[Google Meet Link]: meet.google.com/afe-apxx-wvw [Download title and abstract of the talk]: www.imsc.res.in/~asamal/seminar/ShailzaSingh_Sep22_2020.pdf [Abstract]: Network biology is an investigative and constructive means of understanding the complexities of biology. Substantial progress in the field has resulted in the creation of systems driven synthetic gene circuits which can be used for a tunable response in a cell. These tunable elements can be applied to treat diseased conditions for a transition to a healthy state. Though in its nascent stage of development synthetic biology is beginning to use its constructs to bring engineering approaches using machine learning into biomedicine for treatment of infectious disease. Many engineered peptides/proteins have made their way to therapeutics and diagnostics. I will discuss few success stories from our lab in metabolic, signaling and transcriptional regulatory network wherein we have been able to modulate the gene expression from an anti-inflammatory to a pro-inflammatory phenotype in in vitro L. major infected macrophage model.

Google meet link: meet.google.com/ket-hiwr-wym Turbulence is widely regarded as the last unsolved problem of classical physics. Despite the availability of well-defined governing equations, a tractable framework that predicts the dynamical and statistical properties of turbulence has eluded scientists. In this talk, we discuss how unstable nonchaotic solutions of the Navier-Stokes equation, called Exact Coherent States (ECS), may prove pivotal in developing such a framework. Specifically, we focus on moderately turbulent (quasi-two-dimensional) flows, which are characterized by the fleeting appearance of well-discernible flow patterns called coherent structures. We show that the appearance of coherent structures is related to the dynamical significance of ECS, such as equilibrium or time-periodic flows. Using these special solutions, we then construct a low-dimensional model for flow evolution and forecast turbulence for a short duration. Analyzing their statistical significance, we also show that frequently appearing ECS capture statistical averages (e.g., rate of energy dissipation) of turbulent flows accurately. Finally, we discuss how a network of dynamical connections between ECSs constrains long-term flow dynamics and provides a tractable deterministic picture of turbulence.

Suppose for each prime p we are given a set A_p (possibly empty) of residue classes mod p. Use these and the Chinese Remainder Theorem to form a set A_q of residue classes mod q, for any integer q. Under very mild hypotheses, we show that for a typical integer q, the residue classes in A_q will become equidistributed. The prototypical example (which this generalises) is Hooley's theorem that the roots of a polynomial congruence mod n are equidistributed on average over n. I will also discuss generalisations of such results to higher dimensions, and when restricted to integers with a given number of prime factors. (Joint work with Emmanuel Kowalski.) Google meet link for this talk is meet.google.com/bfk-yreu-qqw

Webinar, Join at: https://bluejeans.com/938282144. This talk will start with an overview of the relatively young field of QBF proof complexity, explaining the QBF proof system QURes, and an assessment of existing lower bound techniques. In the main part of the talk, I will describe a characterisation of QURes proof size in terms of a model in circuit complexity called term decision lists, yielding very direct connections between circuit lower bounds and QURes proof size lower bounds. Joint work with Olaf Beyersdorff, Joshua Blinkhorn, Tomáš Peitl.

Zoom link: https://us02web.zoom.us/j/86865846431 Let $M\geq 2$ be any integer. Consider the set $\text{GL}(n,q)^M=\{x^M|x\in \text{GL}(n,q)\}$, which is the set of all $M^{th}$ powers in the group $\text{GL}(n,q)$. In this talk, we will obtain generating functions for (a) the proportion of regular and regular semsimple elements in $\text{GL}(n,q)^M$, assuming $(M,q)=1$, (b) the proportion of semisimple and all elements which are $M^{th}$ powers when $(M,q)=1$, and $M$ is a power of a prime. Time permitting we will also discuss the other extreme, where we assume $M$ is a prime and $q$ is a power of $M$. This is a joint work with Dr. Anupam Singh.