Relevant bibliographies by topics / Matrice partitions

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Matrice partitions'

Author: Grafiati
Published: 22 June 2023

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Journal articles on the topic "Matrice partitions"

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Carayol, Cécile. "La Ligne rouge de Hans Zimmer. Matrice d’un « nouvel Hollywood » électro-minimaliste et contemplatif." Revue musicale OICRM 5, no. 2 (November 30, 2018): 79–102. http://dx.doi.org/10.7202/1054148ar.

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À travers une étude comparative de plusieurs films au contexte narratif contemplatif comme La Ligne Rouge (Terrence Malick, 1998), partition-matrice qui a marqué une nette évolution dans l’esthétique zimmerienne, Hannibal (Ridley Scott, 2001), Da Vinci Code (de Ron Howard, 2006) « synthèse la plus raffinée des influences du minimalisme » (Berthomieu 2013, p. 698), jusqu’à des partitions que Hans Zimmer a composées pour Christopher Nolan comme Inception (2010) et Interstellar (2014), cet article montre de quelle manière Zimmer parvient pleinement à imposer un nouveau courant musical à Hollywood en intégrant une écriture épurée imprégnée notamment par le minimalisme d’Arvo Pärt à des boucles élaborées par des synthétiseurs ou des sons électroniques : si les hommages ciblés à des oeuvres d’Arvo Pärt sont propices à souligner le tourment intérieur ou le recueillement sombre, Zimmer reprend également des principes plus généraux de cette forme de minimalisme – souvent une oscillation immuable et répétée à l’infini autour d’un accord parfait mineur – presque systématiquement mêlés à cette énergie créative de timbres hybrides, afin de créer une autre temporalité apportant une forme d’inéluctable à l’image tout en maintenant empathie et synchronisme discret comme soutiens à l’action (La Ligne rouge, Batman Begins, Da Vinci Code, Inception). La quinte – seule, en ostinato ou répétée sur un motif – quintessence du tintinnabuli zimmerien (au-delà de l’accord parfait pärtien), souligne l’instant suspendu (La Ligne rouge, Hannibal, Interstellar), tandis qu’une forme de radicalisation de ce minimalisme qui va parfois jusqu’à la négation de toute mélodie, remplacée par une note unique, devenue texture abstraite, ou par un cluster diatonique en blend mode (Da Vinci Code, Interstellar), évoque le désespoir, la mort, ou le néant. Loin d’être un « monde » qui « se réduit alors au vide d’un présent sans rêve » (Berthomieu 2004, p. 75), l’écriture électro-minimaliste et contemplative de Zimmer, marquée par une cohérence narrative forte, est connectée au programme esthétique des films auxquels elle se destine.
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Tomescu, Mihaela Aurelia, Lorentz Jäntschi, and Doina Iulia Rotaru. "Figures of Graph Partitioning by Counting, Sequence and Layer Matrices." Mathematics 9, no. 12 (June 18, 2021): 1419. http://dx.doi.org/10.3390/math9121419.

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A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented with colors. Following this fundamental idea, it was proposed to color the graphs according to the partitions of the graph vertices. Two alternative cases were identified: when the order of the sets in the partition is relevant (the sets are distinguished by their positions) and when the order of the sets in the partition is not relevant (the sets are not distinguished by their positions). The two isomers of C28 fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures.
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Lambkin, Christine L. "Partitioned Bremer support localises significant conflict in bee flies (Diptera : Bombyliidae : Anthracinae)." Invertebrate Systematics 18, no. 4 (2004): 351. http://dx.doi.org/10.1071/is04004.

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Partitioned Bremer support examination of combined cladistic analyses indicates nodes at which the support from the partitions differs, and also identifies the location of character disagreement generated by the combination of data matrices. Significant character incongruence was found between mtDNA sequence data and adult morphological characters from three tribes of bee flies (Diptera : Bombyliidae : Anthracinae : Villini, Anthracini, Exoprosopini). Partitioned Bremer support quantitatively reveals the location of significant conflict between characters from the different partitions. Examination of several partitioned support measures show which characters contributed to the disagreement at that node. A very high value of increased support at another node occurred upon combination of the data partitions and was also examined using these support measures.
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Zhang, Yi, Xinwang Liu, Jiyuan Liu, Sisi Dai, Changwang Zhang, Kai Xu, and En Zhu. "Fusion Multiple Kernel K-means." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 9109–17. http://dx.doi.org/10.1609/aaai.v36i8.20896.

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Multiple kernel clustering aims to seek an appropriate combination of base kernels to mine inherent non-linear information for optimal clustering. Late fusion algorithms generate base partitions independently and integrate them in the following clustering procedure, improving the overall efficiency. However, the separate base partition generation leads to inadequate negotiation with the clustering procedure and a great loss of beneficial information in corresponding kernel matrices, which negatively affects the clustering performance. To address this issue, we propose a novel algorithm, termed as Fusion Multiple Kernel k-means (FMKKM), which unifies base partition learning and late fusion clustering into one single objective function, and adopts early fusion technique to capture more sufficient information in kernel matrices. Specifically, the early fusion helps base partitions keep more beneficial kernel details, and the base partitions learning further guides the generation of consensus partition in the late fusion stage, while the late fusion provides positive feedback on two former procedures. The close collaboration of three procedures results in a promising performance improvement. Subsequently, an alternate optimization method with promising convergence is developed to solve the resultant optimization problem. Comprehensive experimental results demonstrate that our proposed algorithm achieves state-of-the-art performance on multiple public datasets, validating its effectiveness. The code of this work is publicly available at https://github.com/ethan-yizhang/Fusion-Multiple-Kernel-K-means.
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Adm, Mohammad, Shaun Fallat, Karen Meagher, Shahla Nasserasr, Sarah Plosker, and Boting Yang. "Achievable multiplicity partitions in the inverse eigenvalue problem of a graph." Special Matrices 7, no. 1 (January 1, 2019): 276–90. http://dx.doi.org/10.1515/spma-2019-0022.

