Orthogonal Lattice Research Articles

An analytical approach to neuronal connectivity

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $\Delta$, it is possible to obtain the accurate number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial spread of network connections. In addition, most such networks are characterized by the interesting phenomenon where the connections are progressively shifted along the spatial domain where the network is embedded. It is also shown that the number of cycles follows a power law with their respective length. Morphological measurements for characterization of the spatial distribution of connections, including the adjacency matrix spectral density and the lacunarity of the connections, are suggested. The potential of the proposed approach is illustrated with respect to digital images of real neuronal cells.

Crystal Structure and Morphology of Poly(11-undecalactone) Solution-Grown Single Crystals

Solution-grown lamellar single crystals of poly(11-undecalactone) (PUDL) have been prepared in 1-hexanol. The lozenge and hexagonal-shaped single crystals were grown simultaneously, and these crystals gave well-resolved electron diffraction diagrams from which the orthogonal reciprocal lattice with the parameters a* = 1.346 nm-1, b* = 2.004 nm-1, and γ* = 90° could be determined. The growth faces of both crystals were considered as mainly {110}, and the average chain-folding direction was parallel to these growth planes, suggesting that the hexagonal crystal has pseudohexagonal symmetry but actual orthogonal packing of the PUDL molecules. The diffraction analysis combined with X-ray and electron diffraction diagrams indicated that PUDL crystallized in the orthorhombic system which had the lattice parameters of a = 0.743 ± 0.001 nm, b = 0.499 ± 0.001 nm, and c(chain axis) = 1.519 ± 0.003 nm. There are two chains per unit cell, which existed in an antiparallel arrangement. The fiber repeat distance is appropriate for an all-trans backbone conformation for the straight stems. Molecular packing of this structure has been studied in detail, taking into account both diffraction data and energy calculations. The setting angles, with respect to a axis, were 59° for the corner and center chains according to intensity measurements and structure factor calculations. A final model was obtained to yield R = 0.173 with X-ray diffraction data and R = 0.152 with electron diffraction data. A brief comparison is also made with related polymer structures.

Anomalous magnetism in three-dimensional orthogonal dimer lattice system: (Ba 1− xSr x) 2Ru 3O 9 ( x≈0.35)

The magnetic and transport properties of a new cubic KSbO 3-type ruthenate, (Ba 1− x Sr x ) 2Ru 3O 9 ( x≈0.35), have been investigated. The crystal structure has a singular geometry in which ruthenium atoms form an ideal three-dimensional orthogonal dimer lattice. The magnetic susceptibility is Pauli-paramagnetic but exhibits an anomalous temperature dependence reminiscent of a gap-like behavior. The resistivity exhibits a metallic behavior, except for a rise at low temperature.

Single-trabecula building block for large-scale finite element models of cancellous bone.

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) 'building-block' of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of approximately 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of approximately 30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.

The effects of intra-dimer Dzyaloshinsky–Moriya interaction on the properties ofSrCu2(BO3)2 in an external magnetic field

The two-dimensional spin-gap systemSrCu2(BO3)2 shows unique physical properties due to the strong quantum fluctuationsthat follow from its low-dimensionality and its very special topology. Themagnetic properties of this material, e.g. dimer singlet ground state, analmost localized triplet and magnetization plateaux, are well described by aspin-1/2 antiferromagnetic Heisenberg model on the orthogonal dimer lattice. Recently, an unusualangular dependence of the shifts at the B sites with the external magnetic fieldrotated in the (110) plane, which indicates the presence of a field-induced staggeredmoment, has been observed by nuclear magnetic resonance. Such a behaviourcannot be explained by the Heisenberg model alone. We include an intra-dimerDzyaloshinsky–Moriya interaction as well as an anisotropic gyromagnetic tensorin the orthogonal dimer model, and we show that the observed field-inducedstaggered moment can be very well described with physically reasonable values of theparameters.

