30,943 research outputs found
The subgroup growth spectrum of virtually free groups
For a finitely generated group denote by the growth
coefficient of , that is, the infimum over all real numbers such
that . We show that the growth coefficient of a virtually
free group is always rational, and that every rational number occurs as growth
coefficient of some virtually free group. Moreover, we describe an algorithm to
compute
Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis
Motivated by the recent demonstration of its use as a tool for the detection
and characterization of phase-shape correlations in multivariate time series,
we show that eigenvalue decomposition can also be applied to a matrix of
indices of bivariate phase synchronization strength. The resulting method is
able to identify clusters of synchronized oscillators, and to quantify their
strength as well as the degree of involvement of an oscillator in a cluster.
Since for the case of a single cluster the method gives similar results as our
previous approach, it can be seen as a generalized Synchronization Cluster
Analysis, extending its field of application to more complex situations. The
performance of the method is tested by applying it to simulation data.Comment: Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually
available Jan 200
Asymptotics of relative heat traces and determinants on open surfaces of finite area
The goal of this paper is to prove that on surfaces with asymptotically cusp
ends the relative determinant of pairs of Laplace operators is well defined. We
consider a surface with cusps (M,g) and a metric h on the surface that is a
conformal transformation of the initial metric g. We prove the existence of the
relative determinant of the pair under suitable
conditions on the conformal factor. The core of the paper is the proof of the
existence of an asymptotic expansion of the relative heat trace for small
times. We find the decay of the conformal factor at infinity for which this
asymptotic expansion exists and the relative determinant is defined. Following
the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of
determinants on compact surfaces, we prove Polyakov's formula for the relative
determinant and discuss the extremal problem inside a conformal class. We
discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51
page
Lorentz invariance violation and charge (non--)conservation: A general theoretical frame for extensions of the Maxwell equations
All quantum gravity approaches lead to small modifications in the standard
laws of physics which lead to violations of Lorentz invariance. One particular
example is the extended standard model (SME). Here, a general phenomenological
approach for extensions of the Maxwell equations is presented which turns out
to be more general than the SME and which covers charge non--conservation
(CNC), too. The new Lorentz invariance violating terms cannot be probed by
optical experiments but need, instead, the exploration of the electromagnetic
field created by a point charge or a magnetic dipole. Some scalar--tensor
theories and higher dimensional brane theories predict CNC in four dimensions
and some models violating Special Relativity have been shown to be connected
with CNC and its relation to the Einstein Equivalence Principle has been
discussed. Due to this upcoming interest, the experimental status of electric
charge conservation is reviewed. Up to now there seem to exist no unique tests
of charge conservation. CNC is related to the precession of polarization, to a
modification of the --Coulomb potential, and to a time-dependence of the
fine structure constant. This gives the opportunity to describe a dedicated
search for CNC.Comment: To appear in Physical Review
Overview of the 2005 cross-language image retrieval track (ImageCLEF)
The purpose of this paper is to outline efforts from the 2005 CLEF crosslanguage image retrieval campaign (ImageCLEF). The aim of this CLEF track is to explore
the use of both text and content-based retrieval methods for cross-language image retrieval. Four tasks were offered in the ImageCLEF track: a ad-hoc retrieval from an historic photographic collection, ad-hoc retrieval from a medical collection, an automatic image annotation task, and a user-centered (interactive) evaluation task that is explained in the iCLEF summary. 24 research groups from a variety of backgrounds and nationalities (14 countries) participated in ImageCLEF. In this paper we describe the ImageCLEF tasks, submissions from participating groups and summarise the main fndings
Ray-tracing in pseudo-complex General Relativity
Motivated by possible observations of the black hole candidate in the center
of our galaxy and the galaxy M87, ray-tracing methods are applied to both
standard General Relativity (GR) and a recently proposed extension, the
pseudo-complex General Relativity (pc-GR). The correction terms due to the
investigated pc-GR model lead to slower orbital motions close to massive
objects. Also the concept of an innermost stable circular orbit (ISCO) is
modified for the pc-GR model, allowing particles to get closer to the central
object for most values of the spin parameter than in GR. Thus, the
accretion disk, surrounding a massive object, is brighter in pc-GR than in GR.
Iron K emission line profiles are also calculated as those are good
observables for regions of strong gravity. Differences between the two theories
are pointed out.Comment: revised versio
Comment on 'Stability of the semiclassical Einstein equation'
Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev.
D 40, (1989) 315] are corrected.Comment: 3 pages, LaTeX, reprinted from Phys. Rev. D 50 (1994) 545
Improving LLR Tests of Gravitational Theory
Accurate analysis of precision ranges to the Moon has provided several tests
of gravitational theory including the Equivalence Principle, geodetic
precession, parameterized post-Newtonian (PPN) parameters and ,
and the constancy of the gravitational constant {\it G}. Since the beginning of
the experiment in 1969, the uncertainties of these tests have decreased
considerably as data accuracies have improved and data time span has
lengthened. We are exploring the modeling improvements necessary to proceed
from cm to mm range accuracies enabled by the new Apache Point Observatory
Lunar Laser-ranging Operation (APOLLO) currently under development in New
Mexico. This facility will be able to make a significant contribution to the
solar system tests of fundamental and gravitational physics. In particular, the
Weak and Strong Equivalence Principle tests would have a sensitivity
approaching 10, yielding sensitivity for the SEP violation parameter
of , general relativistic effects would
be tested to better than 0.1%, and measurements of the relative change in the
gravitational constant, , would be % the inverse age of the
universe. Having this expected accuracy in mind, we discusses the current
techniques, methods and existing physical models used to process the LLR data.
We also identify the challenges for modeling and data analysis that the LLR
community faces today in order to take full advantage of the new APOLLO ranging
station.Comment: 15 pages, 3 figures, talk presented at 2003 NASA/JPL Workshop on
Fundamental Physics in Space, April 14-16, 2003, Oxnard, C
Interaction-induced Renormalization of Andreev Reflection
We analyze the charge transport between a one-dimensional weakly interacting
electron gas and a superconductor within the scaling approach in the basis of
scattering states. We derive the renormalization group equations, which fully
account for the intrinsic energy dependence due to Andreev reflection. A strong
renormalization of the corresponding reflection phase is predicted even for a
perfectly transparent metal-superconductor interface. The interaction-induced
suppression of the Andreev conductance is shown to be highly sensitive to the
normal state resistance, providing a possible explanation of experiments with
carbon-nanotube/superconductor junctions by Morpurgo et al. [Science 286, 263
(2001)].Comment: 4 pages, 2 figure
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