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A facsimile data compression system, called combined symbol matching (CSM), is presented. The system operates in two modes: facsimile and symbol recognition. In the facsimile mode, a symbol blocking operator isolates document symbols such as alphanumeric characters and other recurring binary patterns. The first symbol encountered is placed in a library, and as each new symbol is detected, it is compared with each entry of the library. If the comparison is within a tolerance, the library identification code is transmitted along with the symbol location coordinates. Otherwise, the new symbol is placed in the library and its binary pattern is transmitted. Nonisolated symbols are left behind as a residue, and are coded by a two-dimensional run-length coding method. In the symbol recognition mode, the library is prerecorded and each entry is labeled with its ASCII code. As each character is recognized, only the ASCII code in transmitted. Computer simulation results are presented for the CCITT standard documents. With text-predominate documents, the compression ratio obtained with the CSM algorithm in the facsimile mode exceeds that obtained with the best run-length coding techniques by a factor of two or more and is comparable for graphics-predominate documents. In the symbol recognition mode, compression ratios of 250:1 have been achieved on business letter documents.

Confusion matrices are a convenient and widely accepted means of tabulating results from experiments in which subjects choose responses to various stimuli. This paper is relevant to studies in which the recognition and confusability characteristics of a large set of possible stimuli are tested in order to select the smaller subset of stimuli that will eventually be presented to the user (e.g., selecting sculpted pushbuttons or command words for voice-interactive systems). Rather than applying cluster analyses, this paper demonstrates how to formulate optimization models from the information contained in a confusion matrix. Four binary integer programming models are proposed that when solved, yield the subset of stimuli exhibiting minimum total confusion. The models are solvable using widely available software on a microcomputer. A sizable example from the literature is solved and discussed, and directions for algorithmic research are recommended.

Based on sequential tracking, a machine composed of three sequentially connected automata is proposed for recognizing a plane shape given by binary pattern. The first automaton detects 10 kinds of quasi-local features which constitute a complete set of features in two consecutive lines. The second automaton integrates these features and segments a contour into letter L shaped segments which are considered as primitives for description of a shape. These L-type segments are arranged to form the structure. The third automaton extracts global features such as connectivity, hole, and concavity, where attribution of a hole to a blob is somewhat generally treated and some degree of closure of a concavity is described. Thus the systematic feature extraction of a plane shape and the simple and essential description of that shape is given.

Connectivity preservation is essential for operations like thinning or shrinking of binary patterns. In this note we present a test function which can be used to check whether a given 0-setting local operator of the conjunctive type (defined by a single template of 3 × 3 elements) disconnects an arbitrary size binary pattern or not. A similar test does not work for 1-setting operators.

A modification is proposed to the Safe Point Thinning Algorithm (SPTA) to speed it up. The modified algorithm was implemented on a single processor. It was then implemented on the Homogeneous Multiprocessor Proper under two techniques: data decomposition and function decomposition. Experimental results show that with our modification and multiprocessor implementations, the SPTA was considerably speeded up.

The effect of run order in different substructures of a pattern on binary pattern learning is investigated. Thirty-six subjects learned binary patterns by the serial anticipation method. Run lengths and order of the runs in odd and even numbered positions respectively were systematically varied. Latency times of anticipation, prediction errors and number of presentations to a criterion indicated that the order of runs in odd numbered position has a greater effect on grasping the pattern than the order of runs in even numbered position. This effect is explained by the particular phenomenal dominance relationship of the two substructures.

The pattern recognition technique utilizing adaptive binary pattern classifiers has been applied to the interpretation of infrared spectra. The binary pattern classifiers have been trained to determine the chemical classes of x-y digitized infrared spectra. High predictive abilities have been obtained in classifying unknown spectra. A new training procedure for binary pattern classifiers has been developed, and it has been used to classify ir spectra into chemical classes. Pattern classifiers trained in the conventional way and by the new procedure have been used in conjunction with feature selection, and it is shown that a small fraction of the data is necessary to classify these infrared spectra successfully into chemical classes.

The paper describes a new class of distance mappings for binary images, which are based on a border-to-border distance rather than on the distance between an individual point and the border of an object. It is shown how these mappings can be used to calculate efficiently meaningful features like the “line-shapeness” or “compactness” of objects within binary images or to characterize binary images in a global sense. The algorithms involved are well suited for conventional sequential processors.

