[CvGmt News] seminario di "Equazioni Differenziali alle Derivate Parziali" + Seminario di "Analisi"
Agnese Di Castro
dicastro at mail.dm.unipi.it
Tue Feb 18 19:05:52 CET 2014
Cari colleghi,
vi comunichiamo che domani, mercoledi' 19 febbraio alle ore 16.00 nell'aula riunioni, presso il Dipartimento di Matematica (Univerista' di Pisa), il Prof. Michael Ruzhansky (Imperial College London) presentera' un seminario dal titolo:
"On wave equations and loss of regularity"
e alle ore 17.00 il Prof. Massimo Fornasier (Technische Universitat Munchen) presentera' un seminario dal titolo:
"Consistency of probability measure quantization by means of power repulsion-attraction potentials"
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
ω to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually Γ-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-definite 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 flows. To model situations
where the given probability is affected by noise, we additionally consider a
modified energy, with the addition of a regularizing total variation term
and we investigate again its point mass approximations in terms of Γ-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.
Saluti
Agnese & Bozhidar
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