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Abstract Associated to a graph G is a set 𝒮(G) of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are free to be chosen. If G has n vertices, then the multiplicities of the eigenvalues of any matrix in 𝒮 (G) partition n; this is called a multiplicity partition. We study graphs for which a multiplicity partition with only two integers is possible. The graphs G for which there is a matrix in 𝒮 (G) with partitions [n − 2, 2] have been characterized. We find families of graphs G for which there is a matrix in 𝒮 (G) with multiplicity partition [n − k, k] for k ≥ 2. We focus on generalizations of the complete multipartite graphs. We provide some methods to construct families of graphs with given multiplicity partitions starting from smaller such graphs. We also give constructions for graphs with matrix in 𝒮 (G) with multiplicity partition [n − k, k] to show the complexities of characterizing these graphs.
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Liu, Jiyuan, Xinwang Liu, Siwei Wang, Sihang Zhou, and Yuexiang Yang. "Hierarchical Multiple Kernel Clustering." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8671–79. http://dx.doi.org/10.1609/aaai.v35i10.17051.

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Current multiple kernel clustering algorithms compute a partition with the consensus kernel or graph learned from the pre-specified ones, while the emerging late fusion methods firstly construct multiple partitions from each kernel separately, and then obtain a consensus one with them. However, both of them directly distill the clustering information from kernels or graphs to partition matrices, where the sudden dimension drop would result in loss of advantageous details for clustering. In this paper, we provide a brief insight of the aforementioned issue and propose a hierarchical approach to perform clustering while preserving advantageous details maximumly. Specifically, we gradually group samples into fewer clusters, together with generating a sequence of intermediary matrices of descending sizes. The consensus partition with is simultaneously learned and conversely guides the construction of intermediary matrices. Nevertheless, this cyclic process is modeled into an unified objective and an alternative algorithm is designed to solve it. In addition, the proposed method is validated and compared with other representative multiple kernel clustering algorithms on benchmark datasets, demonstrating state-of-the-art performance by a large margin.
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Zoghlami, Mohamed Ali, Minyar Sassi Hidri, and Rahma Ben Ayed. "Consensus-Driven Cluster Analysis: Top-Down and Bottom-Up Based Split-and-Merge Classifiers." International Journal on Artificial Intelligence Tools 26, no. 04 (August 2017): 1750018. http://dx.doi.org/10.1142/s021821301750018x.

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Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Typically, the goal is searching for the socalled median (or consensus) partition, i.e. the partition that is most similar, on average, to all the input partitions. In this paper we address the problem of combining multiple fuzzy clusterings without access to the underlying features of the data while basing on inter-clusters similarity. We are concerned of top-down and bottom-up based consensus-driven fuzzy clustering while splitting and merging worst clusters. The objective is to reconcile a structure, developed for patterns in some dataset with the structural findings already available for other related ones. The proposed classifiers consider dispersion and dissimilarity between the partitions as well as the corresponding fuzzy proximity matrices. Several illustrative numerical examples, using both synthetic data and those coming from available machine learning repositories, are also included. The experimental component of the study shows the efficiency of the proposed classifiers in terms of quality and runtime.
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Dalfó, Cristina, and Miquel Àngel Fiol. "A general method to obtain the spectrum and local spectra of a graph from its regular partitions." Electronic Journal of Linear Algebra 36, no. 36 (July 12, 2020): 446–60. http://dx.doi.org/10.13001/ela.2020.5225.

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It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also the local spectra, of a graph from the quotient matrices of some of its regular partitions, is proposed. Moreover, from such partitions, the $C$-local multiplicities of any class of vertices $C$ is also determined, and some applications of these parameters in the characterization of completely regular codes and their inner distributions are described. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.
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Shen, Shuhui, and Xiaojun Zhang. "Constructions of Goethals–Seidel Sequences by Using k-Partition." Mathematics 11, no. 2 (January 6, 2023): 294. http://dx.doi.org/10.3390/math11020294.

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In this paper, we are devoted to finding Goethals–Seidel sequences by using k-partition, and based on the finite Parseval relation, the construction of Goethals–Seidel sequences could be transformed to the construction of the associated polynomials. Three different structures of Goethals–Seidel sequences will be presented. We first propose a method based on T-matrices directly to obtain a quad of Goethals–Seidel sequences. Next, by introducing the k-partition, we utilize two classes of 8-partitions to obtain a new class of polynomials still remaining the same (anti)symmetrical properties, with which a quad of Goethals–Seidel sequences could be constructed. Moreover, an adoption of the 4-partition together with a quad of four symmetrical sequences can also lead to a quad of Goethals–Seidel sequences.
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Benatia, Akrem, Weixing Ji, Yizhuo Wang, and Feng Shi. "Sparse matrix partitioning for optimizing SpMV on CPU-GPU heterogeneous platforms." International Journal of High Performance Computing Applications 34, no. 1 (November 14, 2019): 66–80. http://dx.doi.org/10.1177/1094342019886628.