A parallel implementation of exact Euclidean distance transform based on exact dilations

This article reports the effective implementation of the exact Euclidean distance transform in a distributed system based on standard PCs, by using a simple data exchange protocol. The approach is based on the concept of exact distances, namely the denumerable set of distances found on the orthogonal lattice. The exact dilation algorithm, introduced recently, involves the successive scanning of the image elements for consecutive exact distance values, while assigning these values to empty neighboring pixels. The use of data compression methodology, as well as the quantitative characterization of the parallel efficiency, are also investigated and discussed considering several image sizes and the quantity of foreground elements. Among the obtained results, we have that the latter parameter strongly affects the overall performance and that the compressing strategy represents a potentially useful resource for increasing the overall processing efficiency.

Photonic band gap analysis using finite-difference frequency-domain method

A finite-difference frequency-domain (FDFD) method is applied for photonic band gap calculations. The Maxwell's equations under generalized coordinates are solved for both orthogonal and non-orthogonal lattice geometries. Complete and accurate band gap information is obtained by using this FDFD approach. Numerical results for 2D TE/TM modes in square and triangular lattices are in excellent agreements with results from plane wave method (PWM). The accuracy, convergence and computation time of this method are also discussed.

Aquaporin-4 square array assembly: opposing actions of M1 and M23 isoforms.

Osmotic homeostasis in the brain involves movement of water through aquaporin-4 (AQP4) membrane channels. Perivascular astrocyte end-feet contain distinctive orthogonal lattices (square arrays) assembled from 4- to 6-nm intramembrane particles (IMPs) corresponding to individual AQP4 tetramers. Two isoforms of AQP4 result from translation initiation at methionine residues M1 and M23, but no functional differences are known. In this study, Chinese hamster ovary cells were transfected with M1, M23, or M1+M23 isoforms, and AQP4 expression was confirmed by immunoblotting, immunocytochemistry, and immunogold labeling. Square array organization was examined by freeze-fracture electron microscopy. In astrocyte end-feet, >90% of 4- to 6-nm IMPs were found in square arrays, with 65% in arrays of 13-30 IMPs. In cells transfected with M23, 95% of 4- to 6-nm IMPs were in large assemblies (rafts), 85% of which contained >100 IMPs. However, in M1 cells, >95% of 4- to 6-nm IMPs were present as singlets, with <5% in incipient arrays of 2-12 IMPs. In M1+M23 cells, 4- to 6-nm IMPs were in arrays of intermediate sizes, resembling square arrays in astrocytes. Structural cross-bridges of 1 x 2 nm linked >90% of IMPs in M23 arrays ( approximately 1,000 cross-bridges per microm2) but were rarely seen in M1 cells. These studies show that M23 and M1 isoforms have opposing effects on intramembrane organization of AQP4: M23 forms large square arrays with abundant cross-bridges; M1 restricts square array assembly.

Theory of the Orthogonal Dimer Heisenberg Spin Model for SrCu2(BO3)2

AbstractFor Abstract see ChemInform Abstract in Full Text.

Quantum quincunx in cavity quantum electrodynamics

We introduce the quantum quincunx, which physically demonstrates the quantum walk and is analogous to Galton's quincunx for demonstrating the random walk. In contradistinction to the theoretical studies of quantum walks over orthogonal lattice states, we introduce quantum walks over nonorthogonal lattice states (specifically, coherent states on a circle) to demonstrate that the key features of a quantum walk are observable albeit for strict parameter ranges. A quantum quincunx may be realized with current cavity quantum electrodynamics capabilities, and precise control over decoherence in such experiments allows a remarkable decrease in the position noise, or spread, with increasing decoherence.

Spinodal equation of state for rutileTiO2

We present a general computational scheme to extend the spinodal equation of state [Garcia Baonza et al., Phys. Rev. B 51, 28 (1995)] to the interpretation of the cell parameters response to hydrostatic pressure in orthogonal lattices. As an important example, we analyze the pressure (formula presented)–volume (formula presented)–temperature (T) data of the rutile phase of (formula presented) We show that results of ab initio perturbed ion calculations and very recent x-ray-diffraction experiments of isothermal compression on this system closely follow the spinodal conduct. The computational scheme permits the incorporation of temperature effects in the static calculation as well as in the room-temperature experimental data. Overall, we find highly consistent results and good theory-experiment agreement for a significant series of observables, including structural parameters, (formula presented) diagram, bulk modulus, linear compressibilities, and thermal-expansion coefficient. The observed discrepancies in the pressure first derivative of the bulk modulus can be traced back to the difference between the theoretical and the experimental spinodal pressure. © 2003 The American Physical Society.

