Democratic corporate governance within fluctuating cooperative banks: A multidisciplinary diagnosis and proposition of orientations.

The democratic question became of an ardent actuality within cooperative banks since the end of the 1990's. Founding element of human-sized organizations that were the first mutual or cooperative Caisses, is democracy running the risk to dissolve by necessity in the mature and hybrid giants that are the big banking cooperative groups nowadays? The present article unveils a multidisciplinary synthesis made possible by the conjunction of three researchers studying cooperative banks through three complementary angles: law, economy and management. After a first inventory of the possible symptoms of the disappearance of democracy inherent to the cooperative project, a more differentiating diagnosis is proposed, followed by an outline of some working leads for a creative evolution of cooperative democracy.Democracy; bank;cooperative; pluridisciplinarity; new cooperative paradigm

Renormalizability of Liouville Quantum Gravity at the Seiberg bound

Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d Riemannian metrics $e^{\phi(z)}dz^2$, conjecturally describing scaling limits of discrete $2d$-random surfaces. The law of the random field $\phi$ in LQFT depends on weights $\alpha\in \mathbb{R}$ that in classical Riemannian geometry parametrize power law singularities in the metric. A rigorous construction of LQFT has been carried out in \cite{DKRV} in the case when the weights are below the so called Seiberg bound: $\alpha<Q$ where $Q$ parametrizes the random surface model in question. These correspond to conical singularities in the classical setup. In this paper, we construct LQFT in the case when the Seiberg bound is saturated which can be seen as the probabilistic version of Riemann surfaces with cusp singularities. Their construction involves methods from Gaussian Multiplicative Chaos theory at criticality

Liouville Quantum Gravity on the Riemann sphere

In this paper, we rigorously construct $2d$ Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov "Quantum Geometry of bosonic strings". We also establish some of its fundamental properties like conformal covariance under PSL$_2(\mathbb{C})$-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quantum Gravity.Comment: Added conjectures relating Liouville quantum field theory to random planar map and optimal conditions in order to ensure existence of the unit volume Liouville measur

Distributed image reconstruction for very large arrays in radio astronomy

Current and future radio interferometric arrays such as LOFAR and SKA are characterized by a paradox. Their large number of receptors (up to millions) allow theoretically unprecedented high imaging resolution. In the same time, the ultra massive amounts of samples makes the data transfer and computational loads (correlation and calibration) order of magnitudes too high to allow any currently existing image reconstruction algorithm to achieve, or even approach, the theoretical resolution. We investigate here decentralized and distributed image reconstruction strategies which select, transfer and process only a fraction of the total data. The loss in MSE incurred by the proposed approach is evaluated theoretically and numerically on simple test cases.Comment: Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014 IEEE 8th, Jun 2014, Coruna, Spain. 201

In-line flow-induced vibrations of a rotating cylinder

The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the direction parallel to the current and subjected to a forced rotation about its axis, are investigated by means of two- and three-dimensional numerical simulations, at a Reynolds number equal to 100 based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to 2 (first vibration region), then the body and the flow are steady until a rotation rate close to 2.7 where a second vibration region begins. Each vibration region is characterized by a specific regime of response. In the first region, the vibration amplitude follows a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency). The maximum vibration amplitudes, even though considerably augmented by the rotation relative to the non-rotating body case, remain lower than 0.1 cylinder diameters. Due to their trends as functions of the reduced velocity and to the fact that they develop under a condition of wake-body synchronization or lock-in, the responses of the rotating cylinder in this region are comparable to the vortex-induced vibrations previously described in the absence of rotation. The symmetry breaking due to the rotation is shown to directly impact the structure displacement and fluid force frequency contents. In the second region, the vibration amplitude tends to increase unboundedly with the reduced velocity. It may become very large, higher than 2.5 diameters in the parameter space under study. Such structural oscillations resemble the galloping responses reported for non-axisymmetric bodies. They are accompanied by a dramatic amplification of the fluid forces compared to the non-vibrating cylinder case. It is shown that body oscillation and flow unsteadiness remain synchronized and that a variety of wake topologies may be encountered in this vibration region. The low-frequency, large-amplitude responses are associated with novel asymmetric multi-vortex patterns, combining a pair and a triplet or a quartet of vortices per cycle. The flow is found to undergo three-dimensional transition in the second vibration region, with a limited influence on the system behaviour. It appears that the transition occurs for a substantially lower rotation rate than for a rigidly mounted cylinder

Flow-induced vibrations of a rotating cylinder

The flow-induced vibrations of a circular cylinder, free to oscillate in the cross-flow direction and subjected to a forced rotation about its axis, are analysed by means of two- and three-dimensional numerical simulations. The impact of the symmetry breaking caused by the forced rotation on the vortex-induced vibration (VIV) mechanisms is investigated for a Reynolds number equal to 100, based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate freely up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to 4. Under forced rotation, the vibration amplitude exhibits a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency) and reaches 1.9 diameters, i.e. three times the maximum amplitude in the non-rotating case. The free vibrations of the rotating cylinder occur under a condition of wake–body synchronization similar to the lock-in condition driving non-rotating cylinder VIV. The largest vibration amplitudes are associated with a novel asymmetric wake pattern composed of a triplet of vortices and a single vortex shed per cycle, the TCS pattern. In the low-frequency vibration regime, the flow exhibits another new topology, the U pattern, characterized by a transverse undulation of the spanwise vorticity layers without vortex detachment; consequently, free oscillations of the rotating cylinder may also develop in the absence of vortex shedding. The symmetry breaking due to the rotation is shown to directly impact the selection of the higher harmonics appearing in the fluid force spectra. The rotation also influences the mechanism of phasing between the force and the structural response

Infinite-dimensional flats in the space of positive metrics on an ample line bundle

We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded filtration F of the section ring of L, the set of bounded decreasing convex functions on the support of the Duistermaat--Heckman measure of F embeds L^p-isometrically into the space of bounded positive metrics on L with respect to Darvas' d_p distance for all p\in[1,\infty), and in particular with respect to the Mabuchi metric (p=2)