Lattice Viewpoint Research Articles

A note on groups with a large permodularly embedded subgroup

It is known that if G is a group such that the centre factor group G/ζ(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G/\\zeta (G)$$\\end{document} is polycyclic, then also the commutator subgroup G′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G'$$\\end{document} is polycyclic. The aim of this paper is to describe this situation from a lattice point of view. It is proved that if G is a group admitting a permodularly embedded non-periodic subgroup P such that the interval [G/P] is a polycyclic lattice, then G contains a polycyclic normal subgroup N such that G/N is quasihamiltonian.

Efficient Decoder Design for Low-Density Lattice Codes From the Lattice Viewpoint

Efficient Decoder Design for Low-Density Lattice Codes From the Lattice Viewpoint

Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2

The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners K and K', analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal Fe$_3$Sn$_2$, without spin-orbit coupling we identify two energetically split helical nodal lines winding along $z$ in the vicinity of K and K' resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. The effect of spin-orbit coupling is found to resemble that of a Kane-Mele term, where the nodal lines can either be fully gapped to quasi-two-dimensional massive Dirac fermions, or remain gapless at discrete Weyl points depending on the ferromagnetic moment orientation. Aside from numerically establishing Fe$_3$Sn$_2$ as a model Dirac kagome metal, our results provide insights into materials design of topological phases from the lattice point of view, where paradigmatic low dimensional lattice models often find realizations in crystalline materials with three-dimensional stacking.

2-connections, a Lattice Point of View

We show that the transition laws for a 2-connection can be recovered by discretizing the base 2-space of a 2-bundle into an Euclidean hypercubic lattice. The aim of this work is to serve as an example of how important results in higher gauge theory, which have been derived in a continuous setting, can also be derived in the lattice scheme.

Lattices of coarse structures

We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.

Algebraic approach to the study of zero modes of Haldane pseudopotentials

We consider lattice Hamiltonians that arise from putting Haldane pseudopotentials into a second quantized or "guiding-center-only" form. These are fascinating examples for frustration free lattice Hamiltonians. This is so since even though their highest density zero energy ground states, the Laughlin states, are known to have matrix-product structure (with unbounded bond dimension), the frustration free character of these lattice Hamiltonians seems obscure, {\em unless} one goes back to the original first quantized picture of analytic lowest Landau level wave functions. This step involves putting back additional degrees of freedom associated with dynamical momenta, and one wonders whether the addition of these degrees of freedom is truly necessary to recognize the frustration free character of the underlying lattice Hamiltonian. Fundamentally, these degrees of freedom have nothing to do with spectrum of a "guiding-center-only" Hamiltonian. Moreover, such constructions are unfamiliar and not available in the study of simpler (finite range) frustration free lattice Hamiltonians with matrix product ground states (of finite bond dimension). That the zero mode properties of "lattice versions" of pseudopotentials can be understood from a polynomial-free, intrinsically lattice point of view is also suggested by the fact that these pseudopotentials are constructed from an algebra of reasonably simply looking operators. Here we show that zero mode properties, and hence the frustration free character, of these lattice Hamitlonians can be understood as a consequence of algebraic structures that these operators are part of. We believe that our results will deepen insights into parent Hamiltonians of matrix product states with infinite bond dimensions, as could be of use, especially, in the study of fractional Chern insulators.

Multiple-antenna differential lattice decoding

From a lattice viewpoint, Clarkson, Sweldens and Zheng significantly reduced the complexity of multiantenna differential decoding. Their approximate decoding algorithm, however, has not unleashed the full potential of lattice decoding. In this paper, we present several improved algorithms, generally referred to as differential lattice decoding (DLD), for multiantenna communication. We first analyze two distinct approximate DLD algorithms, and then develop an algorithm that exactly finds the closest lattice point in the Euclidean space. This exact DLD is subsequently augmented by local search to compensate for the remaining approximation. The small amount of extra complexity of the exact or augmented DLD is rewarded by a clear performance gain. We find that employing basis reduction is very effective to reduce the overall decoding complexity for high lattice dimensions. Moreover, the dimension of the lattice defined in this paper is independent of the number of receive antennas, which results in not only lower complexity, but also better performance for a multiantenna receiver.

QCD and hadron structure: A lattice point of view

QCD and hadron structure: A lattice point of view

QCD and hadron structure: A lattice point of view

Computations of structure functions on the lattice are discussed. We show how moments of parton distribution functions can be obtained from lattice simulations in a fully non-perturbative fashion. Moreover, values of renormalization group invariant matrix elements are evaluated that can serve to compute scal dependent matrix elements in any desired renormalization scheme in the continuum. We give an outlook on several lattice calculations related to structure functions, including generalized parton distributions, form factors and dynamical fermions.

THE LATTICE STRUCTURE OF PRERADICALS II: PARTITIONS

We continue the study of the preradicals of a ring in the lattice point of view. We introduce several interesting preradicals associated to a given preradical and some partitions of the whole lattice in terms of preradicals. As an application, we also give some classification theorems.

