[Forum SIS] avviso di seminario

[Domenico Marinucci]

AVVISO DI SEMINARIO

Dipartimento di Matematica

Università di Roma Tor Vergata

Giovedì 14 Giugno Ore 12

Aula Dal Passo



Speaker: Victor Panaretos (EPFL)

DOUBLY SPECTRAL ANALYSIS OF FUNCTIONAL TIME SERIES AND DNA MOLECULAR 
DYNAMICS

The Karhunen-Loève (KL) expansion has evolved into the workhorse of
functional data analysis: the Fourier representation it affords on the
one hand serves as a basis for motivating methodology by analogy to
multivariate statistics; and, on the other hand, appears as the natural
means of regularization in problems such as regression, testing and
prediction, which are ill-posed in the functional case. With the aim of
obtaining a similarly canonical representation of dependent functional
data, we develop a doubly spectral analysis of a stationary functional
stochastic process, decomposing it into an integral of uncorrelated
functional frequency components (Cramér representation), each of which
is in turn expanded into a KL series. This Cramér-Karhunen-Loève
representation separates temporal from intrinsic curve variation, and it
is seen to yield a harmonic principal component analysis when truncated:
a finite dimensional proxy of the time series that optimally captures
both within and between curve variation. Empirical versions are
introduced, and a rigorous analysis of their large-sample behaviour is
provided under Brillinger mixing conditions. Our work is motivated by
and applied to the study of the molecular dynamics of short strands of
DNA; specifically, we consider the problem of determining whether the
dynamics of such strands in solution are significantly affected by small
perturbations of their base-pair composition, based on molecular
dynamics simulations. (Based on joint work with Shahin Tavakoli, now at
Warwick).

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Domenico Marinucci
Dipartimento di Matematica
Università di Roma Tor Vergata
https://www.mat.uniroma2.it/~marinucc/
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