Probabilistically checkable proofs with zero knowledge

We continue the study of the trade‐off between the length of probabilistically checkable proofs (PCPs) and their query complexity, establishing the following main results (which refer to proofs of satisfiability of circuits of size n): 1. We present PCPs of length $\exp(o(\log\log n)^2)\cdot n$ that can be verified by making $o(\log\log n)$ Boolean queries. 2. For every \epsilon>0, we present PCPs of length $\exp(\log^\epsilon n)\cdot n$ that can be verified by making a constant number of Boolean queries. In both cases, false assertions are rejected with constant probability (which may be set to be arbitrarily close to 1). The multiplicative overhead on the length of the proof, introduced by transforming a proof into a probabilistically checkable one, is just quasi polylogarithmic in the first case (of query complexity $o(\log\log n)$), and is $2^{(\log n)^\epsilon}$, for any $\epsilon > 0$, in the second case (of constant query complexity). Our techniques include the introduction of a new variant of PCPs that we call “robust PCPs of proximity.” These new PCPs facilitate proof composition, which is a central ingredient in the construction of PCP systems. (A related notion and its composition properties were discovered independently by Dinur and Reingold.) Our main technical contribution is a construction of a “length‐efficient” robust PCP of proximity. While the new construction uses many of the standard techniques used in PCP constructions, it does differ from previous constructions in fundamental ways, and in particular does not use the “parallelization” step of Arora et al. [J. ACM, 45 (1998), pp. 501–555]. The alternative approach may be of independent interest. We also obtain analogous quantitative results for locally testable codes. In addition, we introduce a relaxed notion of locally decodable codes and present such codes mapping k information bits to codewords of length $k^{1+\epsilon}$ for any $\epsilon>0$.

The "direct-product code" of a function $f$ gives its values on all $k$-tuples $(f(x_1),\dots, f(x_k))$. This basic construct underlies "hardness amplification" in cryptography, circuit complexity, and probabilistically checkable proofs (PCPs). Goldreich and Safra [SIAM J. Comput., 29 (2000), pp. 1132--1154] pioneered its local testing and its PCP application. A recent result by Dinur and Goldenberg [Proceedings of the Forty-Ninth Annual IEEE Symposium on Foundations of Computer Science, 2008, pp. 613--622] enabled for the first time testing proximity to this important code in the "list-decoding" regime. In particular, they give a $2$-query test which works for polynomially small success probability $1/k^{\alpha}$ and show that no such test works below success probability $1/k$. Our main result is a $3$-query test which works for exponentially small success probability $\exp({-k^{\alpha}})$. Our techniques (based on recent simplified decoding algorithms for the same code [R. Impagliazzo et al., Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, 2008, pp. 579--588]) also allow us to considerably simplify the analysis of the 2-query test of [Proceedings of the Forty-Ninth Annual IEEE Symposium on Foundations of Computer Science, 2008, pp. 613--622]. We then show how to derandomize their test, achieving a code of polynomial rate, independent of $k$, and success probability $1/k^{\alpha}$. Finally, we show the applicability of the new tests to PCPs. Starting with a 2-query PCP with a projection property over an alphabet $\Sigma$ and with soundness error $1-\delta$, Rao [Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, 2008, pp. 1--10] (building on Raz's ($k$-fold) parallel repetition theorem [R. Raz, SIAM J. Comput., 27 (1998), pp. 763--803] and Holenstein's proof [T. Holenstein, Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, 2007, pp. 411--419] obtains a new 2-query PCP over the alphabet $\Sigma^k$ with soundness error $\exp(-\delta^2 k)$. Our techniques yield a 2-query PCP with soundness error $\exp(-\delta \sqrt{k})$. Our PCP construction turns out to be essentially the same as the miss-match proof system defined and analyzed by Feige and Kilian [SIAM J. Comput., 30 (2000), pp. 324--346] but with simpler analysis and exponentially better soundness error.

Philosophical PerspectivesEarly View ORIGINAL ARTICLE Modal Pluralism and Higher-Order Logic Justin Clarke-Doane, Corresponding Author Justin Clarke-Doane [email protected] Columbia University & Institute for Advanced Study, Princeton Correspondence Justin Clarke-Doane, Columbia University & Institute for Advanced Study, Princeton. Email: [email protected] William McCarthy, Columbia University. Email: [email protected]Search for more papers by this authorWilliam McCarthy, Corresponding Author William McCarthy [email protected] Columbia University Correspondence Justin Clarke-Doane, Columbia University & Institute for Advanced Study, Princeton. Email: [email protected] William McCarthy, Columbia University. Email: [email protected]Search for more papers by this author Justin Clarke-Doane, Corresponding Author Justin Clarke-Doane [email protected] Columbia University & Institute for Advanced Study, Princeton Correspondence Justin Clarke-Doane, Columbia University & Institute for Advanced Study, Princeton. Email: [email protected] William McCarthy, Columbia University. Email: [email protected]Search for more papers by this authorWilliam McCarthy, Corresponding Author William McCarthy [email protected] Columbia University Correspondence Justin Clarke-Doane, Columbia University & Institute for Advanced Study, Princeton. Email: [email protected] William McCarthy, Columbia University. Email: [email protected]Search for more papers by this author First published: 02 March 2023 https://doi.org/10.1111/phpe.12165Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Early ViewOnline Version of Record before inclusion in an issue RelatedInformation