Least-squares spline resampling to a hexagonal lattice

Abstract Resampling is a common operation in digital image processing systems. The standard procedure involves the (conceptual) reconstruction of a continuous image succeeded by sampling on the new lattice sites. When the reconstruction is done by classical interpolation functions, results might be sub-optimal because the information loss is not minimized. In the particular case of subsampling (i.e., resampling to a coarser lattice), aliasing artifacts might arise and produce disturbing moire patterns. This paper first introduces a spline model for different orders, both for orthogonal and hexagonal lattices. Next, an expression for a least-squares approximation is derived which can be applied to convolution-based resampling. Experimental results for a printing application demonstrate the feasibility of the proposed method and are compared against the standard approach. Our technique can be applied to general least-squares resampling between regular lattices.

A one-dimensional chain state of vortex matter.

Magnetic flux penetrates isotropic type II superconductors in flux-quantized vortices, which arrange themselves into a lattice structure that is independent of the direction of the applied field. In extremely anisotropic high-transition-temperature (high-Tc) superconductors, a lattice of stacks of circular 'pancake' vortices forms when a magnetic field is applied perpendicular to the copper oxide layers, while an orthogonal elongated lattice of elliptical Josephson vortices forms when the applied field is parallel to the layers. Here we report that when a tilted magnetic field is applied to single crystals of Bi2Sr2CaCu2O8+delta, these lattices can interact to form a new state of vortex matter in which all stacks of pancake vortices intersect the Josephson vortices. The sublattice of Josephson vortices can therefore be used to manipulate the sublattice of pancake vortices. This result explains the suppression of irreversible magnetization by in-plane fields as seen in Bi2Sr2CaCu2O8+delta crystals, a hitherto mysterious observation. The ability to manipulate sublattices could be important for flux-logic devices, where a 'bit' might be represented by a pancake vortex stack, and the problem of vortex positioning is overcome through sublattice interactions. This also enables the development of flux transducers and amplifiers, considerably broadening the scope for applications of anisotropic high-Tc superconductors.

Superresolution ISAR imaging using 2‐D autoregressive lattice filters

AbstractA new efficient algorithm to obtain high‐resolution ISAR images in the case of limited frequency band and small angular section is presented. The method is based on the two‐dimensional (2‐D) autoregressive modeling of 2‐D Cartesian frequency backscattered data using 2‐D orthogonal lattice filters. ISAR images obtained for an experimental target are included to validate this technique. © 2002 John Wiley &amp; Sons, Inc. Microwave Opt Technol Lett 32: 81–85, 2002.

Body-centred tetragonal martensite formed from Au 7Cu 5Al 4β phase

The Al–Au–Cu system contains a ternary β electron compound with a nominal stoichiometry of Au 7Cu 5Al 4. At elevated temperatures this compound has a predominantly B2 structure, with some additional next-nearest neighbour ordering of the L2 1 type. The high-temperature phase transforms displacively and reversibly to martensite, with nominal M s and A s temperatures of 23 and 79°C, respectively. It is shown here that the martensite phase is body-centred tetragonal with c/ a<1. The orthogonal lattice is, however, evidently affected by a small degree of additional modulation. This martensite is fundamentally different from the classic 9R and 18R-type martensite of copper-base β phase alloys, and also from the trigonal martensites formed in AuCd and TiNi, and appears rather to be of the same type as the tetragonal martensites of Ni 2MnGa and La 2AgIn.

