Cette recherche s'applique uniquement aux ressources en bibliothèque.
159 résultats
Trier par:
Ajouter à la liste:
Étendre à toutes les références (sans texte intégral)
    • Article
    Sélectionner

    What Does a Random Contingency Table Look Like?

    Barvinok, Alexander
    Combinatorics, Probability and Computing, 2010, Vol.19(4), pp.517-539 [Revue évaluée par les pairs]
    Cambridge University Press
    Disponible
    Plus…
    Titre: What Does a Random Contingency Table Look Like?
    Auteur: Barvinok, Alexander
    Echelle: 2010
    Collection: 20100212
    Sujet: Matrix Methods ; Integers ; Matrices ; Tables (Data) ; Combinatorial Analysis ; Sums ; Contingency ; Mathematical Analysis ; Mathematics of Computing (General) (Ci);
    Description: Let R = ( r 1 , . . ., r m ) and C = ( c 1 , . . ., c n ) be positive integer vectors such that r 1 + ⋯ + r m = c 1 + ⋯ + c n . We consider the set Σ( R , C ) of non-negative m × n integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure. We prove that a random table D ∈ Σ( R , C ) is close with high probability to a particular matrix (‘typical table’) Z defined as follows. We let g ( x ) = ( x + 1)ln( x + 1) − x ln x for x ≥ 0 and let g ( X ) = ∑ i,j g ( x ij ) for a non-negative matrix X = ( x ij ). Then g ( X ) is strictly concave and attains its maximum on the polytope of non-negative m × n matrices X with row sums R and column sums C at a unique point, which we call the typical table Z .
    Précédemment: 20102010070212
    Fait partie de: Combinatorics, Probability and Computing, 2010, Vol.19(4), pp.517-539
    Classement: 201007
    Identifiant: 0963-5483 (ISSN); 1469-2163 (E-ISSN); 10.1017/S0963548310000039 (DOI)

    • Livre
    Sélectionner

    Integer points in polyhedra

    Barvinok, Alexander
    Zürich : European Mathematical Society
    2008
    Recherche de la disponibilité
    Plus…
    Chargement
    Erreur de chargement
    Titre: Integer points in polyhedra / Alexander Barvinok
    Auteur: Barvinok, Alexander
    Editeur: Zürich : European Mathematical Society
    Date: 2008
    Collation: 189 p. : ill.
    Collection: Zurich lectures in advanced mathematics
    Documents dans cette collection: Zurich lectures in advanced mathematics
    Classification: ams 52
    ams 05
    IMATH C-4
    Identifiant: 9783037190524 (ISBN)
    No RERO: R004842596
    Permalien:
    http://data.rero.ch/01-R004842596/html?view=FR_V1

    • Livre
    Sélectionner

    A course in convexity

    Barvinok, Alexander
    Providence R.I. : American Mathematical Society
    [2002]
    Recherche de la disponibilité
    Plus…
    Chargement
    Erreur de chargement
    Titre: A course in convexity / Alexander Barvinok
    Auteur: Barvinok, Alexander
    Editeur: Providence R.I. : American Mathematical Society
    Date: [2002]
    Collation: X, 366 p. : ill. ; 26 cm
    Collection: Graduate studies in mathematics ; vol. 54
    Documents dans cette collection: Graduate studies in mathematics
    Classification: ams 52
    IMATH C-4
    Identifiant: 0821829688 (ISBN)
    No RERO: R003318037
    Permalien:
    http://data.rero.ch/01-R003318037/html?view=FR_V1

    • Article
    Sélectionner

    Computing the Partition Function for Perfect Matchings in a Hypergraph

    Barvinok, Alexander, Samorodnitsky, Alex
    Combinatorics, Probability and Computing, 2011, Vol.20(6), pp.815-835 [Revue évaluée par les pairs]
    Cambridge University Press
    Disponible
    Plus…
    Titre: Computing the Partition Function for Perfect Matchings in a Hypergraph
    Auteur: Barvinok, Alexander; Samorodnitsky, Alex
    Echelle: 2011
    Collection: 20111017
    Sujet: Paper ; Mathematics;
    Description: Given non-negative weights w S on the k -subsets S of a km -element set V , we consider the sum of the products w S 1 ⋅⋅⋅ w S m over all partitions V = S 1 ∪ ⋅⋅⋅ ∪ S m into pairwise disjoint k -subsets S i . When the weights w S are positive and within a constant factor of each other, fixed in advance, we present a simple polynomial-time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman–Minc bounds for permanents. We also discuss applications to counting of perfect and nearly perfect matchings in hypergraphs.
    Précédemment: 20112011111017
    Fait partie de: Combinatorics, Probability and Computing, 2011, Vol.20(6), pp.815-835
    Classement: 201111
    Identifiant: 0963-5483 (ISSN); 1469-2163 (E-ISSN); 10.1017/S0963548311000435 (DOI)

    • Plusieurs versions

    Matrices with prescribed row and column sums

    Barvinok, Alexander
    Linear Algebra and Its Applications, 2012, Vol.436(4), pp.820-844 [Revue évaluée par les pairs]

    • Plusieurs versions

    A bound for the number of vertices of a polytope with applications

    Barvinok, Alexander
    Combinatorica, 2013, Vol.33(1), pp.1-10 [Revue évaluée par les pairs]

    • Article
    Sélectionner

    Thrifty Approximations of Convex Bodies by Polytopes

    Barvinok, Alexander
    International Mathematics Research Notices, 2014, Vol. 2014(16), pp.4341-4356 [Revue évaluée par les pairs]
    Oxford University Press
    Disponible
    Plus…
    Titre: Thrifty Approximations of Convex Bodies by Polytopes
    Auteur: Barvinok, Alexander
    Sujet: Mathematics;
    Description: Given a convex body containing the origin in its interior and a real number τ >1, we seek to construct a polytope P ⊂ C with as few vertices as possible such that C ⊂ τP . Our construction is nearly optimal for a wide range of d and τ . In particular, we prove that if C =− C , then for any 1> ϵ >0 and τ =1+ ϵ one can choose P having roughly ϵ − d /2 vertices and for one can choose P having roughly d 1/ ϵ vertices. Similarly, we prove that if is a convex body such that − C ⊂ μC for some μ ≥1, then one can choose P having roughly (( μ +1)/( τ −1)) d /2 vertices provided ( τ −1)/( μ +1)≪1.
    Fait partie de: International Mathematics Research Notices, 2014, Vol. 2014(16), pp.4341-4356
    Identifiant: 1073-7928 (ISSN); 1687-0247 (E-ISSN); 10.1093/imrn/rnt078 (DOI)

    • Plusieurs versions

    On testing Hamiltonicity of graphs

    Barvinok, Alexander
    Discrete Mathematics, 06 January 2015, Vol.338(1), pp.53-58 [Revue évaluée par les pairs]

    • Plusieurs versions

    Computing the Permanent of (Some) Complex Matrices

    Barvinok, Alexander
    Foundations of Computational Mathematics, 2016, Vol.16(2), pp.329-342 [Revue évaluée par les pairs]

    • Plusieurs versions

    Concentration of the mixed discriminant of well-conditioned matrices

    Barvinok, Alexander
    Linear Algebra and Its Applications, 15 March 2016, Vol.493, pp.120-133 [Revue évaluée par les pairs]