I recently obtained a PhD in Electrical Engineering from Stanford. While there, I was very fortunate to be advised by Greg Valiant and Tsachy Weissman, and also had the singular honour of working with Mary Wootters.
Theoretical work
Low-degree phase transitions for detecting a planted clique in sublinear time [arxiv]
Jay Mardia, Kabir Aladin Verchand, Alexander S. Wein
Logspace Reducibility From Secret Leakage Planted Clique [arxiv]
Jay Mardia
Is the space complexity of planted clique recovery the same as that of detection? [arxiv] [8 min talk] [25 min talk] [ITCS 2021]
Jay Mardia
Finding Planted Cliques in Sublinear Time [arxiv]
Jay Mardia, Hilal Asi, Kabir Aladin Chandrasekher
Concentration Inequalities for the Empirical Distribution of Discrete Distributions : Beyond the Method of Types [arxiv] [Information and Inference]
Jay Mardia, Jiantao Jiao, Ervin Tánczos, Robert D. Nowak, Tsachy Weissman
Repairing Multiple Failures for Scalar MDS Codes [arxiv] [IEEE Transactions on Information Theory] (Part of a line of work excellently presented in this [talk] by Mary Wootters)
Jay Mardia, Burak Bartan, Mary Wootters
Practical work
Overcoming high nanopore basecaller error rates for DNA storage via basecaller-decoder integration and convolutional codes [biorxiv] [GitHub] [ICASSP 2020]
Shubham Chandak, Joachim Neu, Kedar Tatwawadi, Jay Mardia, Billy Lau, Matthew Kubit, Reyna Hulett, Peter Griffin, Mary Wootters, Tsachy Weissman, Hanlee Ji
Improved read/write cost tradeoff in DNA-based data storage using LDPC codes [biorxiv] [Allerton 2019] ([Slides], [poster], and [talk] by Shubham at ISMB / ECCB 2019)
Shubham Chandak, Kedar Tatwawadi, Billy Lau, Jay Mardia, Matthew Kubit, Joachim Neu, Peter Griffin, Mary Wootters, Tsachy Weissman, Hanlee Ji
Course Projects
Implementation and analysis of stabilizer codes in pyQuil [code] [report] (Spring 2019, CS269Q)
Shubham Chandak, Jay Mardia, Meltem Tolunay
Stabilizer codes form a large family of quantum error correcting codes that includes well-known codes such as the Shor code, Steane code, CSS codes and toric codes. In this work, we build a framework for encoding and decoding of general stabilizer codes on pyQuil and test specific single qubit codes with standard quantum noise models.
Professional Activities
Visits: Simons Institute - Computational Complexity of Statistical Inference (Aug-Dec 2021) and EPFL / ETH Zurich - Swiss Winter School on Lower Bounds and Communication Complexity (Feb 2020)
Journal Reviewer: Journal of Machine Learning Research, Information and Inference, IEEE Communications Letters, IEEE Transactions on Information Theory
Conference Reviewer: STOC, ITW, SODA, ICASSP, NeurIPS ITML, ISIT
Teaching at Stanford: TA for Randomized Algorithms and Probabilistic Analysis (CS 265) (Autumn 2020-21), Information Theory (EE 276) (Winter 2020-21), and Information-theoretic Lower Bounds in Data Science (EE 378C) (Spring 2020-21)
Grading: Grader for Scaling Blockchains EE 374 (Spring 2019-2020)
Contact: jmardia [at] stanford [dot] edu