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Acceleration of Affine Hybrid Transformations [chapter]

Bernard Boigelot, Frédéric Herbreteau, Isabelle Mainz
2014 Lecture Notes in Computer Science  
This work addresses the computation of the set of reachable configurations of linear hybrid automata.  ...  This approach is complete over Multiple Counters Systems (MCS), and is able to accelerate hybrid transformations that are out of scope of existing techniques.  ...  The affine space of smallest dimension that contains a given set is unique, and known as the affine hull of this set.  ... 
doi:10.1007/978-3-319-11936-6_4 fatcat:x2yldez6zfho5hlzgektpxlvaa

Algorithms for graded injective resolutions and local cohomology over semigroup rings

David Helm, Ezra Miller
2005 Journal of symbolic computation  
Let Q be an affine semigroup generating Z d , and fix a finitely generated Z d -graded module M over the semigroup algebra k[Q] for a field k.  ...  We provide an algorithm to compute a minimal Z d -graded injective resolution of M up to any desired cohomological degree.  ...  Both authors were partially supported by the National Science Foundation.  ... 
doi:10.1016/j.jsc.2004.11.009 fatcat:bswrxgbwj5dvzp7j6nxb53oox4

Power to the Points: Validating Data Memberships in Clusterings [article]

Parasaran Raman, Suresh Venkatasubramanian
2013 arXiv   pre-print
It is also efficient: assigning an affinity score to a point depends only polynomially on the number of clusters and is independent of the number of points in the data.  ...  It is these labels that are then used for downstream analysis (either focusing on individual clusters, or identifying representatives of clusters and so on).  ...  We show different ways in which identifying points that are "unstable" can enhance or illuminate downstream clustering tasks, and validate the notion of a local affinity score against clusterings where  ... 
arXiv:1305.4757v1 fatcat:4hhjc43qjfcgpotdrdzt2d7bya

Algorithms for graded injective resolutions and local cohomology over semigroup rings [article]

David Helm, Ezra Miller
2003 arXiv   pre-print
Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k.  ...  We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired cohomological degree.  ...  Both authors were partially supported by the National Science Foundation.  ... 
arXiv:math/0309256v1 fatcat:uhizw2f23bax7py2jccyzpuanu

Towards Verification of Uncertain Cyber-Physical Systems

Carna Radojicic, Christoph Grimm, Axel Jantsch, Michael Rathmair
2017 Electronic Proceedings in Theoretical Computer Science  
We define a symbolic model and representation of uncertain computations: Affine Arithmetic Decision Diagrams.  ...  We demonstrate the approach by analyzing a water-level monitor with uncertainties, self-diagnosis, and error-reactions.  ...  Acknowlegement This work is funded, in part, within the ANCONA project (16ES021) within the program IKT 2020 by the German Ministry of Education and Research (BMBF) and by Robert Bosch AG, Intel AG, and  ... 
doi:10.4204/eptcs.247.1 fatcat:3g7knqzurbbnddnwu5uez2gy5q

Power to the Points: Validating Data Memberships in Clusterings

Parasaran Raman, Suresh Venkatasubramanian
2013 2013 IEEE 13th International Conference on Data Mining  
It is based on techniques from the theory of interpolation, coupled with sampling and estimation algorithms from high dimensional computational geometry.  ...  It is also efficient: assigning an affinity score to a point depends only polynomially on the number of clusters and is independent both of the size and dimensionality of the data.  ...  Fix burn-in parameter b Run Hit-And-Run for d steps on T K, ending in z = z 0 for i = 1 . . . m do Set z i to be result of one Hit-And-Run move from z i−1 Return (T −1 z 1 , . . . , T −1 z m ). then pick  ... 
doi:10.1109/icdm.2013.147 dblp:conf/icdm/RamanV13 fatcat:5xge7b74k5botg5h4576mgawd4

Voronoi Diagram of Orthogonal Polyhedra in Two and Three Dimensions [chapter]

Ioannis Z. Emiris, Christina Katsamaki
2019 Lecture Notes in Computer Science  
We construct the exact Voronoi diagram inside an orthogonal polyhedron with holes defined by such polyhedra.  ...  Our approach avoids creating full-dimensional elements on the Voronoi diagram and yields a skeletal representation of the input object.  ...  We thank Evanthia Papadopoulou for commenting on a preliminary version of the paper and Bernard Mourrain for collaborating on software.  ... 
doi:10.1007/978-3-030-34029-2_1 fatcat:ei6ofbgiafcu7c76sulcbrg2sm

