Posts by Collection



Neuberg Locus and its Properties

Published in Journal of Classical Geometry, 2013

Neuberg Locus and its properties.

Recommended citation: Banerjee, Debdyuti and Mukherjee, Sayan. "Neuberg Locus And Its Properties." Journal of Classical Geometry, Volume 2 (26) (2013).

Expected return time to the initial state for biochemical systems with linear cyclic chains: unidirectional and bidirectional reactions

Published in Sādhanā, 2019

Maximum subgraphs without hypergraph families.

Recommended citation: Mukherjee, Sayan; Ghosh, Debraj and De, Rajat K. "Expected return time to the initial state for biochemical systems with linear cyclic chains: unidirectional and bidirectional reactions." Sādhanā (Springer India) Volume 44, Issue 1, Pages 1-12 (2019).

Neural Sequence Transformation

Published in Computer Graphics Forum; Pacific Graphics Conference 2021, 2021

Using neural networks to perform sequence transformation.

Recommended citation: Mukherjee, Sabyasachi; Mukherjee, Sayan; Hua, Binh-Son; Umetani, Nobuyuki and Meister, Daniel. "Neural Sequence Transformation." Computer Graphics Forum (Wiley), Volume 40, Issue 7, Pages 131-140 (2021).

Stylized Rendering as a Function of Expectation

Published in ACM Transactions on Graphics (SIGGRAPH 2024), 2024

A step towards integrating non-photorealistic stylizations into physically-based rendering systems.

Recommended citation: Rex West and Sayan Mukherjee. "Stylized Rendering as a Function of Expectation." ACM Trans. Graph. 43, 4, Article 96 (July 2024), 19 pages.


Tight Query Complexity Bounds for Learning Graph Partitions


Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for $n\ge k\ge 2$, learning the components of an $n$-vertex hidden graph with $k$ components requires at least $(k-1)n-\binom k2$ membership queries. Our result improves on the best known information-theoretic bound of $\Omega(n\log k)$ queries, and exactly matches the query complexity of the algorithm introduced by Reyzin and Srivastava, 2007 for this problem. Additionally, we introduce an oracle that can learn the number of components of $G$ in asymptotically fewer queries than learning the full partition, thus answering another question posed by the same authors. Lastly, we introduce a more applicable version of this oracle, and prove asymptotically tight bounds of $\widetilde\Theta(m)$ queries for both learning and verifying an $m$-edge hidden graph $G$ using it.


Teaching Assistant

Undergraduate course, University of Illinois at Chicago, Department of Mathematics, Statistics and Computer Science, 2016

Below are the different courses I have taught for at UIC during my Ph.D. from Fall 2016 to Spring 2021. You can find materials relevant to / used during these courses in their respective webpages below. Note that all courses do not have webpages with supplemental material.