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Sparse matrix–vector multiplication (SpMV) kernel dominates the computing cost in numerous applications. Most of the existing studies dedicated to improving this kernel have been targeting just one type of processing units, mainly multicore CPUs or graphics processing units (GPUs), and have not explored the potential of the recent, rapidly emerging, CPU-GPU heterogeneous platforms. To take full advantage of these heterogeneous systems, the input sparse matrix has to be partitioned on different available processing units. The partitioning problem is more challenging with the existence of many sparse formats whose performances depend both on the sparsity of the input matrix and the used hardware. Thus, the best performance does not only depend on how to partition the input sparse matrix but also on which sparse format to use for each partition. To address this challenge, we propose in this article a new CPU-GPU heterogeneous method for computing the SpMV kernel that combines between different sparse formats to achieve better performance and better utilization of CPU-GPU heterogeneous platforms. The proposed solution horizontally partitions the input matrix into multiple block-rows and predicts their best sparse formats using machine learning-based performance models. A mapping algorithm is then used to assign the block-rows to the CPU and GPU(s) available in the system. Our experimental results using real-world large unstructured sparse matrices on two different machines show a noticeable performance improvement.
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Dissertations / Theses on the topic "Matrice partitions"

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Quéré, Romain. "Quelques propositions pour la comparaison de partitions non strictes." Phd thesis, Université de La Rochelle, 2012. http://tel.archives-ouvertes.fr/tel-00950514.

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Cette thèse est consacrée au problème de la comparaison de deux partitions non strictes (floues/probabilistes, possibilistes) d'un même ensemble d'individus en plusieurs clusters. Sa résolution repose sur la définition formelle de mesures de concordance reprenant les principes des mesures historiques développées pour la comparaison de partitions strictes et trouve son application dans des domaines variés tels que la biologie, le traitement d'images, la classification automatique. Selon qu'elles s'attachent à observer les relations entre les individus décrites par chacune des partitions ou à quantifier les similitudes entre les clusters qui composent ces partitions, nous distinguons deux grandes familles de mesures pour lesquelles la notion même d'accord entre partitions diffère, et proposons d'en caractériser les représentants selon un même ensemble de propriétés formelles et informelles. De ce point de vue, les mesures sont aussi qualifiées selon la nature des partitions comparées. Une étude des multiples constructions sur lesquelles reposent les mesures de la littérature vient compléter notre taxonomie. Nous proposons trois nouvelles mesures de comparaison non strictes tirant profit de l'état de l'art. La première est une extension d'une approche stricte tandis que les deux autres reposent sur des approches dite natives, l'une orientée individus, l'autre orientée clusters, spécifiquement conçues pour la comparaison de partitions non strictes. Nos propositions sont comparées à celles de la littérature selon un plan d'expérience choisi pour couvrir les divers aspects de la problématique. Les résultats présentés montrent l'intérêt des propositions pour le thème de recherche qu'est la comparaison de partitions. Enfin, nous ouvrons de nouvelles perspectives en proposant les prémisses d'un cadre qui unifie les principales mesures non strictes orientées individus.
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Barsukov, Alexey. "On dichotomy above Feder and Vardi's logic." Electronic Thesis or Diss., Université Clermont Auvergne (2021-...), 2022. https://tel.archives-ouvertes.fr/tel-04100704.

