Golden Jubilee Colloqium series in Mathematics

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Speaker : Prof. Manjul Bhargava

Princeton University

Title: Gauss Composition Laws and their applications

Date : Monday 10 March 2008

Time : 2:30 p.m.

Venue : Ramanujan Hall (Room 214)

Abstract: In 1801 Gauss laid down a remarkable law of composition on

integral binary quadratic forms. This discovery, known as Gauss

composition, not only had a profound influence on elementary number

theory but also laid the foundations for ideal theory and modern

algebraic number theory. Even today, Gauss composition remains one of

the best ways of understanding ideal class groups of quadratic fields.

The question arises as to whether there might exist similar laws of com-

position on other spaces of forms that could shed light on the structure

of other algebraic number rings and fields. In this talk we describe

several such higher analogues of Gauss composition, and we discuss

some of their recent applications.

2. Statistics Seminar

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Speaker: Prof. B.K. Sinha,

Indian Statistical Institute, Kolkata

Title: Statistical Surveillance: Issues, Models and Methods with

Applications

Date and Time: March 11th(Tue)3.00pm-4.30pm

Venue: Ramanujan Hall, Department of

Mathematics, IIT Bombay

Abstract:

Surveillance is the art and science of online monitoring of a process to

detect changes [in the process], if any, as quickly as possible and at the

same time, to keep desired control on the false alarms. Most of the

processes being stochastic in nature, there are many challenging

statistical issues involved. Also there are numerous application areas

wherein surveillance is a major concern. For example, issues in medical

sciences [complicated cases of pregnancies] and public health [emission of

radiation from hazardous pollutants in air / surface / water] have widely

attracted the attention of researchers. Security issues may often be

challenging and these are taking an alarming shape in some countries in

recent times. It is suggested that continuous time monitoring is easier to

handle than discrete time monitoring.

Since the processes need to be monitored over [discrete / continuous] time

domains, longitudinal models play a fundamental role in any critical study

of surveillance. There can be instances of a .sub-optimal. record as

against an expected .generic. record at one point of time which needs

immediate detection. Also this can lead to a false alarm altogether.

Detecting a .true. change scenario as against a .false alarm. scenario has

posed challenging statistical issues.

Characterizing surveillance in statistical terms is an exercise in

statistical inference using sequential observations arising out of a

process wherein the nature of statistical hypotheses are continuously

changing. Moreover, the twin issues of .detection. of a true shift and

keeping a .control on false alarm. need to be addressed. There are a

number of alternative strategies to meet these objectives, mainly from the

point of view of data-use. Simpler but less efficient methods use most

recently available data, thereby simplifying the data analysis and meeting

one or the other of the stated objectives. These methods are suitable for

detection of .large. changes. Other methods use the entire available data

and naturally seek to provide better results on the surveillance issues.

Also important is the concept of .weighted. observations, since most

recent data are likely to gain more importance in the study of

surveillance.

Detecting a .true. change [immediately after it has taken place] and

again, at the same time, controlling a .false. signaling [about such a

change] are the twin requirements for a sound statistical technique to

meet. Most research have centered around these two points of concern.

Traditional statistical procedures do not necessarily take into account

the time point of alarm nor the delay in alarms. Statistical evaluation of

a surveillance method rests on computation of the chance of successful

detection of a true change along with that of expected delay for such

detection. Also it rests on the chance of raising a false alarm.

The concept of a baseline has also gained importance in the study of

surveillance. If it is too low, too many false alarms might surface up. On

the other hand, if it is too high, it will slower the detection process.

There is thus a strong ground for studying the aspect of robustness of

statistical surveillance procedures.

Surveillance may create a fundamentally different situation [for its

detection] when more than one changes occur in the process. In this talk,

I will review the literature on this fascinating topic.

3. Popular Lecture Series in Statistics

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Speaker: Prof. B.K. Sinha

Indian Statistical Institute, Kolkata

Title: On Some Statistical Aspects of Agreement Among Measurements

Date and Time: March 13th(Thur) during 3.00-4.00pm

Venue: Ramanujan Hall, Department of Mathematics, IIT Bombay.

Abstract:

One of the important aspects of interest for researchers in scientific

investigations may be to objectively examine the inter-observer variation

in quantitative and/or qualitative studies. Similar interest may exist in

examining the variation in a variable between two measurement techniques,

the established one and the test one. As an attempt in this direction,

scientists unknowingly may rely on inappropriate agreement analysis such

as simple correlation/association analysis, instead of examining known

limitations of such analysis in this regard.

This technical and, yet, popular talk is aimed at discussing

methodologically appropriate techniques used in agreement analysis, with

real data sets.

Tony Puthenpurakal

Convener

SCC.