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Approximate Inclusion-Exclusion

1990
*
Combinatorica
*

The

doi:10.1007/bf02128670
fatcat:n7dt3hdd3rf37gtl7mgkrsn7ba
*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. ...##
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Approximate inclusion-exclusion

1990
*
Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90
*

The

doi:10.1145/100216.100250
dblp:conf/stoc/LinialN90
fatcat:pkoti32z4ng7nifjuqx3vvpuju
*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. ...##
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On approximate inclusion-exclusion

2008
*
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
*

The

doi:10.2140/iig.2008.6.249
fatcat:cnfhx3od4vedrj4rtquwu4wzxm
*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. ...##
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A note on approximate inclusion-exclusion

1997
*
Discrete Applied Mathematics
*

Adopting the notation of [As := niE,_Ai we have by

doi:10.1016/s0166-218x(96)00048-0
fatcat:7v2yur24pjan3fonwnfimb7rpq
*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}. ...##
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Aq-Analog of Approximate Inclusion–Exclusion

1998
*
Advances in Applied Mathematics
*

Their starting point was the classical

doi:10.1006/aama.1997.0568
fatcat:yl73lfdfure2bft4ylpp3o36di
*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 ...##
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Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions

2008
*
2008 23rd Annual IEEE Conference on Computational Complexity
*

The

doi:10.1109/ccc.2008.18
dblp:conf/coco/Sherstov08a
fatcat:7pvqk4o3mrhebijm2y7fivwkjy
*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*. ...##
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Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions

2009
*
Computational Complexity
*

I am also thankful to Ronald for a stimulating discussion on how quantum arguments can contribute short and simple proofs in classical

doi:10.1007/s00037-009-0274-4
fatcat:htk7crh46bdche2a7o7qbytc2y
*approximation*theory. ... . 1*Inclusion*/*exclusion*. ...*Approximation*vs. orthogonality. ...##
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Quasiparticle random phase approximation with inclusion of the Pauli exclusion principle

2000
*
Physical Review C
*

A special attention is paid to the violation of the Pauli

doi:10.1103/physrevc.61.044319
fatcat:mez5canq2zftxc34bmcsmztm5e
*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. ...##
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Inclusion–exclusion principle for belief functions

2014
*
International Journal of Approximate Reasoning
*

The

doi:10.1016/j.ijar.2014.04.018
fatcat:ziwmfbyuv5dazenop4gpodzlzy
*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. ...##
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Inclusion and Exclusion Approximations of Copolymer Solids Applied to Calculation of Solid−Liquid Transitions

2002
*
Industrial & Engineering Chemistry Research
*

Such an

doi:10.1021/ie0107791
fatcat:uffwf436dfbj7acqn7ezdalnam
*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*. ...##
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Learning DNF by approximating inclusion-exclusion formulae

*
Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
*

*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. ...

##
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Challenges and Opportunities in High-dimensional Variational Inference
[article]

2021
*
arXiv
*
pre-print

Therefore, for moderate-to-high-dimensional posteriors we recommend using the (mode-seeking)

arXiv:2103.01085v2
fatcat:s5crnua7pnhnjlltjotkypsn24
*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. ...##
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QE Neutrino CC Cross Sections off [sup 16]O

2007
*
AIP Conference Proceedings
*

of

doi:10.1063/1.2834496
fatcat:ohfq6ukopzfqfm6phc764ws47m
*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. ...##
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The semi-classical approach to the exclusive electron scattering

1998
*
Nuclear Physics A
*

The

doi:10.1016/s0375-9474(98)00160-2
fatcat:7anjuexuivaonff6x24pi4qlg4
*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 ...##
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Eigenvalue inclusion regions from inverses of shifted matrices

2008
*
Linear Algebra and its Applications
*

The numerical

doi:10.1016/j.laa.2008.08.016
fatcat:t6i5laxzpjgojfnbn2btsa5inq
*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 ...
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