We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra Mn might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is quite intricate, it admits a simple, lattice structure representation.

We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices and countable lattices and all finite lattices.

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a f...

If L is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex ∆(L) (definition recalled below). Lattice-theoretically, the resulting object is a subdirect product of copies of L. We note properties of this construction and of some variants, and pose several questions. For M3 the 5-element nondistributive modular lattice...

This paper develops several lattice structures for RLS Laguerre adaptive filtering including a posteriori and a priori based lattice filters with error-feedback, array-based lattice filters, and normalized lattice filters. All structures are efficient in that their computational cost is proportional to the number of taps, albeit some structures require more multiplications or divisions than oth...

The implementation of fiber-optic lattice structures incorporating single-mode fibers and directional couplers was presented by Behzad Moslehi et al (1984). These fiber structures can be used to perform various high-speed time domain and frequency domain functions such as matrix operations and frequency filtering. They introduce the concept of lattice structure optical filters. Lattice structur...

Seueral techniquesare available for implementingascalardigitaffilter using lattice and ladder structures which are known to yield low noise realizations. Ofthese, the lattice and ladder structures proposed by Gray and Markel have the advantage of being interimlly scaled Block implementation of a scalar digitalfilteroflers a number of advantages. Inthis pnpet, new algorithms to realize block dig...

COMPOSITIONS OF SPECIES STEFAN FORCEY Abstract. An extension of the Tamari lattice to the multiplihedra is discussed, along with projections to the composihedra and the Boolean lattice. The multiplihedra and composihedra are sequences of polytopes that arose in algebraic topology and category theory. Here we describe them in terms of the composition of combinatorial species. We de ne lattice st...