The white block skipping (WBS) method of coding binary facsimile images consists of breaking each scan line into N picture-element (pel) blocks, then using "0" as the code word for all-white blocks and "1" followed by the binary pattern in the block for non-all-white blocks. In the first part of this paper, we derive (based on a first-order Markov source model) the optimum block size N and its corresponding minimum bit rate as functions of the average white and black run lengths of the image. In the second part of this paper, we propose a modified coding scheme where all-white scan lines are essentially skipped. This modified scheme is found to be as efficient as run length coding for transmitting texts.

A heuristic reconstruction algorithm is described, by which binary matrices can be produced from their two orthogonal projections. It is necessary for proper reconstruction that the binary pattern corresponding to the binary matrix bex- andy-directionally connected. By this method a large class of binary matrices can be reconstructed. It is proved that after a finite number of iterative steps this algorithm produces all thex- andy-directionally connected binary patterns belonging to the given two projections. Finally, some remarks on the implementation of this algorithm and results are presented.

Binary image pattern matching is used widely in character and symbol recognition, and to determine pattern positions [1, 2]. Binary level deviation and superposition of noise have been reported as the causes of inaccuracy in matching between the template and image patterns. As a result, measures have been reported to solve this problem. However, these measures have not been entirely effective. There still remain problems of pattern change due to sampling deviation and error in matching caused by this change. This paper presents a method to prevent sampling errors by using Boke processing [3, 4]. Also, the matching errors which occur due to binary pattern sampling are analyzed and measures to reduce them are proposed.

A method has been proposed in the spoken word recognition, which utilizes the frequency-time pattern inherent to the word. However, in the application of the method for speech by unspecified speakers, normalization is required, in contrast to the case of specified speakers, since the formant in the pattern may be shifted along the frequency-axis due to the individual difference of harmonization organs of the speakers. The method including the formant normalization or nonlinear conversion of the frequency-axis contains a larger computational complexity, and is not suited to a large vocabulary of words. From such a viewpoint, this paper proposes a method, in which a common weighted average dictionary is constructed by superposing the binary local-peak patterns of speakers, absorbing their individual differences into a dictionary. The individual differences of speakers are also overcome by matching with the dictionary the binary pattern with an allowable width along the frequency-axis centered around the local peak of the input speech. The weighted average dictionary is only a pattern set representing the frequency of the local peaks inherent in the word, and the storage of data requires less memory capacity. Since the input pattern is matched based on the binary pattern set, the computational complexity is also reduced. With 110 words of 0A command as the sample speech, both male and female speech is used as the inputs. When the input speakers are restricted, a recognition rate of 97 percent was obtained for restricted speakers and nearly 92 percent was obtained for unrestricted speakers.

We introduce in this paper the P-sequences which are integer sequences characterizing binary trees and generating lexicographically all the binary trees in -order. We compute the rank of a P-sequence by a direct formula and not by an algorithm. Furthermore, we introduce the L-sequences which generate directly and lexicographically all the binary trees on A -order, also called natural order. Ranking and unranking algorithms are provided.

Presents a two chip imaging system for optical character recognition (OCR) applications. It consists of a 64/spl times/24 photodiode array providing directly a binary pattern. The image quality is enhanced by means of a separate signal processing chip which performs centering of the image and delivers control signals for further on-line character recognition. The two chips are part of a fully integrated OCR wand.

The frequency of occurrence of logic functions of binary N-tuples can be observed from sequences of binary patterns. The logic functions considered here are AND, NOR, NAND, OR, and an odd-even parity check; and the frequency parameters are expressed as real matrix transformations on the probabilities of the patterns. Some properties, inverses, and interrelationships among the parameter sets are given, along with fast algorithms to facilitate computational processes. The results permit the outputs of convenient hardware logic operations to be converted into other parameters for smoothing, detection, or inference purposes, or to estimate the pattern probabilities by inversion. A measure of association among binary patterns is given as one characteristic feature which can be derived from the observed parameters.