A Homographic Framework for the Fusion of Multi-view Silhouettes

Saad M. Khan, Pingkun Yan, Mubarak Shah
2007 2007 IEEE 11th International Conference on Computer Vision  
Using planar homographies and foreground likelihood information from a set of arbitrary views, we show that visual hull intersection can be performed in the image plane without requiring to go in 3D space  ...  Object structure is finally segmented out by minimizing an energy functional over the surface of the object in a level sets formulation.  ...  Acknowledgement We would like to thank Kevin Boulanger for providing the 3D point rendering code and Pavel Babenko for the GPU optimizations. This work is supported in part by the the U.S.  ... 
doi:10.1109/iccv.2007.4408897 dblp:conf/iccv/KhanYS07 fatcat:3zupts5myzhcppae536nre65cm

Bregman Voronoi Diagrams: Properties, Algorithms and Applications [article]

Frank Nielsen, Jean-Daniel Boissonnat, Richard Nock
2007 arXiv   pre-print
We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams  ...  We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently.  ...  The work by the second author has been partially supported by the project GeoTopAl (1555) of the Agence Nationale de la Recherche (ANR).  ... 
arXiv:0709.2196v1 fatcat:7juz25kny5fi3g45qkag3c4xze

Bregman Voronoi Diagrams

Jean-Daniel Boissonnat, Frank Nielsen, Richard Nock
2010 Discrete & Computational Geometry  
We also introduce extensions of these diagrams, e.g., k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connection with Bregman Voronoi diagrams  ...  We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently.  ...  This research has been partially supported by the Agence Nationale de la Recherche (project GAIA 07-BLAN-0328-04) and DIGITEO (project GAS 2008-16D).  ... 
doi:10.1007/s00454-010-9256-1 fatcat:lik3travqzdfhbm2md3p2t5mfi

Refinement to Certify Abstract Interpretations: Illustrated on Linearization for Polyhedra

Sylvain Boulmé, Alexandre Maréchal
2018 Journal of automated reasoning  
Based on ring rewriting strategies and interval arithmetic, this procedure partitions the variable space to infer precise affine terms which over-approximate polynomials.  ...  Like standard refinement calculi, it introduces data-refinement diagrams. These diagrams relate "abstract states" computed by the analyzer to "concrete states" of the input program.  ...  (y − z) + 10.z" is approximated by the affine program below.  ... 
doi:10.1007/s10817-018-9492-2 fatcat:bq2ztwbt5nhilesotkqanxsikq

Reflections on Termination of Linear Loops [chapter]

Shaowei Zhu, Zachary Kincaid
2021 Lecture Notes in Computer Science  
First, we show that every loop that can be expressed as a transition formula in linear integer arithmetic has a best model as a deterministic affine transition system.  ...  Second, we show that for any linear dynamical system f with integer eigenvalues and any integer arithmetic formula G, there is a linear integer arithmetic formula that holds exactly for the states of f  ...  This work was supported in part by the NSF under grant number 1942537 and by ONR under grant N00014-19-1-2318.  ... 
doi:10.1007/978-3-030-81688-9_3 fatcat:udmwdykxonesvk7o3xa3vi77oi

Missile autopilot robustness using the real multiloop stability margin

KEVIN A. WISE
1993 Journal of Guidance Control and Dynamics  
The angles from 3 to 2, denoted z 32, and from 3 to 4, denoted z 34, are computed. Any point with an angle greater than z 32 and less than z 34 is placed in the set {x,,y,}.  ...  Starting with anchor point 1, the angles from 1 to 2, denoted z 12, and from 1 to 4, denoted z 14, are computed.  ... 
doi:10.2514/3.21010 fatcat:brhbdlcuizhpvnedtbr474vp7m

Least Significant Digit First Presburger Automata [article]

Jérôme Leroux
2006 arXiv   pre-print
Since 1969 C-MST69,S-SMJ77, we know that any Presburger-definable set P-PCM29 (a set of integer vectors satisfying a formula in the first-order additive theory of the integers) can be represented by a  ...  However, the problem of deciding if a FDVA represents such a set, is a well-known hard problem first solved by Muchnik in 1991 with a quadruply-exponential time algorithm.  ...  Number Decision Diagrams (NDD) Recall [WB00] that a Number Decision Diagram (NDD) A in basis r and in dimension m that represents a r-definable set X ⊆ Z m is a finite automaton over the alphabet Σ r that  ... 
arXiv:cs/0612037v1 fatcat:7aywdgoqenatdd7nwnagadbw2m

Convex Language Semantics for Nondeterministic Probabilistic Automata [article]

Gerco van Heerdt, Justin Hsu, Joël Ouaknine, Alexandra Silva
2018 arXiv   pre-print
from the threshold problem.  ...  For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking language equivalence is undecidable by reduction  ...  Separating NPAs and DPAs: Unary Alphabet We now turn to the unary case. A weighted language over a unary alphabet can be represented by a sequence u i = u 0 , u 1 , . . . of real numbers.  ... 
arXiv:1805.11550v1 fatcat:5e53ifggtzbvvlbfhdvukis5gu
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