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Approximate Inclusion-Exclusion
1990
Combinatorica
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The Inclusion-Exclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. ...
When the sizes of all intersections are only given approximately, good bounds are derived on how well the size of the union may be approximated. ...
This prompted our interest in approximate versions of the inclusion-exclusion formula. ...
doi:10.1007/bf02128670
fatcat:n7dt3hdd3rf37gtl7mgkrsn7ba
Approximate inclusion-exclusion
1990
Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90
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The Inclusion-Exclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. ...
When the sizes of all intersections are only given approximately, good bounds are derived on how well the size of the union may be approximated. ...
This prompted our interest in approximate versions of the inclusion-exclusion formula. ...
doi:10.1145/100216.100250
dblp:conf/stoc/LinialN90
fatcat:pkoti32z4ng7nifjuqx3vvpuju
On approximate inclusion-exclusion
2008
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
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The inclusion-exclusion formula expresses the size of the union of a family of sets in terms of the sizes of intersections of all subfamilies. In [2] N. Linial and N. ...
Nisan use linear programming to approximate the size of the union when the intersection sizes are known only for certain subfamilies. ...
At this point we can ask whether it is possible to give an approximate inclusion-exclusion formula. ...
doi:10.2140/iig.2008.6.249
fatcat:cnfhx3od4vedrj4rtquwu4wzxm
A note on approximate inclusion-exclusion
1997
Discrete Applied Mathematics
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Adopting the notation of [As := niE,_Ai we have by inclusion-exclusion MS = IAsl -U(A~ n Ai) = u -r = (-l)n+' at,) it is clear that inequalities ( 1.1) and ( 1.2) necessarily hold. ...
[l] have recently investigated the problem of approximating u:=\U~=,Ail given only the values zZ'(k,n):={as: /SI < k}. ...
doi:10.1016/s0166-218x(96)00048-0
fatcat:7v2yur24pjan3fonwnfimb7rpq
Aq-Analog of Approximate Inclusion–Exclusion
1998
Advances in Applied Mathematics
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Their starting point was the classical inclusion᎐exclusion formula and their main result was that a good approximation may be obtained if and only if sufficiently many terms from the inclusion᎐exclusion ...
Nisan whose article '' Approximate Inclusion᎐Exclusion'' 14 has served as a model for this work. changes in a significant way around q: if k F O q , ny1 Ž .' then any approximation may err by a factor ...
doi:10.1006/aama.1997.0568
fatcat:yl73lfdfure2bft4ylpp3o36di
Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions
2008
2008 23rd Annual IEEE Conference on Computational Complexity
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The approximate inclusion-exclusion problem, due to Linial and Nisan (1990) , is to estimate Pr[A 1 ∪· · ·∪A n ] given Pr[ i∈S A i ] for all |S | k. ...
Its key ingredient is the Approximation/Orthogonality Principle, a certain equivalence of approximation and orthogonality in a Euclidean space, recently proved by the author in the context of quantum lower ...
This problem, due to Linial and Nisan [10] , is known as approximate inclusion-exclusion. ...
doi:10.1109/ccc.2008.18
dblp:conf/coco/Sherstov08a
fatcat:7pvqk4o3mrhebijm2y7fivwkjy
Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions
2009
Computational Complexity
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I am also thankful to Ronald for a stimulating discussion on how quantum arguments can contribute short and simple proofs in classical approximation theory. ...
. 1 Inclusion/exclusion. ...
Approximation vs. orthogonality. ...
doi:10.1007/s00037-009-0274-4
fatcat:htk7crh46bdche2a7o7qbytc2y
Quasiparticle random phase approximation with inclusion of the Pauli exclusion principle
2000
Physical Review C
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A special attention is paid to the violation of the Pauli exclusion principle (PEP) in solving the QRPA equation. ...
Limitations of the Quasiparticle Random Phase Approximation (QRPA) are studied within an exactly solvable model, with a two body interaction of Fermi type. ...
This is usually called the "quasiboson approximation" (QBA). The QBA violates the Pauli exclusion principle (PEP) and this affects severely the theory. ...
doi:10.1103/physrevc.61.044319
fatcat:mez5canq2zftxc34bmcsmztm5e
Inclusion–exclusion principle for belief functions
2014
International Journal of Approximate Reasoning
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The inclusion-exclusion principle is a well-known property of set cardinality and probability measures, that is instrumental to solve some problems such as the evaluation of systems reliability or of uncertainty ...