Algorithms for reconstruction of a two-dimensional binary pattern Z from its row-projection vector A and column-projection vector B have been developed by Chang. The projection set (A,B) is said to be unique, nonunique, or inconsistent if it determines one binary pattern, more than one binary pattern, or no binary pattern. A binary patern Z is said to be ambiguous if there exists another pattern with the same projections, otherwise it is unambiguous. Two characterization questions of binary patterns and their projections are posed. First, given Z what is the necessary and sufficient condition for Z to be ambiguous, or unambiguous? Second, given (A,B), what is the necessary and sufficient condition for (A,B) to be unique, nonunique, or inconsistent? These two combinational questions are discussed and efficient algorithms to answer them are derived from some ideas of Ryser.

Different types of two-dimensional carriers have been used to binarize images. The binary pattern can be decomposed in sub-patterns related to one-dimensional carriers, although the two-dimensional carrier cannot be decomposed in one-dimensional ones.

Golay hexagonal pattern transforms are position independent local operators for use in transforming or altering binary images. The hexagonal tessellation is preferred because it removes the connectivity ambiguity present in the square or checkerboard tessellation. Golay transforms also may be applied to multilevel or "gray" images by encoding such images as a registered stack of binary image planes. The general Golay transform creates a new binary image (the output image) from as many as three stacked input images. Simpler Golay transforms merely alter the binary pattern contained in a single image plane, i.e., the same plane acts as both input and output. Because it is slow and cumbersome to perform Golay transforms using a general-purpose computer, fast special-purpose computers have been built for this purpose which may be programmed in a new image processing language called Glol (Golay logic language). It has been found, using both synthetic images as well as images taken from the real world, that Golay transforms are useful in feature enhancement and extraction. Several illustrative examples are provided.

The problem of reconstructing binary patterns from their shadows or projections is treated. Two algorithms are formulated. For the two-view case, both algorithms give a perfect reconstruction if and only if the pattern is two-view unambiguous. It is also shown that n views are sufficient, but not necessary, to reconstruct any n × n binary pattern. Experimental results for the four-view reconstruction of 25 × 25 binary patterns indicate that one of the algorithms has good convergency behavior.

The application of a conditional probability computer to the steady-state optimization of a simple chemical process has been investigated. On the basis of the work of previous investigators, the memory structure of the conditional probability computer was modified in a way designed to accelerate the learning process and improve the predictive capabilities of the computer. The proposed modifications were studied by optimizing an analog simulation of a simple chemcial process subjected to a variety of uncontrolled disturbances. The investigations served to delineate some of the special problems encountered in the application of a binary pattern recognition device such as the conditional probability computer to process optimization. The proposed modifications were successful in achieving significant acceleration in the learning process and improvement in predictive capabilities over that offered by a conventional conditional probability computer. (Author)

A piecewise-linear pattern classifier is applied to the interpretation of low resolution mass spectral data. A criterion for internal generation of new weight vectors based on periodic evaluation of a function is tested. Results are presented for classification problems pertaining to molecular formula and structural information and are compared with results from a binary pattern classifier.

Given the horizontal and vertical projections of a finite binary pattern f , can we reconstruct the original pattern f ? In this paper we give a characterization of patterns that are reconstructable from their projections. Three algorithms are developed to reconstruct both unambiguous and ambiguous patterns. It is shown that an unambiguous pattern can be perfectly reconstructed in time m × n and that a pattern similar to an ambiguous pattern can also be constructed in time m × n , where m , n are the dimensions of the pattern frame.

Two information processing models of the perception of binary patterns are outlined. The H (k-span) model assumes S er;aluates the transitional uncertainty associated with the different k-tuples constituting the pattern. The H (run-span) model assumes S codes the pattern into runs and then evaluates the transitional uncertainty associated with the pattern’s run-tuples. Both models give a measure of the complexity of a pattern. The models are tested by using the complexity measures to predict various response indices of pattern complexity; e.g. judged pattern complexity, mean number of words to describe a pattern, accuracy of recall of a pattern. H (run-span) proved to be highly correlated with all of the pattern complexity indices. H (k-span) received only moderate support.

This paper proposes a novel design for a parallel nonadaptive binary pattern classifier. The structure employs random-pulse (stochastic) computing elements to economically realize multimodal nonlinear discriminant functions similar in form to those used in potential function classifiers. The technique achieves efficient hardware utilization by employing a READ-ONLY memory (ROM) without addressing circuits to store modes and simultaneously execute parallel stochastic multiplications required in discriminant function computations.

Binary data arising from graphical information can be compressed by using a linear transformation. If the linear transformation is based on a binary field (modulo 2), the compressed data is also binary. This allows digital transmission and less complicated encoding/decoding equipment.

