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On the Lattice Smoothing Parameter Problem [article]

Kai-Min Chung, Daniel Dadush, Feng-Hao Liu, Chris Peikert
2014 arXiv   pre-print
It plays a central role in the best known worst-case/average-case reductions for lattice problems, a wealth of lattice-based cryptographic constructions, and (implicitly) the tightest known transference  ...  the GapSVP problem.  ...  in NPcoNP for factors γ ≥ c √ n [AR04] , as well as the results for approximating the Covering Radius Problem, whose 2-approximation is in AM but is in coAM only for γ ≥ c n/ log n, and in NPcoNP  ... 
arXiv:1412.7979v1 fatcat:qsc5bo43ercfrhjboyt3fpmrni

On the Lattice Smoothing Parameter Problem

Kai-Min Chung, Daniel Dadush, Feng-Hao Liu, Chris Peikert
2013 2013 IEEE Conference on Computational Complexity  
It plays a central role in the best known worst-case/average-case reductions for lattice problems, a wealth of lattice-based cryptographic constructions, and (implicitly) the tightest known transference  ...  More formally, for an approximation factor γ ≥ 1 and some 0 < ε < 1 (which may both be functions of the lattice dimension n), we define γ-GapSPP ε to be the promise problem in which YES instances are lattices  ...  in NPcoNP for factors γ ≥ c √ n [AR04] , as well as the results for approximating the Covering Radius Problem, whose 2-approximation is in AM but is in coAM only for γ ≥ c n/ log n, and in NPcoNP  ... 
doi:10.1109/ccc.2013.31 dblp:conf/coco/ChungDLP13 fatcat:rjb2enmta5eubacj75rd3t74gi

A Subexponential Algorithm for ARRIVAL [article]

Bernd Gärtner, Sebastian Haslebacher, Hung P. Hoang
2021 arXiv   pre-print
The problem is in NPcoNP but not known to be in P. The currently best algorithms have runtime 2^Θ(n) where n is the number of vertices.  ...  The ARRIVAL problem is to decide the fate of a train moving along the edges of a directed graph, according to a simple (deterministic) pseudorandom walk.  ...  ARRIVAL is arguably the simplest problem in NPcoNP that is not known to be in P.  ... 
arXiv:2102.06427v3 fatcat:zajvz7drovauppe3w2gt5u5u2u

Preparation of Cobalt Nanoparticles

Aliya F. Khusnuriyalova, Maria Caporali, Evamarie Hey-Hawkins, Oleg G. Sinyashin, Dmitry G. Yakhvarov
2021 European Journal of Inorganic Chemistry  
, and application of transition metal nanoparticles (NPs), which are widely used in physical, chemical, engineering, and biomedical processes.  ...  In this minireview, we summarise the most successful and most efficient methods for obtaining Co NPs, including chemical and physical aspects of their preparation.  ...  of RAS, and the testing of the catalytic activity has been done in Kazan Federal  ... 
doi:10.1002/ejic.202100367 fatcat:szwnrtnu5fg23p4d76tdnuoa34

Shrunk subspaces via operator Sinkhorn iteration [article]

Cole Franks, Tasuku Soma, Michel X. Goemans
2022 arXiv   pre-print
A recent breakthrough in Edmonds' problem showed that the noncommutative rank can be computed in deterministic polynomial time, and various algorithms for it were devised.  ...  Finding a shrunk subspace plays a key role in applications, such as separation in the Brascamp-Lieb polytope, one-parameter subgroups in the null-cone membership problem, and primal-dual algorithms for  ...  Membership in the rank-2 BL polytope is in NPcoNP. The idea of the first result is as follows.  ... 
arXiv:2207.08311v1 fatcat:xmqfmbmuorhntei6lueyiathda

Cobalt magnetic nanoparticles as theranostics: Conceivable or forgettable?

Claudia Petrarca, Anna Maria Poma, Giulia Vecchiotti, Giovanni Bernardini, Qiao Niu, Anna Giulia Cattaneo, Mario Di Gioacchino, Enrico Sabbioni
2020 Nanotechnology Reviews  
In our opinion, it would be worth to further exploit the potential of finely tunable properties of CoB NPs in in vivo systems in order to establish a systematic database of properties and effects suitable  ...  Nevertheless, experimental evidences documenting the in vivo toxicity of engineered CoB NPs remain very few.  ...  a capping agent for the synthesized nanoparticles [36] .  ... 
doi:10.1515/ntrev-2020-0111 fatcat:6afcyms62bdctc45wl4j63byse

How hard is it to approximate the Jones polynomial? [article]

Greg Kuperberg
2014 arXiv   pre-print
In this article, we show that any value-dependent approximation of the Jones polynomial at these non-lattice roots of unity is #P-hard.  ...  In our argument, the result follows fairly directly from the universality result and Aaronson's theorem that PostBQP = PP [arXiv:quant-ph/0412187].  ...  In fact, recognizing the unknot is in NP [18] , and in coNP assuming the generalized Riemann hypothesis [29] .  ... 
arXiv:0908.0512v2 fatcat:zhglvduc5rhallsqplqcyl2xfa

