Wednesday, February 28, 2018
Public Access

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February 2018
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2:00pm [2:00pm]Niranjan Balachandran
Title: A function field analogue of a theorem of Sarkozy, due to B Green. Speaker: Niranjan Balachandran Date-Time: Wednesday, February 28 2018, 2 PM to 3.30 PM Venue: Ramanujan Hall Abstract: In the late 70s Sarkozy proved the following theorem: Given a polynomial f(T) over the integers with f(0)=0, there exists a constant c_f such that for any set $A\subset [n]$ of size at least $n/(log n)^{c_f}$ there exist distinct $a,b\in A$ such that $a-b=f(x)$ for some $x$. In 2016, Ben Green proved a function field analog of the same result but with a much better bound for $|A|$: Given a polynomial $F\in\bF_q[T]$ of degree $k$ with $F(0)=0$, there exists $0 q^{(1-c)n}$ there exist $\alpha(T)\neq\beta(T)$ in $A$ such that $\alpha(T)-\beta(T)=F(\gamma(T))$ for some $\gamma(T)\in\bF_q[T]$. We will see a proof of this result.

4:00pm [4:00pm]Prof. Ujjwal Das, IIM Udaipur
Time and Date: 28th Feb 2018, 4-5 pm Venue: Ramanujan Hall Speaker : Prof. Ujjwal Das, IIM Udaipur Title: Modeling Interval Censored Competing Risks Data with Missing Causes of Failure Missing causes of failure are quite frequent in survival and reliability studies. Surprisingly for interval censored data, this problem has not been investigated much, albeit in lifetime studies such data occur frequently. In this article, interval censored competing risks data are analyzed when some of the causes of failure are missing. The proposed technique uses vertical modeling, an approach that utilizes the data to extract information to the maximum possible extent, especially when some causes of failure are missing. The maximum likelihood estimates of the model parameters are obtained. Through a Monte Carlo simulation study, the performance of the point and interval estimators are assessed. It is observed through the simulation study that the proposed analysis performs better than the complete case analysis. Such analysis is particularly relevant for smaller sample sizes, as carrying out a complete case analysis in those cases may have a significant impact on the inferential procedures. Through Monte Carlo simulations, the effect of a possible model misspecification is also assessed on the cumulative incidence function which is an important statistic in the framework of competing risks. The proposed method has been illustrated on a real data set.