5 Dicembre, 2008 11:00

Stima efficiente di curve in più dimensioni mediante splines di regressione con nodi liberi

Dott.ssa Laura Sangalli, MOX, Dipartimento di Matematica, Politecnico di Milano

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

Si considera il problema di stima efficiente di una curva tridimensionale, a partire da una sua osservazione discreta e affetta da errore. Viene sviluppata una tecnica di regressione basata su spline con nodi liberi, e cioè spline in cui il numero e la posizione dei nodi non sono prefissati, ma scelti in maniera adattiva ai dati. La tecnica proposta è confrontata con un metodo di regressione classico, la regressione polinomiale locale, via simulazioni e applicazioni al dataset del Progetto Aneurisk. Viene mostrato che le spline di regressione tridimensionali con nodi liberi producono stime più accurate ed efficienti.

26 Novembre, 2008 15:00

Sensitivity analysis as an ingredient of modeling.

Stefano Tarantola e Marco Ratto, Joint Research Center, European Commission, Ispra

Aula Seminari III piano Dipartimento

abstract

abstract

Nineteen years after Science’s review of sensitivity analysis methods in 1989 (System analysis
at molecular scale, by H. Rabitz) we search Science Online to identify and then review all
recent articles on "sensitivity analysis". In spite of the considerable developments which have
taken place in this discipline, of the good practices which have emerged, and of existing
guidelines for sensitivity analysis issued on both sides of the Atlantic, we could not find
other than very primitive sensitivity analysis tools, based on "one-factor-at-a-time" (OAT)
approaches.
In the context of model corroboration or falsification, this use of OAT methods is illicit and
unjustified, unless the model under analysis is proved to be linear.
We show that available good practices, such as variance-based measures and others, are
able to overcome OAT shortcomings and easy to implement. These methods also allow the
concept of factors importance to be defined rigorously, thus making the factors importance
ranking univocal. We analyse the requirements of sensitivity analysis in the context of
modelling, and present best available practices.
In the second talk, we describe smoothing methods for emulation and sensitivity analysis
including summary of tensor product cubic splines and reproducing kernel Hilbert spaces
(RKHS); recursive algorithm to estimate tensor product cubic splines; equivalence between
recursive and en-bloc algorithms; and the problem of heteroskedasticity

26 Novembre, 2008 15:00

Seminari FDS

Numeri figurati

R. Betti, Dipartimento di Matematica - Politecnico di Milano

Laboratorio Didattico FDS

Nineteen years after Science’s review of sensitivity analysis methods in 1989 (System analysis
at molecular scale, by H. Rabitz) we search Science Online to identify and then review all
recent articles on "sensitivity analysis". In spite of the considerable developments which have
taken place in this discipline, of the good practices which have emerged, and of existing
guidelines for sensitivity analysis issued on both sides of the Atlantic, we could not find
other than very primitive sensitivity analysis tools, based on "one-factor-at-a-time" (OAT)
approaches.
In the context of model corroboration or falsification, this use of OAT methods is illicit and
unjustified, unless the model under analysis is proved to be linear.
We show that available good practices, such as variance-based measures and others, are
able to overcome OAT shortcomings and easy to implement. These methods also allow the
concept of factors importance to be defined rigorously, thus making the factors importance
ranking univocal. We analyse the requirements of sensitivity analysis in the context of
modelling, and present best available practices.
In the second talk, we describe smoothing methods for emulation and sensitivity analysis
including summary of tensor product cubic splines and reproducing kernel Hilbert spaces
(RKHS); recursive algorithm to estimate tensor product cubic splines; equivalence between
recursive and en-bloc algorithms; and the problem of heteroskedasticity

21 Novembre, 2008 

Sezione di Geometria, Algebra e loro applicazioni

Automata theoretic methods in inverse semigroups

Akihiro Yamamura, Akita University

Aula Seminari F.Saleri , VI Piano, Dip.Mat.

Nineteen years after Science’s review of sensitivity analysis methods in 1989 (System analysis
at molecular scale, by H. Rabitz) we search Science Online to identify and then review all
recent articles on "sensitivity analysis". In spite of the considerable developments which have
taken place in this discipline, of the good practices which have emerged, and of existing
guidelines for sensitivity analysis issued on both sides of the Atlantic, we could not find
other than very primitive sensitivity analysis tools, based on "one-factor-at-a-time" (OAT)
approaches.
In the context of model corroboration or falsification, this use of OAT methods is illicit and
unjustified, unless the model under analysis is proved to be linear.
We show that available good practices, such as variance-based measures and others, are
able to overcome OAT shortcomings and easy to implement. These methods also allow the
concept of factors importance to be defined rigorously, thus making the factors importance
ranking univocal. We analyse the requirements of sensitivity analysis in the context of
modelling, and present best available practices.
In the second talk, we describe smoothing methods for emulation and sensitivity analysis
including summary of tensor product cubic splines and reproducing kernel Hilbert spaces
(RKHS); recursive algorithm to estimate tensor product cubic splines; equivalence between
recursive and en-bloc algorithms; and the problem of heteroskedasticity

