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Some approximations in Model Checking and Testing [article]

M.C. Gaudel and R. Lassaigne and F. Magniez and M. de Rougemont
2013 arXiv   pre-print
We present some notions of approximation with their logic and statistics backgrounds, which yield several techniques for model checking and testing: Bounded Model Checking, Approximate Model Checking,  ...  Approximate Black-Box Checking, Approximate Model-based Testing and Approximate Probabilistic Model Checking.  ...  In bounded model checking, some upper bounds on the execution paths to witness some error are stated for some class of formulas. The method is polynomial in the size of the model. 2.  ... 
arXiv:1304.5199v1 fatcat:ytly2coo4jgfxerjndgyhm47gy

Partial Order Resolution of Event Logs for Process Conformance Checking [article]

Han van der Aa, Henrik Leopold, Matthias Weidlich
2020 arXiv   pre-print
Moreover, to reduce the runtime of conformance checking based on partial order resolution, we introduce an approximation method that comes with a bounded error in terms of accuracy.  ...  To cope with the order uncertainty in real-world data, we present several estimators for this task, incorporating different notions of behavioral abstraction.  ...  Confidence Intervals Based on statistical distributions established for expected conformance values, we further derive statistical bounds in the form of a confidence interval for the estimation of P conf  ... 
arXiv:2007.02416v1 fatcat:plb7f5cq3zbu7hsx3jvwpheygm

Reachset Conformance Testing of Hybrid Automata

Hendrik Roehm, Jens Oehlerking, Matthias Woehrle, Matthias Althoff
2016 Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control - HSCC '16  
Additionally, we present a test selection algorithm that uses a coverage measure to reduce the number of test cases for conformance testing.  ...  For this reason, a common approach is to formally verify abstractions of (parts of) the original system.  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers as well as Christoph Gladisch, Thomas Heinz and Christian Heinzemann for their valuable comments and suggestions to improve the quality  ... 
doi:10.1145/2883817.2883828 dblp:conf/hybrid/RoehmOWA16 fatcat:pxhgj63h3rah7b3i73wbuno7sm

The Augmented Synthetic Control Method [article]

Eli Ben-Michael, Avi Feller, Jesse Rothstein
2020 arXiv   pre-print
We bound the estimation error of this approach under different data generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise.  ...  Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate.  ...  Section 5 bounds the estimation error under a linear model and a linear factor model, the standard setting for SCM.  ... 
arXiv:1811.04170v3 fatcat:4visdb6hyfegnn7ie73ipeowpi

An a posteriori error analysis for a coupled continuum pipe-flow/Darcy model in Karst aquifers: anisotropic and isotropic discretizations [article]

Koffi Wilfrid Houedanou
2017 arXiv   pre-print
This paper presents an a posteriori error analysis for a coupled continuum pipe-flow/Darcy model in karst aquifers.  ...  From the finite element solution, the error estimators are constructed and based on the residual of model equations.  ...  Then the error is bounded globally from above by Commentary 6.1. (Upper error bound-conforming case) The upper error bound (55) contains an alignment measure m Notation 2.1. Model problem.  ... 
arXiv:1702.08814v2 fatcat:n7c72jkqgncalenrg4dsmpivpu

Anisotropic cosmologies containing isotropic background radiation

Saulo Carneiro, Guillermo Mena Marugán
2001 Physical Review D, Particles and fields  
Using these results, we are also able to construct approximate solutions for shear-free cosmological models with rotation.  ...  bounds derived from rotation of galaxies.  ...  An independent estimate ω ∼ 10 −21 s −1 can be obtained from the analysis of the rotation of galaxies [30] .  ... 
doi:10.1103/physrevd.64.083502 fatcat:wjgoxe7sszeo5p4qadya6keioa

Nonconforming P1 elements on distorted triangulations: Lower bounds for the discrete energy norm error [article]

Peter Oswald
2018 arXiv   pre-print
., optimal-order discrete H^1 norm best approximation error estimates for H^2 functions hold for arbitrary triangulations.  ...  However, similar estimates for the error of the Galerkin projection for second-order elliptic problems show a dependence on the maximum angle of all triangles in the triangulation.  ...  and upper bounds for the Galerkin energy norm error (or, equivalently, the error of best approximation by conforming P1 elements in the H 1 norm) have been obtained.  ... 
arXiv:1607.05983v2 fatcat:54pon74qabb2tm7o4o6bu4skxa