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On dit d'un sous-ensemble de NP qu'il présente une dichotomie s'il contient des problèmes qui sont soit résolubles en temps polynomial (dans Ptime), soit difficiles (NP-complets). La classe des problèmes de satisfaction de contraintes (CSP) finis est un sous-ensemble bien connu de NP qui présente une telle dichotomie. La classe de complexité NP n'a pas de dichotomie à moins que P = NP. Pour ces deux classes, il existe des logiques qui leur sont associées. -- NP est capturé par la logique Existentielle du second ordre (ESO) par le théorème de Fagin, c'est-à-dire qu'un problème est dans NP si et seulement s'il est exprimable par une formule ESO.-- CSP est un sous-ensemble de la logique de Feder et Vardi, le fragment monotone, monadique et sans inégalités de SNP, lui-même un fragment syntaxique de ESO (MMSNP); et, pour chaque formule de MMSNP, il existe un problème CSP équivalent via des réductions polynomiales.Ceci implique que la logique ESO, tout comme NP, n'a pas de dichotomie, à contraster avec le fait que MMSNP a une dichotomie tout comme CSP. L'objectif principal de cette thèse est d'étudier les propriétés de dichotomie de sous-ensembles de NP qui contiennent strictement CSP ou MMSNP.Feder et Vardi ont prouvé que si nous omettons une des trois propriétés qui définissent MMSNP, à savoir être monotone, monadique ou omettre les inégalités, alors la logique résultante n'a pas de dichotomie. Comme leurs preuves restent parfois sommaires, nous revisitons ces résultats et fournissons des preuves détaillées. Le fragment guardé et monotone de SNP (GMSNP) est une extension connue de MMSNP qui est obtenue en relâchant la restriction "monadique" de MMSNP. Nous définissons de manière similaire une nouvelle logique appelée MMSNP avec des inégalités gardées, en relâchant la restriction d'être "sans inégalités". Nous prouvons qu'elle est strictement plus expressive que MMSNP et qu'elle possède également une dichotomie.Il existe une logique MMSNP₂ qui étend MMSNP de la même manière que MSO₂ étend la logique monadique du second ordre (MSO). On sait que MMSNP₂ est un fragment de GMSNP et que ces deux classes ont toutes deux une dichotomie ou n'en ont pas. Nous revisitons ce résultat et le renforçons en prouvant que, en ce qui concerne le fait d'avoir une dichotomie, sans perte de généralité, on peut considérer seulement les problèmes MMSNP₂ sur des signatures à un élément, au lieu des problèmes GMSNP sur des signatures finies arbitraires.Nous cherchons à prouver l'existence d'une dichotomie pour les MMSNP₂ en construisant en temps polynomial, pour tout problème MMSNP₂, un problème MMSNP équivalent. Nous rencontrons quelques obstacles pour construire une telle équivalence. Cependant, si nous permettons aux formules MMSNP d'être composées d'un nombre dénombrable de conjonctions négatives, nous prouvons qu'une telle équivalence existe. De plus, la formule MMSNP infinie correspondante a la propriété d'être "régulière". Cette propriété de régularité signifie que, dans un certain sens, cette formule est essentiellement finie. Il est connu que les problèmes MMSNP réguliers peuvent être exprimés par CSP sur des modèles oméga-catégoriques. De plus, il existe une caractérisation de la dichotomie algébrique pour les CSP oméga-catégoriques qui décrivent des problèmes MMSNP. Si l'on parvient à étendre cette caractérisation algébrique sur les problèmes réguliers MMSNP, alors notre résultat fournirait une dichotomie algébrique pour MMSNP₂. (...)
A subset of NP is said to have a dichotomy if it contains problem that are either solvable in P-time or NP-complete. The class of finite Constraint Satisfaction Problems (CSP) is a well-known subset of NP that follows such a dichotomy. The complexity class NP does not have a dichotomy unless P = NP. For both of these classes there exist logics that are associated with them. -- NP is captured by Existential Second-Order (ESO) logic by Fagin's theorem, i.e., a problem is in NP if and only if it is expressible by an ESO sentence.-- CSP is a subset of Feder and Vardi's logic, Monotone Monadic Strict NP without inequalities (MMSNP), and for every MMSNP sentence there exists a P-time equivalent CSP problem. This implies that ESO does not have a dichotomy as well as NP, and that MMSNP has a dichotomy as well as CSP. The main objective of this thesis is to study subsets of NP that strictly contain CSP or MMSNP with respect to the dichotomy existence.Feder and Vardi proved that if we omit one of the three properties that define MMSNP, namely being monotone, monadic or omitting inequalities, then the resulting logic does not have a dichotomy. As their proofs remain sketchy at times, we revisit these results and provide detailed proofs. Guarded Monotone Strict NP (GMSNP) is a known extension of MMSNP that is obtained by relaxing the "monadic" restriction of MMSNP. We define similarly a new logic that is called MMSNP with Guarded inequalities, relaxing the restriction of being "without inequalities". We prove that it is strictly more expressive than MMSNP and that it also has a dichotomy.There is a logic MMSNP₂ that extends MMSNP in the same way as MSO₂ extends Monadic Second-Order (MSO) logic. It is known that MMSNP₂ is a fragment of GMSNP and that these two classes either both have a dichotomy or both have not. We revisit this result and strengthen it by proving that, with respect to having a dichotomy, without loss of generality, one can consider only MMSNP₂ problems over one-element signatures, instead of GMSNP problems over arbitrary finite signatures.We seek to prove the existence of a dichotomy for MMSNP₂ by finding, for every MMSNP₂ problem, a P-time equivalent MMSNP problem. We face some obstacles to build such an equivalence. However, if we allow MMSNP sentences to consist of countably many negated conjuncts, then we prove that such an equivalence exists. Moreover, the corresponding infinite MMSNP sentence has a property of being "regular". This regular property means that, in some sense, this sentence is still finite. It is known that regular MMSNP problems can be expressed by CSP on omega-categorical templates. Also, there is an algebraic dichotomy characterisation for omega-categorical CSPs that describe MMSNP problems. If one manages to extend this algebraic characterisation onto regular MMSNP, then our result would provide an algebraic dichotomy for MMSNP₂.Another potential way to prove the existence of a dichotomy for MMSNP₂ is to mimic the proof of Feder and Vardi for MMSNP. That is, by finding a P-time equivalent CSP problem. The most difficult part there is to reduce a given input structure to a structure of sufficiently large girth. For MMSNP and CSP, it is done using expanders, i.e., structures, where the distribution of tuples is close to a uniform distribution. We study this approach with respect to MMSNP₂ and point out the main obstacles. (...)
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Fonseca, Tiago. "Matrices à signes alternants, boucles denses et partitions planes." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00521884.

