He has been credited with coining the terms stringology and sparsification. He has published over 200 scientific papers and is listed as an ISI highly cited researcher.
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Nikhil Srivastava attended Union College in Schenectady, New York, graduating summa cum laude with a bachelor of science degree in mathematics and computer science in 2005. He received a PhD in computer science from Yale University in 2010 (his dissertation was called "Spectral Sparsification and Restricted Invertibility").
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Simple sparsification improves sparse denoising autoencoders in denoising highly corrupted images. In International Conference on Machine Learning (pp. 432-440). The need for efficient image restoration methods has grown with the massive production of digital images and movies of all kinds, often taken in poor conditions.Antoni Buades, Bartomeu Coll, Jean-Michel Morel.
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Integral equation approaches have become particularly popular for interconnect extraction due to sparsification techniques, also sometimes called matrix compression, acceleration, or matrix-free techniques, which have brought nearly O(n) growth in storage and solution time to integral equation methods.L. Greengard. The Rapid Evaluation of Potential Fields in Particle Systems. M.I.T. Press, Cambridge, Massachusetts, 1988.
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Differentially Private Federated Learning: A Client Level Perspective Robin C. Geyer and al., 2018 Other research activities focus on the reduction of the bandwidth during training through sparsification and quantization methods, where the machine learning models are sparsified and/or compressed before they are shared with other nodes. Recent research advancements are starting to consider real-word propagating channels as in previous implementations ideal channels were assumed.
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It is not possible for sk to equal s∞ for any finite k: as showed, there exists a constant α such that sk ≤ s∞(1 − α/k). Therefore, if the exponential time hypothesis is true, there must be infinitely many values of k for which sk differs from sk + 1. An important tool in this area is the sparsification lemma of , which shows that, for any ε > 0, any k-CNF formula can be replaced by O(2εn) simpler k-CNF formulas in which each variable appears only a constant number of times, and therefore in which the number of clauses is linear. The sparsification lemma is proven by repeatedly finding large sets of clauses that have a nonempty common intersection in a given formula, and replacing the formula by two simpler formulas, one of which has each of these clauses replaced by their common intersection and the other of which has the intersection removed from each clause.
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Yaroslavtsev completed his PhD in computer science in three years in 2013 at Pennsylvania State University, advised by Sofya Raskhodnikova. His dissertation was titled Efficient Combinatorial Techniques in Sparsification, Summarization and Testing of Large Datasets. After an ICERM institute postdoctoral fellowship at Brown University, he joined the University of Pennsylvania in the first cohort of fellows at the Warren Center for Network and Data Science, founded by Michael Kearns. In 2016, Yaroslavtsev joined the faculty at Indiana University in the Department of Computer Science and founded the Center for Algorithms and Machine Learning (CAML) at Indiana University.
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By applying the sparsification lemma and then using new variables to split the clauses, one may then obtain a set of O(2εn) 3-CNF formulas, each with a linear number of variables, such that the original k-CNF formula is satisfiable if and only if at least one of these 3-CNF formulas is satisfiable. Therefore, if 3-SAT could be solved in subexponential time, one could use this reduction to solve k-SAT in subexponential time as well. Equivalently, if sk > 0 for any k > 3, then s3 > 0 as well, and the exponential time hypothesis would be true. The limiting value s∞ of the sequence of numbers sk is at most equal to sCNF, where sCNF is the infimum of the numbers δ such that satisfiability of conjunctive normal form formulas without clause length limits can be solved in time O(2δn).
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