An empirical method employing computerized pattern recognition techniques has been applied previously to the generation of simulated mass spectra of small organic molecules. The techniques have been improved in two ways to yield superior performance. First, a method for training adaptive binary pattern classifiers using an iterative least squares approach is used. Second, a feature extraction technique known as an attribute inclusion algorithm is used to investigate the importance of multiple features in the molecular descriptions.

In this paper, it is shown that if k>=3, any finite k-symbols pattern whose lengthis greater than 1 can be generted strictly monotonously from the primitive pattern by some sequence of parallel transformations of a k-symbols scope-n tessellation automaton for any n>=2. It is also shown that any nonzero finite binary pattern can be generated monotonously from the primitive pattern by some sequence of parallel transformations of a binary scope-n tessellation automaton for any n>=3.

Support Vector Machine (SVM) is originally designed for linear binary pattern recognition. According to defect of common SVM, the Least square SVM is discussed to classify the small samples. In fault diagnosis, multi-category faults are common. Many multi-category SVMs are introduced in this paper briefly, and then an immune guided decision tree SVM (DTSVM) is presented which takes into account the fault occurring frequency. It proposes a fault isolation algorithm which adopts immune memory to optimize the configuration of DTSVM. Simulation and examples show that this method is useful in fault isolation. The kernel functions play an important role in the classification. The choice of kernel function and its parameters is neither easy nor trivial. In this paper, we have researched the kernel function of RBF and its effect on classification.

This paper proposes a probabilistic similarity index as a proximity measure between binary feature vectors. Different situations of binary features are analyzed and applications of the new index to questionnaire analysis is reported.Binary vectors are the most frequently used data format in computer science. Pattern recognition problems, such as questionnaire data analysis, require that the association between binary pattern vectors or feature vectors be measured. Many association measures, including the simple matching coefficient and the Jaccard coefficient, have been proposed.Consider two binary vectors of size n, V1 = [V1(i)] and V2 = [V2(i)], i = 1,2,…,n; where V1(i)e{0,1}, V2(i)e{0,1}. Let the vectors represent two features where the i-th components correspond to the i-th pattern. We wish to assess the association between these two vectors. We define the elements of the contingency table as follows. All the summations are for i from 1 through n. n1 = S V1(i) n2 = S V2(i) n00 = S [1-Vt(i)][1-V2(i)] n01 = S [1-V1(i)]V2(i) n10 = S V1(i)[1-V2(i)] n11 = S V1(i)V2(i).Various elements of the contingency table have been used to measure the similarity between V1 and V2. They differ in the coding of (0,1) and in the emphasis placed on the 0-0 and 1-1 matches. In the situation where the coding of 0 and 1 is meaningful and consistent between the vectors, in which (1,1) matches and (0,0) matches are equally important, the elements n11 and n00 are directly involved in the computation of the similarity, while n01 and n10 are not. Indices like the simple matching coefficient are suitable in this case.If the labeling of 0 and 1 is arbitrary, as when the labels simply denote two distinct states, or as when the two binary vectors represent two binary partitions of the same set, several well-known indices, such as Hubert's G, can be reduced to the binary case for this situation.The third situation arises in many questionnaire problems, where the coding of 0 and 1 is meaningful and significant, and n11 is treated differently from n00. Consider a questionnaire in which each participant responds to several “yes-no” questions. The answers are coded 0 or 1, where “1” means “yes” and “0” means “no” or “not clear”, “don't remember”, or even “missing data”. The (1,1) matches are significant, while (0,1), (1,0), and (0,0) matches are not. The Jaccard coefficient is an example of an index suitable for this situation. We are mainly interested in this situation in this paper.Probabilistic measures of association are based on the unusualness of the proximity. This paper discusses the application of a new probabilistic similarity index to questionnaire data analysis. This index is defined as the cumulative probability, under a random permutation hypothesis, that a random labeling of components within a vector has at most the observed number of matches. The permutation null hypothesis is defined as Ho(p): all permutations of V2, r(V2)'s, are equally likely. The baseline population under Ho(p) is Op = {r(V2): S(V2) is a permutation of V2}.A new similarity index T is defined as the cumulative probability that a random permutation of V2 has at most the same number of (1,1) matches with V1 as the original V2 has with V1, i.e., T = H(n11), where H is the cumulative hypergeometric probability.The probabilistic similarity index defined under this model has clear statistical significance and its critical value for testing the null hypothesis can be easily computed. This unique property of probabilistic proximity measures frees the researcher from Monte Carlo study and provides a natural threshold for vector correspondence. The proposed similarity index is self-standardized and thus does not require a correction for randomness. A pipelined architecture is available for computing this similarity index efficiently.Applications of this probabilistic similarity index to a questionnaire data analysis problem is reported. The application of a randomized version of this index is reported elsewhere [1,2]. Its performance is compared with some well known similarity measures. Its advantages and limitations are demonstrated.

