Liouville theory and uniformization of four-punctured sphere

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.Comment: 17 pages, no figure

Non-invasive computer-assisted measurement of knee alignment

The quantification of knee alignment is a routine part of orthopaedic practice and is important for monitoring disease progression, planning interventional strategies, and follow-up of patients. Currently available technologies such as radiographic measurements have a number of drawbacks. The aim of this study was to validate a potentially improved technique for measuring knee alignment under different conditions. An image-free navigation system was adapted for non-invasive use through the development of external infrared tracker mountings. Stability was assessed by comparing the variance (F-test) of repeated mechanical femoro-tibial (MFT) angle measurements for a volunteer and a leg model. MFT angles were then measured supine, standing and with varus-valgus stress in asymptomatic volunteers who each underwent two separate registrations and repeated measurements for each condition. The mean difference and 95% limits of agreement were used to assess intra-registration and inter-registration repeatability. For multiple registrations the range of measurements for the external mountings was 1° larger than for the rigid model with statistically similar variance (p=0.34). Thirty volunteers were assessed (19 males, 11 females) with a mean age of 41 years (range: 20-65) and a mean BMI of 26 (range: 19-34). For intra-registration repeatability, consecutive coronal alignment readings agreed to almost ±1°, with up to ±0.5° loss of repeatability for coronal alignment measured before and after stress maneuvers, and a ±0.2° loss following stance trials. Sagittal alignment measurements were less repeatable overall by an approximate factor of two. Inter-registration agreement limits for coronal and sagittal supine MFT angles were ±1.6° and ±2.3°, respectively. Varus and valgus stress measurements agreed to within ±1.3° and ±1.1°, respectively. Agreement limits for standing MFT angles were ±2.9° (coronal) and ±5.0° (sagittal), which may have reflected a variation in stance between measurements. The system provided repeatable, real-time measurements of coronal and sagittal knee alignment under a number of dynamic, real-time conditions, offering a potential alternative to radiographs

Optimal detection of changepoints with a linear computational cost

We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the genome, or in finance as we observe time-series over longer periods. We consider the common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalised likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations. This compares favourably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the Binary Segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data.Comment: 25 pages, 4 figures, To appear in Journal of the American Statistical Associatio

Constitutive association of BRCA1 and c-Abl and its ATM-dependent disruption after irradiation

BRCA1 plays an important role in mechanisms of response to double-strand breaks, participating in genome surveillance, DNA repair, and cell cycle checkpoint arrests. Here, we identify a constitutive BRCA1-c-Abl complex and provide evidence for a direct interaction between the PXXP motif in the C terminus of BRCA1 and the SH3 domain of c-Abl. Following exposure to ionizing radiation (IR), the BRCA1-c-Abl complex is disrupted in an ATM-dependent manner, which correlates temporally with ATM-dependent phosphorylation of BRCA1 and ATM-dependent enhancement of the tyrosine kinase activity of c-Abl. The BRCA1-c-Abl interaction is affected by radiation-induced modification to both BRCA1 and c-Abl. We show that the C terminus of BRCA1 is phosphorylated by c-Abl in vitro. In vivo, BRCA1 is phosphorylated at tyrosine residues in an ATM-dependent, radiation-dependent manner. Tyrosine phosphorylation of BRCA1, however, is not required for the disruption of the BRCA1-c-Abl complex. BRCA1-mutated cells exhibit constitutively high c-Abl kinase activity that is not further increased on exposure to IR. We suggest a model in which BRCA1 acts in concert with ATM to regulate c-Abl tyrosine kinase activity

A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise

We prove a functional non-central limit theorem for jump-diffusions with periodic coefficients driven by strictly stable Levy-processes with stability index bigger than one. The limit process turns out to be a strictly stable Levy process with an averaged jump-measure. Unlike in the situation where the diffusion is driven by Brownian motion, there is no drift related enhancement of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit

H(3)+ correlators from Liouville theory

We prove that arbitrary correlation functions of the H(3)+ model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H(3)+ model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) coset model in terms of correlation functions in Liouville theory.Comment: 24 pages, v3: minor changes, references adde

Liouville field theory with heavy charges. II. The conformal boundary case

We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit computation is given for the one point function providing the first one loop check of the bootstrap formula.Comment: LaTeX 26 page

Development of a real-time PCR assay for the specific detection and identification of Streptococcus pseudopneumoniae using the recA gene

AbstractWe sequenced the evolutionarily conserved genes 16S rRNA, atpD, tuf, and recA from Streptococcus pseudopneumoniae, Streptococcus pneumoniae, Streptococcus mitis, and Streptococcus oralis. Phylogenetic analysis revealed that recA provided good resolution between these species, including discrimination of the novel species S. pseudopneumoniae. By contrast, the more conserved 16S rRNA, tuf and atpD are not sufficiently discriminatory. Therefore, recA sequences were used to develop a real-time PCR assay with a locked nucleic acid-mediated TaqMan probe for the specific detection and identification of S. pseudopneumoniae. The PCR assay showed excellent specificity and a detection limit of <10 genome copies for the detection and identification of S. pseudopneumoniae strains, which makes it a promising tool for molecular identification and epidemiological studies. In conclusion, this article describes for the first time a PCR assay for the specific identification of S. pseudopneumoniae