The mortar finite element method for Bingham fluids

Patrick Hild
2001 Mathematical Modelling and Numerical Analysis  
In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method.  ...  Afin d'approcher ce problème régi par une inéquation variationnelle, nous appliquons la méthode non conforme deséléments finis avec joints.  ...  error bound obtained in the conforming case (see [15] ).  ... 
doi:10.1051/m2an:2001110 fatcat:x446prpspbajxplnyzwnnjbp7u

Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme

Meiqun Jiang, Xingye Yue
2007 Mathematical Modelling and Numerical Analysis  
Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul. 1 (2003) 260-303].  ...  In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented.  ...  Chen for many inspiring discussions on this topic. They'd also like to thank the referees for their valuable comments and suggestions.  ... 
doi:10.1051/m2an:2007044 fatcat:sz27fmvutjddnliehbpb2m2fvu

Finite element approximation of elliptic homogenization problems in nondivergence-form

Yves C R Capdeboscq, Timo Sprekeler, Endre Süli
2019 Mathematical Modelling and Numerical Analysis  
We propose and rigorously analyze a numerical scheme based on finite element approximations for such nondivergence-form homogenization problems.  ...  We use uniform $W^{2,p}$ estimates to obtain corrector results for periodic homogenization problems of the form $A(x/\varepsilon):D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition  ...  The authors thank the anonymous referees for their helpful comments and constructive suggestions.  ... 
doi:10.1051/m2an/2019093 fatcat:ludwjzdhorgltncv7ftq72r2yy

A posteriori error analysis for a boundary element method with non-conforming domain decomposition [article]

Catalina Domínguez, Norbert Heuer
2013 arXiv   pre-print
Assuming a saturation property, we establish quasi-reliability and efficiency of the error estimator in comparison with the error in a natural (non-conforming) norm.  ...  We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions.  ...  This amounts to an error estimate like ( 6 ) for the non-conforming method (5) in a different norm. The proof of this bound is essentially an intermediate result from [8] . Proposition 4.4.  ... 
arXiv:1307.7310v1 fatcat:hbv4yrvrzjello2prazmvbqkbu

Practical persistent scatterer processing validation in the course of the Terrafirma project

Nico Adam, Alessandro Parizzi, Michael Eineder, Michele Crosetto
2009 Journal of Applied Geophysics  
Two independent and complementary strategies for the validation are foreseen in the validation project in order to drive sustainability.  ...  In principle, the lower bound for the deformation deviation an end user can expect ordering a test site processing from different OSPs is reported.  ...  Additionally, we thank Richard Bamler and the anonymous reviewers for the constructive suggestions which greatly helped to improve this paper.  ... 
doi:10.1016/j.jappgeo.2009.07.002 fatcat:lsrgedurx5bd5boognfc3thkye

Convergence of the {${\rm ACM}$} finite element scheme for plate bending problems

Fumio Kikuchi
1975 Publications of the Research Institute for Mathematical Sciences  
When the shape of the domain is rectangular and the exact solution is sufficiently smooth, Z, 2~e rror bounds of moments and deflection and error of eigenvalue are all at the order of square of the maximum  ...  Convergence rates of the ACM non-conforming scheme are evaluated.  ...  Let u hi be the approximation of u i defined above. Then u hi -u i satisfies the same error estimates as hold for u h -u in To obtain a lower bound, we use the same u h and u as in Lemma 11.  ... 
doi:10.2977/prims/1195191694 fatcat:en3epsdh5vac5dcgysve2hbdse

Critical exponents of the 3d Ising and related models from conformal bootstrap

Ferdinando Gliozzi, Antonio Rago
2014 Journal of High Energy Physics  
Likewise we obtain the scaling dimensions of six scalars and four spinning operators for the 3d critical Ising model.  ...  The constraints of conformal bootstrap are applied to investigate a set of conformal field theories in various dimensions.  ...  Rychkov for useful discussions and insights.  ... 
doi:10.1007/jhep10(2014)042 fatcat:esd2ng4klreplcnvpzulqvribi


2011 Biocomputing 2012  
of conformations and, simultaneously, provides estimates for the uncertainty in properties calculated from the model.  ...  This problem requires one to consider a large number of conformations in order to ensure that the model adequately represents the range of structures that the protein can adopt.  ...  An important feature of the algorithm is that it provides a built-in error check in the form of an uncertainty parameter, or posterior uncertainty, which is related to the error in the estimated population  ... 
doi:10.1142/9789814366496_0009 fatcat:hoz2qygipzdcxbzok35zu5ucuy
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