately suggested minimizing the sum of squares of subdiagonal elements, which is, of course, the truly natural generalization of the Jacobi method. For the next 15 minutes he investigated the case when it would be impossible to make an improvement for a particular pivotal element and found that these cases were of measure zero. “I recoded my procedure for the 701 and tried many other matrices of various sizes. I myself never had a failure, but it has since been demonstrated that the method will indeed fail for a class of matrices. Hence, a proof is clearly impossible. However, I think a statistical proof is possible, along lines suggested by Kogbetliantz, which, however, I have not been able to find. I do not think von Neumann's variation of the method would fail. (However, it is more complicated and time consuming.)”

The result obtained in the paper on the cell of the honey bee, read November 26, 1885, by which the side of one of the lozenges composing the cell was found to be three times the difference between the two parallel edges forming the sides of one of the trapeziums of the prism, gives a very simple method for constructing the figure as follows. On a straight line take a part AD, and lay off DC equal to twice AD, from D erect a perpendicular, and with radius AC = 3DA cut off DP; AC and AP are sides of the lozenge ACEP, which fulfils the required conditions. It is manifest that from this lozenge the remaining two lozenges and also the six trapeziums can he immediately constructed.

In a 1967 publication, D. P. Gaver studied a probabilistic model of a multiprogramming computer system. His results have been utilized recently by a number of authors. However, we have observed that Gaver's results contain inconsistencies. These inconsistencies are discussed in detail and a correction suggested and verified through an independent derivation.

A comment on Schild, A., I. Fredman. 1961. On scheduling tasks with associated linear loss functions. Management Sci. 7 (3, April) 280–285.

I would like to comment on the Yarnold and Nehnevajsa article (Yarnold, K. W., Jiri Nehnevajsa. 1961. Analytical methods for determination of training-device requirements. Opns Res. 9 535–545.) appearing in the July–August 1961 issue. The comments fall into two categories: first based on the authors' assumption that “training devices” operate by improving the temporal-accuracy performance of a system's human links, and a second set of comments based on another assumption (mine) that humans can be trained by “training devices” continually to make improvements in and better diagnose problems of the entire man-machine system.

We have read with much interest the paper “Automatic Segmentation of Cyclic Program Structures Based on Connectivity and Processor Timing” by T. C. Lowe [ Comm. ACM 13 , 1 (Jan. 1970), 3-6, 9], and we congratulate the author on the clarity of his exposition. However, we're afraid we must question the technique he describes.