Statistics Seminar: STA 290
Tuesday, November 1st, 2011 at 3.10pm, MSB 1143 (Statistics Seminar Room)
Speaker: Victor Panaretos (Institute of Mathematics of the Ecole Polytechniqe Fédérale de Lausanne, Switzerland)
Title: Second-Order Comparison of Functional Populations and the Mechanical Properties of DNA
Abstract: A key question in theinvestigation of the molecular dynamics of DNA is whether its mechanicalproperties at persistence length are significantly affected by itsbase-pair composition. This question is studied by looking at the mechanical behavior of short closed strands of DNA called minicircles. These short strands can be modeled as random curves in space, and their corresponding mechanical properties, or flexibility, can be formalized through functional notions of dispersion capturing aspects of the second-order behaviour of the random curves. Motivated by this setup, we introduce the notion of a dispersion operator and consider the problem of comparing the dispersion operators of two functional populations. The covariance operator is a particular instance of a dispersion operator. An M-test based on the Hilbert-Schmidt norm of a score operator contrasting the dispersion operators of the two samples is developed. It is seen to involve aspects of ill-posed inverse problems and regularization is applied through spectral truncation. The procedure is applied to a sample of DNA minicircles obtained via the electron microscope.