Filling regions in raster images is the term given to the problem of extracting a connected region (that contains some preselected seed pixel) and filling it with some color. A connected region is formally defined as the collection of all pixels that are in the transitive closure of a pixel-connectivity operator that is applied to the seed. For example, the 4-pixel-connectivity operator selects all pixels that are (spatially) 4-connected to the pixel operand, and have the same color. This problem can be solved relatively easily if the fill color is distinguishable so that every pixel, once colored (i.e. flagged OLD) will not be considered again. In binary images, the fill “color” is usually a binary pattern and therefore, a “colored” pixel may still have its previous (e.g., black or white) color. This fact makes the problem non-trivial.In this paper, a region to be filled is represented as a connected directed a-cyclic planar graph in which nodes are regular regions (defined below) that are easy to handle. An arc connects a regular region to its neighbor below which shares a common horizontal sub-boundary. Based on this abstract representation of a region, a formulation of the filling problem is developed as a variant of graph traversing. The difficulties imposed by filling with a binary pattern, and the avoidance of an explicit description of the graph are explored and a solution is presented. This solution utilizes the frame buffer (that is used to display the image) for improved efficiency of a graph traversal algorithm.This method turns out to be similar to [Lieberman-78], that is shown here to be incorrect. The complexity of the new algorithm is 0(N*L+ N*Log N), compared to 0(N*L*Log N) there, where N is the number of nodes in the graph and L is the average composite degree of each node. A proof of correctness for the new algorithm is given too.

Symbolic substitution is a method of computing based on parallel binary pattern replacement, that can be implemented with simple optical components and regular free-space interconnection schemes. A two-dimensional pattern is searched for in parallel in an array and is replaced with another pattern. Pattern transformation rules can be applied sequentially or in parallel to realize complex functions. When the substitution space is modified to be loge SIT connected for N binary spots, and masks are allowed to customize the system, then optical digital circuits using symbolic substitution for network interconnects can be made nearly as efficient in terms of gate count and circuit depth as conventional arbitrary interconnection schemes allow. We describe an optical setup that requires no more than a fanin and fanout of two using optically nonlinear logic devices and a free space interconnection scheme based on symbolic substitution.

Binary pattern classification that may be implemented using optical hardware and neural network algorithms is considered. Pattern classification problems that have no concise description (as in classifying handwritten characters) or no concise computation (as in NP-complete problems) are expected to be particularly amenable to this approach. For example, optical processors that efficiently classify binary patterns in accordance with their Boolean function complexity might be designed. As a candidate for such a design, an optical neural network model is discussed that is designed for binary pattern classification and that consists of an optical resonator with a dynamic multiplex-recorded reflection hologram and a phase conjugate mirror with thresholding and gain. In this model, learning or training examples of binary patterns may be recorded on the hologram such that one bit in each pattern marks the pattern class. Any input pattern, including one with an unknown class or marker bit, will be modified by a large number of parallel interactions with the reflection hologram and nonlinear mirror. After perhaps several seconds and 100 billion interactions, a steady-state pattern may develop with a marker bit that represents a minimum-Boolean-complexity classification of the input pattern. Computer simulations are presented that illustrate progress in understanding the behavior of this model and in developing a processor design that could have commanding and enduring performance advantages compared to current pattern classification techniques.

Presentation of images on some kinds of electronic displays requires a binary output. Several so-called halftone techniques are used to binarize graytone images. Among these we have studied implicit passive methods. In electronic half toning the images are presented on a discrete raster.

