Notiziario Scientifico
Settimana dal 17 al 23 febbraio 2014
Martedì 18 febbraio 2014
Martedì 18 febbraio 2014
Mercoledì 19 febbraio 2014
Mercoledì 19 febbraio 2014
Giovedì 20 febbraio 2014
Venerdì 21 febbraio 2014
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 9 del venerdì precedente la settimana di pubblicazione.
Ore 14:30, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
We present some recent results about the existence of positive and sign-changing solutions for the
Brezis-Nirenberg problem. In particular we exhibit a new kind of blowing-up solution and a
sign-changing tower of bubbles.
Ore 15:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
The Shape from Shading problem is a well known ill-posed problem. Several contributions have
addressed the case of Lambertian surfaces improving the model with the introduction of perspective
deformations or studying the corresponding photometric stereo problem. In our study we focus the
attention on a different improvement which is intended to reduce the assumptions on the properties
of the surface dealing with more general (and real) non-Lambertian surfaces. Our goal is to find a
unique model which should be flexible enough to handle many different kinds of real images. As a
starting point for this rather big project, we consider the basic model of a single nonlinear
partial differential equation (PDE) where we need to introduce new terms to tackle the general
non-Lambertian case. In particular, in this talk we will consider the non-Lambertian diffusive
Oren-Nayar reflectance model and the specular Phong model, we will construct semi-Lagrangian
approximation schemes for the corresponding nonlinear PDEs and we will compare their performances
with the classical Lambertian model in terms of some error indicators on a series of benchmarks
images.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
We prove some results about the singularities of Satake compactifications of classical moduli
spaces, this will give an insight into the relation among solutions of the Schottky problem in
different genera. The moduli space A_g lies in the boundary of A^S_[g+m] for every m. We will show
that the intersection between M^S_[g+m] and A_g contains the m-th infinitesimal neighbourhood of M_g
in A_g, this implies that stable equations for M_g do not exist. In particular, given two
inequivalent positive even unimodular quadratic forms P and Q, there is a curve whose period matrix
distinguishes between the theta series of P and Q; we are able to compute its genus in the rank 24
case. On the other hand, the intersection of A_g and Hyp^S_[g+m] is transverse: this enables us to
write down many new stable equations for Hyp_g in terms of theta series. Our work relies upon some
formulae for the first order part of the period matrix of some degenerations.
Ore 15:00, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
I will talk about recent results concerning the stability of some dissipative systems, precisely
conformally symplectic systems. I will start with the description of a suitable KAM theory, which
allows to prove the persistence of invariant attractors. The proof is constructive and it provides
efficient algorithms to evaluate the breakdown threshold of quasi-periodic attractors. Applications
to model problems are provided. Most of these works are done in collaboration with R. Calleja and R.
de la Llave.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
Ore 11:00, Aula 34 (quarto piano), Dipartimento di Scienze Statistiche
DNA is now routinely used in criminal investigations and court cases, although DNA samples taken at
crime scenes are of varying quality and therefore present challenging problems for their
interpretation. We present a statistical model for the quantitative peak information obtained from
an electropherogram (EPG) of a forensic DNA sample and illustrate its potential use for the analysis
of criminal cases. In contrast to most previously used methods, we directly model the peak height
information and incorporates important artefacts associated with the production of the EPG. Our
model has a number of unknown parameters, and we show that these can be estimated by the method of
maximum likelihood in the presence of multiple unknown contributors, and their approximate standard
errors calculated; the computations exploit a Bayesian network representation of the model. A case
example from a UK trial, as reported in the literature, is used to illustrate the efficacy and use
of the model, both in finding likelihood ratios to quantify the strength of evidence, and in the
deconvolution of mixtures for the purpose of finding likely profiles of one or more unknown
contributors to a DNA sample. Our model is readily extended to simultaneous analysis of more than
one mixture as illustrated in a case example. We show that combination of evidence from several
samples may give an evidential strength close to that of a single source trace and thus modelling of
peak height information provides for a potentially very efficient mixture analysis. Joint work with
Robert Cowell, Therese Graversen and Steffen Lauritzen
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