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

Labor Market Pooling, Outsourcing and Labor Contracts

Economic regions, such as urban agglomerations, face external demand and price shocks that produce income risk. Workers in large and diversified agglomerations may benefit from reduced wage volatility, while firms may outsource the production of intermediate goods and realize benefits from Chamberlinian externalities. Firms may also protect workers from wage risks through fixed wage contracts. This paper explores the relationships between firms’ risks, workers’ contracts, and the structure of production in cities.labor market, labor contracts, Chamberlinian externalities

Reduction for constrained variational problems on 3D null curves

We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of symmetries lead to the integration by quadratures of the extremals. Explicit solutions are found in terms of elliptic functions and integrals.Comment: 16 page

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

Sulphur and Carbon Isotopes as Tracers of Past Sub-seafloor Microbial Activity

Microbial life below the seafloor has changed over geological time, but these changes are often not obvious, as they are not recorded in the sediment. Sulphur (S) isotope values in pyrite extracted from a Plio- to Holocene sequence of the Peru Margin (Ocean Drilling Program, ODP, Site 1229) show a down-core pattern that correlates with the pattern of carbon (C) isotopes in diagenetic dolomite. Early formation of the pyrite is indicated by the mineralogical composition of iron, showing a high degree of pyritization throughout the sedimentary sequence. Hence, the S-record could not have been substantially overprinted by later pyrite formation. The S- and C-isotope profiles show, thus, evidence for two episodes of enhanced microbial methane production with a very shallow sulphate-methane transition zone. The events of high activity are correlated with zones of elevated organic C content in the stratigraphic sequence. Our results demonstrate how isotopic signatures preserved in diagenetic mineral phases provide information on changes of past biogeochemical activity in a dynamic sub-seafloor biosphere

A Time-Dependent Dirichlet-Neumann Method for the Heat Equation

We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves with Dirichlet boundary conditions followed by subdomain solves with Neumann boundary conditions. However, each subdomain problem is now in space and time, and the interface conditions are also time-dependent. Using a Laplace transform argument, we show for the heat equation that when we consider finite time intervals, the Dirichlet-Neumann method converges, similar to the case of Schwarz waveform relaxation algorithms. The convergence rate depends on the length of the subdomains as well as the size of the time window. In this discussion, we only stick to the linear bound. We illustrate our results with numerical experiments.Comment: 9 pages, 5 figures, Lecture Notes in Computational Science and Engineering, Vol. 98, Springer-Verlag 201

High Dimensional Classification with combined Adaptive Sparse PLS and Logistic Regression

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection, which combined constitute a powerful framework for classification, as well as data visualization and interpretation. However, current proposed combinations lead to instable and non convergent methods due to inappropriate computational frameworks. We hereby propose a stable and convergent approach for classification in high dimensional based on sparse Partial Least Squares (sparse PLS). Results: We start by proposing a new solution for the sparse PLS problem that is based on proximal operators for the case of univariate responses. Then we develop an adaptive version of the sparse PLS for classification, which combines iterative optimization of logistic regression and sparse PLS to ensure convergence and stability. Our results are confirmed on synthetic and experimental data. In particular we show how crucial convergence and stability can be when cross-validation is involved for calibration purposes. Using gene expression data we explore the prediction of breast cancer relapse. We also propose a multicategorial version of our method on the prediction of cell-types based on single-cell expression data. Availability: Our approach is implemented in the plsgenomics R-package.Comment: 9 pages, 3 figures, 4 tables + Supplementary Materials 8 pages, 3 figures, 10 table

Sur un theoreme fondamental dans la theorie des equations differentielles

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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