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Acceleration of Affine Hybrid Transformations
[chapter]

2014
*
Lecture Notes in Computer Science
*

This work addresses the

doi:10.1007/978-3-319-11936-6_4
fatcat:x2yldez6zfho5hlzgektpxlvaa
*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*. ...##
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Algorithms for graded injective resolutions and local cohomology over semigroup rings

2005
*
Journal of symbolic computation
*

Let

doi:10.1016/j.jsc.2004.11.009
fatcat:bswrxgbwj5dvzp7j6nxb53oox4
*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. ...##
###
Power to the Points: Validating Data Memberships in Clusterings
[article]

2013
*
arXiv
*
pre-print

It is also efficient: assigning an

arXiv:1305.4757v1
fatcat:4hhjc43qjfcgpotdrdzt2d7bya
*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 ...##
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Algorithms for graded injective resolutions and local cohomology over semigroup rings
[article]

2003
*
arXiv
*
pre-print

Let

arXiv:math/0309256v1
fatcat:uhizw2f23bax7py2jccyzpuanu
*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. ...##
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Towards Verification of Uncertain Cyber-Physical Systems

2017
*
Electronic Proceedings in Theoretical Computer Science
*

We define a symbolic model

doi:10.4204/eptcs.247.1
fatcat:3g7knqzurbbnddnwu5uez2gy5q
*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*...##
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Power to the Points: Validating Data Memberships in Clusterings

2013
*
2013 IEEE 13th International Conference on Data Mining
*

It is based on techniques

doi:10.1109/icdm.2013.147
dblp:conf/icdm/RamanV13
fatcat:5xge7b74k5botg5h4576mgawd4
*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 ...##
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Voronoi Diagram of Orthogonal Polyhedra in Two and Three Dimensions
[chapter]

2019
*
Lecture Notes in Computer Science
*

We construct the exact Voronoi

doi:10.1007/978-3-030-34029-2_1
fatcat:ei6ofbgiafcu7c76sulcbrg2sm
*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. ...##
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A Homographic Framework for the Fusion of Multi-view Silhouettes

2007
*
2007 IEEE 11th International Conference on Computer Vision
*

Using planar homographies

doi:10.1109/iccv.2007.4408897
dblp:conf/iccv/KhanYS07
fatcat:3zupts5myzhcppae536nre65cm
*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. ...##
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Bregman Voronoi Diagrams: Properties, Algorithms and Applications
[article]

2007
*
arXiv
*
pre-print

We also introduce extensions of these

arXiv:0709.2196v1
fatcat:7juz25kny5fi3g45qkag3c4xze
*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). ...##
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Bregman Voronoi Diagrams

2010
*
Discrete & Computational Geometry
*

We also introduce extensions of these

doi:10.1007/s00454-010-9256-1
fatcat:lik3travqzdfhbm2md3p2t5mfi
*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). ...##
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Refinement to Certify Abstract Interpretations: Illustrated on Linearization for Polyhedra

2018
*
Journal of automated reasoning
*

Based on ring rewriting strategies

doi:10.1007/s10817-018-9492-2
fatcat:bq2ztwbt5nhilesotkqanxsikq
*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. ...##
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Reflections on Termination of Linear Loops
[chapter]

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

doi:10.1007/978-3-030-81688-9_3
fatcat:udmwdykxonesvk7o3xa3vi77oi
*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. ...##
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Missile autopilot robustness using the real multiloop stability margin

1993
*
Journal of Guidance Control and Dynamics
*

The angles

doi:10.2514/3.21010
fatcat:brhbdlcuizhpvnedtbr474vp7m
*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*. ...##
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Least Significant Digit First Presburger Automata
[article]

2006
*
arXiv
*
pre-print

Since 1969 C-MST69,S-SMJ77, we know that any Presburger-definable

arXiv:cs/0612037v1
fatcat:7aywdgoqenatdd7nwnagadbw2m
*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 ...##
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Convex Language Semantics for Nondeterministic Probabilistic Automata
[article]

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*. ...

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