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