634 research outputs found
Conformal constraints for anomalous dimensions of leading twist operators
Leading-twist operators have a remarkable property that their divergence
vanishes in a free theory. Recently it was suggested that this property can be
used for an alternative technique to calculate anomalous dimensions of
leading-twist operators and allows one to gain one order in perturbation theory
so that, i.e., two-loop anomalous dimensions can be calculated from one-loop
Feynman diagrams, etc. In this work we study feasibility of this program on a
toy-model example of the theory in six dimensions. Our conclusion
is that this approach is valid, although it does not seem to present
considerable technical simplifications as compared to the standard technique.
It does provide one, however, with a very nontrivial check of the calculation
as the structure of the contributions is very different.Comment: 14 pages, 6 figure
Electroproduction of tensor mesons in QCD
Due to multiple possible polarizations hard exclusive production of tensor
mesons by virtual photons or in heavy meson decays offers interesting
possibilities to study the helicity structure of the underlying short-distance
process. Motivated by the first measurement of the transition form factor
at large momentum transfers by the BELLE
collaboration we present an improved QCD analysis of this reaction in the
framework of collinear factorization including contributions of twist-three
quark-antiquark-gluon operators and an estimate of soft end-point corrections
using light-cone sum rules. The results appear to be in a very good agreement
with the data, in particular the predicted scaling behavior is reproduced in
all cases.Comment: 27 pages, 5 figure
Semantic Stability in Social Tagging Streams
One potential disadvantage of social tagging systems is that due to the lack
of a centralized vocabulary, a crowd of users may never manage to reach a
consensus on the description of resources (e.g., books, users or songs) on the
Web. Yet, previous research has provided interesting evidence that the tag
distributions of resources may become semantically stable over time as more and
more users tag them. At the same time, previous work has raised an array of new
questions such as: (i) How can we assess the semantic stability of social
tagging systems in a robust and methodical way? (ii) Does semantic
stabilization of tags vary across different social tagging systems and
ultimately, (iii) what are the factors that can explain semantic stabilization
in such systems? In this work we tackle these questions by (i) presenting a
novel and robust method which overcomes a number of limitations in existing
methods, (ii) empirically investigating semantic stabilization processes in a
wide range of social tagging systems with distinct domains and properties and
(iii) detecting potential causes for semantic stabilization, specifically
imitation behavior, shared background knowledge and intrinsic properties of
natural language. Our results show that tagging streams which are generated by
a combination of imitation dynamics and shared background knowledge exhibit
faster and higher semantic stability than tagging streams which are generated
via imitation dynamics or natural language streams alone
Two-loop conformal generators for leading-twist operators in QCD
QCD evolution equations in minimal subtraction schemes have a hidden
symmetry: One can construct three operators that commute with the evolution
kernel and form an algebra, i.e. they satisfy (exactly) the
commutation relations. In this paper we find explicit expressions for these
operators to two-loop accuracy going over to QCD in non-integer
space-time dimensions at the intermediate stage. In this way conformal symmetry
of QCD is restored on quantum level at the specially chosen (critical) value of
the coupling, and at the same time the theory is regularized allowing one to
use the standard renormalization procedure for the relevant Feynman diagrams.
Quantum corrections to conformal generators in effectively
correspond to the conformal symmetry breaking in the physical theory in four
dimensions and the commutation relations lead to nontrivial constraints
on the renormalization group equations for composite operators. This approach
is valid to all orders in perturbation theory and the result includes
automatically all terms that can be identified as due to a nonvanishing QCD
-function (in the physical theory in four dimensions). Our result can be
used to derive three-loop evolution equations for flavor-nonsinglet
quark-antiquark operators including mixing with the operators containing total
derivatives. These equations govern, e.g., the scale dependence of generalized
hadron parton distributions and light-cone meson distribution amplitudes.Comment: 36 page
Heat kernel estimates for general boundary problems
We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in R d Rd . They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on fi nite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed
Discovering Beaten Paths in Collaborative Ontology-Engineering Projects using Markov Chains
Biomedical taxonomies, thesauri and ontologies in the form of the
International Classification of Diseases (ICD) as a taxonomy or the National
Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in
acquiring, representing and processing information about human health. With
increasing adoption and relevance, biomedical ontologies have also
significantly increased in size. For example, the 11th revision of the ICD,
which is currently under active development by the WHO contains nearly 50,000
classes representing a vast variety of different diseases and causes of death.
This evolution in terms of size was accompanied by an evolution in the way
ontologies are engineered. Because no single individual has the expertise to
develop such large-scale ontologies, ontology-engineering projects have evolved
from small-scale efforts involving just a few domain experts to large-scale
projects that require effective collaboration between dozens or even hundreds
of experts, practitioners and other stakeholders. Understanding how these
stakeholders collaborate will enable us to improve editing environments that
support such collaborations. We uncover how large ontology-engineering
projects, such as the ICD in its 11th revision, unfold by analyzing usage logs
of five different biomedical ontology-engineering projects of varying sizes and
scopes using Markov chains. We discover intriguing interaction patterns (e.g.,
which properties users subsequently change) that suggest that large
collaborative ontology-engineering projects are governed by a few general
principles that determine and drive development. From our analysis, we identify
commonalities and differences between different projects that have implications
for project managers, ontology editors, developers and contributors working on
collaborative ontology-engineering projects and tools in the biomedical domain.Comment: Published in the Journal of Biomedical Informatic
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