Pattern Matrix Research Articles

Expectations and Stability with Gross Complements

Arrow and Nerlove (1958) have found that when all commodities, both present and future, in a continuous time general equilibrium model of a competitive economy, are gross substitutes, then stability with “static” expectations is equivalent to stability with “adaptive” expectations. It is found here that we may extend the Arrow-Nerlove result that the stability behaviour of the system is unaffected by the selection of the more sophisticated adaptive expectations over static expectations, provided the substitute-complement relationship of commodities, both present and future, fits into the Morishima (1952) matrix pattern. In addition, a counterexample is exhibited which establishes that the Arrow-Nerlove result does not hold in general and the choice of adaptive versus static expectations can affect stability…

Developmental Assessment of Pattern Detection of Matrices

GAINES, ROSSLYN. Developmental Assessment of Pattern Detection of Matrices. CHILD DEVELOPMENT, 1977, 48,445-451. The purpose of this study is to examine if there are developmental changes in skill and speed of detection of variation in matrix patterns. The sample comprised 215 subjects: 93 kindergartners, 30 fifth-grade students, 30 high school sophomores, 32 nonartists, and 30 professional artists. A complex matrix was used, requiring the multiplication of asymmetrical transitive relations involving double asymmetry. The results showed that detection of matrix patterns did not increase with age using smaller 3 x 3 stimulus arrays in the matrix format, but that there were differences when the larger 4 x 4 matrix format was used.

Basic T matrix patterns for 2-port linear transformation networks in the real domain

Well known 2-port linear transformation networks, e.g. convertors and invertors, are related by both continuous and discrete transformations. These are shown as patterns on two graphs using T matrix elements. This leads to the development of further networks that are needed to complete the continuous transformation pattern.

Ovarian Tumors: Tumors and Tumor-Like Conditions of the Ovaries, Fallopian Tubes and Ligaments of the Uterus

This is an informative and useful book that, in addition to discussing ovarian tumors, has several chapters on tumors of the fallopian tubes and the accessory ligaments of the uterus. Concepts new to some American surgeons and pathologists include systemic carcinoma and the role of enzymatically active cells of ovarian stroma in relation to neoplasms. The introduction to incidence, diagnosis, treatment, and prognosis is effective and concise. The principal failing of the book here is the absence of a chapter on development of the ovary. The detailed and diverse nature of the ovary leads easily to confusion and disagreement. In several instances this may be due to lack of attention to recent ultrastructural work. For example, adenomatoid tumors now seem to be mesotheliomas with a special matrix pattern, and granular cell myoblastoma is a tumor of Schwann cells of neural crest origin and is mistakenly identified here with neurilemmoma. Elsewhere

A model of neural code for taste quality

The 80 chorda tympani single fibers were selected following the rate of appearance of each response type of units for four taste stimuli in arbitrarily selected 400 fibers in the rat. These 80 fibers were distributed in the matrix with 80 squares in order of the units with sucrose, NaCl, acid and quinine sensitivities from left to right, and also with the intention to make the monotonic function for each quality accomplished by putting the units in appropriate columns. Thus, we could satisfactorily demonstrate the possibility to represent the pictures of across fiber response patterns quantitatively as bar graphs in the matrix. As the matrix patterns for 0.01 M to 0.1 M NaCl were almost the same, the matrix pattern is considered to represent only the taste quality. The matrix patterns obtained for DL-alanine, Na-saccharin, MSG and AgNO 3 were well consistent with results of electrophysiological, behavioral and psychophysical studies.

Symmetry, gestalt and information theory: a critique.

A criticism of a recent analysis of matrix pattern perception is advanced. It is pointed out that a fair test of the equivalence for performance of different forms of redundancy must be framed in terms of the measure of transmitted information.

Filamentous and matrix components of skeletal muscle Z-disks.

AbstractThe fine structural appearance of Z‐disk lattices in vertebrate skeletal “fast” muscle varies depending upon whether osmium or glutaraldehyde has been employed as the primary fixative. Prior investigators have attributed the differences to change in the extent of actin filament overlap within the Z‐disk and/or to rearrangement of Z‐disk filaments.Adult frog and young newt “fast” muscle has been studied under various degrees of stretch, with several different aldehyde and osmium fixation procedures, and after plastic section digestion techniques utilizing Pronase or pepsin. Serial cross sections of Z‐disks were correlated with oriented cross and longitudinal sections. Fixation with collidine‐buffered osmium and veronal acetate‐buffered glutaraldehyde seems to provide the greatest and most distinctly contrasting differences. A consistently arranged phase, the filamentous lattice, can be discerned after either fixation. However, a second phase, termed “Z‐disk matrix,” appears variable, perhaps due to extraction during primary osmium fixation procedures. Glutaraldehyde‐fixed frog muscle Z‐disks display a copious matrix, one which is seldom totally depleted by osmium fixation. In young newt muscle Z‐disks, little matrix is present after glutaraldehyde fixation and none of it remains after primary osmium. In Z‐disks fixed by either method, matrix that is retained appears to be deposited in lattice‐like patterns. It is suggested that these matrix patterns, or their loss, are the basis for the varying images of Z‐disks observed under diferent fixation conditions and that the filamentous lattice is relatively stable. The Z‐disk is more rapidly obliterated by Pronase or pepsin digestion than is any other muscle component, including actin (which appears notably unreactive). The rapid digestion effect is limited to the region postulated to include the matrix phase. Models for the structural interrelationship of filamentous and matrix phases are discussed and compared to prior Z‐disk models.

