Laplacian eigenvectors and eigenvalues and almost equitable partitions

Relations between Laplacian eigenvectors and eigenvalues and the existence of almost equitable partitions (which are generalizations of equitable partitions) are presented. Furthermore, on the basis of some properties of the adjacency eigenvectors of a graph, a necessary and sufficient condition for the graph to be primitive strongly regular is introduced. © 2006 Elsevier Ltd. All rights reserved.

Stratégies intermédiales et autoreprésentation dans l'oeuvre littéraire et les dessins-partitions d'Unica Zürn

Par son recours à diverses formes d’expression, Unica Zürn (1916-1970) redynamise l’espace de la feuille en le faisant activement participer à l’écriture de soi. Le « je » semble en effet se démultiplier grâce à des jeux « anagrammatiques » sur les divers signes mobilisés, qu’ils soient alphabétiques, picturaux ou musicaux. L’autoreprésentation s’inscrit alors au sein d’une œuvre pluridisciplinaire inusitée, qui renouvelle l’esthétique quelque peu « essoufflée » du mouvement surréaliste. Cette attitude vis-à-vis de la feuille, où plusieurs signes « décomposables » et « recomposables » se partagent l’espace, est observable tant dans l’œuvre littéraire que picturale d’Unica Zürn. Le processus de création par la lettre, le trait et la note de musique, tend à revaloriser le support matériel utilisé par l’effacement des frontières entre les disciplines artistiques, qui appelle un regard distancié du lecteur/spectateur sur l’œuvre. Afin d’interpréter les travaux de Zürn dans la pluralité des moyens artistiques qui y sont déployés, l’approche intermédiale sera favorisée. Dans le premier chapitre de ce mémoire, il s’agira d’abord de voir comment s’articule un certain dialogue entre le discours des chercheurs de l’intermédialité et l’œuvre d’Unica Zürn. Le rapport à l’objet sera notre porte d’entrée dans la matière intermédiale. Par un retour à la matérialité de l’expérience médiatique, nous constaterons que Zürn met à l’avant-scène les instruments et supports de la création, ce qui mène à une représentation distorsionnée de soi, de l’espace et du temps. Une fois le parallèle établi entre les concepts de l’intermédialité et les travaux de Zürn, nous nous concentrerons sur le pan musical de l’œuvre pluridisciplinaire de l’auteure-artiste. Le second chapitre traitera de l’intrusion du sonore dans l’univers textuel, qui se fera notamment par la réappropriation de l’opéra Norma, de Vincenzo Bellini. Cette réécriture s’intitule Les jeux à deux et prend une distance considérable par rapport au texte originel. Elle s’accompagne de dessins effectués par l’auteure-artiste à même les partitions de l’opéra. Le regard multiple posé sur l’œuvre zürnienne permettra de comprendre que l’écriture palimpseste participe du processus d’autoreprésentation, tout en élaborant un discours sur la rencontre entre littérature, dessin et musique, ainsi que sur l’influence de cette juxtaposition sur le débordement des frontières médiatiques traditionnelles.

Partitions spectrales optimales pour les problèmes aux valeurs propres de Dirichlet et de Neumann

Les façons d'aborder l'étude du spectre du laplacien sont multiples. Ce mémoire se concentre sur les partitions spectrales optimales de domaines planaires. Plus précisément, lorsque nous imposons des conditions aux limites de Dirichlet, nous cherchons à trouver la ou les partitions qui réalisent l'infimum (sur l'ensemble des partitions à un certain nombre de composantes) du maximum de la première valeur propre du laplacien sur tous ses sous-domaines. Dans les dernières années, cette question a été activement étudiée par B. Helffer, T. Hoffmann-Ostenhof, S. Terracini et leurs collaborateurs, qui ont obtenu plusieurs résultats analytiques et numériques importants. Dans ce mémoire, nous proposons un problème analogue, mais pour des conditions aux limites de Neumann cette fois. Dans ce contexte, nous nous intéressons aux partitions spectrales maximales plutôt que minimales. Nous cherchons alors à vérifier le maximum sur toutes les $k$-partitions possibles du minimum de la première valeur propre non nulle de chacune des composantes. Cette question s'avère plus difficile que sa semblable dans la mesure où plusieurs propriétés des valeurs propres de Dirichlet, telles que la monotonicité par rapport au domaine, ne tiennent plus. Néanmoins, quelques résultats sont obtenus pour des 2-partitions de domaines symétriques et des partitions spécifiques sont trouvées analytiquement pour des domaines rectangulaires. En outre, des propriétés générales des partitions spectrales optimales et des problèmes ouverts sont abordés.

Partitions selection strategy for set of clustering solutions

Clustering is a difficult task: there is no single cluster definition and the data can have more than one underlying structure. Pareto-based multi-objective genetic algorithms (e.g., MOCK Multi-Objective Clustering with automatic K-determination and MOCLE-Multi-Objective Clustering Ensemble) were proposed to tackle these problems. However, the output of such algorithms can often contains a high number of partitions, becoming difficult for an expert to manually analyze all of them. In order to deal with this problem, we present two selection strategies, which are based on the corrected Rand, to choose a subset of solutions. To test them, they are applied to the set of solutions produced by MOCK and MOCLE in the context of several datasets. The study was also extended to select a reduced set of partitions from the initial population of MOCLE. These analysis show that both versions of selection strategy proposed are very effective. They can significantly reduce the number of solutions and, at the same time, keep the quality and the diversity of the partitions in the original set of solutions. (C) 2010 Elsevier B.V. All rights reserved.