Boolean Algebra from the Lattice Point of View

Using lattices, presents Boolean Algebra, which is usually introduced using its postulate‐oriented approach. Relationships among sets, relations, lattices and Boolean algebra are shown to form a distributive but not complemented lattice. Provides examples together with corresponding Hasse diagrams. References useful application areas.

Maximum likelihood sequence estimation from the lattice viewpoint

Considers the problem of data detection in multilevel lattice-type modulation systems in the presence of intersymbol interference and additive white Gaussian noise. The conventional maximum likelihood sequence estimator using the Viterbi algorithm has a time complexity of O(m/sup /spl nu/+1/) operations per symbol and a space complexity of O(/spl delta/m/sup /spl nu//) storage elements, where m is the size of input alphabet, /spl nu/ is the length of channel memory, and /spl delta/ is the truncation depth. By revising the truncation scheme and viewing the channel as a linear transform, the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point. From this lattice viewpoint, the lattice sequence estimator for PAM systems is developed, which has the following desired properties: 1) its expected time-complexity grows as /spl delta//sup 2/ as SNR/spl rarr//spl infin/; 2) its space complexity grow as /spl delta/; and 3) its error performance is effectively optimal for sufficiently large m. A tight upper bound on the symbol error probability of the new estimator is derived, and is confirmed by the simulation results of an example channel. It turns out that the estimator is effectively optimal for m/spl ges/4 and the loss in signal-to-noise ratio is less than 0.5 dB even for m=2. Finally, limitations of the proposed estimator are also discussed. >

地形データを用いた土木施設の景観影響評価指標

This study aims to develop new indices that indicate the effect of infurastructure on landscape.The first index ‘Nomal visual size’ is the area of the projection of elements on the standized screen like a solid angle. The second is ‘Total visual size’, that is the sumation of all the nomal visual size of elements that are looked from the lattice view point on the earth. These indices have a merit which can compare with all cases.These indices are tested in the case study of S dam and its reservoir project in Yamanashi prefecture. They are available and some characteristics are found.

Functional dependencies in relational databases: A lattice point of view

A lattice theoretic approach is developed to study the properties of functional dependencies in relational databases. Particular attention is paid to the analysis of the semilattice of closed sets, the lattice of all closure operations on a given set and to a new characterization of normal form relation schemes. Relation schemes with restrictions on functional dependencies are also studied.

Color-dielectric models from a lattice point of view.

We study the color-dielectric model, introduced by Nielsen and Patkos, using lattice gauge theory. We argue that the collective color-dielectric field, which is introduced by a block-spinning method, approaches zero in the vacuum for confining theories for a sufficiently large averaging size of the block-spinning box, as a consequence of the area-law behavior of Wilson loops. Increasing the box size increases the effective potential height for quarks, but decreases the resolving power of the effective theory. Estimates show that there exists an optimal choice of the size of the box suitable for a mean-field description of hadrons within the color-dielectric models with confinement. This yields a limit for the maximum momentum scales for which these models are applicable. This limit poses no difficulties for construction of phenomenological models.

Conformal techniques, bosonization and tree-level string amplitudes

Calculational tools are provided allowing the determination of tree-level amplitudes for processes involving fermions and bosons in heterotic and superstring theories. A simple representation is given of the cocycle operators that are needed for bosonization of conformal operators, including spin fields and ghosts. This permits explicit computation of all correlation functions. The general m-boson, 2 n-fermion tree-level scattering amplitude in the open superstring is derived and a typical calculation of a four-point amplitude in the o(16) × o(16) heterotic string is presented in manifestly Lorentz-covariant form. An analysis of the branch-cut singularities in the o(16) × o(16) model is performed. In addition, the covariant form of the “new formalism” is developed. Particular attention is given to a lattice viewpoint of these results.

Unusual magnetic properties in two copper(II) chelates of Schiff bases derived from .alpha.-amino acids: a dimeric interaction in a structural linear chain

Abstract : Ordinarily one expects the structural and magnetic properties of a given substance to be intimately related, with the dimensionality of the magnetic or electrical interactions that are present reflecting the lattice dimensionality. For example, a cluster of two interacting magnetic ions should obey a theoretical model whose statistics treat only the pair of interacting spins. Systems in which there are interactions between a small number of spins in a definable cluster within a macroscopic crystal are considered to be zero-dimensional (O-D) from a lattice viewpoint. Each cluster is assumed to be isolated from neighboring clusters in the crystal structure, and interactions of spins of the individual clusters with the spins on neighboring clusters are assumed to be absent. This basic idea may be generalized to include one dimensional chains (1-D) and two-dimensional layers (2-D). Eventually such a process leads to the ultimate reality of a three-dimensional (3-D) crystal structure in which there are more or less equally interacting near neighbors. (Author)