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Cette thèse est consacrée à l'étude d'identités qu'on observe à l'interface entre le domaine des modèles intégrables en physique statistique et la combinatoire. L'histoire a commencé quand Mills, Robbins et Rumsey étudiaient des Matrices à Signes Alternants (ASM). En 1982, ils proposèrent une formule d'énumération. Pendant qu'ils cherchaient une preuve de cette formule ils découvrirent l'existence d'autres objets comptés par la même formule : les Partitions Planes Totalement Symétriques Auto-Complémentaires (TSSCPP). C'est seulement quelques années plus tard que Zeilberger fut capable de prouver cette égalité, prouvant que les deux objets sont comptés par la même formule. La même année, Kuperberg utilise l'intégrabilité quantique (notion venue de la physique statistique) pour donner une preuve plus simple. En 2001, Razumov et Stroganov conjecturèrent une intrigante relation entre les ASM et l'état fondamental du modèle de spins XXZ (pour Delta=-1/2), lui aussi intégrable. Cette conjecture a été démontrée en 2010 par Cantini et Sportiello. L'objectif principal de ce manuscrit est de comprendre le rôle de l'intégrabilité dans cette histoire, notamment le rôle joué par l'équation de Knizhnik-Zamolodchikov quantique. Grâce à cette équation nous avons été capables de démontrer plusieurs conjectures combinatoires, dont une version raffinée de l'équalité entre le nombre des TSSCPP et des ASM proposée en 1986 par Mills, Robbins et Rumsey et certains propriétés des composantes du vecteur fondamental du modèle XXZ. Est présentée aussi une série de nouvelles conjectures concernant l'état fondamental.
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Dinis, Da Fonseca Tiago. "Matrices de signe alternant, boucles denses et partitions planes." Paris 6, 2010. http://www.theses.fr/2010PA066281.

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Cette thèse est consacrée à l'étude d'identités qu'on observe à l'interface entre le domaine des modèles intégrables en physique statistique et la combinatoire. L'histoire commence quand Mills, Robbins et Rumsey étudiaient des Matrices de Signe Alternant (ASM). En 1982, ils proposèrent une formule d'énumeration. Pendant qu'ils cherchaient une preuve de cette formule ils découvrirent l'existence d'autres objets comptés par la même formule : les Partitions Planes Totalement Symétriques Auto-Complementaires (TSSCPP). C'est seulement quelques années plus tard que Zeilberger fut capable de prouver cet équalité, prouvant que tout les deux objets sont comptés par la même formule. La même année, Kuperberg utilise l'integrabilité quantique (notion venu de la physique statistique) pour donner une preuve plus simple. En 2001, Razumov et Stroganov conjecturèrent une intrigante relation entre les ASM et l'état fondamental du modèle de spins XXZ (pour Delta=-1/2), lui aussi intégrable. Cette conjecture fut démontrée en 2010 par Cantini et Sportiello. L'objectif principal de ce manuscrit est de comprendre le rôle de l'intégrabilité dans cette histoire, notamment, le rôle joué par l'équation Knizhnik-Zamolodchikov quantique. Grâce à cette équation nous avons été capables de démontrer plusieurs conjectures combinatoires, dont une version raffinée de l'équalité entre le nombre des TSSCPP et des ASM proposée en 1986 par Mills, Robbins et Rumsey et certains propriétés des composantes du vecteur fondamental du modèle XXZ. Est présentée aussi une série de nouvelles conjectures concernant l'état fondamental.
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Cheballah, Hayat. "Combinatoire des matrices à signes alternants et des partitions planes." Paris 13, 2011. http://www.theses.fr/2011PA132054.

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Cette thèse se situe dans le domaine de la combinatoire bijective et est consacrée à la construction d’une bijection explicite entre deux familles d’objets combinatoires : les matrices à signes alternants (ASMs) et les partitions planes totalement symétriques auto-complémentaires (TSSCPPs). L’histoire a commencé lorsque Milis, Robbins et Rumsey étudiaient les ASMs et proposèrent une formule d’énumération en 1982. Durant leurs recherches, ils découvrirent l’existence d’autres objets comptés par la même formule : les TSSCPPs. Dix ans plus tard, une preuve non bijective de l’équiénumération de ces deux familles fut donnée par Zeilberger. Pour ce faire, Zeilberger utilise deux sous classes de motif de Gelfand-Tsetlin ; les triangles Gog et les triangles Magog. Pendant ces dernières années les recherches se sont multipliées afin de donner une preuve bijective du théorème de Zeilberger. Citons notamment les travaux de Krattenthaler qui construit une bijection explicite entre les trapézoïdes Gog et Magog à une ligne. L’étape suivante, celle des trapézoïdes à deux lignes, semblait inaccessible. L’objectif de cette thèse est de résoudre ce problème grace à l’utilisation d’un outil fondamental en combinatoire, l’involution de Schiitzenberger. Nous avons pour cela défini des nouvelles statistiques sur les triangles Gog et les triangles Magog et nous montrons expérimentalement que la bijection que nous construisons respecte ces statistiques. Nous présentons également de nouvelles conjectures sur ces statistiques.
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Pierce, Virgil. "The asymptotic expansion of the partition function of random matrices." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280566.

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We explore two methods for calculating the Taylor Coefficients of the terms of the asymptotic expansion of the partition function of random matrices for specific even potentials. The first of these methods applies to the leading order term. We show that this term has an elementary form in terms of a solution to an algebraic equation. This generates a general formula for the Taylor Coefficients of this term. Next we exploit the relationship between orthogonal polynomials and the Toda Lattice Equations to derive ODE's for the general terms of the expansion of the partition function of random matrices, which leads to a method of calculating the Taylor Coefficients of these functions.
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Cabanal-Duvillard, Thierry. "Probabilités libres et calcul stochastique : application aux grandes matrices aléatoires." Paris 6, 1999. http://www.theses.fr/1999PA066594.

