Contact:

<my first name>91089<at>gmail<dot>com

Bossone 604, 3100 Market Street, Philadelphia PA


About MeI am pursuing PhD at Drexel University under Dr. John Walsh. I am part of Adaptive Signal Processing and Information Theory Research Group (ASPITRG). I obtained my undergraduate degree in Electronics and Telecommunication Engineering from Mumbai University, India.

My research interests lie in the intersection of Information Theory, Algorithms and Combinatorics. I am also interested in efficient and parallel implementations of algorithms. I am working on Characterization of Region of Entropic Vectors and Computation of rate regions for multi-source network coding which are ASPITRG projects supported very graciously by NSF under CCF-1421828, CCF-1016588 and CCF-1053702. 

Computation is the main tool I use to develop intuition about theoretical statements. I develop a lot of Software in C, C++, OpenMP, MPI, Python, Cython, MATLAB/Octave and more recently in GAP

My relatively latest resume can be found here.

Software:

ITCP (Information Theoretic Converse Prover):  GAP package for converse proofs in network coding. In particular, this software can generate statements of the converse coding theorems for network coding rate regions. Uses symchm and qsopt_ex-interface (see below). Those who have dabbled with computer assisted proofs of network coding rate regions and/or non-Shannon-type information inequalities, have probably come across ITIP and XITIP, which are softwares that can verify whether a putative inequality bounding a network coding rate region is implied by a collection of linear information inequalities and a collection of linear constraints on the entropy function. ITCP takes this business one step further, with the ability to produce all inequalities bounding a network coding rate region that are implied by a collection of linear information inequalities and network coding constraints on the entropy function, thus solving a generation problem instead of the much easier verification problem. Apart from network coding rate region outer bounds, it supports computation of lower bounds on worst case information ratio in secret sharing and upper bounds on guessing numbers of directed graphs. (git repopdf documentationtheoretical description)

symchm:  GAP package capable of computing exact projections of polyhedra, using an algorithm called chm. If symmetries of the projection are known, they can be exploited reduce complexity. This software offers a strong alternative to Fourier-Motzkin variable elimination when the input polyhedron dimension is exponentially large compared to the projection dimension. With a little bit of tinkering, this software can be used to solve Multi-objective Linear Programs (MOLPs). (git repopdf documentation

qsopt_ex-interface:   GAP package that provides an interface to rational LP solver qsopt_ex by Espinoza et. al., allowing one to solve LPs from within a GAP session. 

ITAP (Information Theoretic Achievability Prover): A  GAP package for achievability proofs in network coding and secret sharing with linear codes. (git repo, pdf documentationtheoretical description)

chm (Convex Hull Method): A general purpose C library for polyhedral projection. Uses rational arithmetic and rational linear programming. ( more about this here)

orbiter-mod: A C++ enumerator of subspace arrangements aka vector linear codes, based on Anton Betten's orbiter. This is supposed to be the core for a C++ version of ITAP (an under-construction git repo can be found here)

setops: A tiny library for handling sets with bit-wise operations. (more about this here)

sagemath: I was lucky to be one of the participants in Google Summer of Code (GSoC) 2014 for SageMath where I worked on augmenting the matroids package in sage. I implemented the visualization routines (ticket #16449), efficient minor checking (ticket #16545) and network code enumeration (ticket #16546). My mentors for this project were Stefan van Zwam and Rudi Pendavingh. More about this here: Stefan's blog post

Publications:

[0] Jayant Apte, John MacLaren Walsh, "Explicit Polyhedral Bounds on Network Coding Rate Regions via Entropy Function Region: Algorithms, Symmetry, and Computation", submitted, IEEE Transactions on Information Theory, Paper

[1] Jayant Apte, John MacLaren Walsh, "Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding ", submitted, IEEE Transactions on Information Theory, Paper

[2] Jayant Apte, Qi Chen, John MacLaren Walsh, "Symmetries in the Entropy Space", accepted, 2016 IEEE Information Theory Workshop, Paper, Computer-assisted proofs

[3] Jayant Apte, John MacLaren Walsh, “Symmetry in Network Coding”, accepted, International Symposium on Information Theory (ISIT) 2015, Hong Kong Paper (extended version)

[4] Jayant Apte, John MacLaren Walsh, "Exploiting Symmetry in Computing Polyhedral Bounds on Network Coding Rate Regions", accepted, International Symposium on Network Coding (NetCod) 2015, Sydney, Australia Paper (extended version)

[5] Jayant Apte, C. Li, John MacLaren Walsh, “Algorithms for Computing Network Coding Rate Regions via Single Element Extensions of Matroids”, IEEE International Symposium on Information Theory (ISIT) 2014, Honolulu, Hawaii, Program Paper Talk

[6] Jayant Apte, C. Li, John MacLaren Walsh, Steven Weber, “Exact Repair Problems With Multiple Sources”, 48th Annual Conference on Information Sciences and Systems (CISS) 2014, Princeton, NJ,  Program Paper Talk

[7] C. Li, Jayant Apte, John MacLaren Walsh, Steven Weber, “A New Computational Approach for Determining Rate Regions and Optimal Codes for Coded Networks”, IEEE International Symposium on Network Coding (NetCod), Calgary, Canada, Jun. 7-9, 2013 Program Paper

Talks:
Based on B. D. McKay, Isomorph-free exhaustive generation, Journal of Algorithms, 26 (1998) 306-324.

Based on Jim Geelen, Bert Gerards and Geoff Whittle, Solving Rota's conjecture, Notices of the American Mathematical Society, Aug 17, 2014: 736–743

Based on Chen, Qi; Yeung, Raymond W., Partition Symmetrical Entropy Functions, arXiv:1407.7405v1 [cs.IT]

Based on Katrin Herr, R. Bödi, Symmetries in linear and integer linear programming, Oberwolfach Report 38/2010

Based on D. Bremner, M. D. Sikiric, and A. Schurmann. Polyhedral representation conversion up to symmetries. CoRR, abs/math/0702239, 2007

Based on FRITZ, T., & CHAVES, R. (2013). Entropic Inequalities and Marginal Problems. IEEE transactions on information theory, 59(2), 803-817.

Based on K. Fukuda and A. Prodon. Double description method revisited. Technical report, Department of Mathematics, Swiss Federal Institute of Technology, Lausanne, Switzerland, 1995 and
Catherine Lassez and Jean-Louis Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In Bruce Donald, Deepak Kapur, and Joseph Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence. Academic Press, 1992.

Based on David Avis, lrs: A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm, in Gil Kalai and Günter M. Ziegler, editors, Polytopes - Combinatorics and Computation 
2000 

Based on A.G. Dimakis, P. B. Godfrey, Y. Wu, M. J. Wainwright and K. Ramchandran, Network Coding for Distributed Storage Systems, IEEE Transactions on Information Theory, Vol. 56(9), 4539-4551, Sept. 2010. 

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