Lattice Matrices Research Articles

On compositions of lattice matrices

In this paper, we give some properties of compositions of matrices whose elements belong to a distributive lattice. We also construct an idempotent matrix from a given matrix, and factor a matrix into a product of a square matrix and a rectangular matrix of the same dimension, this square matrix has reflexivity and transitivity. The main results obtained in this paper are generalizations of previous results on fuzzy matrices by Ragab, Emam and Hashimato.

Optimal construction of reduced pyramids for lossless and progressive image coding

Reduced pyramids, including in particular pyramids without analysis filters, are known to produce excellent results when used for lossless signal and image compression. The present paper presents a methodology for the optimal construction of such pyramids by selecting the interpolation synthesis post-filters so as to minimize the error variance at each level of the pyramid. This establishes optimally efficient interpolative pyramidal lossless compression. It also has the added advantage of producing lossy replicas of the original which, at lower resolutions, retain as much similarity to the original as possible. This is highly useful for the progressive coding of signals or images needed for many applications such as fast browsing through image databases or hybrid lossless/lossy medical image coding. The general optimization methodology is developed first, for a general family of reduced pyramids. Subsequently, this is applied to the optimization of pyramids in this family formed using separable, two-dimensional (2-D) quincunx and three-dimensional (3-D) face-centered orthorhombic lattice sampling matrices. It is shown that this family includes in particular the well known 2-D and 3-D "hierarchical interpolation" (HINT) techniques which have been particularly popular for the lossless compression of medical records. Optimal versions of these techniques are determined for 2-D and 3-D images characterized by separable or isotropic correlation functions. The advantages of the developed methods are demonstrated by experimental evaluation. It is shown that the method outperforms the HINT method for the lossless compression of 3-D images. It is also shown to outperform all other known interpolative coders and to produce results comparable to the best predictive lossless coder of 2-D images.

Effects of Vasoactive Mediators on the Rat Lung Pericyte: Quantitative Analysis of Contraction on Collagen Lattice Matrices

Pericytes are contractile cells of the microvasculature which may contribute to the hypotension and increase in permeability that are present during inflammation and late-stage sepsis. The purpose of this study was to examine the contractile effects, if any, of septic modulators on the lung pericyte. Contractile effects were qualitatively examined using a previously developed silicone rubber method. This study further demonstrates a quantitative method for measuring the contraction of lung pericytes cultured on a collagen lattice. Contraction was measured by the change in collagen matrix area in response to vasoactive stimuli. Bradykinin and serotonin significantly increased contraction in a dose-dependent manner, with a maximum increase in contraction twice that of control. Forskolin and adenosine caused relaxation, also in a significant dose-dependent manner, with a maximum decrease in contraction of 80 and 30–40%, respectively. Histamine had no effect on contractility in either the silicone rubber or the collagen lattice assay. These results show that the lung pericyte, like the retinal pericyte, is a contractile cell and can be stimulated to contract or relaxin vitroby the presence of certain inotropic agents present during inflammation and sepsis. These responses may play a role in microvascular regulation.

Lattice matrices, intersection of ring families and dicuts

Lattice matrices are 0/1-matrices used in the description of certain lattice polyhedra and related to dicuts in a graph. The incidence matrix A I of a so-called intersection of two ring families and the incidence matrix A D of all dicuts of a graph are examples of such matrices. After showing that any lattice matrix A can be obtained from some matrix A I by deletion or some A D by contraction, we first describe the convex hull of the rows of A I, CONV( A I), as the solution set of a system x⩾0, Bx⩽1, Rx⩽0, which is tdi. We then derive the main result, the description of CONV( A) by another tdi system. As applications, the polyhedral description of all dicuts in a graph, CONV( A D), and that of all convex sets of bounded length in a poset are established.

Multigrid inversion of lattice fermion operators

A ground state decomposition method for multigrid inversion of lattice fermion matrices is discussed and tested for staggered fermions coupled to U(1) gauge fields in two dimensions.

Transmission Electron Microscopy studies of the structure of martensitic interfaces in Cu-Zn: Diffraction contrast

A Cu-38.6%Zn alloy was treated at 870°C and quenched in ice brine(10% NaOH) to produce martensitic transformation. The parent phase is bcc structure and the martensite phase is 9R close-packed structure. The orientation relationship of the parent phase and martensite was determined by the Kikuchi pattern and diffraction pattern. The experimental lattice deformation matrix can then be deduced from the orientation relationship and assumed correspondence. The lattice deformation matrices determined from experiment and calculated from CRAB martensite crystallography theory are as follows:As shown in Figure 1, a set of dislocations is observed in the martensitic interface whose Burgers vector is determined to be l/3[101]b by the two beam technique. The direction and the average spacing of these dislocations determined from experiment are [.49 . .47]b and 5±1nm respectively. This set of dislocations is consistent with the lattice invariant shear l/3[101]b on the ( 01)b plane with the magnitude 0.022 used in the CRAB martensite crystallography which corresponds to an anticoherency dislocation array with the spacing of 7.75nm and in the direction [.514,. ,.514]b. The habit plane determined from experiment is (.13,.65,.75 )b and close to (.13,.68,.72)b from the prediction of CRAB martensite crystallography.

Das zweikorrelationen-modell bei dichten kugelpackungen in T 3…6-B 0…4 mischungen

A model is given for the binding in certain phases which are homotypic to close-packings. The structure of VNi 3 shows that the core electrons of the minor component tend to contract the structure while the valence electrons tend to dilate it. Good commensurability of both electron spatial correlations gives energetically low structures; this is particularly favourable at a valence electron concentration of 1.5, where the factorial commensurability of the lattice matrices of the correlations are connected by the factor 2. Factorial commensurability may be conserved while changing the composition if the structures are related by abnormal shears. When the valence electron concentration increases over 1.5 a straining stress arises perpendicular to a close-packed plane. The stress, depending on its strength, may cause a change of sub-structure stacking sequence, a change of support number of the plane and finally a loss of translation symmetry of the close-packed planes. By these mechanisms several structures may be interpreted energetically which at present are not interpreted by any other model.

The theory of switching nets

The paper develops a strictly mathematical, unified theory of combinational switching networks, with the aid of linear graph theory and lattice algebra. The theory is based on the concept of a lattice-weighted, directed linear graph, termed switching net. The advantages of using lattice algebra, rather than Boolean algebra are emphasized. A calculus of lattice matrices is outlined in Section II, and then applied to the study of switching nets (Section III). A suitable formulation of Ashenhurst's uniqueness theorem, and a modified version of its proof are given in Section IV. In Section V switching net theory is extended to multi-terminal and reiterative nets, generalizing results due to M.L. Tsetlin and A.Sh. Blokh.

Powers of a matrix over a lattice

Let M==jaijjJ be an nXn matrix with elements in a lattice in which meet, join, and inclusion are denoted by ab, a+b, and aCb, respectively. Two nXn lattice matrices M and M' are said to be equal if aij=a', i, j= 1, 2, , n, and if aijCa', i, j= 1, 2, , n, then we shall write MCM'. The n2 elements of M will be called independent provided P1C Ek.=2 Pk, where P1, P2, * * *, P, are any products of elements aij of M, implies P1CPm for some mn such that 2 <m<r.