Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions

We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory.Comment: 9 pages, LaTeX, some misprints are corrected, to be published in Phys. Lett.

On conformal Jordan cells of finite and infinite rank

This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite rank to one of lower rank. A conformal Jordan cell of rank one corresponds to a primary field. This offers a picture in which any finite conformal Jordan cell of a given conformal weight may be obtained from a universal covering cell of the same weight but infinite rank.Comment: 9 pages, LaTeX, v2: typo corrected, comments added, version to be publishe

A Logarithmic Conformal Field Theory Solution For Two Dimensional Magnetohydrodynamics In Presence of The Alf'ven Effect

When Alf`ven effect is peresent in magnetohydrodynamics one is naturally lead to consider conformal field theories, which have logarithmic terms in their correlation functions. We discuss the implications of such logarithmic terms and find a unique conformal field theory with centeral charge $c=-\frac{209}{7}$, within the border of the minimal series, which satisfies all the constraints. The energy espectrum is found to be \newline $E(k)\sim k^{-\frac{13}{7}} \log{k}$.Comment: Latex, 9 page

Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

We study a set of chiral symmetries contained in degenerate operators beyond the `minimal' sector of the c(p,q) models. For the operators h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ], for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of a spin j representation of SU(2). We give a free-field construction of these operators which makes this structure explicit and allows their OPEs to be calculated directly without any use of screening charges. The first non-trivial chiral field in this series, at j=1/2, is a fermionic or para-fermionic doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra and we calculate the vacuum character of these triplet models.Comment: 23 pages Late

Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a =$ behave as $|x_1 -x_2|^{\xi_a}$ with $\xi_a = a$ for length scales $|x_1-x_2| << \sigma$. The length scale $\sigma$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.Comment: 13 pages, 9 figure

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference

Extended chiral algebras in the SU(2)_0 WZNW model

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde

Long range correlation in cosmic microwave background radiation

We investigate the statistical anisotropy and Gaussianity of temperature fluctuations of Cosmic Microwave Background radiation (CMB) data from {\it Wilkinson Microwave Anisotropy Probe} survey, using the multifractal detrended fluctuation analysis, rescaled range and scaled windowed variance methods. The multifractal detrended fluctuation analysis shows that CMB fluctuations has a long range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of temperature fluctuation of CMB is mainly due to the long-range correlations and the map is consistent with a Gaussian distribution.Comment: 10 pages, 7 figures, V2: Added comments, references and major correction

Radiographers supporting radiologists in the interpretation of screening mammography: a viable strategy to meet the shortage in the number of radiologists.

BackgroundAn alternative approach to the traditional model of radiologists interpreting screening mammography is necessary due to the shortage of radiologists to interpret screening mammograms in many countries.MethodsWe evaluated the performance of 15 Mexican radiographers, also known as radiologic technologists, in the interpretation of screening mammography after a 6 months training period in a screening setting. Fifteen radiographers received 6 months standardized training with radiologists in the interpretation of screening mammography using the Breast Imaging Reporting and Data System (BI-RADS) system. A challenging test set of 110 cases developed by the Breast Cancer Surveillance Consortium was used to evaluate their performance. We estimated sensitivity, specificity, false positive rates, likelihood ratio of a positive test (LR+) and the area under the subject-specific Receiver Operating Characteristic (ROC) curve (AUC) for diagnostic accuracy. A mathematical model simulating the consequences in costs and performance of two hypothetical scenarios compared to the status quo in which a radiologist reads all screening mammograms was also performed.ResultsRadiographer's sensitivity was comparable to the sensitivity scores achieved by U.S. radiologists who took the test but their false-positive rate was higher. Median sensitivity was 73.3 % (Interquartile range, IQR: 46.7-86.7 %) and the median false positive rate was 49.5 % (IQR: 34.7-57.9 %). The median LR+ was 1.4 (IQR: 1.3-1.7 %) and the median AUC was 0.6 (IQR: 0.6-0.7). A scenario in which a radiographer reads all mammograms first, and a radiologist reads only those that were difficult for the radiographer, was more cost-effective than a scenario in which either the radiographer or radiologist reads all mammograms.ConclusionsGiven the comparable sensitivity achieved by Mexican radiographers and U.S. radiologists on a test set, screening mammography interpretation by radiographers appears to be a possible adjunct to radiologists in countries with shortages of radiologists. Further studies are required to assess the effectiveness of different training programs in order to obtain acceptable screening accuracy, as well as the best approaches for the use of non-physician readers to interpret screening mammography

Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some detail the partially massless version of new massive gravity, a theory with several special properties that we call "partially massless gravity".Comment: 34 pages, 2 figures; v2: added references; v3: Several rewordings in the introduction and section 2, added references. Matches published versio