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Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs [article]

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof
2016 arXiv   pre-print
Two sets A, B ⊆{0, 1}^n form a Uniquely Decodable Code Pair (UDCP) if every pair a ∈ A, b ∈ B yields a distinct sum a+b, where the addition is over Z^n.  ...  For sufficiently small ϵ, this bound significantly improves previous bounds by Urbanke and Li [Information Theory Workshop '98] and Ordentlich and Shayevitz [2014, arXiv:1412.8415], which upper bound β  ...  We now upper bound |η(P )|.  ... 
arXiv:1605.00462v1 fatcat:bp6uutjjznan3l42c36vi7xcfq

Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
The zero-error capacity of the BAC is equal to the maximum size of the product of the code sizes of a uniquely decodable code pair (UDCP): a pair A, B ⊆ {0, 1} n such that |A + B| = |A| · |B| where A +  ...  Let us bound the number of possibilities for a + b and b − a for pairs (a, b) ∈ W d .  ... 
doi:10.1109/isit.2016.7541316 dblp:conf/isit/AustrinKKN16 fatcat:se3b7rvz6ng33lwaqpm2ekiy2u

Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof
2018 IEEE Transactions on Information Theory  
For the size of the sumset of such a pair, van Tilborg has given an upper bound in the general case.  ...  Two sets of 0-1 vectors of fixed length form a uniquely decodeable code pair if their Cartesian product is of the same size as their sumset, where the addition is pointwise over integers.  ...  The zero-error capacity of the BAC is equal to the maximum size of the product of the code sizes of a uniquely decodable code pair (UDCP): a pair A, B ⊆ {0, 1} n such that |A + B| = |A| · |B| where A +  ... 
doi:10.1109/tit.2017.2688378 fatcat:gvdup6qgobguvjxc6slwj54xva

Optimal (2, n) visual cryptographic schemes

Mausumi Bose, Rahul Mukerjee
2006 Designs, Codes and Cryptography  
The image cannot be decoded from any single share but any two participants can together decode it visually, without using any complex decoding mechanism.  ...  For a practically useful range of n, we also obtain optimal schemes with the smallest possible pixel expansion.  ...  Acknowledgment We thank the referees for very constructive suggestions.  ... 
doi:10.1007/s10623-006-0011-9 fatcat:f5sdoxq26rbdhfjpxpsbrc4icq

ℓ_p-Spread and Restricted Isometry Properties of Sparse Random Matrices [article]

Venkatesan Guruswami, Peter Manohar, Jonathan Mosheiff
2022 arXiv   pre-print
Namely, every nonzero x ∈ X is "robustly non-sparse" in the following sense: x is εx_2-far in ℓ_2-distance from all δ n-sparse vectors, for positive constants ε, δ bounded away from 0.  ...  This "ℓ_2-spread" property is the natural counterpart, for subspaces over the reals, of the minimum distance of linear codes over finite fields, and corresponds to X being a Euclidean section of the ℓ_  ...  Acknowledgements We thank Sidhanth Mohanty for helpful discussions about the works of [BDH18, Bor19, BC19, MOP20a, MOP20b, OW20], and Yuval Peled for helpful discussions about convergence theorems for  ... 
arXiv:2108.13578v2 fatcat:rg5xhaa3xzbghiogjrarebgl4m

Efficient High Quality Rendering of Point Sampled Geometry [article]

Mario Botsch, Andreas Wiratanaya, Leif Kobbelt
2002 Symposium on Rendering  
We propose a highly efficient hierarchical representation for point sampled geometry that automatically balances sampling density and point coordinate quantization.  ...  For our application we cannot use this scheme since it does not provide a hierarchical representation and no guaranteed upper bound on the memory requirements.  ...  j ) encode(S, B j , i − 1) decode(bounding box B, recursion level i) if i = 0 write center position of B else split B into octants B 1 , . . . , B 8 read byte code [χ 1 · · · χ 8 ] for j = 1, . . . , 8  ... 
doi:10.2312/egwr/egwr02/053-064 fatcat:cdir27uaefhz3hfhgnd5ht4vmy

Decoding from Pooled Data: Sharp Information-Theoretic Bounds

Ahmed El Alaoui, Aaditya Ramdas, Florent Krzakala, Lenka Zdeborová, Michael I. Jordan
2019 SIAM Journal on Mathematics of Data Science  
We establish almost matching upper and lower bounds on the minimum number of queries m such that there is no solution other than the planted one with probability tending to 1 as n tends to infinity.  ...  We thank I-Hsiang Wang for sharing the slides of his talk at ITA. We thank Cris Moore for bringing the work of Achlioptas and Naor [AN05] to our attention.  ...  We thank Andrea Sportiello for suggesting the interpolation method that is used in our second proof of Proposition 6. We thank Nikhil Srivastava for bringing the survey [Big97]  ... 
doi:10.1137/18m1183339 dblp:journals/simods/AlaouiRKZJ19 fatcat:fcruanho7jgmvbryrbuiplejku

