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Subject: CVGMT weekly bulletin

Weekly bulletin of http://cvgmt.sns.it/

--- Summary ---

* Seminars by: Fornasier
* New papers by: Percivale, Maddalena, Tomarelli
* Modified papers by: Garroni, De Luca, Ponsiglione, Alberti, Gobbino, DeSimone, Pinamonti, Maddalena, Alicandro, Granieri, Valdinoci, Crippa, Bianchini

--- Seminars next week ---

* Wednesday 19 feb 2014
time: 17:00
Aula Riunioni - Department of Mathematics, University of Pisa

Consistency of probability measure quantization by means of power repulsion-attraction potentials
Massimo Fornasier 

Abstract. In this talk we present the study of the consistency of a variational method
for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials.
The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given probability measure
? to be quantized. Then we show that the discrete functionals, de?ning the discrete quantizers as their minimizers, actually ?-converge to the target energy with respect to the narrow topology on the space of probability
measures. A key ingredient is the reformulation of the target functional
by means of a Fourier representation, which extends the characterization of
conditionally positive semi-de?nite functions from points in generic
position to probability measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy
in terms of uniform moment bounds, which already found applications in the
asymptotic analysis of corresponding gradient ?ows. To model situations
where the given probability is affected by noise, we additionally consider a
modi?ed energy, with the addition of a regularizing total variation term
and we investigate again its point mass approximations in terms of ?-convergence. We show that such a discrete measure representation of the
total variation can be interpreted as an additional nonlinear potential,
repulsive at a short range, attractive at a medium range, and at a long
range not having effect, promoting a uniform distribution of the point
masses.

--- New Papers ---

* Maddalena, Percivale, Tomarelli: Adhesion of Soft Nonlinear Elastic Membranes

--- Modified Papers ---

* Gobbino, Granieri: Sul Problema della Gittata Ottimale 2

* Pinamonti, Valdinoci: A Lewy-Stampacchia Estimate for variational inequalities in the Heisenberg group

* Alberti, Bianchini, Crippa: A uniqueness result for the continuity equation in two dimensions

* Alberti, DeSimone: Quasistatic evolution of sessile drops and contact angle hysteresis

* Granieri: Metric Currents and Geometry of Wassserstein Spaces

* Alberti, Bianchini, Crippa: Structure of level sets and Sard-type properties of Lipschitz maps

* Alicandro, Ponsiglione: Ginzburg-Landau functionals and  renormalized energy: A revised  $\Gamma$-convergence approach

* Granieri, Maddalena: Transport Problems ans Disintegration Maps

* Granieri, Maddalena: A Metric Approach to Elastic Reformations

* Alicandro, De Luca, Garroni, Ponsiglione: Metastability and dynamics  of discrete topological singularities in two dimensions: a $\Gamma$-convergence approach

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