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Thüne, Mario. "Eigenvalues of Matrices and Graphs." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-120713.

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The interplay between spectrum and structure of graphs is the recurring theme of the three more or less independent chapters of this thesis. The first chapter provides a method to relate the eigensolutions of two matrices, one being the principal submatrix of the other, via an arbitrary annihilating polynomial. This is extended to lambda-matrices and to matrices the entries of which are rational functions in one variable. The extension may be interpreted as a possible generalization of other known techniques which aim at reducing the size of a matrix while preserving the spectral information. Several aspects of an application in order to reduce the computational costs of ordinary eigenvalue problems are discussed. The second chapter considers the straightforward extension of the well known concept of equitable partitions to weighted graphs, i.e. complex matrices. It provides a method to divide the eigenproblem into smaller parts corresponding to the front divisor and its complementary factor in an easy and stable way with complexity which is only quadratic in matrix size. The exploitation of several equitable partitions ordered by refinement is discussed and a suggestion is made that preserves hermiticity if present. Some generalizations of equitable partitions are considered and a basic procedure for finding an equitable partition of complex matrices is given. The third chapter deals with isospectral and unitary equivalent graphs. It introduces a construction for unitary equivalent graphs which contains the well known GM-switching as a special case. It also considers an algebra of graph matrices generated by the adjacency matrix that corresponds to the 1-dimensional Weisfeiler-Lehman stabilizer in a way that mimics the correspondence of the coherent closure and the 2-dimensional Weisfeiler-Lehman stabilizer. The algebra contains the degree matrix, the (combinatorial, signless and normalized) Laplacian and the Seidel matrix. An easy construction produces graph pairs that are simultaneously unitary equivalent w.r.t. that algebra.
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Bagatini, Alessandro. "Matrix representation for partitions and Mock Theta functions." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/150232.

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Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem.
In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.
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Bas, Erdeniz Ozgun. "Load-Balancing Spatially Located Computations using Rectangular Partitions." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306909831.

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Books on the topic "Matrice partitions"

1

Claudio, Procesi, ed. Topics in hyperplane arrangements, polytopes and box-splines. New York: Springer, 2011.

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Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. Providence, Rhode Island: American Mathematical Society, 2016.

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Su, Zhonggen. Random Matrices and Random Partitions Normal Convergence. World Scientific Publishing Co Pte Ltd, 2015.

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Parametric state space structuring. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Guhr, Thomas. Replica approach in random matrix theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.8.

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This article examines the replica method in random matrix theory (RMT), with particular emphasis on recently discovered integrability of zero-dimensional replica field theories. It first provides an overview of both fermionic and bosonic versions of the replica limit, along with its trickery, before discussing early heuristic treatments of zero-dimensional replica field theories, with the goal of advocating an exact approach to replicas. The latter is presented in two elaborations: by viewing the β = 2 replica partition function as the Toda lattice and by embedding the replica partition function into a more general theory of τ functions. The density of eigenvalues in the Gaussian Unitary Ensemble (GUE) and the saddle point approach to replica field theories are also considered. The article concludes by describing an integrable theory of replicas that offers an alternative way of treating replica partition functions.
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Keating, Jon, and Nina Snaith. Random permutations and related topics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.25.

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This article considers some topics in random permutations and random partitions highlighting analogies with random matrix theory (RMT). An ensemble of random permutations is determined by a probability distribution on Sn, the set of permutations of [n] := {1, 2, . . . , n}. In many ways, the symmetric group Sn is linked to classical matrix groups. Ensembles of random permutations should be given the same treatment as random matrix ensembles, such as the ensembles of classical compact groups and symmetric spaces of compact type with normalized invariant measure. The article first describes the Ewens measures, virtual permutations, and the Poisson-Dirichlet distributions before discussing results related to the Plancherel measure on the set of equivalence classes of irreducible representations of Sn and its consecutive generalizations: the z-measures and the Schur measures.
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Marino, Marcos. Quantum chromodynamics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.32.

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This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.
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Concini, Corrado De, and Claudio Procesi. Topics in Hyperplane Arrangements, Polytopes and Box-Splines. Springer London, Limited, 2010.

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Book chapters on the topic "Matrice partitions"

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Hildenbrandt, Regina. "Partitions-requirements-matrices." In Operations Research Proceedings 2001, 303–10. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-50282-8_38.

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Beck, J., and J. Spencer. "Balancing Matrices with Line Shifts II." In Irregularities of Partitions, 23–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-61324-1_2.

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Zhang, Fuzhen. "Partitioned Matrices." In Universitext, 29–58. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-5797-2_2.

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Hackbusch, Wolfgang. "Matrix Partition." In Hierarchical Matrices: Algorithms and Analysis, 83–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47324-5_5.

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Harville, David A. "Submatrices and Partitioned Matrices." In Matrix Algebra From a Statistician’s Perspective, 13–22. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/0-387-22677-x_2.

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Harville, David A. "Submatrices and Partitioned Matrices." In Matrix Algebra: Exercises and Solutions, 7–10. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0181-3_2.