Excitation of two-dimensional plasmons with cross-grating couplers

We have prepared cross-grating gate electrodes on top of a two-dimensional electron system in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ heterostructures, which act as grating couplers. In addition to the well-known two-dimensional plasmon modes at ${\ensuremath{\omega}}_{P}{(q}_{1})$ and ${\ensuremath{\omega}}_{P}{(2q}_{1}),$ with wave vector ${q}_{1}=2\ensuremath{\pi}/a,$ where a is the grating period, we observe an excitation at ${\ensuremath{\omega}}_{P}(\sqrt{2}{q}_{1}).$ This plasma excitation oscillates in the diagonal direction with respect to the cross-grating structure, and is formed by a superposition of the plasmons in the orthogonal lattice directions with wave vectors ${q}_{x}$ and ${q}_{y}.$

Robust Skeletonization through Exact Euclidean Distance Transform and its Application to Neuromorphometry

This paper presents how robust 1-pixel-wide and 8-connected skeletons can be obtained simultaneously with exact distance transform calculation. The proposed approach is based on the new concept of exact dilation. Two alternative algorithms for exact Euclidean distance transform calculation allowing exact dilation are described: a simpler approach based on the SEDR (sorted exact distance representation) data structure, which allows exact distance transform calculation; and a more effective strategy based on border propagation. In both techniques the distances are assigned strictly according to sequences of increasing exact distances in the orthogonal lattice. Because of the high accuracy allowed by such procedures, progressive dilations, high quality and accurate 1-pixel-wide and 8-connected skeletons can be obtained corresponding to the frontiers between previously labelled distinct connected objects. Although this method can be useful for determining generalized Dirichlet tessellations, which is also illustrated in this article, its full potential is harnessed by previously segmenting the contours of connected objects by removing their points corresponding to curvature peaks, which are obtained by using an effective multi-scale curvature estimation technique. In such a way, not only high-quality 1-pixel-wide and 8-connected skeletons are obtained for any shape, but also the whole approach becomes considerably robust to small distortions in the object contours, thus avoiding one of the great shortcomings in traditional skeletonization methods. The application of such methods to an important problem in computational neuroscience and neuromorphometry, namely the automated extraction of tapered dendrograms, is described and illustrated. Considerations regarding distances in orthogonal lattices, typical problems in skeletonization, and the practical implementation of the proposed techniques are also included.

2D FIR Wiener filter realisation using orthogonallattice structures

A new realisation algorithm for 2D FIR Wiener filters is proposed. The reduced-order 2D orthogonal lattice filter structure is used as the principal component as in the 1D case. A numerical example is included to verify the formulation.

Three–dimensional integrable lattices in Euclidean spaces: conjugacy and orthogonality

It is shown that the discrete Darboux system, descriptive of conjugate lattices in Euclidean spaces, admits constraints on the (adjoint) eigenfunctions which may be interpreted as discrete orthogonality conditions on the lattices. Thus, it turns out that the elementary quadrilaterals of orthogonal lattices are cyclic. Orthogonal lattices on lines, planes and spheres are discussed and the underlying integrable systems in one, two and three dimensions are derived explicitly. A discrete analogue of Bianchi's Ribaucour transformation is set down and particular orthogonal lattices are given. As a by–product, discrete Dini surfaces are obtained.

Assembly of connexins and MP26 in lens fiber plasma membranes studied by SDS-fracture immunolabeling

The SDS-fracture immunolabeling technique, unlike conventional freeze-fracture, provides direct evidence for the biochemical nature of membrane constituents. SDS-fracture immunolabeling shows that during differentiation of lens fiber cells the onset of junctional assembly is characterized by the presence of small clusters and linear arrays comprising connexins alpha3 and alpha8. At this initial stage MP26, a major fiber membrane constituent, appears to be colocalized with these two connexins. The application of double-immunogold labeling reveals that when large junctional plaques are assembled MP26 becomes mainly associated with the periphery of the junctional domains. This type of distribution suggests that MP26 may play a role in the clustering and gathering of connexons. In aged nuclear fiber membranes connexins, MP26 and their proteolytic derivatives form an orthogonal lattice of repeating subunits.