arXiv subjects

Martin Kurth

Publications and source records attributed to Martin Kurth.

9 recordsLinked to original sources

arXiv2008

Voting power and Qualified Majority Voting with a "no vote" option

In recent years, enlargement of the European Union has led to increased interest in the allocation of voting weights to member states with hugely differing population numbers. While the eventually agreed voting scheme lacks any strict mathematical basis, the Polish government suggested a voting scheme based on the Penrose definition of voting power, leading to an allocation of voting weights proportional to the square root of the population (the "Jagiellonian Compromise"). The Penrose definition of voting power is derived from the citizens' freedom to vote either "yes" or "no". This paper defines a corresponding voting power based on "yes", "no" and "abstain" options, and it is found that this definition also leads to a square root law, and to the same optimal vote allocation as the Penrose scheme.

math.GM↗

arXiv2008

Square root voting in the Council of the European Union: Rounding effects and the Jagiellonian Compromise

In recent years, enlargement of the European Union has brought with it renewed discussion of voting arrangements in the Council of the EU. During these negotiations, the Polish government proposed a voting scheme that gives each country a voting weight proportional to the square root of its population, and sets a quota according to an optimality condition ("Jagiellonian Compromise"). In this paper, the optimal quota is found exactly for the current population data from the 27 EU member states, and it is found that rounding of the voting weights can be used to improve the voting scheme.

math.GM↗

arXiv2006

Toward a Collection-based Metadata Maintenance Model

In this paper, the authors identify key entities and relationships in the operational management of metadata catalogs that describe digital collections, and they draft a data model to support the administration of metadata maintenance for collections. Further, they consider this proposed model in light of other data schemes to which it relates and discuss the implications of the model for library metadata maintenance operations.

cs.DL↗

arXiv2003

Non-perturbative renormalization of the static axial current in quenched QCD

We non-perturbatively calculate the scale dependence of the static axial current in the Schroedinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. The bare current in the O(a) improved theory as well as in the original Wilson regularization is thus connected to the renormalization group invariant one. The latter may then be related to the current at the B-scale defined such that its matrix elements differ from the physical (QCD) ones by O(1/M). At present, a (probably small) perturbative uncertainty enters in this step. As an application, we renormalize existing unimproved data on F_B^{bare} and extrapolate to the continuum limit. We also study an interesting function h(d/L,u) derived from the Schroedinger functional amplitude describing the propagation of a static quark-antiquark pair.

hep-lat↗

arXiv2002

Non-perturbative determination of Z_A^{stat} in quenched QCD

We non-perturbatively calculate the renormalization factor of the static axial vector current in O(a) improved quenched lattice QCD. Its scale dependence is mapped out in the Schroedinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. We also obtain Z_A^{stat} for Wilson fermions in order to renormalize existing unimproved data on F_B^{bare} non-perturbatively.

hep-lat↗

arXiv2001

Heavy Quark Effective Theory at one-loop order: An explicit example

We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the difference between the full and the effective theory in the continuum limit. In the full theory we find a term non-analytic in 1/m, revealing the asymptotic character of the 1/m-expansion. In general, deviations from the m-to-infinity limit turn out to be small and are well described by the first non-trivial terms when m is a factor 2-3 above the external scale. We also investigate the mass dependence of discretization errors, and find that the behaviour of the correlation functions at finite lattice spacing differs significantly from that in the continuum limit when the quark mass is large.

hep-lat↗

arXiv2001

An explicit example of HQET at one-loop order of perturbation theory

As an explicit example of HQET, we construct correlation functions containing a heavy-light axial current, both in the static approximation and in full QCD. This enables us to investigate the size of finite mass effects. As we use the lattice regularisation, we can also check the mass dependence of discretisation errors.

hep-lat↗

arXiv2000

Renormalization and O(a)-improvement of the static-light axial current

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schrödinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its relation to other schemes is computed to 1-loop order and the 2-loop anomalous dimension is derived. In finite volume renormalization schemes such as the SF-scheme, the renormalization scale dependence of the renormalized quantities is described by the step scaling function which can be computed by MC- simulations. We evaluate its lattice spacing effects in perturbation theory.

hep-lat↗

arXiv1999

Renormalization of the static-light axial current

We discuss the determination of the heavy-light axial current renormalization in the static approximation, using a new method based on the Schrödinger Functional (SF). Previous perturbative results for the renormalization constant are confirmed.

hep-lat↗