Three fermions with six single particle states can be entangled in two inequivalent ways

Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single particle states we propose the Pl\"ucker relations as a sufficient and necessary condition of separability.Comment: 23 pages LATE

Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra "dilatonic" coordinate, whose rotation, Lorentz and conformal groups are SO(d-1), SO(d-1,1) XSO(1,1) and SO(d,2)XSO(2,1), respectively. The generalized spacetimes described by simple Jordan algebras of degree three correspond to extensions of Minkowskian spacetimes in the critical dimensions (d=3,4,6,10) by a dilatonic and extra (2,4,8,16) commuting spinorial coordinates, respectively. The Freudenthal triple systems defined over these Jordan algebras describe conformally covariant phase spaces. Following hep-th/0008063, we give a unified geometric realization of the quasiconformal groups that act on their conformal phase spaces extended by an extra "cocycle" coordinate. For the generic Jordan family the quasiconformal groups are SO(d+2,4), whose minimal unitary realizations are given. The minimal unitary representations of the quasiconformal groups F_4(4), E_6(2), E_7(-5) and E_8(-24) of the simple Jordan family were given in our earlier work hep-th/0409272.Comment: A typo in equation (37) corrected and missing titles of some references added. Version to be published in JHEP. 38 pages, latex fil

Small Orbits

We study both the "large" and "small" U-duality charge orbits of extremal black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras and their associated Freudenthal triple systems, in order to derive the minimal charge representatives, their stabilizers and the associated "moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2 and N = 4 theories coupled to an arbitrary number of vector multiplets, as well as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered as part of the general N = 2 sequence, albeit with an additional triality symmetry, the ST^2 and T^3 models demand a separate treatment, since their representative Jordan algebras are Euclidean or only admit non-zero elements of rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter coupled N = 3, and "pure" N = 5 theories.Comment: 40 pages, 9 tables. References added. Expanded comments added to sections III. C. 1. and III. F.

Srs2 promotes synthesis-dependent strand annealing by disrupting DNA polymerase δ-extending D-loops.

Synthesis-dependent strand annealing (SDSA) is the preferred mode of homologous recombination in somatic cells leading to an obligatory non-crossover outcome, thus avoiding the potential for chromosomal rearrangements and loss of heterozygosity. Genetic analysis identified the Srs2 helicase as a prime candidate to promote SDSA. Here, we demonstrate that Srs2 disrupts D-loops in an ATP-dependent fashion and with a distinct polarity. Specifically, we partly reconstitute the SDSA pathway using Rad51, Rad54, RPA, RFC, DNA Polymerase δ with different forms of PCNA. Consistent with genetic data showing the requirement for SUMO and PCNA binding for the SDSA role of Srs2, Srs2 displays a slight but significant preference to disrupt extending D-loops over unextended D-loops when SUMOylated PCNA is present, compared to unmodified PCNA or monoubiquitinated PCNA. Our data establish a biochemical mechanism for the role of Srs2 in crossover suppression by promoting SDSA through disruption of extended D-loops

Size effects in statistical fracture

We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and fiber bundle models and discuss their limitations. Next, we review energetic and geometric approaches to fracture size effects for specimens with a flaw. Finally, we overview the numerical simulations of lattice models and compare with theoretical models.Comment: review article 19 pages, 5 figure

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Differences in the biological carbon pump at three subtropical ocean sites

We report primary production of organic matter and organic carbon removal from three subtropical open ocean time-series stations, two located in the Atlantic and one in the Pacific, to quantify the biological components of the oceanic carbon pump. We find that within subtropical gyres, export production varies considerably despite similar phytoplankton biomass and productivity. We provide evidence that the removal of organic carbon is linked to differences in nutrient input into the mixed layer, both from eddy induced mixing and dinitrogen fixation. These findings contribute to our knowledge of the spatial heterogeneity of the subtropical oceans, which make up more than 50% of all ocean area and are thought to spread in the course of CO2- induced global warming

Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups

We show that there is a remarkable connection between the harmonic superspace (HSS) formulation of N=2, d=4 supersymmetric quaternionic Kaehler sigma models that couple to N=2 supergravity and the minimal unitary representations of their isometry groups. In particular, for N=2 sigma models with quaternionic symmetric target spaces of the form G/HXSU(2) we establish a one-to-one mapping between the Killing potentials that generate the isometry group G under Poisson brackets in the HSS formulation and the generators of the minimal unitary representation of G obtained by quantization of its geometric realization as a quasiconformal group. Quasiconformal extensions of U-duality groups of four dimensional N=2, d=4 Maxwell-Einstein supergravity theories (MESGT) had been proposed as spectrum generating symmetry groups earlier. We discuss some of the implications of our results, in particular, for the BPS black hole spectra of 4d, N=2 MESGTs.Comment: 20 pages; Latex file: references added; minor cosmetic change

Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n=9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5,...,9 for the quadratic Casimir operator, in each case providing a formula (see eq. (11) to (15)) for the dimensions of the representations in the family as a function of D=dim g. This generalises previous results for powers j and Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the dimension formulas are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos correcte

Educating Health Professionals about Disability: A Review of Interventions

Health professionals need to understand the human rights and health needs of disabled people. This review of evidence on interventions demonstrates that a range of often innovative approaches have been trialled. Lectures by faculty are less effective in changing attitudes than contact with disabled people themselves. Existing examples of good practice need to be scaled up, and better and more long-term evaluations of impact are required