Golden Jubilee Colloqium series in Mathematics
Speaker : Prof. Manjul Bhargava
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
Speaker: Prof. B.K. Sinha,
Indian Statistical Institute, Kolkata
Title: Statistical Surveillance: Issues, Models and Methods with
Date and Time: March 11th(Tue)3.00pm-4.30pm
Venue: Ramanujan Hall, Department of
Mathematics, IIT Bombay
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
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
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.
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.