Few examples of macromolecular crystals containing lattice-translocation defects have been published in the literature. Lattice translocation and twinning are believed to be two common but different crystal-growth anomalies. While the successful use of twinned data for structure determination has become relatively routine in recent years, structure determination of crystals with lattice-translo...

We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...

We study two-dimensional Dirac fermions in a random non-Abelian vector potential by using lattice regularization. We consider U(N) random vector potential for large N . The ensemble average with respect to random vector potential is taken by using lattice supersymmetry which we introduced before in order to investigate phase structure of supersymmetric gauge theory. We show that a phase transit...

–A simple independent method for geometrical construction of two-dimensional coincidence site lattices (CSL) based on vector representation of lattice sites is put forward. In this method, the construction of such CSLs is achieved by mutual rotation of a unique vector, termed a sigma generating vector, which has the magnitude of a non-prime integer and is present in an identically oriented supe...

We report a scheme to exploit low radiative loss plasmonic resonance by combining a dark (subradiant) mode and a lattice resonance. We theoretically demonstrate that such dark-mode lattice resonances in periodic arrays of nanodisks or plasmonic crystals can be excited by vertically incident light beams. We investigate the excitation of lattice resonances in a finite sized, square-lattice plasmo...

Two-lattice polyhedra are a special class of lattice polyhedra that include network 4ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of components of a vector in a 2-lattice polyhedron is equal to the minimum capacity of a cover for the polyhedron. For special classes of 2-lattice ...

In this paper we propose a visual speech recognition network based on Support Vector Machines. Each word of the dictionary is described as a temporal sequence of visemes. Each viseme is described by a support vector machine, and the temporal character of speech is modeled by integrating the support vector machines as nodes into a Viterbi decoding lattice. Experiments conducted on a small visual...

This paper describes new vector indexing algorithms for Lattice Vector Quantization (LVQ). The techniques described apply to a large class of lattices such as Z n , A n , D n , D ++ n (including as special cases the Gosset Lattice E 8 , and the lattice of Barnes-wall 1 6), widely used in signal compression. Relying on a partitioning of the events sources, based on a notion of leaders, they allo...

The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A variant of SVP (commonly studied in computatio...