An n-bit Gray code is a circular listing of the 2 n-bit strings so that successive strings differ only in one bit position. An n-bit antipodal Gray code has the additional property that the complement of any string appears exactly n steps away in the list. The problem of determining for which values of n antipodal Gray codes can exist was posed by Hunter Snevily, who showed them to be possible ...

A Gray code is a Hamilton path H on the n-cube, Q n. By labeling each edge of Q n with the dimension that changes between its incident vertices, a Gray code can be thought of as a sequence H = t 1 ; t 2 ; : : : ; t N-1 (with N = 2 n and each t i satisfying 1 t i n). The sequence H deenes an (undirected) graph of transitions, G H , whose vertex set is f1; 2; : : : ; ng and whose edge set E(G H) ...

The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a cube, with regions, surfaces, lines and vertices labelled by Gray category data. These can be viewed as a generalisation of ribbon diagrams. The Gray categories present two types of duals, which are extended to functor...

The OK-quantization theory determines the minimum gray level by using the reproducibility of an image histogram. In many cases, it is ascertained by the human sense of sight that the minimum gray level obtained from this theory is appropriate. However, in order to put the OK-quantization theory into practical use, it is necessary to perform a validity evaluation of this theorem using a computer...

The human brain develops with a nonlinear contraction of gray matter across late childhood and adolescence with a concomitant increase in white matter volume. Across the adult population, properties of cortical gray matter covary within networks that may represent organizational units for development and degeneration. Although gray matter covariance may be strongest within structurally connecte...

Non-genetic phenotypic variations play a critical role in the adaption to environmental changes in microbial organisms. Candida albicans, a major human fungal pathogen, can switch between several morphological phenotypes. This ability is critical for its commensal lifestyle and for its ability to cause infections. Here, we report the discovery of a novel morphological form in C. albicans, refer...

Propagation of incoherently soliton pairs in photorefractive crystals under steady-state conditions is studied. These soliton states can be generated when the two mutually incoherent optical beams with the same polarization and wavelength incident on the biased photorefractive crystal. Such soliton pairs can exist in bright-bright, dark-dark, gray-gray as well as in bright-dark types. In this p...

Representations are formalized as encodings that map the search space to the vertex set of a graph. We define the notion of bit equivalent encodings and show that for such encodings the corresponding Walsh coefficients are also conserved. We focus on Gray codes as particular types of encoding and present a review of properties related to the use of Gray codes. Gray codes are widely used in conj...

At the early onset of the 20th century, several studies already reported that the gray matter was implicated in the histopathology of multiple sclerosis (MS). However, as white matter pathology long received predominant attention in this disease, and histological staining techniques for detecting myelin in the gray matter were suboptimal, it was not until the beginning of the 21st century that ...