Relaxing order basis computation

International audienceThe computation of an order basis (also called sigma basis) is a fundamental tool for linear algebra with polynomial coefficients. Such a computation is one of the key ingredients to provide algorithms which reduce to polynomial matrices multiplication. This has been the case for column reduction or minimal nullspace basis of polynomial matrix over a field. In this poster, we are interested in the application of order basis to compute minimal matrix generators of a linear matrix sequence. In particular, we focus on the linear matrix sequence used in the Block Wiedemann algorithm

Relaxation to equilibrium driven via indirect control in Markovian dynamics

We characterize to what extent it is possible to modify the stationary states of a quantum dynamical semigroup, that describes the irreversible evolution of a two-level system, by means of an auxiliary two-level system. We consider systems that can be initially entangled or uncorrelated. We find that the indirect control of the stationary states is possible, even if there are not initial correlations, under suitable conditions on the dynamical parameters characterizing the evolution of the joint system.Comment: revtex4, 7 page

Normalization procedure for relaxation studies in NMR quantum information processing

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a "loss of purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.Comment: 9 pages, 5 figures, to appear in QI

Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner

The magnification behaviour of a generalized family of self-organizing feature maps, the Winner Relaxing and Winner Enhancing Kohonen algorithms is analyzed by the magnification law in the one-dimensional case, which can be obtained analytically. The Winner-Enhancing case allows to acheive a magnification exponent of one and therefore provides optimal mapping in the sense of information theory. A numerical verification of the magnification law is included, and the ordering behaviour is analyzed. Compared to the original Self-Organizing Map and some other approaches, the generalized Winner Enforcing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.Comment: 6 pages, 5 figures. For an extended version refer to cond-mat/0208414 (Neural Computation 17, 996-1009

Local Spacetime Physics from the Grassmannian

A duality has recently been conjectured between all leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM and the residues of a contour integral with a natural measure over the Grassmannian G(k,n). In this note we show that a simple contour deformation converts the sum of Grassmannian residues associated with the BCFW expansion of NMHV tree amplitudes to the CSW expansion of the same amplitude. We propose that for general k the same deformation yields the (k-2) parameter Risager expansion. We establish this equivalence for all MHV-bar amplitudes and show that the Risager degrees of freedom are non-trivially determined by the GL(k-2) "gauge" degrees of freedom in the Grassmannian. The Risager expansion is known to recursively construct the CSW expansion for all tree amplitudes, and given that the CSW expansion follows directly from the (super) Yang-Mills Lagrangian in light-cone gauge, this contour deformation allows us to directly see the emergence of local space-time physics from the Grassmannian.Comment: 22 pages, 13 figures; v2: minor updates, typos correcte