Fluorescence imaging has become an indispensable technique in cancer research because it can reveal informative molecular, cellular, anatomical, and functional insights. Development of advanced fluorescent probes with superior sensitivity and biological selectivity for fluorescence imaging is thus imperative. To move forward in this direction, we developed an easy self-assembly method for fabricating aptamer- anchored rubrene-loaded organic fluorescent nanoprobes. The aptamer-modified organic nanoprobes integrated the best features of the organic light-emitting materials and the aptamers, thus endowing them with excellent cell-targeting capability, high stability, and good biocompatibility. By using this general method, a variety of biocompatible and highly bright organic fluorescent nanoprobes based on novel organic light-emitting materials with specific recognition could be easily constructed for real-time biosensing and long-term biomedical imaging. © 2019 Chinese Chemical Society.

The PCP (i.e., Probabilistically Checkable Proofs) Theorem [8, 7, 22, 5, 4] states that any mathematical proof can be converted to a format that can be checked by a veri er making only a constant number of queries to the proof. The veri er picks the queries in a randomized way and might err with low probability.

Science as a Craft Industry

During the first two weeks of December of 2005, NATO sponsored an Advanced Study Institute (ASI) In Istanbul, Turkey. Part of this ASI involved a case study of a terrorist attack, where a chemical was assumed to be dumped into Sulunger Lake in Turkey. This chapter documents the response developed by the ASI participants to this scenario, in terms of hydrodynamic transport, ecosystem effects, and decision making.

"Baxter, Prof. Rodney James, (born 8 Feb. 1940), Professor in the Department of Theoretical Physics, Institute of Advanced Studies, and in the School of Mathematical Sciences, 1981–2002, Visiting Fellow in the School of Mathematical Sciences, since 2002, Australian National University" published on by Oxford University Press.

November 01 2018 Leon Battista Alberti and His Somniatic Troubles Mark Jarzombek Mark Jarzombek Mark Jarzombek is Professor of History and Theory of Architecture at the MIT School of Architecture and Planning. He has an architecture diploma from the ETH and a PhD from the History, Theory and Criticism of Architecture and Art program at MIT. He has published widely on numerous topics and has been a fellow at CASVA, the Institute for Advanced Study, the Canadian Center for Architecture, and the Sterling and Francine Clark Art Institute. His books include the textbook A Global History of Architecture (Wiley Press, 2006) and The Architecture of First Societies: A Global Perspective (Wiley Press, 2013). Search for other works by this author on: This Site Google Scholar Author and Article Information Mark Jarzombek Mark Jarzombek is Professor of History and Theory of Architecture at the MIT School of Architecture and Planning. He has an architecture diploma from the ETH and a PhD from the History, Theory and Criticism of Architecture and Art program at MIT. He has published widely on numerous topics and has been a fellow at CASVA, the Institute for Advanced Study, the Canadian Center for Architecture, and the Sterling and Francine Clark Art Institute. His books include the textbook A Global History of Architecture (Wiley Press, 2006) and The Architecture of First Societies: A Global Perspective (Wiley Press, 2013). Online Issn: 2572-7338 Print Issn: 1091-711X © 2015 Mark Jarzombek2015Mark Jarzombek Thresholds (2015) (43): 102–309. https://doi.org/10.1162/thld_a_00060 Cite Icon Cite Permissions Share Icon Share Facebook Twitter LinkedIn MailTo Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Search Site Citation Mark Jarzombek; Leon Battista Alberti and His Somniatic Troubles. Thresholds 2015; (43): 102–309. doi: https://doi.org/10.1162/thld_a_00060 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsThresholds Search Advanced Search This content is only available as a PDF. © 2015 Mark Jarzombek2015Mark Jarzombek Article PDF first page preview Close Modal You do not currently have access to this content.

