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

A simple model for heterogeneous flows of yield stress fluids

Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a non-monotonous local constitutive curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress $\Sigma$, we find homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate curve. Under controlled macroscopic shear rate $\dot{\Gamma}$, shear banding is predicted within a range of values of $\dot{\Gamma}$. For small shear rates, stick slip can also be observed. These qualitative behaviours are robust when changing the boundary conditions.Comment: 13 pages, 13 figure

Alpha- and beta-adrenergic mediation of changes in metabolism and Na/K exchange in rat brown fat

Double- and triple-barreled ion-sensitive microelectrodes were used to measure changes in extracellular K+ and Na+ concentrations ([K+]o, [Na+]o) in brown fat. Redox states of different respiratory enzymes were measured simultaneously in order to correlate ion movements with metabolic activity. Trains of stimuli applied to the efferent nerves evoked two distinct increases in [K+]o. A first, small, rapid increase occurred within 10 s and accompanied a first, rapid membrane depolarization. A second, slow increase of [K+]o occurred several minutes after stimulation and accompanied a second, slow depolarization. A few seconds after stimulation onset, while the membrane was repolarizing and shifts in redox states indicated increases in lipolysis and respiration, [K+]o decreased. The [K+]o decrease was accompanied by an increase in [Na+]o, and could be partly blocked by ouabain. Phentolamine, an alpha-antagonist that blocks the first depolarization, also blocked the first, rapid [K+]o increase and part of the subsequent decrease. Propranolol, a beta-antagonist, had little effect on the first depolarization and the first increase in [K+]o, but blocked part of the subsequent [K+]o decrease and the second, slow [K+]o increase. The changes in [K+]o were almost completely abolished in the presence of both antagonists. It is concluded that brown adipocytes take up K+ and simultaneously lose Na+ in response to the interaction of noradrenaline with alpha- and beta-receptors, and this indicates a very early stimulation of the Na+ pump

Non-invasive quantification of lower limb mechanical alignment in flexion

Objective: Non-invasive navigation techniques have recently been developed to determine mechanical femorotibial alignment (MFTA) in extension. The primary aim of this study was to evaluate the precision and accuracy of an image-free navigation system with new software designed to provide multiple kinematic measurements of the knee. The secondary aim was to test two types of strap material used to attach optical trackers to the lower limb. Methods: Seventy-two registrations were carried out on 6 intact embalmed cadaveric specimens (mean age: 77.8 ± 12 years). A validated fabric strap, bone screws and novel rubber strap were used to secure the passive tracker baseplate for four full experiments with each knee. The MFTA angle was measured under the conditions of no applied stress, valgus stress, and varus stress. These measurements were carried out at full extension and at 30°, 40°, 50° and 60° of flexion. Intraclass correlation coefficients, repeatability coefficients, and limits of agreement (LOA) were used to convey precision and agreement in measuring MFTA with respect to each of the independent variables, i.e., degree of flexion, applied coronal stress, and method of tracker fixation. Based on the current literature, a repeatability coefficient and LOA of ≤3° were deemed acceptable. Results: The mean fixed flexion for the 6 specimens was 12.8° (range: 6–20°). The mean repeatability coefficient measuring MFTA in extension with screws or fabric strapping of the baseplate was ≤2°, compared to 2.3° using rubber strapping. When flexing the knee, MFTA measurements taken using screws or fabric straps remained precise (repeatability coefficient ≤3°) throughout the tested range of flexion (12.8–60°); however, using rubber straps, the repeatability coefficient was >3° beyond 50° flexion. In general, applying a varus/valgus stress while measuring MFTA decreased precision beyond 40° flexion. Using fabric strapping, excellent repeatability (coefficient ≤2°) was observed until 40° flexion; however, beyond 50° flexion, the repeatability coefficient was >3°. As was the case with precision, agreement between the invasive and non-invasive systems was satisfactory in extension and worsened with flexion. Mean limits of agreement between the invasive and non-invasive system using fabric strapping to assess MFTA were 3° (range: 2.3–3.8°) with no stress applied and 3.9° (range: 2.8–5.2°) with varus and valgus stress. Using rubber strapping, the corresponding values were 4.4° (range: 2.8–8.5°) with no stress applied, 5.5° (range: 3.3–9.0°) with varus stress, and 5.6° (range: 3.3–11.9°) with valgus stress. Discussion: Acceptable precision and accuracy may be possible when measuring knee kinematics in early flexion using a non-invasive system; however, we do not believe passive trackers should be mounted with rubber strapping such as was used in this study. Flexing the knee appears to decrease the precision and accuracy of the system. The functions of this new software using image-free navigation technology have many potential clinical applications, including assessment of bony and soft tissue deformity, pre-operative planning, and post-operative evaluation, as well as in further pure research comparing kinematics of the normal and pathological knee

Gender homophily from spatial behavior in a primary school: a sociometric study

We investigate gender homophily in the spatial proximity of children (6 to 12 years old) in a French primary school, using time-resolved data on face-to-face proximity recorded by means of wearable sensors. For strong ties, i.e., for pairs of children who interact more than a defined threshold, we find statistical evidence of gender preference that increases with grade. For weak ties, conversely, gender homophily is negatively correlated with grade for girls, and positively correlated with grade for boys. This different evolution with grade of weak and strong ties exposes a contrasted picture of gender homophily

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

Characterization of a dense aperture array for radio astronomy

EMBRACE@Nancay is a prototype instrument consisting of an array of 4608 densely packed antenna elements creating a fully sampled, unblocked aperture. This technology is proposed for the Square Kilometre Array and has the potential of providing an extremely large field of view making it the ideal survey instrument. We describe the system,calibration procedures, and results from the prototype.Comment: 17 pages, accepted for publication in A&