Generalized external indexes for comparing data partitions with overlapping categories

There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833-841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. (c) 2010 Elsevier B.V. All rights reserved.

Ergodic properties of triangle partitions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MODEL PARTITIONS AND COMPACT TEST CASE SUITES

We present a generalized test case generation method, called the G method. Although inspired by the W method, the G method, in contrast, allows for test case suite generation even in the absence of characterization sets for the specification models. Instead, the G method relies on knowledge about the index of certain equivalences induced at the implementation models. We show that the W method can be derived from the G method as a particular case. Moreover, we discuss some naturally occurring infinite classes of FSM models over which the G method generates test suites that are exponentially more compact than those produced by the W method.

A unified approach to modeling multivariate binary data using copulas over partitions

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

Content Classification of Multimedia Documents using Partitions of Low-Level Features

Audio-visual documents obtained from German TV news are classified according to the IPTC topic categorization scheme. To this end usual text classification techniques are adapted to speech, video, and non-speech audio. For each of the three modalities word analogues are generated: sequences of syllables for speech, “video words” based on low level color features (color moments, color correlogram and color wavelet), and “audio words” based on low-level spectral features (spectral envelope and spectral flatness) for non-speech audio. Such audio and video words provide a means to represent the different modalities in a uniform way. The frequencies of the word analogues represent audio-visual documents: the standard bag-of-words approach. Support vector machines are used for supervised classification in a 1 vs. n setting. Classification based on speech outperforms all other single modalities. Combining speech with non-speech audio improves classification. Classification is further improved by supplementing speech and non-speech audio with video words. Optimal F-scores range between 62% and 94% corresponding to 50% - 84% above chance. The optimal combination of modalities depends on the category to be recognized. The construction of audio and video words from low-level features provide a good basis for the integration of speech, non-speech audio and video.

Rare earth and other chemical element contents and partitions in bottom sediments, micronodules, and nodules from the bioproductive zone of the Pacific Ocean

Concentrations and compositions of rare earth elements (REE) in three micronodule fractions (50-250, 250-500, and >500 ?m), coexisting macronodules, and host sediments were studied. Samples were collected at three sites (Guatemala Basin, Peru Basin, and northern equatorial Pacific) located in elevated bioproductivity zones of surface waters. Influence of micronodule size is dominant for REE compositions and subordinate for REE concentrations. For example, Ce concentration inversely correlates with micronodule size and drops to the lowest value in macronodules and host sediments. Decrease of Ce concentration is generally accompanied by Mn/Fe increase in micro- and macronodules. Hence, the role of diagenetic source of material directly correlates with micronodule sizes. Contribution of the diagenetic source is maximal for macronodules. REE composition distinctions for micronodules and macronodules can be attributed to variations of hydrogenic iron oxyhydroxides and diagenetic (hydrothermal) iron hydroxophosphates that are the major REE carriers in ferromanganese ore deposits. Relationship and general trend in chemistry of coexisting macronodules suggest that they can represent products of the initial stage of nodule formation.

Nest choice in laying hens: Effects of nest partitions and social status.

Nest choice in loose-housed laying hens is influenced by nest characteristics, position and social factors. We examined the relative preference of laying hens for two group-nests differing in the presence or absence of a partition in the middle of the nest and whether this was influenced by social status. We hypothesized that hens would prefer the partitioned nest as it provides more enclosure, and that social status would affect nest choice. Relative preference for the nests was assessed in a free choice preference test conducted in two consecutive trials each with eight groups of 20 hens from 18 to 31 weeks of age. The hens were individually marked and had access to two commercial group-nests (49 × 114 cm), one of which contained an internal wooden partition (30 × 10 cm) which divided the nest in two halves. At 28 weeks of age, the position of the nests was switched. The number of eggs laid was recorded daily. On one day each at 24 and 28 weeks of age (after the nest switch) video recordings were made of the first 5 h of daylight. From these videos we recorded the number of nest visits per egg per nest and the number of nest visits for individual hens. On one day each at 24 and 27 weeks of age we also recorded videos from within the nests to assess individual nest choice for egg-laying. In addition, we recorded aggressive interactions between individual hens during the first hour of light on one day each at 18, 24 and 27 weeks of age to establish social status. We found a relative preference for the partition nest with a greater proportion of eggs laid in these nests as well as fewer nest visits per egg. The hens were also consistent in their egg-laying location over the two days of observation. After the nest switch, however, the hens did not switch egg laying location and the number of visits per egg no longer differed between nests suggesting that the preference for the partitioned nest was only important at the beginning of lay. In addition, although social rank had no impact on preference of nest type, lower ranking hens performed more nest visits and laid their eggs slightly later on the second observation day (week 27 of age) compared with higher ranking hens. Therefore, the use of partitions could improve the attractiveness of group-nests.