Biomagnetism and Ferritin Final Report

Methods for determining iron content in frog embryos and ferritin in rat intestine section

Geometry of all supersymmetric type I backgrounds

We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9,1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in the subgroup Sigma(P) of Spin(9,1) which preserves the space of parallel spinors P. Given a solution of the gravitino Killing spinor equation with L parallel spinors, L = 1,2,3,4,5,6,8, the dilatino Killing spinor equation allows for solutions with N supersymmetries for any 0 < N =< L. Moreover for L = 16, we confirm that N = 8,10,12,14,16. We find that in most cases the Bianchi identities and the field equations of type I backgrounds imply a further reduction of the holonomy of the supercovariant connection. In addition, we show that in some cases if the holonomy group of the supercovariant connection is precisely the isotropy group of the parallel spinors, then all parallel spinors are Killing and so there are no backgrounds with N < L supersymmetries.Comment: 73 pages. v2: minor changes, references adde

Mutation-Periodic Quivers, Integrable Maps and Associated Poisson Algebras

We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra of a special family of functions associated with these maps. A bi-Hamiltonian structure is derived and used to construct a sequence of Poisson commuting functions and hence show complete integrability. Canonical coordinates are derived, with the map now being a canonical transformation with a sequence of commuting invariant functions. Compatibility of a pair of these functions gives rise to Liouville's equation and the map plays the role of a B\"acklund transformation.Comment: 17 pages, 7 figures. Corrected typos and updated reference detail

Biopsy pathology of the breast second edition

British Journal of Cancer (2002) 87, 1055–1055. doi:10.1038/sj.bjc.6600586 www.bjcancer.co

Quantum Error Correction and Orthogonal Geometry

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.Comment: RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have changed the statement of Theorem 2 to correct it -- we now get worse rates than we previously claimed for our quantum codes. Minor changes have been made to the rest of the pape

Quantum Error Correction via Codes over GF(4)

The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.Comment: Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor error

Asymptotic enumeration of incidence matrices

We discuss the problem of counting {\em incidence matrices}, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with $n$ ones as $n\to\infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.Comment: jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda