Colloquium:

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Speaker: M. Boratynski,

University of Bari, Italy

Date and Time: Tuesday, April 15, 2008 at 4 p.m.

Title: ``Invariant tubular neighborhood theorem for affine

varieties''

Venue: Ramanujan Hall

Abstract

The topic of the talk is the algebraic geometry analogue of the

Invariant tubular neighborhood theorem which concerns the action

of compact Lie groups on differential manifolds.

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Seminar

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Title: A graphical method to compare the efficiencies of cluster

randomized designs

Speaker: Prof. Siuli Mukhopadhyay

Department of Mathematics, IIT-B

Time: 3-4 pm

Date 15 April

Room 113

Abstract

The purpose of this talk is to compare efficiencies of several cluster

randomized designs using the method of quantile dispersion graphs (QDGs).

A

cluster randomized design is considered whenever

subjects are randomized at a group level but analyzed at the individual

level. A prior knowledge of

the correlation existing between subjects within the same cluster is

necessary to design these cluster

randomized trials. Using the QDG approach we are able to compare several

cluster randomized designs

without requiring any information on the intracluster correlation. For a

given design, quantiles of

the power function are obtained for several effect sizes. The quantiles

depend on the intracluster

correlation present in the model. The dispersion of these quantiles over

the

space of the unknown

intracluster correlation is determined, and then depicted by the QDGs. Two

applications of the

proposed methodology are presented.

Tony J. Puthenpurakal

Convener

SCC