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### Approximate Inclusion-Exclusion

Nathan Linial, Noam Nisan
1990 Combinatorica
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.  ...

### Approximate inclusion-exclusion

N. Linial, N. Nisan
1990 Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90
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.  ...

### On approximate inclusion-exclusion

Andreas Klein, Klaus Metsch
2008 Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
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.  ...

### A note on approximate inclusion-exclusion

Avraham A Melkman, Solomon E Shimony
1997 Discrete Applied Mathematics
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}.  ...

### Aq-Analog of Approximate Inclusion–Exclusion

Marios Mavronicolas
Their starting point was the classical inclusionexclusion formula and their main result was that a good approximation may be obtained if and only if sufficiently many terms from the inclusionexclusion  ...  Nisan whose article '' Approximate InclusionExclusion'' 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  ...

### Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions

Alexander A. Sherstov
2008 2008 23rd Annual IEEE Conference on Computational Complexity
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.  ...

### Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions

Alexander A. Sherstov
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 approximation theory.  ...  . 1 Inclusion/exclusion.  ...  Approximation vs. orthogonality.  ...

### Quasiparticle random phase approximation with inclusion of the Pauli exclusion principle

F. Šimkovic, A. A. Raduta, M. Veselský, Amand Faessler
2000 Physical Review C
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.  ...

### Inclusion–exclusion principle for belief functions

F. Aguirre, S. Destercke, D. Dubois, M. Sallak, C. Jacob
2014 International Journal of Approximate Reasoning
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.  ...

### Inclusion and Exclusion Approximations of Copolymer Solids Applied to Calculation of Solid−Liquid Transitions

2002 Industrial & Engineering Chemistry Research
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.  ...

### Learning DNF by approximating inclusion-exclusion formulae

J. Tarui, T. Tsukiji
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.  ...

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

Akash Kumar Dhaka, Alejandro Catalina, Manushi Welandawe, Michael Riis Andersen, Jonathan Huggins, Aki Vehtari
2021 arXiv   pre-print
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.  ...

### QE Neutrino CC Cross Sections off [sup 16]O

A. V. Butkevich, S. A. Kulagin, Geralyn P. Zeller, Jorge G. Morfin, Flavio Cavanna
2007 AIP Conference Proceedings
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.  ...

### The semi-classical approach to the exclusive electron scattering

W.M. Alberico, G. Chanfray, J. Delorme, M. Ericson, A. Molinari
1998 Nuclear Physics A
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  ...

### Eigenvalue inclusion regions from inverses of shifted matrices

Michiel E. Hochstenbach, David A. Singer, Paul F. Zachlin
2008 Linear Algebra and its Applications
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  ...
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