Inclusion-exclusion for monotone functions In this section, we show that the inclusion-exclusion principle can be applied to evaluate some events of interest for monotone functions, and we provide an illustration ...
These conditions allow us to check, once a formula has been put in DNF, whether or not the inclusion/exclusion principle applies. ...
doi:10.1016/j.ijar.2014.04.018
fatcat:ziwmfbyuv5dazenop4gpodzlzy
Inclusion and Exclusion Approximations of Copolymer Solids Applied to Calculation of Solid−Liquid Transitions
2002
Industrial & Engineering Chemistry Research
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Such an inclusion model is compared to an exclusion model hypothesizing exclusion of the comonomer units from the crystalline domain. ...
Furthermore, the inclusion parameters, the fold energy and the energy penalty, are found to be solvent-and composition-independent, while the exclusion parameter, the crystallizability, is found to be ...
We refer to this approximation as the inclusion approximation. ...
doi:10.1021/ie0107791
fatcat:uffwf436dfbj7acqn7ezdalnam
Learning DNF by approximating inclusion-exclusion formulae
Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
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Approximating Inclusion-Exclusion Formulae Our positive and negative results for learning DNF are built on positive and negative results for approximating the inclusion-exclusion formula, respectively, ...
From 9 and the inclusion-exclusion formula, we can extend 3 to for any nonempty set S f 1; : : : ; n 0 g with 0 jSj k and any a i 2 f 0; 1g with i 2 S. ...
doi:10.1109/ccc.1999.766279
dblp:conf/coco/TaruiT99
fatcat:m2iyr7wgeveofadninp3fwwkim
Challenges and Opportunities in High-dimensional Variational Inference
[article]
2021
arXiv
pre-print
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Therefore, for moderate-to-high-dimensional posteriors we recommend using the (mode-seeking) exclusive KL divergence since it is the easiest to optimize, and improving the variational family or using model ...
parameter transformations to make the posterior and optimal variational approximation more similar. ...
By drawing a connection between importance sampling and the Figure 1 : Illustration of a mean-field approximation with exclusive (mode-seeking) and inclusive (mass-covering) divergences. ...
arXiv:2103.01085v2
fatcat:s5crnua7pnhnjlltjotkypsn24
QE Neutrino CC Cross Sections off [sup 16]O
2007
AIP Conference Proceedings
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2007 pre-print arXiv:0711.3223v1 fatcat:u4x4ztkzxjgvxp3ihiddnszupm
of inclusive and total cross sections. ...
The charged-current quasi-elastic scattering of muon neutrino on oxygen target is computed for neutrino energy between 200 MeV and 2.5 GeV using different approximations: the Plane Wave Impulse Approximation ...
We found a significant nuclear-model dependence of the exclusive, inclusive and total cross sections for neutrino energy E ν ≤ 1 GeV. ...
doi:10.1063/1.2834496
fatcat:ohfq6ukopzfqfm6phc764ws47m
The semi-classical approach to the exclusive electron scattering
1998
Nuclear Physics A
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The exclusive scattering is found to be quite sensitive to the mean field final states interaction, unlike the inclusive one. ...
The semiclassical approach, successfully applied in the past to the inelastic, inclusive electron scattering off nuclei, is extended to the treatment of exclusive processes. ...
Introduction The plane wave impulse approximation (PWIA) has been a framework extensively employed in analysing the exclusive (or semi-inclusive) processes of inelastic scattering of electrons off nuclei ...
doi:10.1016/s0375-9474(98)00160-2
fatcat:7anjuexuivaonff6x24pi4qlg4
Eigenvalue inclusion regions from inverses of shifted matrices
2008
Linear Algebra and its Applications
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The numerical approximation of the inclusion sets for large matrices is also examined. ...
We consider eigenvalue inclusion regions based on the field of values, pseudospectra, Gershgorin region, and Brauer region of the inverse of a shifted matrix. ...
In addition to an inclusion region, it is suggestive here to speak of its boundary as an inclusion or exclusion curve, depending on whether it is the boundary of a bounded inclusion or exclusion region ...
doi:10.1016/j.laa.2008.08.016
fatcat:t6i5laxzpjgojfnbn2btsa5inq
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