Feature extraction algorithms

This paper describes methods for extracting pattern-synthesizing features. A set of patterns is expressed as a Boolean matrix, allowing the problem of feature extraction to be viewed as one of factoring this matrix. Feature extraction methods based on matrix factorization and pattern intersection are presented. Attribute inclusion is defined to be the implication of the presence of one attribute by that of another, and an algorithm for obtaining features correlated by inclusion is discussed.

Pattern Classification with an Optical PAPA Device

An optical PAPA (Automatic Programmer and Analyzer of Probabilities) device using a coherent optical system was made. Each random mask used for the classification of the input patterns consists of the several elements of the matrix pattern of diffraction gratings with particular azimuthal orientation theta of grating lines. Therefore, the transmitted light through the input pattern and random masks is theta modulated and is used to make the filter for classification. Horizontal and vertical line patterns and Japanese characters were classified with proper accuracy. Problems of the selection of random masks, characteristics of a photographic emulsion and errors of classification are also discussed.

Morphogenetic substratum for differentiation of cartilage in tissue culture.

WE report here a new system for studying the development of cartilage from post foetal mesenchymal cells in vitro. The chondrocytes develop under the influence of the matrix pattern of a substratum prepared from decalcified bone. In this system, a chemically defined medium is introduced and embryo extracts are avoided in order to exclude all the soluble or particulate material that may be present in cultures of skeletal tissue1–5.

Sparsity-Directed Decomposition for Gaussian Elimination on Matrices

This is a concise critical survey of the theory and practice relating to the ordered Gaussian elimination on sparse systems. A new method of renumbering by clusters is developed, and its properties described. By establishing a correspondence between matrix patterns and directed graphs, a sequential binary partition is used to decompose the nodes of a graph into clusters. By appropriate ordering of the nodes within each cluster and by selecting clusters, one at a time, both optimal ordering and a useful form of matrix banding are achieved. Some results pertaining to the compatibility between optimal ordering for sparsity and the usual pivoting for numerical accuracy are included.

Comparison of coefficients and grouping procedures in numerical analysis of soil trace element data

Using published trace element data for 28 Queensland soils, numerical analyses were carried out with five different non-probabilistic coefficients. Four different hierarchical sorting strategies were applied to two of the matrices. The nature of the groups finally delineated depended mainly upon choice of similarity coefficient. Simple matching coefficient, non-metric coefficient, mean character difference and Euclidean distance (all “magnitude” coefficients) generated similar matrix patterns but correlation coefficient (“pattern” coefficient) gave a different pattern. Euclidean distance appeared to be most sensitive to skewness in attribute distribution and to the presence of aberrant attribute values. The same groups appeared consistently at the lower levels of the dendrograms produced by application of centroid, furthest-neighbour, and flexible sorting strategies to a particular matrix (examples are given, using Euclidean distance and correlation coefficient-similarity matrices based on transformed data). Relationships between groups at higher levels of the dendrograms should be treated with caution as they varied markedly with changes in sorting strategy and with transformation of the data. It is suggested tentatively that, for soil studies using quantitative data, the raw data should be transformed to approach normal distribution before processing. Standardization is necessary to render data dimensionless. Choice of similarity coefficient depends upon the objective of the analyst but two well-defined types are evident in the five considered in this paper. Choice of sorting strategy does not appear to be critical but it is probably desirable to base final groups on those which appear consistently when different sorting strategies are used. Rigid adherence to the phenon concept is not feasible.

Seriation of Anthropological Data: A Computer Program for Matrix-Ordering

A new digital computer program has been developed for the seriation of anthropological data. The program facilitates and refines procedures in the application of certain matrix-ordering approaches, such as the Brainerd-Robinson technique. The new program has special advantages for obtaining the best ordering of a case that is inherent in the data, together with special provisions for experimentation. Some of the innovations consist of working with the whole matrix pattern from start to finish, more exhaustive row-column comparisons, provision for specifying different ordering criteria, consistent utilization of a chosen criterion for matrix evaluation as well as for row-column placement, and a means of lessening the effect of input-order bias. The program is designed to produce a close approximation of an ideal model in order to place data collections as accurately as possible on a continuum of similarity for purposes such as chronological ordering and the expression of intercultural relationships.

Genetic parameters of British Large White bacon pigs

Estimates of heritabilities and genetic correlations among 35 measurements and scores of British Large White bacon pigs are reported. The data came from pigs tested at the five National Progeny Testing Stations during the period autumn 1957 to spring 1959, and comprised full records on 1936 pigs from 200 sires. Independent analyses were carried out for each sex, and adjustments were made to the data for differences among stations, six-monthly periods and weight at slaughter.Genetic parameters were estimated from sire components of variation and covariation obtained by conventional heirarchical analyses of variance and covariance. Estimates of the heritabilities and their standard errors are given in Table 2, and of genetic and phenotypic correlations in Table 3. These estimates, which agree in general with other estimates in the literature,, indicate that a large part of the variation and covariation is of genetic origin and that carcass traits, growth rate and food conversion efficiency are amenable to change by selection. Moreover, no serious antagonisms were found to exist with regard to improvement by selection.An attempt has been made to summarise the correlation matrix pattern among 24 of the more important traits by using a principal component analysis. The first two principal components account for a disproportionate fraction of the correlation pattern especially of the genetic correlation matrix. Two principal components are given for each trait; the first may be associated with measurements of fat depth.

Assimilation of information from dot and matrix patterns.

Assimilation of information from dot and matrix patterns.