D6.2 - Preliminary conclusions about Federated Learning applied to clinical data

Federico Álvarez, Santiago Zazo, Juan Parras, Alejandro Almodóvar, Patricia Alonso, Enrico Giampieri, Gastone Castellani, Lorenzo Sani, Cesare Rollo, Tiziana Sanavia, Anders Krogh, Íñigo Prada-Luengo (+3 others)
2021 Zenodo  
Some preliminary code from all partners has been uploaded to a common repository to start creating a pool of methods and tools to foster incoming synergies.  ...  After a preliminary introductory section where the fundamental procedures and limitations are described, we detail the well-known mathematical foundation of Federated Learning for convex problems.  ...  One is that the representations of samples (as well as the samples of course) can be kept private to the nodes and only the decoder and other parameters need to be communicated between nodes.  ... 
doi:10.5281/zenodo.5862590 fatcat:trd6rdi7pzcq7gcta62jcitwua

DRIVE: One-bit Distributed Mean Estimation [article]

Shay Vargaftik, Ran Ben Basat, Amit Portnoy, Gal Mendelson, Yaniv Ben-Itzhak, Michael Mitzenmacher
2021 arXiv   pre-print
MM and RBB were supported in part by a gift to the Center for Research on Computation and Society at Harvard University.  ...  We thank Moshe Gabel, Mahmood Sharif, Yuval Filmus and, the anonymous reviewers for helpful comments and suggestions.  ...  Lemma 6 relies on Chebyshev's inequality and allows us to bound the vNMSE for all d. Lemma 7 gives a sharper bound for large dimensions using the Bernstein's inequality. Lemma 6.  ... 
arXiv:2105.08339v5 fatcat:xq2hgeinjvhc5hlod2ftmj6y2i

Domain adaptation for holistic skin detection [article]

Aloisio Dourado, Frederico Guth, Teofilo Emidio de Campos, Li Weigang
2020 arXiv   pre-print
Furthermore, we provide experimental support for the counter-intuitive superiority of holistic over local approaches for human skin detection.  ...  Human skin detection in images is a widely studied topic of Computer Vision for which it is commonly accepted that analysis of pixel color or local patches may suffice.  ...  The target only results are expected to be an upper bound in performance when 100% of the training labels are used because there is no domain change, but they may suffer from the reduced training set size  ... 
arXiv:1903.06969v2 fatcat:6gpp3maszrg6lli464fu2vvysm

Community Detection and Stochastic Block Models [article]

Emmanuel Abbe
2022 arXiv   pre-print
This monograph surveys the recent developments that establish the fundamental limits for community detection in the SBM, both with respect to information-theoretic and computational tradeoffs, and for  ...  The main results discussed are the phase transitions for exact recovery at the Chernoff-Hellinger threshold, the phase transition for weak recovery at the Kesten-Stigum threshold, the optimal SNR-mutual  ...  The encoder is a linear code that takes the XOR of any pair of bits, so that N = n 2 and the code is R = n/N ∼ 2/n.  ... 
arXiv:1703.10146v2 fatcat:olhrolrol5c67glzmhg42pnyei

High Performance Algorithms for Quantum Gravity and Cosmology [article]

William J. Cunningham
2018 arXiv   pre-print
The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or graphs.  ...  Finally, we consider the vacuum selection problem in string theory, where we show a network-centered approach yields a dynamical mechanism for vacuum selection in the context of multiverse cosmology.  ...  This allows each computer to choose unique random pairs, though it introduces a small amount of overhead.  ... 
arXiv:1805.04463v1 fatcat:xbk732bbzjeann2fpefo5ongdi

Nanopore sequencing of DNA concatemers reveals higher-order features of chromatin structure [article]

Netha Ulahannan, Matthew Pendleton, Aditya S Deshpande, Stefan Schwenk, Julie M Behr, Xiaoguang Dai, Carly Tyer, Priyesh Rughani, Sarah Kudman, Emily Adney, Huasong Tian, David Wilkes (+6 others)
2019 bioRxiv   pre-print
Our results establish Pore-C as the most simple and scalable assay for the genome-wide assessment of combinatorial chromatin interactions, with additional applications for cancer rearrangement reconstruction  ...  ACKNOWLEDGEMENTS We thank Jane Skok for helpful comments on the manuscript.  ...  Marcin Imielinski is supported by a Burroughs Wellcome Fund Career Award for Medical Scientists, Doris Duke Clinical Foundation Clinical Scientist Development Award, Starr Cancer Consortium Award, Melanoma  ... 
doi:10.1101/833590 fatcat:aamus4z5gfagfiwtom3ujgneca

Physics-based Deep Learning [article]

Nils Thuerey and Philipp Holl and Maximilian Mueller and Patrick Schnell and Felix Trost and Kiwon Um
2022 arXiv   pre-print
As much as possible, all topics come with hands-on code examples in the form of Jupyter notebooks to quickly get started.  ...  This is a good setup to figure out an upper bound and reasonable range for the learning rate as the most central hyperparameter.  ...  Alternatively, this learned model reduction code focuses on the encoding and decoding aspects.  ... 
arXiv:2109.05237v3 fatcat:pz7ot63dlbdkriihkwloefk3im

RF Impairments in Wireless Transceivers: Phase Noise, CFO, and IQ Imbalance – A Survey

Amirhossein Mohammadian, Chintha Tellambura
2021 IEEE Access  
Furthermore, we discuss artificial intelligence (AI) approaches for developing estimation and compensation algorithms for RF impairments.  ...  Wireless transceivers for mass-market applications must be cost effective. We may achieve this goal by deploying non-ideal low-cost radio frequency (RF) analog components.  ...  Then ML or sphere-decoding methods are deployed for decoding the space-frequency code.  ... 
doi:10.1109/access.2021.3101845 fatcat:ete2cakeerdjrahum3gcuuexwe
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