6 Novembre, 2008 11:00

Sezione di Analisi

Risultati di regolarità per soluzioni di equazioni ellittiche degeneri non lineari

Maria Manfredini, Università di Bologna

Aula seminari MOX

abstract

abstract

Per ulteriori informazioni contattare:
Marco Bramanti, tel. 02 2399 4567
e-mail marco.bramanti@polimi.it

4 Novembre, 2008 14:15

Sezione di Analisi

Precondizionatori di Schwarz multilivello in elettrocardiologia computazionale

Prof. Simone Scacchi, Dipartimento di Matematica, Universita di Pavia

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

In questo seminario saranno presentati alcuni risultati sulla scalabilita' e l'efficienza di precondizionatori di Schwarz multilivello per il modello Bidominio dell'elettrocardiologia computazionale. Questo modello e' costituito da un sistema degenere di due equazioni alle derivate parziali paraboliche di diffusione-reazione, che descrivono l'attivita' bioelettrica del tessuto cardiaco. A causa della natura degenere e multiscala del problema, la discretizzazione con elementi finiti in spazio e metodi semi-impliciti in tempo porta alla soluzione di sistemi lineari mal condizionati. Per ridurre i costi computazionali richiesti dalla soluzione di questi sistemi, verranno introdotti dei precondizionatori basati su tecniche di domain decomposition di tipo Schwarz multilivello. Saranno presentati risultati di convergenza per questi metodi e test numerici a conferma delle stime teoriche

30 Ottobre, 2008 11:30

Sezione di Analisi

Stabilità e ricostruzione per il problema inverso della corrosione

Dott. Eva Sincich, Università di Trieste

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

Durante il seminario verra´ discusso un problema inverso che trova applicazione nell´individuazione della corrosione superficiale nei metalli. Il problema inverso consiste nella determinazione di un coefficiente in una condizione al bordo (che descrive il danno dovuto alla corrosione) dalle misurazioni elettrostatiche effettuate su una porzione del bordo accessibile all´ispezione. Verranno presentati dei risultati di stabilita´ e di ricostruzione per entrambe le condizioni al bordo che modellano il fenomeno, ovvero per la condizione lineare di Robin e per la condizione non lineare di Butler e Volmer

27 Ottobre, 2008 16:00

Sezione di Analisi

Stable discretizations of partial differential equations and their geometrical foundations

Prof. Douglas N. Arnold, McKnight Presidential Professor, School of Mathematics, University of Minnesota at Minneapolis

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

Partial differential equations (PDE) are among the most useful mathematical modeling tools, and numerical discretization of PDE--approximating them by problems which can be solved on computers--is one of the most important and widely used approaches to simulating the physical world. A vastly developed technology is built on such discretizations. Nonetheless, fundamental challenges remain in the design and understanding of effective methods of discretization for certain important classes of PDE problems.

The accuracy of a simulation depends on the consistency and stability of the discretization method used. While consistency is usually elementary to establish, stability of numerical methods can be subtle, and for some key PDE problems the development of stable methods is extremely challenging. After illustrating the situation through simple (but
surprising) examples, we will describe a powerful new approach--the finite element exterior calculus--to the design and understanding of discretizations for a variety of elliptic PDE problems. This approach achieves stability by developing discretizations which are compatible with the geometrical and topological structures, such as de Rham cohomology and Hodge decompositions, which underlie well-posedness of the PDE problem being solved

23 Ottobre, 2008 10:00

Sezione di Analisi

Modelling Petroleum Systems from Source to Trap

prof. Maik Inthorn, SINTEF, Norway

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

SINTEF is Scandinavias largest independent research institute. At the Basin Modelling Department of the division for petroleum research software is developed that shall help in the prediction of the location of hydrocarbon accumulations. Different software tools have been developed over the last 20 years to describe petroleum systems from the source rock to the hydrocarbon accumulation in traps. Processes like generation, expulsion and migration of hydrocarbons are represented. The software is used by many companies all around the world. An overview is given and source rock modelling will be described as an example

23 Ottobre, 2008 15:00

Seminari FDS

Modelli matematici: un’introduzione elementare

S. Salsa, Dipartimento di Matematica - Politecnico di Milano

Laboratorio Didattico FDS

SINTEF is Scandinavias largest independent research institute. At the Basin Modelling Department of the division for petroleum research software is developed that shall help in the prediction of the location of hydrocarbon accumulations. Different software tools have been developed over the last 20 years to describe petroleum systems from the source rock to the hydrocarbon accumulation in traps. Processes like generation, expulsion and migration of hydrocarbons are represented. The software is used by many companies all around the world. An overview is given and source rock modelling will be described as an example