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Tail bounds for occupancy and the satisfiability threshold conjecture

Anil Kamath, Rajeev Motwani, Krishna Palem, Paul Spirakis
1995 Random structures & algorithms (Print)  
Our motivating application is the following well-known conjecture on threshold phenomenon for the satisfiability problem.  ...  We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis.  ...  Acknowledgements We are grateful to Svante Janson and Joel Spencer for technical discussions regarding occupancy bounds in general, and for valuable help in the proof of Occupancy Bound 2.  ... 
doi:10.1002/rsa.3240070105 fatcat:norvetkdnzfnxppgptdmofglpm

Tail bounds for occupancy and the satisfiability threshold conjecture

A. Kamath, R. Motwani, K. Palem, P. Spirakis
Proceedings 35th Annual Symposium on Foundations of Computer Science  
Our motivating application is the following well-known conjecture on threshold phenomenon for the satisfiability problem.  ...  We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis.  ...  Acknowledgements We are grateful to Svante Janson and Joel Spencer for technical discussions regarding occupancy bounds in general, and for valuable help in the proof of Occupancy Bound 2.  ... 
doi:10.1109/sfcs.1994.365732 dblp:conf/focs/KamathMPS94 fatcat:qwwlqc3j6za5fn3izup6p7iy7m

Page 1196 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
, Paul (GR-PATR-CT; Patras) Tail bounds for occupancy and the satisfiability threshold conjecture.  ...  The proof uses the tail bounds mentioned above to give an upper bound on the mean of the reciprocal of the number of satisfying truth assignments for y, given that the all true assignment is satisfying  ... 

Balls and Bins: A Study in Negative Dependence

Devdatt P. Dubhashi, Desh Ranjan
1996 BRICS Report Series  
<br />For i in [n], let Bi be the random variable denoting the number of balls in the ith bin. We will often refer to these variables as occupancy numbers.  ...  bounds which are usually derived under the assumption of independence.  ...  Acknowledgements We would like to thank Thomas Lauer and Torben Hagerup for bringing the non-triviality of the problem to our attention and Shiva Chaudhuri, Torben Hagerup and Kurt Mehlhorn for valuable  ... 
doi:10.7146/brics.v3i25.20006 fatcat:inkkk5p7yvc5flwrjztdrfg74q

Balls and bins: A study in negative dependence

Devdatt Dubhashi, Desh Ranjan
1998 Random structures & algorithms (Print)  
Acknowledgements We would like to thank Thomas Lauer and Torben Hagerup for bringing the non-triviality of the problem to our attention and Shiva Chaudhuri, Torben Hagerup and Kurt Mehlhorn for valuable  ...  We are grateful to Colin McDiarmid for reading a previous version of this paper and for many technical remarks and suggestions, including the short proof of the Zero-One Lemma for (−A)..  ...  The rest of the proof is unchanged, and gives the upper tail bound. For the lower tail, we apply the same argument to the variables b i − X i , where b i is an upper bound on the variable X i .  ... 
doi:10.1002/(sici)1098-2418(199809)13:2<99::aid-rsa1>3.0.co;2-m fatcat:227izutacfabxiqegyyp5e2v54

On the classical complexity of sampling from quantum interference of indistinguishable bosons [article]

Valery Shchesnovich
2021 arXiv   pre-print
Lett. 123, 250503 (2019), are usually carried out on a small interferometer, much smaller than the size necessary for the no-collision regime.  ...  There seems to be a scalability issue to the necessary number of bosons on the linear optical platforms and the experiments, such as the recent Boson Sampling with 20 photons on 60-port interferometer  ...  but not necessary bounds on the tails of the distribution.  ... 
arXiv:1904.02013v5 fatcat:gvulp52dufamncrfyvnagbu3rm

Page 5240 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Anil Kamath, Rajeev Motwani, Krishna Palem and Paul Spi- rakis, Tail bounds for occupancy and the satisfiability threshold conjecture (592-603); Andres Albanese, Johannes Blémer, Jeff Edmonds, Michael  ...  dense graphs (24-35); Mario Szegedy, A note on the @ number of Lovasz and the generalized Delsarte bound (36-39); Jeffrey Jackson, An efficient membership-query algorithm for learning DNF with respect  ... 

A Statistical Study of Loss-Delay Tradeoff for RED Queues

H. Yousefi'zadeh, A. Habibi, Xiaolong Li, H. Jafarkhani, C. Bauer
2012 IEEE Transactions on Communications  
Aside from the introduction of many new schemes, the use of TCP-based AQM schemes and in specific RED is anticipated to continue in foreseeable future as the de-facto standard of network congestion control  ...  We discuss the convergence characteristics of our solution and investigate its low complexity characteristics.  ...  The value of q t is then compared to two thresholds, a minimum threshold q min and a maximum threshold q max .  ... 
doi:10.1109/tcomm.2012.050812.100733 fatcat:a2ciyvkcxnhzvcxiznxqrubygy

