Seminar

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Title:

Three popular concentration inequalities in

probabilistic combinatorics.

Speaker:

Prof. Anand Srivastav, University of Kiel, Germany

Day & Date:

Wednesday, March 5, 2008

Time:

Lecture 1: 3.00 PM - 3.50 PM

Tea Break: 3.50 - 4.10 PM

Lecture 2: 4.10 PM - 5.00 PM

Colloquium

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Speaker: Prof. H. N. Mhaskar ,

Department of Mathematics, California State University, Los

Angeles,

Title: EDGE DETECTION AND LOCAL APPROXIMATION USING SPECTRAL DATA

Date: 7 March 2007

Time: 4.00-5.00 p.m

Venue: Ramanujan Hall

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Abstract for Prof Anand Srivastav's talks:

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We will give an introduction to concentration inequalities

(i.e. estimation of large deviations) for sums of independent

and partially dependent random variables in a discrete

setting and their impact on some combinatorial problems,

like discrepancy of 2-colorings of hypergraps, lattice

approximation and subgraph counting. In the first lecture

the well-known Chernov-Hoeffding bounds are introduced.

In the second lecture we will discuss an inequality of

Svante Janson for a sum of partially dependent random variables. If

time permits, we will also discuss a lower tail

due to Janson, Luczak and Ruczinski is discussed.

These lectures shall be expository in nature.

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Abstract for Prof. H. N. Mhaskar's talk

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We discuss the question of identifying local features of a function, such

as

the discontinuities in its derivatives, membership in local smoothness

classes,

etc., given global information about the function in the form of its

Fourier

coefficients with respect to an orthonormal system. We present a unifying

theme for some of the recent work on trigonometric and algebraic

polynomial

frames on the circle, the unit interval, the Euclidean sphere, and a

smooth

manifold in general. Applications include direction finding in phased

array

antennas, estimation of the velocity of the gulf stream, and

semi-supervised

learning of hand written digits.

Tony J. Puthenpurakal

Convener

SCC