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Low-degree test with polynomially small error

Dana Moshkovitz
2016 Computational Complexity  
We show that the Sliding Scale Conjecture in PCP, namely the conjecture that there are PCP verifiers whose error is exponentially small in their randomness, would follow from a derandomization of our parallel  ...  This is known as low degree testing, and is the core of the algebraic approach to construction of PCP.  ...  Acknowledgements This paper originally appeared as "An Approach To The Sliding Scale Conjecture Via Parallel Repetition For Low Degree Testing" [31] .  ... 
doi:10.1007/s00037-016-0149-4 fatcat:sgzrdmg7hzfmdfh323r54n7mhq

The tale of the PCP theorem

Dana Moshkovitz
2012 XRDS Crossroads The ACM Magazine for Students  
One could a-priori hope for polynomially small error (the "projection games conjecture"/"sliding scale conjecture").  ...  In 2002 Khot put forward the Unique Games Conjecture (UGC), which postulates the existence of a certain special PCP to be explained below.  ... 
doi:10.1145/2090276.2090286 fatcat:aim67yzrxrhsnjfs72dkfomzae

The Projection Games Conjecture and the NP-Hardness of ln n-Approximating Set-Cover

Dana Moshkovitz
2015 Theory of Computing  
In the conference version of this paper, the SET-COVER result was conditioned on a conjecture we call "The Projection Games Conjecture" (PGC), a strengthening of the Sliding A preliminary version of this  ...  We establish a tight NP-hardness result for approximating the SET-COVER problem based on a strong PCP theorem.  ...  "Sliding scale" refers to the idea that the error can be decreased as we increase the alphabet size.  ... 
doi:10.4086/toc.2015.v011a007 dblp:journals/toc/Moshkovitz15 fatcat:sg65cikhdre7vdecuqrsmmvjqi

The Projection Games Conjecture and the NP-Hardness of ln n-Approximating Set-Cover [chapter]

Dana Moshkovitz
2012 Lecture Notes in Computer Science  
We suggest the research agenda of establishing new hardness of approximation results based on the "projection games conjecture", i.e., an instantiation of the Sliding Scale Conjecture of Bellare, Goldwasser  ...  Specifically, we show that under the projection games conjecture (in fact, under a quantitative version of the conjecture that is only slightly beyond the reach of current techniques), it is N P-hard to  ...  The projection games conjecture is in fact the Sliding Scale Conjecture of Bellare, Goldwasser, Lund and Russell [BGLR93] instantiated for projection games.  ... 
doi:10.1007/978-3-642-32512-0_24 fatcat:6hrj355lyvadfn7hfnnfplgkju

Polynomially Low Error PCPs with polyloglog n Queries via Modular Composition

Irit Dinur, Prahladh Harsha, Guy Kindler
2015 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15  
The ultimate goal, in this direction, would be to prove polynomial hardness for CSPs with constant arity and polynomial alphabet size (aka the sliding scale conjecture for inverse polynomial soundness  ...  We show that every language in NP has a PCP verifier that tosses O( n) random coins, has perfect completeness, and a soundness error of at most 1/poly(n), while making at most O(poly n) queries into a  ...  [BGLR93] as the "sliding scale" conjecture. 1 One may assume that every local predicate ϕ is satisfiable. Otherwise the question of "x ?  ... 
doi:10.1145/2746539.2746630 dblp:conf/stoc/DinurHK15 fatcat:uyhom4teove3hjqr3fgovnoin4

Disruption of Core Planar Cell Polarity Signaling Regulates Renal Tubule Morphogenesis but Is Not Cystogenic

Koshi Kunimoto, Roy D. Bayly, Eszter K. Vladar, Tyson Vonderfecht, Anna-Rachel Gallagher, Jeffrey D. Axelrod
2017 Current Biology  
Indeed, PCP signaling that is normally downregulated once development is completed is retained in cystic adult kidneys.  ...  Core planar cell polarity (PCP) signaling controls OCD and CE in other contexts, leading to the hypothesis that disruption of PCP signaling interferes with CE and/or OCD to produce PKD.  ...  However, we find that contrary to prior conjecture, not only is disruption of PCP signaling not required for cystogenesis, but PCP signaling is retained in adult cysts when it would otherwise be attenuated  ... 
doi:10.1016/j.cub.2017.09.011 pmid:29033332 pmcid:PMC5683414 fatcat:nlebvufbtng2vomukb24afxuju

Nearly Tight Bounds for Robust Proper Learning of Halfspaces with a Margin [article]

Ilias Diakonikolas and Daniel M. Kane and Pasin Manurangsi
2019 arXiv   pre-print
We study the problem of properly learning large margin halfspaces in the agnostic PAC model.  ...  On the positive side, we give an α = 1.01-approximate proper learner that uses O(1/(ϵ^2γ^2)) samples (which is optimal) and runs in time poly(d/ϵ) · 2^Õ(1/γ^2).  ...  Theorem 3.8 (Dinur-Harsha-Kindler PCP [DHK15]). n −Ω(1) -Gap-polyloglog(n)-CSP is NP-hard. Finally, we state the Sliding Scale Conjecture (SSC) of Bellare et al.  ... 
arXiv:1908.11335v1 fatcat:c2vthrp6azgo3ovtgfjlrgtb7y