Given N, M, and s, a method of generating anNxM binary matrix such that every nonzero x s binary pattern occurs exactly once as its submatrix is presented. This construction is based upon a systematic filling of the matrix with a maximal length recurrent sequence and gives several new solutions yet unreported. 1. Introduction. In this paper we consider the problem of construction of an NxM binary matrixA such thatany s nonzero binarypatternoccurs exactlyonce as its submatrix. Similar problems have been attempted earlier by various authors. Reed and Stewart (5) considered the existence ofA given only and s. Gordon (2) later extended their result andshowed that given any and s, one can always findN and M,N> t,M> s such that all s submatrices (in the toroidal sense) inA are distinct.A is then called a perfect map. All the s nonzero binary patterns are not necessarily the submatrices of a perfect map. However, a perfectmap with parametersM 2 1 and N (2 s'- 1)/M and containing all the x s nonzero binary patterns was exhibited in 12).WhenN andM are relativelyprime, apseudorandom array also gives a perfectmap with the same parameters (3). The toroidal perfect maps of (2), (3) and (5) can be easily converted into nontoroidal ones by repeating the first t- 1 rows after the last row and the first s- 1 columns after the last column. In this paper, we will be concerned only withNxM nontoroidal perfect mapA in which every nonzero binary s pattern occurs exactly once as a submatrix. Obviously, the four parameters are then related as

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

A dual mode facsimile data compression technique, called Combined Symbol Matching (CSM) , is presented. The CSM technique possesses the advantages of symbol recognition and extended run-length coding methods. In operation, a symbol blocking operator isolates valid alphanumeric characters and document symbols. The first symbol encountered is placed in a library, and as each new symbol is detected, it is compared with each entry of the library. If the comparison is within a tolerance, the library identification code is transmitted along with the symbol location coordinates. Otherwise, the new symbol is placed in the library and its binary pattern is transmitted. A scoring system determines which elements of the library are to be replaced by new prototypes once the library is filled. Non-isolated symbols are left behind as a residue, and are coded by a two-dimensional run-length coding method. Simulation results are presented for CCITT standard documents. With text-predominate documents, the CSM compression ratio exceeds that obtained with the best run-length coding techniques by a factor of two or more, and is comparable for graphics-predominate documents.© (1979) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The general problem is as follows: Given a number of binary optical inputs, photodetectors thresholded to provide binary outputs, and a desired functional relationship (memory-free) between the inputs and outputs, find an optimum assembly of passive optical elements that implements the relationship. Here the passive optical elements might be diffracting, shadowing, reflecting, or refracting structures of various numbers, locations, sizes, and shapes; the binary optical inputs might be from a spatial light modulator or an array of laser diodes; the desired relationship might be a combinational logic function with a high proportion of don't-cares (input values or patterns for which the output may be either binary value); and optimality might be specified in terms of maximum fabrication and operating tolerances or minimum complexity. Several aspects of this general problem are considered in the context of optical real-weight and complex-weight threshold logic and optical binary pattern classification.

This chapter deals with a development of ideas stemming from the early work of Bledsoe and Browning (1959) in which a binary pattern field was broken up into several randomly selected sets of n binary points called n-tuples. The scheme is adaptive and requires a set of patterns with which the system can be trained: the training set.

A raster-scan algorithm and the corresponding hardware implementation for the approximation of binary pattern edges with line segments is described. The generated representation is more suitable for processing by conventional microprocessors than raw binary images or chain-code descriptions. The approach is used in an experimental printed wiring board inspection system.

The conditions under which changes in parameters lead to changes in the pattern-generating behaviour of Turing's two-morphogen linear model can be expressed in terms of two reduced rate constants, k ′ 1 and k ′ 4 which represent autocatalytic and self-inhibitory rates in relation to cross-catalysis and cross-inhibition, and the ratio of the diffusivities for the two morphogens. This allows a new type of diagram to be drawn in which a two-dimensional k ′ 1 k ′ 4 space is divided by Turing's conditions into regions where the various morphogenetic behaviours occur. An analysis using this type of diagram is applied to the linear limit of two non-linear models, those of Gierer and Meinhardt and of Tyson's modification of the Brusselator, and is used to clarify what is happening in their non-linear development. Several possible applications are mentioned; to the stability of a simple binary pattern in slime moulds, to the development and decay of a succession of patterns in the imaginal wing discs of Drosophila as treated by Kauffman et al., and to the apparent ease of disturbing the sea urchin blastula to produce a three-part, rather than a two-part pattern.