The Application of Nanosensors in Illicit Drugs Determination: A Review

Lawal Shuaibu, AbduRahman Abdul Audu, Kingsley John Igenepo
2021 Current Journal of Applied Science and Technology  
As highlighted in the in-depth review, the sensors are designed to utilize biological receptors with a transducer component to detect the analyte-biorecognition element interaction which resulted in producing  ...  The utilization of nanomaterials (NMs) to produce nanosensors for detecting drugs in a wide range of materials has attracted global attention.  ...  It is also used in the analysis of biomolecules used as capping and reducing agents in nanofabrication to reveal whether they are involved in synthesis or not [29, 30] .  ... 
doi:10.9734/cjast/2021/v40i2231477 fatcat:z4e4nshbizc6hncuivbxnrbnsm

Common equivalence and size after forgetting [article]

Paolo Liberatore
2021 arXiv   pre-print
Minimizing after forgetting is polynomial-time if the formula is also acyclic and variables cannot be introduced, NP-hard when they can.  ...  Both operations can be expressed in terms of common equivalence, a weakened version of equivalence. In turn, common equivalence can be expressed in terms of forgetting.  ...  Other subclasses are in Post's lattice [CHS07] .  ... 
arXiv:2006.11152v2 fatcat:uuwlko7iejavtp25zm6c6iuzv4

Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes [article]

Peter Bürgisser and Cole Franks and Ankit Garg and Rafael Oliveira and Michael Walter and Avi Wigderson
2019 arXiv   pre-print
This setting captures a diverse set of problems in different areas of computer science, mathematics, and physics.  ...  Our work points to intriguing open problems and suggests further research directions.  ...  [BCMW17] proved that the membership problem for ∆ is in NPcoNP.  ... 
arXiv:1910.12375v1 fatcat:qasr4soxk5gpdouftldqxjpcr4

Strategies for Improving the Functionality of Zeolitic Imidazolate Frameworks: Tailoring Nanoarchitectures for Functional Applications

Yusuf Valentino Kaneti, Saikat Dutta, Md. S. A. Hossain, Muhammad J. A. Shiddiky, Kuo-Lun Tung, Fa-Kuen Shieh, Chia-Kuang Tsung, Kevin C.-W. Wu, Yusuke Yamauchi
2017 Advanced Materials  
6 of ZIFs via the encapsulation of guest species (such as metal and metal oxide NPs and biomolecules) into ZIFs, 7 and hybridization with polymeric matrices to form mixed matrix membranes for industrial  ...  In this progress report, we aim to provide an overview of the extensive strategies which 5 have been developed to improve the functionality of ZIFs, including linker modifications, functional hybridization  ...  types of metal NPs due to their 16 interplay of electronic and lattice effects.  ... 
doi:10.1002/adma.201700213 pmid:28833624 fatcat:5b2gbniagvcw3pft2ucb5lgmmy

Catalyst overcoating engineering towards high-performance electrocatalysis

Qiang Liu, Marco Ranocchiari, Jeroen A. van Bokhoven
2022 Chemical Society Reviews  
The recent advances of applying surface overcoating engineering for designing high-performance electrocatalysts for application in sustainable energy-based electrocatalysis are reviewed.  ...  Fig. 17(a) TEM and (b) HRTEM images of SCEIN/SWNT; the inset in (b) represents the (110) lattice plane of Fe particles in SCEINs.  ...  Instead, Ni was found to strain the NiFe lattice, ascribed to the observation that both Fe-Fe and Ni-Ni bonds shifted in comparison with Fe and Ni foil.  ... 
doi:10.1039/d1cs00270h pmid:34870651 fatcat:innsesjsxnbgtafwqmc3gaqn3y

Operator scaling with specified marginals [article]

Cole Franks
2018 arXiv   pre-print
variables, noncommutative rank of symbolic matrices, and a basic problem in invariant theory (Garg, Gurvits, Oliveira and Wigderson, FOCS, 2016).  ...  The existence of the operator analogues of doubly stochastic scalings of matrices is equivalent to a multitude of problems in computer science and mathematics, such rational identity testing in non-commuting  ...  A polynomial time algorithm for Question 1 would confirm that membership in the Kronecker polytope is in P, whereas it is only known to be in coNPNP [4] .  ... 
arXiv:1801.01412v2 fatcat:vhnat6ea4fflpahgjvszupqro4

Nanoscale Forces and Their Uses in Self-Assembly

Kyle J. M. Bishop, Christopher E. Wilmer, Siowling Soh, Bartosz A. Grzybowski
2009 Small  
organized onto one of the three 1:1 ionic lattices illustrated in (c).  ...  of ionic lattices, U CsCl < U NaCl < U ZnS .  ... 
doi:10.1002/smll.200900358 pmid:19517482 fatcat:mz45wj2xfzgoxkmcdlr4k5x7ki

Deterministic and randomized polynomial-time approximation of radii

Andreas Brieden, Peter Gritzmann, Ravindran Kannan, Victor Klee, László Lovász, Miklós Simonovits
2001 Mathematika  
Our algorithms arise from the observation that the oracle complexity of approximating the radii is closely related to the problem of covering a sphere with a prescribed number of caps, or, equivalently  ...  In most of the problems considered here, the accuracy approaches 0 as n-^oo, and the problem is that of estimating the rapidity of this approach for the best possible oracle-polynomial-time algorithms.  ...  In general, the weak C-containment problem cannot be solved in polynomial time (unless P = coMP), since it is already coNP-complete to decide whether the standard cube is contained in a given affine image  ... 
doi:10.1112/s0025579300014364 fatcat:plolxcpmqze55eqpg642ow254m
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