A complete set of covariants of the four qubit system

We obtain a complete and minimal set of 170 generators for the algebra of SL(2,\C)^{\times 4}-covariants of a binary quadrilinear form. Interpreted in terms of a four qubit system, this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective Hilbert space. Also, this sheds some light on the local unitary invariants, and provides all the possible building blocks for the construction of entanglement measures for such a system.Comment: 14 pages, IOP macros; slightly expanded versio

Entanglement monotones and maximally entangled states in multipartite qubit systems

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. For qubits (or spin 1/2) the combs are automatically invariant under SL(2,\CC). This implies that the {\em filters} obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.Comment: 7 pages, revtex4. Talk presented at the Workshop on "Quantum entanglement in physical and information sciences", SNS Pisa, December 14-18, 200

On the growth of Kronecker coefficients (extended abstract)

We present a new stability phenomenon for Kronecker coefficients, that we call hook stability: the Kronecker coefficients stabilize if we add cells to the first row and first column of each of the indexing partitions, simultaneously. We also show that when we increase the sizes of the first two rows of their three indexing partitions, in some appropriate way, the Kronecker coefficients grow linearly, and we are able to give asymptotic estimates

Nilpotent polynomials approach to four-qubit entanglement

We apply the general formalism of nilpotent polynomials [Mandilara et al, Phys. Rev. A 74, 022331 (2006)] to the problem of pure-state multipartite entanglement classification in four qubits. In addition to establishing contact with existing results, we explicitly show how the nilpotent formalism naturally suggests constructions of entanglement measures invariant under the required unitary or invertible class of local operations. A candidate measure of fourpartite entanglement is also suggested, and its behavior numerically tested on random pure states.Comment: 11 pages, 1 figure. Finalised versio

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control

ESTIMATING THE STOCK OF GLASS EELS IN AN ESTUARY BY MARK-RECAPTURE EXPERIMENTS USING VITAL DYES

Glass eels (Anguilla anguilla) arriving after the fishing season in the Vilaine estuary (France) were caught by boat and at a trapping ladder located at a blocking dam upstream in the estuary. They were marked with Bismarck brown, rhodamine B or neutral red, and released into the estuary. The effect of marking on behaviour, mortality and recapture differed according to the dye and concentration used. The glass eels also differed in response to marking according to their origin. Estuarine glass eels were clearly desynchronized in their selective tidal stream transport and left the release area after a few tidal cycles. Trapped glass eels were less sensitive to marking. They remained in the release area and were recaptured in larger number both in the trapping ladder and in the estuary. These results supported a model of two behavioral fractions in the estuary: flow-carried migrants and active glass eels with stronger rheotactic behaviour. The proportion of active glass eels in the estuary shifted from none for the two weeks after the fishery closure, to 10% value of the total stock. At the trapping ladder, the migration ended in June each year, while a large stock was still present in the estuary. These observations favour the interpretation of a short duration of the active phase at this site followed by the transition towards a more benthic behavior. The daily efficiency of the trapping ladder was calculated as 4% of the active stock from both stock estimations and average recapture rate. This value was consistent with the low annual efficiency of the trapping ladder, calculated as 30% of the estuarine stock of glass eels that arrived after the fishing season

A study of the effectiveness of a phonetic and activity approach to the teaching of spelling in grade four,

Includes appendices. Thesis (M.A.)--Boston Universit

THEMIS as particle detector: Spectropolarimetry of solar flares

The progressive phases of three solar flares have beenobserv ed with THEMIS in July 2000, using the multiline spectropolarimetric MTR mode. A preliminary analysis of the characteristics of the polarization of the Hα and Hβ lines observed at the beginning of the progressive phase of one of these flares is presented