Complex hyperbolic free groups with many parabolic elements

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in ${\rm PU}(2,1)$ such that the boundary loops are mapped to ${\rm PU}(2,1)$. We provide a system of coordinates on the corresponding representation variety, and analyse more specifically those representations corresponding to subgroups of $(3,3,\infty)$-groups. In particular we prove that it is possible to construct representations of the free group of rank two \la a,b\ra in ${\rm PU}(2,1)$ for which $a$, $b$, $ab$, $ab^{-1}$, $ab^2$, $a^2b$ and $[a,b]$ all are mapped to parabolics.Comment: 21 pages, 11 figure

Filtered derivative with p-value method for multiple change-points detection

This paper deals with off-line detection of change points for time series of independent observations, when the number of change points is unknown. We propose a sequential analysis like method with linear time and memory complexity. Our method is based at first step, on Filtered Derivative method which detects the right change points but also false ones. We improve Filtered Derivative method by adding a second step in which we compute the p-values associated to each potential change points. Then we eliminate as false alarms the points which have p-value smaller than a given critical level. Next, our method is compared with the Penalized Least Square Criterion procedure on simulated data sets. Eventually, we apply Filtered Derivative with p-Value method to segmentation of heartbeat time series

Local and Global Convergence of a General Inertial Proximal Splitting Scheme

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally inexpensive proximal operator. We analyze a general family of inertial proximal splitting algorithms (GIPSA) for solving such problems. We establish finiteness of the sum of squared increments of the iterates and optimality of the accumulation points. Weak convergence of the entire sequence then follows if the minimum is attained. Our analysis unifies and extends several previous results. We then focus on $\ell_1$-regularized optimization, which is the ubiquitous special case where the nonsmooth term is the $\ell_1$-norm. For certain parameter choices, GIPSA is amenable to a local analysis for this problem. For these choices we show that GIPSA achieves finite "active manifold identification", i.e. convergence in a finite number of iterations to the optimal support and sign, after which GIPSA reduces to minimizing a local smooth function. Local linear convergence then holds under certain conditions. We determine the rate in terms of the inertia, stepsize, and local curvature. Our local analysis is applicable to certain recent variants of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), for which we establish active manifold identification and local linear convergence. Our analysis motivates the use of a momentum restart scheme in these FISTA variants to obtain the optimal local linear convergence rate.Comment: 33 pages 1 figur

Is There Market Power in the French Comte Cheese Market?

An NEIO approach is used to measure seller market power in the French Comté cheese market, characterised by government-approved supply control. The estimation is performed on quarterly data at the wholesale stage over the period 1985-2005. Three different elasticity shifters are included in the demand specification, and the supply equation accounts for the existence of the European dairy quota policy. The market power estimate is small and statistically insignificant. Monopoly is rejected, as well as weak forms of Cournot oligopoly. Results appear to be robust to the choice of functional form, and suggest little effect of the supply control scheme on consumer prices.Supply control, NEIO, protected designation of origin, Marketing,

About the Efficiency of Input vs. Output Quotas

Output quotas are known to be more efficient than input quotas in transferring surplus from consumers to producers. Input quotas, by distorting the shadow prices of inputs, lead to inefficient production and generate larger deadweight losses, for a given amount of surplus transferred. Yet, input quotas have been a ubiquitous tool in agricultural policy. Practicality considerations, as well as the difficulty to control outputs that heavily depend on stochastic weather conditions, are arguments that help understand why policy makers may favor input quotas over output quotas. In this paper, we offer an additional explanation that rests on efficiency considerations. Assuming that the regulator only has limited knowledge about the market fundamentals (supply and demand elasticities, among others), seeks to transfer at least a given amount of surplus to producers and is influenced by the industry in his choice of the quota level, we show that an input quota becomes the optimal policy.Agricultural and Food Policy, H2, L2, Q1,

A New Class of Cellular Automata for Reaction-Diffusion Systems

We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion, and a probabilistic table-lookup for the reactive part. The applicability of the new CA is demonstrated using the Ginzburg-Landau equation.Comment: 4 pages, RevTeX 3.0 , 3 Figures 214972 bytes tar, compressed, uuencode