1,737,298 research outputs found
Non-Malleable Extractors and Non-Malleable Codes: Partially Optimal Constructions
Full text linkThe recent line of study on randomness extractors has been a great success, resulting in exciting new techniques, new connections, and breakthroughs to long standing open problems in several seemingly different topics. These include seeded non-malleable extractors, privacy amplification protocols with an active adversary, independent source extractors (and explicit Ramsey graphs), and non-malleable codes in the split state model. Previously, the best constructions are given in [Xin Li, 2017]: seeded non-malleable extractors with seed length and entropy requirement O(log n+log(1/epsilon)log log (1/epsilon)) for error epsilon; two-round privacy amplification protocols with optimal entropy loss for security parameter up to Omega(k/log k), where k is the entropy of the shared weak source; two-source extractors for entropy O(log n log log n); and non-malleable codes in the 2-split state model with rate Omega(1/log n). However, in all cases there is still a gap to optimum and the motivation to close this gap remains strong.
In this paper, we introduce a set of new techniques to further push the frontier in the above questions. Our techniques lead to improvements in all of the above questions, and in several cases partially optimal constructions. This is in contrast to all previous work, which only obtain close to optimal constructions. Specifically, we obtain:
1) A seeded non-malleable extractor with seed length O(log n)+log^{1+o(1)}(1/epsilon) and entropy requirement O(log log n+log(1/epsilon)), where the entropy requirement is asymptotically optimal by a recent result of Gur and Shinkar [Tom Gur and Igor Shinkar, 2018];
2) A two-round privacy amplification protocol with optimal entropy loss for security parameter up to Omega(k), which solves the privacy amplification problem completely;
3) A two-source extractor for entropy O((log n log log n)/(log log log n)), which also gives an explicit Ramsey graph on N vertices with no clique or independent set of size (log N)^{O((log log log N)/(log log log log N))}; and
4) The first explicit non-malleable code in the 2-split state model with constant rate, which has been a major goal in the study of non-malleable codes for quite some time. One small caveat is that the error of this code is only (an arbitrarily small) constant, but we can also achieve negligible error with rate Omega(log log log n/log log n), which already improves the rate in [Xin Li, 2017] exponentially.
We believe our new techniques can help to eventually obtain completely optimal constructions in the above questions, and may have applications in other settings
Xin li xue yu jiao yu xin li xue /
No full textCover title.; Special collection from London Missionary Society.; 880-03 Bian zhu zhong zhi jiao yu xin li xue di yi zhang.; Also available in an electronic version via the Internet at http://nla.gov.au/nla.gen-vn455089
Ren zhi xin li xue
No full textBen shu jie shao le ren zhi xin li xue de ji ben yuan ze he fang fa, yi ji dui ge zhong zhong yao ren zhi guo cheng de yan jiu, bao gua zhi jue, zhu yi, ji yi, biao xiang, si wei he yu yan den
Guo li zhong yang da xue jiao yu xue yuan xin li xue xi gai kuang.
No full textCover title.; Special collection from London Missionary Society.; Also available in an electronic version via the Internet at http://nla.gov.au/nla.gen-vn1973394
Critical remarks on Finsler modifications of gravity and cosmology by Zhe Chang and Xin Li
No full textAbstractI do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in [Zhe Chang, Xin Li, Phys. Lett. B 668 (2008) 453] and [Zhe Chang, Xin Li, Phys. Lett. B 676 (2009) 173], respectively). They consider that “In Finsler manifold, there exists a unique linear connection – the Chern connection … It is torsion freeness and metric compatibility …”. There are well-known results (for example, presented in monographs by H. Rund and R. Miron and M. Anastasiei) that in Finsler geometry there exist an infinite number of linear connections defined by the same metric structure and that the Chern and Berwald connections are not metric compatible. For instance, the Chern's one (being with zero torsion and “weak” compatibility on the base manifold of tangent bundle) is not generally compatible with the metric structure on total space. This results in a number of additional difficulties and sophistication in definition of Finsler spinors and Dirac operators and in additional problems with further generalizations for quantum gravity and noncommutative/string/brane/gauge theories. I conclude that standard physics theories can be generalized naturally by gravitational and matter field equations for the Cartan and/or any other Finsler metric compatible connections. This allows us to construct more realistic models of Finsler spacetimes, anisotropic field interactions and cosmology
AIM817709_Supplemental_material_SP4 – Supplemental material for Acupuncture combined with swallowing training for poststroke dysphagia: a meta-analysis of randomised controlled trials
No full textSupplemental material, AIM817709_Supplemental_material_SP4 for Acupuncture combined with swallowing training for poststroke dysphagia: a meta-analysis of randomised controlled trials by Ling Xin Li and Kai Deng in Acupuncture in Medicine</p
AIM817709_Supplemental_material_SP5 – Supplemental material for Acupuncture combined with swallowing training for poststroke dysphagia: a meta-analysis of randomised controlled trials
No full textSupplemental material, AIM817709_Supplemental_material_SP5 for Acupuncture combined with swallowing training for poststroke dysphagia: a meta-analysis of randomised controlled trials by Ling Xin Li and Kai Deng in Acupuncture in Medicine</p
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