Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r) that one usually associates with such a group and hence with a simply-laced Coxeter-Dynkin diagram have a meaningful definition for the non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula for the determinant of the Cartan matrix to all cases. Returning to invariant theory we show that for each irreducible representation i of a binary tetrahedral, octahedral, or icosahedral group one can find a homomorphism into a finite complex reflection group whose defining reflection representation restricts to i.Comment: 19 page

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

Probabilistically Accurate Program Transformations

18th International Symposium, SAS 2011, Venice, Italy, September 14-16, 2011. ProceedingsThe standard approach to program transformation involves the use of discrete logical reasoning to prove that the transformation does not change the observable semantics of the program. We propose a new approach that, in contrast, uses probabilistic reasoning to justify the application of transformations that may change, within probabilistic accuracy bounds, the result that the program produces. Our new approach produces probabilistic guarantees of the form ℙ(|D| ≥ B) ≤ ε, ε ∈ (0, 1), where D is the difference between the results that the transformed and original programs produce, B is an acceptability bound on the absolute value of D, and ε is the maximum acceptable probability of observing large |D|. We show how to use our approach to justify the application of loop perforation (which transforms loops to execute fewer iterations) to a set of computational patterns.National Science Foundation (U.S.) (Grant CCF-0811397)National Science Foundation (U.S.) (Grant CCF-0905244)National Science Foundation (U.S.) (Grant CCF-1036241)National Science Foundation (U.S.) (Grant IIS-0835652)United States. Dept. of Energy (Grant DE-SC0005288

The effective mass of two--dimensional 3He

We use structural information from diffusion Monte Carlo calculations for two--dimensional 3He to calculate the effective mass. Static effective interactions are constructed from the density-- and spin structure functions using sumrules. We find that both spin-- and density-- fluctuations contribute about equally to the effective mass. Our results show, in agreement with recent experiments, a flattening of the single--particle self--energy with increasing density, which eventually leads to a divergent effective mass.Comment: 4 pages, accepted in PR

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

Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc

Comparison of the fragmentation behavior of DNA and LNA single strands and duplexes

DNA and locked nucleic acid (LNA) were characterized as single strands, as well as double stranded DNA‐DNA duplexes and DNA‐LNA hybrids using tandem mass spectrometry with collision‐induced dissociation. Additionally, ion mobility spectrometry was carried out on selected species. Oligonucleotide duplexes of different sequences – bearing mismatch positions and abasic sites of complementary DNA 15‐mers – were investigated to unravel general trends in their stability in the gas phase. Single stranded LNA oligonucleotides were also investigated with respect to their gas phase behavior and fragmentation upon collision‐induced dissociation. In contrast to the collision‐induced dissociation of DNA, almost no base loss was observed for LNAs. Here, backbone cleavages were the dominant dissociation pathways. This finding was further underlined by the need for higher activation energies. Base losses from the LNA strand were also absent in fragmentation experiments of the investigated DNA‐LNA hybrid duplexes. While DNA‐DNA duplexes dissociated easily into single stranded fragments, the high stability of DNA‐LNA hybrids resulted in predominant fragmentation of the DNA part rather than the LNA, while base losses were only observed from the DNA single strand of the hybrid

An elementary stringy estimate of transport coefficients of large temperature QCD

Modeling QCD at large temperature with a simple holographic five dimensional theory encoding minimal breaking of conformality, allows for the calculation of all the transport coefficients, up to second order, in terms of a single parameter. In particular, the shear and bulk relaxation times are provided. The result follows by deforming the AdS background with a scalar dual to a marginally relevant operator, at leading order in the deformation parameter.Comment: 11 pages; v2: comments and references adde