One of the key ingredients of A. Connes’ noncommutative geometry is a generalized Dirac operator which induces a metric(Connes’ distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al , whose Connes’ distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being “naturally” defined has the “local eigenvalue property” and i...

Constrained coding has found widespread use in optical and magnetic data storage devices [9]. Proposals for new storage systems such as holographic storage have caused interest in two-dimensional (2D) and three-dimensional (3D) constrained systems as models of data storage on a surface. One-dimensional constraints were extensively studied and there are several known methodologies for designing ...

Introduction Two-dimensional (2D) spectroscopy has great potential to unambiguously distinguish metabolites [1,2]. J-Resolved magnetic resonance spectroscopy allows the indirect dimension to be encoded following a various number of echo times. Till now, in vivo 2D MRS related studies did not investigate sampling strategies of the indirect dimension as a way of improving the quantification of me...

The aim of this paper is a complete statistical analysis of the two dimensional discrete wavelet transform, 2D DWT. This analysis represents a generalization of the statistical analysis of the 1D DWT, already reported in literature. The probability density function, the correlation and the first two moments of the coefficients of the 2D-DWT are computed. The asymptotic behaviour of this transfo...

The field of two-dimensional filters and their design methods have been approached by many researchers, for more than three decades (Lim, 1990; Lu & Antoniou, 1992). A commonly-used design technique for 2D filters is to start from a specified 1D prototype filter and transform its transfer function using various frequency mappings in order to obtain a 2D filter with a desired frequency response....

We present two free-solution annealed DNA nanostructures consisting of either cross-tile CT1 or CT2. The proposed nanostructures exhibit two distinct structural morphologies, with one-dimensional (1D) nanotubes for CT1 and 2D nanolattices for CT2. When we perform mica-assisted growth annealing with CT1, a dramatic dimensional change occurs where the 1D nanotubes transform into 2D nanolattices d...

Experimental demonstrations of one-dimensional (1D) van der Waals material tellurium (Te) have been presented by Raman spectroscopy under strain and magneto-transport. Raman spectroscopy measurements have been performed under strains along different principle axes. Pronounced strain response along the c-axis is observed due to the strong intrachain covalent bonds, while no strain response is ob...

the translated shapes. Indeed, this allows one to model overlapping objects. The random shape process is called The Boolean model is a random set process in which random shapes are positioned according to the outcomes of an indepenthe grain process and the point process is called the germ dent point process. In the discrete case, the point process is process. We call the union process a germ–gr...

To realize a one-dimensional (1D) system with strong spin-orbit coupling is a big challenge in modern physics, since the electrons in such a system are predicted to exhibit exotic properties unexpected from the 2D or 3D counterparts, while it was difficult to realize genuine physical properties inherent to the 1D system. We demonstrate the first experimental result that directly determines the ...