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Zhang, Fuzhen. "Partitioned Matrices, Rank, and Eigenvalues." In Universitext, 35–72. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1099-7_2.

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Abed, Fidaa, Ioannis Caragiannis, and Alexandros A. Voudouris. "Near-Optimal Asymmetric Binary Matrix Partitions." In Mathematical Foundations of Computer Science 2015, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48054-0_1.

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Alon, Noga, Michal Feldman, Iftah Gamzu, and Moshe Tennenholtz. "The Asymmetric Matrix Partition Problem." In Web and Internet Economics, 1–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45046-4_1.

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Kuang, Da, Jaegul Choo, and Haesun Park. "Nonnegative Matrix Factorization for Interactive Topic Modeling and Document Clustering." In Partitional Clustering Algorithms, 215–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09259-1_7.

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Conference papers on the topic "Matrice partitions"

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Sankhavara, C. D., and H. J. Shukla. "Influence of Partition Location on Natural Convection in a Partitioned Enclosure." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72093.

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In this study, Natural convection heat transfer and fluid flow of square partitioned enclosure with two partitions protruding centrally from the end walls of an enclosure have been analysed numerically using finite element method. The enclosure has opposite isothermal walls at different temperatures. The thickness and length of the partitions is fixed and equal to 1/10 and 1/4 of width of the enclosure respectively. Computation for Rayleigh number in the range of 104 to 106 has been conducted. The influence of different thermal boundary conditions at the end walls and at the partitions is included in the investigation. ‘Standard’ boundary conditions are introduced as more appropriate to simulate situations of practical engineering interest. To solve the relevant governing equations a segregated sequential solution algorithm is used after employing Boussinesq approximation. These equations after discretization were solved by using the tridiagonal matrix algorithm. Results clearly demonstrate that partition location has a significant effect on heat transfer.
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Kang, Zhao, Zipeng Guo, Shudong Huang, Siying Wang, Wenyu Chen, Yuanzhang Su, and Zenglin Xu. "Multiple Partitions Aligned Clustering." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/375.

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Multi-view clustering is an important yet challenging task due to the difficulty of integrating the information from multiple representations. Most existing multi-view clustering methods explore the heterogeneous information in the space where the data points lie. Such common practice may cause significant information loss because of unavoidable noise or inconsistency among views. Since different views admit the same cluster structure, the natural space should be all partitions. Orthogonal to existing techniques, in this paper, we propose to leverage the multi-view information by fusing partitions. Specifically, we align each partition to form a consensus cluster indicator matrix through a distinct rotation matrix. Moreover, a weight is assigned for each view to account for the clustering capacity differences of views. Finally, the basic partitions, weights, and consensus clustering are jointly learned in a unified framework. We demonstrate the effectiveness of our approach on several real datasets, where significant improvement is found over other state-of-the-art multi-view clustering methods.
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Gobel, Andreas, Leslie Ann Goldberg, Colin McQuillan, David Richerby, and Tomoyuki Yamakami. "Counting List Matrix Partitions of Graphs." In 2014 IEEE Conference on Computational Complexity (CCC). IEEE, 2014. http://dx.doi.org/10.1109/ccc.2014.14.

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Langr, Daniel, and Ivan Šimeček. "On Memory Footprints of Partitioned Sparse Matrices." In 2017 Federated Conference on Computer Science and Information Systems. IEEE, 2017. http://dx.doi.org/10.15439/2017f70.

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Qiu, Chen, and Jian S. Dai. "Constraint Stiffness Construction and Decomposition of a SPS Orthogonal Parallel Mechanism." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46811.

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This paper investigates both stiffness analysis and synthesis problems using a physical prototype of one SPS orthogonal parallel mechanism. This parallel mechanism is supported with line-type constraint limbs. In the stiffness analysis, a reciprocal relationship between motions and wrenches is used to design layouts of constraint limbs and construct the corresponding stiffness matrix. In the stiffness synthesis, the developed stiffness matrix is decomposed to obtain configurations of constraint limbs based on existing synthesis algorithms, including direct-recursion and matrix-partition approaches. It is revealed the line-vector based matrix-partition approach can establish an one-to-one correspondence between synthesized results and constraint limbs of the parallel mechanism. Subsequently both types of synthesis approaches are applied to decomposing the developed constraint stiffness matrix. The comparison results suggest the modified matrix-partition approach can obtain decomposed constraint limbs exactly the same as those used to construct the stiffness matrix.
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Sugino, Fumihiko. "U-duality from matrix membrane partition function." In STRING THEORY; 10th Tohwa University International Symposium on String Theory. AIP, 2002. http://dx.doi.org/10.1063/1.1454380.

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Lin, Po Ting, Yu-Cheng Chou, Mark Christian E. Manuel, and Kuan Sung Hsu. "Investigation of Numerical Performance of Partitioning and Parallel Processing of Markov Chain (PPMC) for Complex Design Problems." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34652.