The goal of facsimile bandwidth compression is the efficient transmission of documents achieved by the removal of redundancy in the encoding technique. For the case of printed or typewritten documents, the most powerful encoding technique is the Combined Symbol Matching (CSM) algorithm, which is based on the detection of recurrent patterns (such as alphanumeric characters) in the document being encoded 〈4, 5, 6, 10〉. As the transmitter scans the document, it locates and extracts isolated patterns, transmits them to the receiver, and stores them in a library. Using the received patterns, the receiver also accumulates an exact copy of the transmitter's library. As each new pattern is isolated, it is compared with the library patterns which have been previously encountered. If the pattern is unfamiliar, it is added to the library. However if a "match" is detected, this indicates a recurrence of a pattern, and there is no need to retransmit it, since it is available in the receiver's copy of the library. Therefore, the library entry number (library ID) is transmitted instead, enabling the receiver to reconstruct the pattern from the "prototype" in its library. Since the library ID can be transmitted with far fewer bits than the binary pattern that it points to, a significant bandwidth compression may be attained. For printed documents, the CSM algorithm is typically twice as efficient as the best run-length coding algorithms.

This paper presents a novel design of a non-adaptive binary pattern classifier. The structure employs random-pulse (stochastic) computing elements to realize nonlinear discriminant functions in pattern recognition. A machine design configuration illustrates how a ROM without addressing circuits stores modes and simultaneously executes parallel stochastic multiplications required in discriminant function computations—demonstrating efficient hardware utilization.

Summary.-An attempt was made to obtain a rough estimate of the human S's monitoring span. Sequences of binary digits were flashed to Ss whose task was to indicate the occurrence of a specific pattern of digits. The upper limit of monitoring performance is about 7 digits per second. This paper considers the short-term monitoring of information upon a continuing basis. We have found no direct antecedent task in the literature, although the task resembles a task employed by Bakan (1961) who required his Ss to indicate the occurrence of three successive odd numbers. METHOD Task.-A stream of binary digits, appearing one digic at a time as a 0 or a 1, was presented. The 0 was flashed concentrically with the 1 in order to reduce apparent movement. Each flash of the display also advanced a counter for each S. S's task was to indicate when a particular patrern of digits appeared. For example, in the stream of digits 0001 11 01 0, the triplet pattern 101 occurred upon the eighth digit. Construction of biwy seqrbences.-The sequences had the property that each possible binary patrern of constant length n occurred sequentially once and only once within each sequence. A binary sequence which incorporates all possible patterns of n = 2 is 00110. This sequence concains, in order, the patcerns 00, 01, 21, and 10. Similarly, for n = 3, the sequence 1 1000101 11 contains the patcerns 11 0, 100, 000, 001, 01 0, 101,011, and 11 1. In general, a suitable sequence of length [2" + (n - 1 )] concains all of the binary patterns of length n, once and only once. It is noted that the length of the binary sequence necessarily increases with n by this procedure. Szbbjects.-Five university srudents served together as a crew. The entire crew viewed the display (6 in. high at 6-ft. viewing distance), but each S monitored a different binary pattern. The monitored pattern was available to each S upon a card before and during each sequence. S indicated the occurrence of his monitored pattern with a switch, which stopped his counter. The crew served 90 min. per day over a 12-wk period. Conditions.-In the initial tests three rates of presentation: 2, 1, and 0.5 binary digits per sec.; and three lengths of monitored pattern: 4, 6, and 8 'The research reported in this paper was sponsored by the Air Force Systems Command, Electronic Systems Division, under Project 7682 Man-Computer Information Processing. The paper is identified as ESD-TDR-63-342. Further reproduction is authorized to satisfy needs of the U. S. Government. 'Now at Tufts University.

Two approaches are involved in this study, namely, the multiple-gray-level (direct) approach and the binary-level (indirect) approach. In the direct approach, a new reconstruction method called Minimum Ray-Sum Difference Technique (MRDT) is introduced. The algorithm is applicable for any even number of projections which consist of pairs of perpendicular projections. Comparative studies with respect to other methods1 are conducted. In the indirect approach, a multiple-gray-level pattern is decomposed or coded into a set of dependent or independent binary patterns. Projections are obtained for each binary pattern for processing or transmission. A multiple-gray-level pattern has to be reconstructed. A modified algorithm introduced by Chang2 is used in this study.