ETH-Hardness of Approximating 2-CSPs and Directed Steiner Network

Irit Dinur, Pasin Manurangsi, Marc Herbstritt
2018 Innovations in Theoretical Computer Science  
As a special case of the so-called Sliding Scale Conjecture, Bellare et al. [5] suggested that the answer to this question might be positive.  ...  Alas, despite many efforts by researchers to resolve this conjecture (e.g. [39, 4, 20, 21, 35] ), it still remains open to this day.  ...  Note that, while this latest result comes close to the polynomial sliding scale conjecture, it does not quite resolve the conjecture yet.  ... 
doi:10.4230/lipics.itcs.2018.36 dblp:conf/innovations/DinurM18 fatcat:vduqver5rzcbjn5qkmmlg53noe

Primary decidual zone formation requires Scribble for pregnancy success in mice

Jia Yuan, Shizu Aikawa, Wenbo Deng, Amanda Bartos, Gerd Walz, Florian Grahammer, Tobias B. Huber, Xiaofei Sun, Sudhansu K. Dey
2019 Nature Communications  
Scribble (Scrib) is a scaffold protein with multifunctional roles in PCP, tight junction and Hippo signaling.  ...  This study shows that Scrib is expressed in stromal cells around the implantation chamber following implantation.  ...  Primary antibodies listed in Supplementary Table 2 were used. β-Actin was used as a loading control.  ... 
doi:10.1038/s41467-019-13489-4 pmid:31780662 pmcid:PMC6882879 fatcat:epsxufe43rarphjg2t7p3xyw6u

Variable Selection is Hard [article]

Dean Foster, Howard Karloff, Justin Thaler
2014 arXiv   pre-print
We prove a similar result for a statistical version of the problem in which the data are corrupted by noise.  ...  SAT ∈ PCP 1, [O(log(N )), 2] poly(1/ ) , where = 2 −Ω(log 1− In [14] , Moshkovitz formulates a slight strengthening of the sliding scale conjecture that she calls the Projection Games Conjecture (PGC)  ...  In words, the sliding scale conjecture asserts that SAT has a polynomial-length PCP in which the verifier makes two queries to the proof (note that each query reads an entire symbol from the alphabet Σ  ... 
arXiv:1412.4832v1 fatcat:m2novipbpjcnfh2phnjkvgayxu

Semi-supervised classification with hybrid generative/discriminative methods

Gregory Druck, Chris Pal, Andrew McCallum, Xiaojin Zhu
2007 Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '07  
While prominent semi-supervised learning methods assume low density regions between classes or are subject to generative modeling assumptions, we conjecture that hybrid generative/discriminative methods  ...  allow semi-supervised learning in the presence of strongly overlapping classes and reduce the risk of modeling structure in the unlabeled data that is irrelevant for the specific classification task of  ...  A practical concern is that each component and its gradient may be different in scale.  ... 
doi:10.1145/1281192.1281225 dblp:conf/kdd/DruckPMZ07 fatcat:gqgtz76pnvbrtmb5lm55rrdb2y

Almost-Polynomial Ratio ETH-Hardness of Approximating Densest k-Subgraph [article]

Pasin Manurangsi
2017 arXiv   pre-print
In addition, our result has "perfect completeness", meaning that we prove that it is ETH-hard to even distinguish between the case in which G contains a k-clique and the case in which every induced k-subgraph  ...  of G has density at most 1/n^-1/( n)^c in polynomial time.  ...  In particular, to achieve a polynomial ratio hardness for DkS, it is plausible that one has to prove a long-standing conjecture called the sliding scale conjecture (SSC) [BGLR93] .  ... 
arXiv:1611.05991v2 fatcat:hb7gjbokore37ktl5hc54kebyi

A Framework for Private Matrix Analysis in Sliding Window Model

Jalaj Upadhyay, Sarvagya Upadhyay
2021 International Conference on Machine Learning  
We show the existing framework in the non-private setting is not robust to noise required for privacy.  ...  Prior to our work, no such result was known for sparse and non-negative differentially private PCA even in the static data setting.  ...  The situation in the sliding window model is more complicated, but we believe it is possible to achieve a matching upper bound. In view of this, we conjecture the following. Conjecture 1.  ... 
dblp:conf/icml/UpadhyayU21 fatcat:vir4dnj7hrgcdpo2h2lm4gwmni

Fixed and live visualization of RNAs in Drosophila oocytes and embryos

Evan K. Abbaszadeh, Elizabeth R. Gavis
2016 Methods  
RNA labeling for detection in live cells.  ...  This review presents two methods, single molecule fluorescence in situ hybridization for high resolution quantitative RNA detection in fixed Drosophila oocytes and embryos and genetically encoded fluorescent  ...  To our knowledge, MCP-FP transgenes currently in use in Drosophila derive from pG14-MS2-GFP [25] and PCP-FP transgenes from phage-ubc-nls-ha-pcp-gfp [40] .  ... 
doi:10.1016/j.ymeth.2016.01.018 pmid:26827935 pmcid:PMC4808400 fatcat:xqenntgej5awjobgo2zz6xuxfu

Long-term behavioral and neurodegenerative effects of perinatal phencyclidine administration: implications for schizophrenia

C Wang, J McInnis, M Ross-Sanchez, P Shinnick-Gallagher, J.L Wiley, K.M Johnson
2001 Neuroscience  
An increase in the NMDA receptor NR1 subunit mRNA was also observed in the cortex.  ...  Phencyclidine treatment resulted in a substantial increase in fragmented DNA in the frontal and olfactory cortices consistent with neurodegeneration by an apoptotic mechanism.  ...  TUNEL-positive meningeal cells can be seen in all groups. TUNEL-positive cells are remarkably more numerous in the vehicle/PCP (C) group. Scale bar = 100 Wm.  ... 
doi:10.1016/s0306-4522(01)00384-0 pmid:11720778 fatcat:h7osdjqrrzba3gshnqk7rzihxu
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