The Justiciarship in England 1066–1232. By Francis West, Professorial Fellow, Institute of Advanced Studies, Australian National University. Cambridge Studies in Medieval Life and Thought, N.S., Vol. 12. [Cambridge: at the University Press. 1966. ix, 271 and (bibliography and index) 35 pp. 55s. net.] - Volume 25 Issue 1

The SciencesVolume 22, Issue 9 p. 13-18 In Abstract Terrain Rick Norwood, Rick Norwood Rick Norwood, assistant professor of mathematics at William Paterson College, in New Jersey, recently completed a year at the Institute for Advanced Study, in Princeton. This article originally appeared, in somewhat different form, in The Wilson Quarterly.Search for more papers by this author Rick Norwood, Rick Norwood Rick Norwood, assistant professor of mathematics at William Paterson College, in New Jersey, recently completed a year at the Institute for Advanced Study, in Princeton. This article originally appeared, in somewhat different form, in The Wilson Quarterly.Search for more papers by this author First published: December 1982 https://doi.org/10.1002/j.2326-1951.1982.tb02122.x AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume22, Issue9December 1982Pages 13-18 RelatedInformation

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 43:179-190 (2010) - DOI: https://doi.org/10.3354/cr00909 Trends in temperature and precipitation on the Tibetan Plateau, 1961–2005 Heli Lu1,2,*, Guifang Liu1 1Institute of Natural Resources and Environmental Science, and College of Environment and Planning, Henan University, Kaifeng 475004, China 2United Nations University - Institute of Advanced Studies, Yokohama 220-8502, Japan *Email: cluheli@gmail.com ABSTRACT: We studied the basic characteristics of temperature and precipitation in different climatic zones of the Tibetan Plateau (TP) from 1961–2005, through statistical and spatial analysis. Over the past 45 yr, annual temperature in the TP increased at a rate of 0.265°C decade–1. The rate of temperature increase in winter was double that of spring in almost all zones and the rate of annual temperature increase was demonstrably higher during 1980–2005 than during 1961–1980 and 1961–2005, suggesting that the rate of warming is accelerating. Annual precipitation showed a slight increase (8.21 mm decade–1) across the whole TP. Short (2 to 4 yr), middle (5 to 8 yr), and long (>10 yr) precipitation cycles were found at 32, 11, and 6 stations, respectively. Empirical Orthogonal Function (EOF) analysis revealed different precipitation cycles between the northern and the southern TP, with the boundary along 33°N. For the period 1961–2005, 46 stations showed a warming-wetting trend; the number of stations showing this trend for 1980–2005 was 34% higher than for 1961–1980, suggesting that a warming-wetting trend will dominate the TP in the future. KEY WORDS: Tibetan Plateau · Basic characteristics · Climatic zones Full text in pdf format PreviousNextCite this article as: Lu H, Liu G (2010) Trends in temperature and precipitation on the Tibetan Plateau, 1961–2005. Clim Res 43:179-190. https://doi.org/10.3354/cr00909 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 43, No. 3. Online publication date: October 19, 2010 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2010 Inter-Research.

Competitive Intelligence ReviewVolume 8, Issue 2 p. 90-92 Cl Perspectives Hakluyt & Company: Fitzroy mocleon's last venture Stevan Dedijer, Stevan Dedijer Stevan Dedijer, a SCIP Meritorious Award winner, is one of the founders of modern economic and business intelligence. He is the author of more than 150 papers and reports in the fields of intelligence, security, and “social intelligence.” He was founder and director of the Research Policy Institute at Lund University in Sweden, where he also taught intelligence and security courses, was a Fellow at the Institute of Advanced Studies in Social Sciences in Palo Alto, and has served as a consultant to numerous corporations, governments, and international bodies. He can be reached at Vicka Lovrina 4, Dubrovnik 20000, Croatia; Tel. & Fax: 385-20-411-613.Search for more papers by this author Stevan Dedijer, Stevan Dedijer Stevan Dedijer, a SCIP Meritorious Award winner, is one of the founders of modern economic and business intelligence. He is the author of more than 150 papers and reports in the fields of intelligence, security, and “social intelligence.” He was founder and director of the Research Policy Institute at Lund University in Sweden, where he also taught intelligence and security courses, was a Fellow at the Institute of Advanced Studies in Social Sciences in Palo Alto, and has served as a consultant to numerous corporations, governments, and international bodies. He can be reached at Vicka Lovrina 4, Dubrovnik 20000, Croatia; Tel. & Fax: 385-20-411-613.Search for more papers by this author First published: 16 October 2006 https://doi.org/10.1002/cir.3880080216Citations: 1 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume8, Issue2Summer 1997Pages 90-92 RelatedInformation

After the end of his term as justice, Dieter Grimm moved from Karlsruhe to Berlin where he joined the Faculty of Law of Humboldt University and became permanent fellow and a year later rector of the Wissenschaftskolleg, Institute for Advanced Study. This chapter is devoted to the six years where he directed the Kolleg, the selection of forty fellows from all disciplines and continents for each academic year, the priorities that he set, the recruitments of legal scholars, and the role and impact of legal science in general among the various disciplines.

The Second Workshop on the “Standardisation of Chinese Physics Terminology” was held in Taiwan from 23 to 26 November 2012. It was organised by the Taiwan National Academy of Educational Research, together with the Physical Society of Republic of China (Taiwan), National Taiwan University, China National Committee for Terms in Sciences and Technologies, and the Institute of Advanced Studies (IAS) at Nanyang Technological University, Singapore. This series of workshops was first organized by Institute of Advanced Studies, Singapore in 2011.