Evolutionary algorithms for continuous-space optimisation

Alexandru Agapie, Mircea Agapie, Gheorghita Zbaganu
2013 International Journal of Systems Science  
For the hitting-time of an arbitrary target zone, we provide lower and upper bounds, as well as an asymptotic limit.  ...  We analyze from this viewpoint the (1+1)EA on the inclined plane fitness landscape, and derive a closed-form expression for the probability of occupancy of an arbitrary target zone, at an arbitrary iteration  ...  Acknowledgments The first author acknowledges support from DAAD (German Academic Exchange Service), study and research grant A/10/05445, and from CNCSIS-UEFISCSU, project number 844 PNII -IDEI, code 1778  ... 
doi:10.1080/00207721.2011.605963 fatcat:q66wpt7bjjchdkx3tlw7awbizq

Oblivious AQM and nash equilibria

Debojyoti Dutta, Ashish Goel, John Heidemann
2002 Computer communication review  
equilibrium, and motivating the need for equilibriaaware protocols.  ...  We show that drop-tail and RED do not impose Nash equilibria. We modify RED slightly to obtain an oblivious scheme, VLRED, that imposes a Nash equilibrium, but is not efficient.  ...  We have the following observation: Theorem 5: Any oblivious router mechanism with average bounded buffer occupancy cannot in MAC. Proof: Suppose an oblivious strategy satisfying the above is in MAC.  ... 
doi:10.1145/571697.571709 fatcat:efygr5or2fhexinue25af27f5i

Polluted Bootstrap Percolation with Threshold Two in All Dimensions [article]

Janko Gravner, Alexander E. Holroyd
2017 arXiv   pre-print
Our result partially resolves a conjecture of Morris, and contrasts with the d=2 case, where Gravner and McDonald proved that the critical parameter is q/p^2.  ...  On the cubic lattice Z^d of dimension d>=3 with threshold r=2, we prove that the final density of occupied sites converges to 1 as p and q both approach 0, regardless of their relative scaling.  ...  Janko Gravner was partially supported by the NSF grant DMS-1513340, Simons Foundation Award #281309, and the Republic of Slovenias Ministry of Science program P1-285.  ... 
arXiv:1705.01652v1 fatcat:juxiiifkifcolnxihfow6x55lq

Single α-particle orbits and Bose-Einstein condensation in 12C

T. Yamada, P. Schuck
2005 European Physical Journal A  
orbits as well as the occupation numbers are discussed in detail in comparison with those for the 0^+_1 and 2^+_1 states together with the 1^-_1 and 3^-_1 states.  ...  The α-bosonic properties such as single-α orbits and occupation numbers in J^π=0^+, 2^+, 1^- and 3^- states of ^12C around thethreshold are investigated with the semi-microscopic 3α cluster model.  ...  Suzuki, and A. Tohsaki.  ... 
doi:10.1140/epja/i2005-10168-1 fatcat:exqluej2sfch7i2q2ltztz3hge

Reconfiguration of the proteasome during chaperone-mediated assembly

Soyeon Park, Xueming Li, Ho Min Kim, Chingakham Ranjit Singh, Geng Tian, Martin A. Hoyt, Scott Lovell, Kevin P. Battaile, Michal Zolkiewski, Philip Coffino, Jeroen Roelofs, Yifan Cheng (+1 others)
2013 Nature  
Chen, and Finley laboratory members for suggestions, and C. Mann for antibodies.  ...  This work was supported in part by grants from NIH (5R01GM098672 and 1S10RR026814-01), UCSF Program for Breakthrough Biomedical Research (New Technology Award) to YC; the Johnson Cancer Research Center  ...  Unexpectedly, synthetic Rpt tail peptides bound α pockets with poor specificity, except for Rpt6, which uniquely bound the α2/α3 pocket.  ... 
doi:10.1038/nature12123 pmid:23644457 pmcid:PMC3687086 fatcat:ttqhhdy6xja2vnokm7dfrksqiq

Approximate counting and sampling via local central limit theorems [article]

Vishesh Jain, Will Perkins, Ashwin Sah, Mehtaab Sawhney
2021 arXiv   pre-print
an FPTAS for the number of independent sets of size k ≤ (1-δ) α_c(Δ) n, where α_c(Δ) is the NP-hardness threshold for this problem.  ...  We give an FPTAS for computing the number of matchings of size k in a graph G of maximum degree Δ on n vertices, for all k ≤ (1-δ)m^*(G), where δ>0 is fixed and m^*(G) is the matching number of G, and  ...  Recently, Davies and Perkins [14] showed an analogous threshold for counting independent sets of a given size in bounded degree graphs.  ... 
arXiv:2108.01161v1 fatcat:o4vpapffgvb3xj3hj433uzugha

α+α+tcluster structures andC12(02+)-analog states inB11

Taiichi Yamada, Yasuro Funaki
2010 Physical Review C  
We indicate that the 12.56-MeV state (J^π=1/2^+_2) just above the α+α+t threshold observed in the ^7Li(^7Li,^11B^*)t reaction etc. is of the dilute-cluster-gas-like, and is a strong candidate for the Hoyle-analogue  ...  Full levels up to the 3/2^-_3 and 1/2^+_2 states around the α+α+t threshold (E_x=11.1 MeV) are reproduced consistently with the experimental energy levels.  ...  ACKNOWLEDGMENTS The present authors thank to H. Horiuchi, K. Ikeda, G. Röpke, P. Schuck, and A. Tohaski for valuable discussions and encouragements.  ... 
doi:10.1103/physrevc.82.064315 fatcat:tqodz3lva5bklc6r2a4vduacxm
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