Many a modern engineering system comprises networks of low cost edge de- vices capable of processing large amounts of data under resource constraints such as low compute-power and memory, limited communication bandwidth, and the need for low latency. Under this setting, for tasks such as inference, compression, and communication, classical al- gorithms are often inadequate and a complete paradigm shift to incorporate optimization for the practical constraints is warranted. Motivated by such applications, my research is focused on designing algorithms and lower bounds for statistical inference, compression, learning, and communication under limited data access.
In the first part of the talk, we describe an instance of statistical inference on data that is distributed across nodes and hence access to data is limited. In particular, we character- ize the communication complexity of distributed high dimensional correlation testing. Next, we make use of the idea of limited data access to envision communication under a weaker form of feedback and use it to resolve in part, a 27-year old conjecture regarding the capacity of queue channels. We conclude with a brief outline of ongoing work and future research plans.
(The talk will be in hybrid mode. Details of it are as follows.
The zoom meeting link is
https://zoom.us/j/99598370034
Meeting id:995 9837 0034
Passcode: 941422)
We consider the digital reverse of integers, in particular those of primes. A palindromic prime number is a popular example of a prime whose reverse is also a prime. The infinitude of such primes is one among the open conjectures in the area. We will discuss available partial results on almost primes and build on these to present reversed primes in arithmetic progression. The new results are from my joint work with Yuta Suzuki.
Knots are topological states rigorously identified in closed curves using polynomial invariants. These knots occur naturally in sufficiently long swollen ring polymers or globular ones. The occurrence of knots is known to affect the static, dynamic, and rheological properties of the polymer while, on the other hand, knot formation and knot complexity strongly depend on the physical properties of the polymer itself (e.g., the stiffness). In this talk, I will present how and to what extent the supervised machine learning approaches can be employed to predict the topologically different knotted states of fully flexible ring polymers confined inside a spherical cavity. I will discuss the factors that may influence the predictions, such as the degree of spherical confinement, the length of the polymer chain of the tested configurations (shorter or longer than the trained ones), the topological family (torus/twist) of the knotted states, etc. Finally, I will discuss its applicability in recognizing the physical knots tied in open linear polymer chains.