In this study, an octagonal-based self-organizing network’s lattice structure is proposed to allow more exploration and exploitation in updating the weights for better mapping and classification performances. The neighborhood of the octagonal-based lattice structure provides more nodes for the weights updating than standard hexagonal-based lattice structure. Based on our experiment, the octagon...

Graphene, made of sp^{2} hybridized carbon, is characterized with a Dirac band, representative of its underlying 2D hexagonal lattice. The fundamental understanding of graphene has recently spurred a surge in the search for 2D topological quantum phases in solid-state materials. Here, we propose a new form of 2D material, consisting of sd^{2} hybridized transition metal atoms in hexagonal latti...

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete wavelet transform with real wavelets. Moreover, the hexagonal lattice allows to build wavelets having a more isotropic magnitude than on the C...

A conjecture is given for the exact location of the multicritical point in the phase diagram of the ±J Ising model on the triangular lattice. The result pc = 0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, pc = 0.9327041, again in excellent agree...

A conjecture is given for the exact location of the multicritical point in the phase diagram of the ±J Ising model on the triangular lattice. The result pc = 0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, pc = 0.9327041, again in excellent agree...

Retroviral capsids are composed of hexagonal arrays of the viral CA protein. In this issue of Cell, Ganser-Pornillos et al. (2007) provide a molecular model of the hexagonal HIV-1 CA lattice obtained from a new electron cryomicroscopic reconstruction. This study reveals the three principal stabilizing interfaces in the capsid lattice and explains how two different classes of inhibitors can bloc...

Binary (periodic) aperiodic complementary sequences have been studied extensively due to their wide range of applications in engineering, for example in optics, radar and communications. They are also linked to topics in coding theory, combinatorics and Boolean functions. Complementary sequences have been generalized either by being defined over larger alphabets or by being defined from one dim...

The correlation between structural and optical properties of nanocrystalline ZnO synthesized by the citrate precursor method has been investigated. The Rietveld refinement of X-ray diffraction pattern confirms the P63mc space group and formation of single phase hexagonal wurtzite structure with presence of tensile strain at the lattice site. The presence of Raman active optical phonon mode at 4...

A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed systematically arranged triangles, squares, or hexagons, were investigated numerically and experimentally. Finite-element-based homogenization allowed computation Poisson's ratio, elastic modulus, shear bulk modulus. comprehensive understanding the r...