Macular irregularities of optical coherence tomographic vertical cross sectional images in school age children

The purpose of this study was to compare the incidences of macular irregularities of elementary school (ES) and junior high school (JHS) students. This was a prospective cross-sectional observational study of 122 right eyes of 122 ES students (8–9 years) and 173 right eyes of 173 JHS students (12–13 years). Vertical cross-sectional images of the macula were obtained by optical coherence tomography. The eyes were classified based on the vertical symmetry of the posterior pole, and then sub-classified as convex-, flat-, concave-, or dome-shaped based on the direction of the curvature of the retinal pigment epithelium. One hundred and two eyes (83.6%) were placed in the symmetrical group in the ES students and 149 eyes (86.1%) in the JHS students. Twenty eyes (16.4%) were placed in the asymmetric groups in the ES students and 24 eyes (13.9%) in the JHS students. In symmetrical group, 78 and 118 eyes had a convex-shape (76.4 and 79.2%), followed by 22 and 29 eyes of dome-shaped group (21.6 and 19.4%) in ES and JHS students respectively. Because the incidences of the posterior pole shapes were not significantly different between the groups, it is likely that the macular irregularities develop before the age of ES.

A Comparison of Complete Parts on m-Idempotent Hyperrings

On a particular class of m-idempotent hyperrings, the relation ξ m * is the smallest strongly regular equivalence such that the related quotient ring is commutative. Thus, on such hyperrings, ξ m * is a new representation for the α * -relation. In this paper, the ξ m -parts on hyperrings are defined and compared with complete parts, α -parts, and m-complete parts, as generalizations of complete parts in hyperrings. It is also shown how the ξ m -parts help us to study the transitivity property of the ξ m -relation. Finally, ξ m -complete hyperrings are introduced and studied, stressing on the fact that they can be characterized by ξ m -parts. The symmetry plays a fundamental role in this study, since the protagonist is an equivalence relation, defined using also the symmetrical group of permutations of order n.

Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k-1)N2 for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N2 is the total of points in the image.

On a Property of a Three-Dimensional Matrix

Let be the symmetrical group acting on the set and . Consider the set The main result of this paper is the following theorem. If the number of set entries is more than , then there exist entries such that , , and . The application of this theorem to the three-dimensional assignment problem is considered.

A Complexity Gap for Tree-Resolution

<p>It is shown that any sequence psi_n of tautologies which expresses the<br />validity of a fixed combinatorial principle either is "easy" i.e. has polynomial<br />size tree-resolution proofs or is "difficult" i.e requires exponential<br />size tree-resolution proofs. It is shown that the class of tautologies which<br />are hard (for tree-resolution) is identical to the class of tautologies which<br />are based on combinatorial principles which are violated for infinite sets.<br />Actually it is shown that the gap-phenomena is valid for tautologies based<br />on infinite mathematical theories (i.e. not just based on a single proposition).<br />We clarify the link between translating combinatorial principles (or<br />more general statements from predicate logic) and the recent idea of using<br /> the symmetrical group to generate problems of propositional logic.<br />Finally, we show that it is undecidable whether a sequence psi_n (of the<br />kind we consider) has polynomial size tree-resolution proofs or requires<br />exponential size tree-resolution proofs. Also we show that the degree of<br />the polynomial in the polynomial size (in case it exists) is non-recursive,<br />but semi-decidable.</p><p>Keywords: Logical aspects of Complexity, Propositional proof complexity,<br />Resolution proofs.</p><p> </p>