Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of thes...

We show that orthogonal space-time block codes may be identified with packings on the Grassmann manifold. We describe a general criterion for packings on the Grassmann manifold that yield coherent space-time constellations with the same code properties that make orthogonal space-time block codes so favorable. As an example, we point out that the rate 3/4 orthogonal space-time block code motivat...

While the P vs NP problem is mainly approached form the point of view of discrete mathematics, this paper proposes reformulations into the field of abstract algebra, geometry, fourier analysis and of continuous global optimization which advanced tools might bring new perspectives and approaches for this question. The first one is equivalence of satisfaction of 3-SAT problem with the question of...

By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k ≥ 2. The case k = 2 reduces to the spanning-forest model on the complete graph. Different k are studied at once by using a microcanonical ensemble in which the number of hyperforests is fixed. The low-temperature phase is characterized by the ap...

In this paper, we propose a novel online multi-camera framework for person identification based on gait recognition using Grassmann Discriminant Analysis. We propose an online method wherein the gait space of individuals are created as they are tracked. The gait space is view invariant and the recognition process is carried out in a distributed manner. We assume that only a fixed known set of p...

Face recognition techniques have gained much attention and research interests over the recent years due to their vast applications in security and authentication systems. Some of the popular approaches involve support vector machines (SVM), which can either be a binary or a multiclass classification problem, and subspace learning, where data is assumed to lie on some low dimensional manifold, s...

A close relationship between the determinant, the pfaffian, and the Grassmann algebra is well-known. In this paper, a similar relation between the permanent, the hafnian, and a commutative analogue of the Grassmann algebra is described. Using the latter, some new properties of the hafnian are proved.

A supersymmetric D = 1, N = 1 model with a Grassmann-odd Lagrangian is proposed which, in contrast to the model with an even Lagrangian, contains not only a kinetic term but also an interaction term for the coordinates entering into one real scalar Grassmann-even (bosonic) superfield.

Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Plücker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words. 1. Introduction. In network coding one is looking at the transmission of information through a directed graph with possibly several senders and several receivers [1]. One c...