On quadratic orbital networks

These are some informal remarks on quadratic orbital networks over finite fields. We discuss connectivity, Euler characteristic, number of cliques, planarity, diameter and inductive dimension. We find a non-trivial disconnected graph for d=3. We prove that for d=1 generators, the Euler characteristic is always non-negative and for d=2 and large enough p the Euler characteristic is negative. While for d=1, all networks are planar, we suspect that for d larger or equal to 2 and large enough prime p, all networks are non-planar. As a consequence on bounds for the number of complete sub graphs of a fixed dimension, the inductive dimension of all these networks goes 1 as p goes to infinity.Comment: 13 figures 15 page

B-meson decay constants with domain-wall light quarks and nonperturbatively tuned relativistic b-quarks

We report on our progress to obtain the decay constants f_B and f_Bs from lattice-QCD simulations on the RBC-UKQCD Collaborations 2+1 flavor domain-wall Iwasaki lattices. Using domain-wall light quarks and relativistic b-quarks we analyze data with several partially quenched light-quark masses at two lattice spacings of a approx 0.11 fm and a approx 0.08 fm.Comment: Updated data analysis. 7 pages, 7 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

A broader perspective on point of view: logophoricity in Ogonoid languages

Logophoric marking in the Ogonoid family (Benue-Congo, Niger-Congo) differs significantly from most other logophoric reference systems in that these languages employ distinct verbal suffixes in logophoric domains, in addition to regular participant reference marking. This contrasts other known logophoric reference systems, which typically exhibit two sets of mutually exclusive pronouns, one logophoric and one non-logophoric. It has been commonly held in the literature that the function of logophoric pronouns is not to disambiguate coreference of clausal arguments, but to indicate the expression of a point of view distinct from that articulated using non-logophoric personal pronouns. In this paper, the properties of logophoric reference in Gokana (Hyman and Comrie 1981) and Kana (Ikoro 1996) are introduced before discussing new data from Eleme. Evidence is presented that point of view does not play a role in the use of logophoric marking in Eleme. Rather, it is argued that the logophoric trigger is determined by the interaction of person, number and grammatical relation hierarchies allowing for the development of a unique and comparably pervasive system of coreference

An Alternative Approach to Generalised BV and the Application to Expanding Interval Maps

We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where the weighting used in the transfer operator is not better than piecewise H\"older continuous and the partition on which the map is continuous may possess a countable number of elements. For such weighted transfer operators we give upper bounds for both the spectral radius and for the essential spectral radius

On extremal quantum states of composite systems with fixed marginals

We study the convex set of all bipartite quantum states with fixed marginal states. The extremal states in this set have recently been characterized by Parthasarathy [Ann. Henri Poincar\'e (to appear), quant-ph/0307182, [1]]. Here we present an alternative necessary and sufficient condition for a state with given marginals to be extremal. Our approach is based on a canonical duality between bipartite states and a certain class of completely positive maps and has the advantage that it is easier to check and to construct explicit examples of extremal states. In dimension 2 x 2 we give a simple new proof for the fact that all extremal states with maximally mixed marginals are precisely the projectors onto maximally entangled wave functions. We also prove that in higher dimension this does not hold and construct an explicit example of an extremal state with maximally mixed marginals in dimension 3 x 3 that is not maximally entangled. Generalizations of this result to higher dimensions are also discussed.Comment: 6 pages, to appear in J.Math.Phy