Neural encoding of navigable space involves a network of structures centered on the hippocampus, whose neurons -place cells - encode current location. Input to the place cells includes afferents from the entorhinal cortex, which contains grid cells. These are neurons expressing spatially localized activity patches, or firing fields, that are evenly spaced across the floor in a hexagonal close-p...

The investigation of the lattice-parameter ratios of tetrahedral and hexagonal-rhombohedral inorganic compounds, as reported by Constant & Shlichta [(2003), Acta Cryst. A59, 281-282], has been extended to the structural data found for organic and metal-organic compounds (CSD), for bio-macromolecular crystals (PDB) and for inorganic materials (ICSD). In this first part of the series, the frequen...

Micrographs of mouse liver gap junctions, isolated with detergents, and negatively stained with uranyl acetate, have been recorded by low-irradiation methods. Our Fourier-averaged micrographs of the hexagonal junction lattice show skewed, hexameric connexons with less stain at the threefold axis than at the six indentations between the lobes of the connexon image. These substructural features, ...

CHECKERBOARD codes are two-dimensional binary codes that are designed to satisfy specific constraints [1], [2]. An example is the two-dimensional rectangular binary arrays that satisfy the (d, k) run-length constraint— there are at most k 0’s and the number of 0’s between any neighboring 1’s is at least d in each row and column [3]–[7]. It may naturally arise from data storage on a surface [8],...

We have investigated the temperature dependence of the H parallel to c flux line lattice structural phase transition from square to hexagonal symmetry, in the tetragonal superconductor LuNi2B2C ( T(c) = 16.6 K). At temperatures below 10 K the transition onset field, H2(T), is only weakly temperature dependent. Above 10 K, H2(T) rises sharply, bending away from the upper critical field. This con...

The hexagonal lattice was proposed as an alternative method for image sampling. The hexagonal sampling has certain advantages over the conventionally used square sampling. Hence, the hexagonal lattice has been used in many areas. A hexagonal lattice allows √ 3, dyadic and √ 7 refinements, which makes it possible to use the multiresolution (multiscale) analysis method to process hexagonally samp...

Hexagonal ABO 3 oxides ( A, B = cation) are a class of rich materials for realizing novel quantum phenomena. Their hexagonal symmetry, oxygen trigonal bipyramid coordination, and quasi-two dimensional layering give rise to properties distinct from those the cubic perovskites. As bulk materials, most focus in this has been on rare-earth manganites, RMnO R rare earth); these display coupled ferro...

In this note we give a simple proof of the classical fact that the hexagonal lattice gives the highest density circle packing among all lattices in R2. With the benefit of hindsight, we show that the problem can be restricted to the important class of well-rounded lattices, on which the density function takes a particularly simple form. Our proof emphasizes the role of well-rounded lattices for...

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.