350 research outputs found
Permutation combinatorics of worldsheet moduli space
52 pages, 21 figures52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published version52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published versio
Ranking the Impact of Different Tests on a Hypothesis in a Bayesian Network
Testing of evidence in criminal cases can be limited by temporal or financial constraints or by the fact that certain tests may be mutually exclusive, so choosing the tests that will have maximal impact on the final result is essential. In this paper, we assume that a main hypothesis, evidence for it and possible tests for existence of this evidence are represented in the form of a Bayesian network, and use three different methods to measure the impact of a test on the main hypothesis. We illustrate the methods by applying them to an actual digital crime case provided by the Hong Kong police. We conclude that the Kullback-Leibler divergence is the optimal method for selecting the tests with the highest impact
Strings from Feynman Graph counting : without large N
A well-known connection between n strings winding around a circle and
permutations of n objects plays a fundamental role in the string theory of
large N two dimensional Yang Mills theory and elsewhere in topological and
physical string theories. Basic questions in the enumeration of Feynman graphs
can be expressed elegantly in terms of permutation groups. We show that these
permutation techniques for Feynman graph enumeration, along with the Burnside
counting lemma, lead to equalities between counting problems of Feynman graphs
in scalar field theories and Quantum Electrodynamics with the counting of
amplitudes in a string theory with torus or cylinder target space. This string
theory arises in the large N expansion of two dimensional Yang Mills and is
closely related to lattice gauge theory with S_n gauge group. We collect and
extend results on generating functions for Feynman graph counting, which
connect directly with the string picture. We propose that the connection
between string combinatorics and permutations has implications for QFT-string
dualities, beyond the framework of large N gauge theory.Comment: 55 pages + 10 pages Appendices, 23 figures ; version 2 - typos
correcte
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
We show that the zeroth cohomology of M. Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber
operad. They are parameterized by grt_1, up to one class (or two, depending on
the definitions). More generally, the homotopy derivations of the (non-unital)
E_n operads may be expressed through the cohomology of a suitable graph
complex. Our methods also give a second proof of a result of H. Furusho,
stating that the pentagon equation for grt_1-elements implies the hexagon
equation
The Beta Ansatz: A Tale of Two Complex Structures
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges
Search for the Proton Decay Mode proton to neutrino K+ in Soudan 2
We have searched for the proton decay mode proton to neutrino K+ using the
one-kiloton Soudan 2 high resolution calorimeter. Contained events obtained
from a 3.56 kiloton-year fiducial exposure through June 1997 are examined for
occurrence of a visible K+ track which decays at rest into mu+ nu or pi+ pi0.
We found one candidate event consistent with background, yielding a limit,
tau/B > 4.3 10^{31} years at 90% CL with no background subtraction.Comment: 13 pages, Latex, 3 tables and 3 figures, Accepted by Physics Letters
Neutrino Interactions In Oscillation Experiments
We calculate neutrino induced cross-sections relevant for oscillation
experiments, including the -lepton threshold for quasi-elastic, resonance
and deep inelastic scattering. In addition to threshold effects, we include
nuclear corrections for heavy targets which are moderate for quasi-elastic and
large for single pion production. Nuclear effects for deep inelastic reactions
are small. We present cross sections together with their nuclear corrections
for various channels which are useful for interpreting the experimental results
and for determining parameters of the neutrino sector..Comment: 24 pages, 18 figure
A Study of Cosmic Ray Composition in the Knee Region using Multiple Muon Events in the Soudan 2 Detector
Deep underground muon events recorded by the Soudan 2 detector, located at a
depth of 2100 meters of water equivalent, have been used to infer the nuclear
composition of cosmic rays in the "knee" region of the cosmic ray energy
spectrum. The observed muon multiplicity distribution favors a composition
model with a substantial proton content in the energy region 800,000 -
13,000,000 GeV/nucleus.Comment: 38 pages including 11 figures, Latex, submitted to Physical Review
The Wide-field Infrared Survey Explorer (WISE): Mission Description and Initial On-orbit Performance
The all sky surveys done by the Palomar Observatory Schmidt, the European
Southern Observatory Schmidt, and the United Kingdom Schmidt, the InfraRed
Astronomical Satellite and the 2 Micron All Sky Survey have proven to be
extremely useful tools for astronomy with value that lasts for decades. The
Wide-field Infrared Survey Explorer is mapping the whole sky following its
launch on 14 December 2009. WISE began surveying the sky on 14 Jan 2010 and
completed its first full coverage of the sky on July 17. The survey will
continue to cover the sky a second time until the cryogen is exhausted
(anticipated in November 2010). WISE is achieving 5 sigma point source
sensitivities better than 0.08, 0.11, 1 and 6 mJy in unconfused regions on the
ecliptic in bands centered at wavelengths of 3.4, 4.6, 12 and 22 microns.
Sensitivity improves toward the ecliptic poles due to denser coverage and lower
zodiacal background. The angular resolution is 6.1, 6.4, 6.5 and 12.0
arc-seconds at 3.4, 4.6, 12 and 22 microns, and the astrometric precision for
high SNR sources is better than 0.15 arc-seconds.Comment: 22 pages with 19 included figures. Updated to better match the
accepted version in the A
The classification of isotrivially fibred surfaces with p_g=q=2
An isotrivially fibred surface is a smooth projective surface endowed with a
morphism onto a curve such that all the smooth fibres are isomorphic to each
other. The first goal of this paper is to classify the isotrivially fibred
surfaces with completing and extending a result of Zucconi. As an
important byproduct, we provide new examples of minimal surfaces of general
type with and and a first example with .Comment: Main paper by M.Penegini. Appendix by S.Rollenske. 31 pages, 6
Figures. v2 changed group relations in Theorem 5.2, changes in Theorem 5.7,
new proof of Theorem 4.15, minor corrections of misprint
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