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On the Lattice Smoothing Parameter Problem
[article]
2014
arXiv
pre-print
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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 NP ∩ coNP 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 NP ∩ coNP ...
arXiv:1412.7979v1
fatcat:qsc5bo43ercfrhjboyt3fpmrni
On the Lattice Smoothing Parameter Problem
2013
2013 IEEE Conference on Computational Complexity
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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 NP ∩ coNP 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 NP ∩ coNP ...
doi:10.1109/ccc.2013.31
dblp:conf/coco/ChungDLP13
fatcat:rjb2enmta5eubacj75rd3t74gi
A Subexponential Algorithm for ARRIVAL
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2102.06427v2 fatcat:mzezgliusbfvhd5qrgm3ffboj4Other Versions
The problem is in NP ∩ coNP 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 NP ∩ coNP that is not known to be in P. ...
arXiv:2102.06427v3
fatcat:zajvz7drovauppe3w2gt5u5u2u
Preparation of Cobalt Nanoparticles
2021
European Journal of Inorganic Chemistry
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, 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]
2022
arXiv
pre-print
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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 NP ∩ coNP. The idea of the first result is as follows. ...
arXiv:2207.08311v1
fatcat:xmqfmbmuorhntei6lueyiathda
Cobalt magnetic nanoparticles as theranostics: Conceivable or forgettable?
2020
Nanotechnology Reviews
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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]
2014
arXiv
pre-print
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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
2021
Current Journal of Applied Science and Technology
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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]
2021
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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 NP ∩ coNP. ...
arXiv:1910.12375v1
fatcat:qasr4soxk5gpdouftldqxjpcr4
Strategies for Improving the Functionality of Zeolitic Imidazolate Frameworks: Tailoring Nanoarchitectures for Functional Applications
2017
Advanced Materials
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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
2022
Chemical Society Reviews
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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]
2018
arXiv
pre-print
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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 coNP ∩ NP [4] . ...
arXiv:1801.01412v2
fatcat:vhnat6ea4fflpahgjvszupqro4
Nanoscale Forces and Their Uses in Self-Assembly
2009
Small
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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
2001
Mathematika
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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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