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Divide-and-conquer strategies have been utilized to perform evaluation calculations of complex network systems, such as reliability analysis of a Markov chain. This paper focuses on partitioning of Markov chain for a multi-modular redundant system and the fast calculation using parallel processing. The complexity of Markov chain is first reduced by eliminating the connections with low transition probabilities associated with a threshold parameter. The transition probability matrix is then reordered and partitioned such that a worse-case reliability is evaluated through the calculations in only the diagonal sub-matrices of the transition probability matrix. Since the calculations of the sub-matrices are independent to each other, the numerical efficiency can be greatly improved using parallel computing. The numerical results showed the selection of threshold parameter is a key factor to numerical efficiency. In this paper, the sensitivity of the numerical performance of Partitioning and Parallel-processing of Markov Chain (PPMC) to the threshold parameter has been investigated and discussed.
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Fabregat-Traver, Diego, Paolo Bientinesi, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Automatic Generation of Partitioned Matrix Expressions for Matrix Operations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498598.

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Strofylas, Giorgos A., Georgios I. Mazanakis, Sotirios S. Sarakinos, Georgios N. Lygidakis, and Ioannis K. Nikolos. "On the Use of Improved Radial Basis Functions Methods in Fluid-Structure Interaction Simulations." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66412.

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The development of an efficient partitioned FSI coupling scheme is reported in this paper, aimed to facilitate interaction between an open-source CSD software package and an in-house academic CFD code. The coupling procedure is based on Radial Basis Functions (RBFs) interpolation for both information transfer and mesh deformation, entailing no dependence on connectivities, and hence making it applicable to different type or even intersecting grids. However, the method calls for increased computational resources in its initial formulation; to alleviate this deficiency, appropriate acceleration techniques have been incorporated, namely the Partition of Unity (PoU) approach and a surface-point reduction scheme. The PoU approach was adopted in case of data transfer, localizing the interpolation process and therefore reducing the size of the coupling matrix. An alternative approach was applied to improve the efficiency of the mesh deformation procedure, based on the agglomeration of the flow/structure interface nodes used for the RBFs interpolation method. For the demonstration of the proposed scheme a static aeroelastic simulation of a real bridge model, during its construction phase, was performed. The extracted results exhibit its potential to encounter effectively such complicated test cases, in a computationally efficient way.
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Chou, Chiu-Chih, Thong Nguyen, and Jose E. Schutt-Aine. "Impact of Partition Schemes in Loewner Matrix Macromodeling." In 2020 IEEE Electrical Design of Advanced Packaging and Systems (EDAPS). IEEE, 2020. http://dx.doi.org/10.1109/edaps50281.2020.9312918.

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Reports on the topic "Matrice partitions"

1

Brenan, J. M., K. Woods, J. E. Mungall, and R. Weston. Origin of chromitites in the Esker Intrusive Complex, Ring of Fire Intrusive Suite, as revealed by chromite trace element chemistry and simple crystallization models. Natural Resources Canada/CMSS/Information Management, 2021. http://dx.doi.org/10.4095/328981.

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To better constrain the origin of the chromitites associated with the Esker Intrusive Complex (EIC) of the Ring of Fire Intrusive Suite (RoFIS), a total of 50 chromite-bearing samples from the Black Thor, Big Daddy, Blackbird, and Black Label chromite deposits have been analysed for major and trace elements. The samples represent three textural groups, as defined by the relative abundance of cumulate silicate phases and chromite. To provide deposit-specific partition coefficients for modeling, we also report on the results of laboratory experiments to measure olivine- and chromite-melt partitioning of V and Ga, which are two elements readily detectable in the chromites analysed. Comparison of the Cr/Cr+Al and Fe/Fe+Mg of the EIC chromites and compositions from previous experimental studies indicates overlap in Cr/Cr+Al between the natural samples and experiments done at >1400oC, but significant offset of the natural samples to higher Fe/Fe+Mg. This is interpreted to be the result of subsolidus Fe-Mg exchange between chromite and the silicate matrix. However, little change in Cr/Cr+Al from magmatic values, owing to the lack of an exchangeable reservoir for these elements. A comparison of the composition of the EIC chromites and a subset of samples from other tectonic settings reveals a strong similarity to chromites from the similarly-aged Munro Township komatiites. Partition coefficients for V and Ga are consistent with past results in that both elements are compatible in chromite (DV = 2-4; DGa ~ 3), and incompatible in olivine (DV = 0.01-0.14; DGa ~ 0.02), with values for V increasing with decreasing fO2. Simple fractional crystallization models that use these partition coefficients are developed that monitor the change in element behaviour based on the relative proportions of olivine to chromite in the crystallizing assemblage; from 'normal' cotectic proportions involving predominantly olivine, to chromite-only crystallization. Comparison of models to the natural chromite V-Ga array suggests that the overall positive correlation between these two elements is consistent with chromite formed from a Munro Township-like komatiitic magma crystallizing olivine and chromite in 'normal' cotectic proportions, with no evidence of the strong depletion in these elements expected for chromite-only crystallization. The V-Ga array can be explained if the initial magma responsible for chromite formation is slightly reduced with respect to the FMQ oxygen buffer (~FMQ- 0.5), and has assimilated up to ~20% of wall-rock banded iron formation or granodiorite. Despite the evidence for contamination, results indicate that the EIC chromitites crystallized from 'normal' cotectic proportions of olivine to chromite, and therefore no specific causative link is made between contamination and chromitite formation. Instead, the development of near- monomineralic chromite layers likely involves the preferential removal of olivine relative to chromite by physical segregation during magma flow. As suggested for some other chromitite-forming systems, the specific fluid dynamic regime during magma emplacement may therefore be responsible for crystal sorting and chromite accumulation.
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