Methods of Regularities Searching Based on Optimal Partitioning

The purpose of discussed optimal valid partitioning (OVP) methods is uncovering of ordinal or continuous explanatory variables effect on outcome variables of different types. The OVP approach is based on searching partitions of explanatory variables space that in the best way separate observations with different levels of outcomes. Partitions of single variables ranges or two-dimensional admissible areas for pairs of variables are searched inside corresponding families. Statistical validity associated with revealed regularities is estimated with the help of permutation test repeating search of optimal partition for each permuted dataset. Method for output regularities selection is discussed that is based on validity evaluating with the help of two types of permutation tests.

Generating More Boundary Elements of Subset Projections

Composition problem is considered for partition constrained vertex subsets of n dimensional unit cube E^n . Generating numerical characteristics of E^n subsets partitions is considered by means of the same characteristics in 1 − n dimensional unit cube, and construction of corresponding subsets is given for a special particular case. Using pairs of lower layer characteristic vectors for E^(1-n) more characteristic vectors for E^n are composed which are boundary from one side, and which take part in practical recognition of validness of a given candidate vector of partitions.

Large Distinct Part Sizes in a Random Integer Partition

A partition of a positive integer n is a way of writing it as the sum of positive integers without regard to order; the summands are called parts. The number of partitions of n, usually denoted by p(n), is determined asymptotically by the famous partition formula of Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P on the set of all partitions of n assuming that the probability 1/p(n) is assigned to each n-partition. The symbols E and V ar will be further used to denote the expectation and variance with respect to the measure P . Thus, each conceivable numerical characteristic of the parts in a partition can be regarded as a random variable.

On Local Uniform Topological Algebras

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.

On Thom Polynomials for A4(−) via Schur Functions

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.

Evaluation of wind-induced internal pressure in low-rise buildings: A multi scale experimental and numerical approach

Hurricane is one of the most destructive and costly natural hazard to the built environment and its impact on low-rise buildings, particularity, is beyond acceptable. The major objective of this research was to perform a parametric evaluation of internal pressure (IP) for wind-resistant design of low-rise buildings and wind-driven natural ventilation applications. For this purpose, a multi-scale experimental, i.e. full-scale at Wall of Wind (WoW) and small-scale at Boundary Layer Wind Tunnel (BLWT), and a Computational Fluid Dynamics (CFD) approach was adopted. This provided new capability to assess wind pressures realistically on internal volumes ranging from small spaces formed between roof tiles and its deck to attic to room partitions. Effects of sudden breaching, existing dominant openings on building envelopes as well as compartmentalization of building interior on the IP were systematically investigated. Results of this research indicated: (i) for sudden breaching of dominant openings, the transient overshooting response was lower than the subsequent steady state peak IP and internal volume correction for low-wind-speed testing facilities was necessary. For example a building without volume correction experienced a response four times faster and exhibited 30–40% lower mean and peak IP; (ii) for existing openings, vent openings uniformly distributed along the roof alleviated, whereas one sided openings aggravated the IP; (iii) larger dominant openings exhibited a higher IP on the building envelope, and an off-center opening on the wall exhibited (30–40%) higher IP than center located openings; (iv) compartmentalization amplified the intensity of IP and; (v) significant underneath pressure was measured for field tiles, warranting its consideration during net pressure evaluations. The study aimed at wind driven natural ventilation indicated: (i) the IP due to cross ventilation was 1.5 to 2.5 times higher for Ainlet/Aoutlet>1 compared to cases where Ainlet/Aoutlet<1, this in effect reduced the mixing of air inside the building and hence the ventilation effectiveness; (ii) the presence of multi-room partitioning increased the pressure differential and consequently the air exchange rate. Overall good agreement was found between the observed large-scale, small-scale and CFD based IP responses. Comparisons with ASCE 7-10 consistently demonstrated that the code underestimated peak positive and suction IP.

Phase and partitioning behavior of phenols and polycyclic aromatic hydrocarbons in offshore oil and gas produced water

Produced water constitutes the largest volume of waste from offshore oil and gas operations and is composed of a wide range of organic and inorganic compounds. Although treatment processes have to meet strict oil in water regulations, the definition of “oil” is a function of the analysis process and may include aliphatic hydrocarbons which have limited environmental impact due to degradability whilst ignoring problematic dissolved petroleum species. This thesis presents the partitioning behavior of oil in produced water as a function of temperature and salinity to identify compounds of environmental concern. Phenol, p-cresol, and 4-tert-butylphenol were studied because of their xenoestrogenic power; other compounds studied are polycyclic aromatic hydrocarbon PAHs which include naphthalene, fluorene, phenanthrene, and pyrene. Partitioning experiments were carried out in an Innova incubator for 48 hours, temperature was varied from 4ﾟC to 70ﾟC, and two salinity levels of 46.8‰ and 66.8‰ were studied. Results obtained showed that the dispersed oil concentration in the water reduces with settling time and equilibrium was attained at 48 h settling time. Polycyclic aromatic hydrocarbons (PAHs) partitions based on dispersed oil concentration whereas phenols are not significantly affected by dispersed oil concentration. Higher temperature favors partitioning of PAHs into the water phase. Salinity has negligible effect on partitioning pattern of phenols and PAHs studied. Simulation results obtained from the Aspen HYSYS model shows that temperature and oil droplet distribution greatly influences the efficiency of produced water treatment system.

Prospecção química e avaliação biológica de Banisteriopsis laevifolia (Malpighiaceae)

The Banisteriopsis genus is widespread in traditional medicine. This work aims to contribute with information about the chemical composition and on the evaluation of the biological activity of the essential oil, the ethanol extract of the leaves and partitions of the Banisteriopsis laevifolia. The phytochemical screeningtest of ethanol extract and partitions of leaves indicated the presence of flavonoids, terpenoids, saponins, phenols and steroids compounds. Nitrogenous compounds, characteristic of some species of this family, were not detected. Flavonoids were the predominant metabolite, with the highest concentrations on the partitions ethyl acetate and n-butanol. The antibacterial activity, antifungal and cytotoxicity of the essetial oil, ethanol extract and partitions were assyed by microdilution broth method (MBM), where the minimum inhibitory concentrations (MIC) were calculated. The ethanol extract and partitions did not inhibit growth against to Gram positive bacteria tested, with MIC less than 400 mg L-1. For the Gram negative bacteria tested, the hexane and hydroethanol partitios were more effective against F. nucleatum bacteria (MIC 100 ug mL-1). The ethanol extract showed antifungal activity with MIC of 31.2 mg L-1. Ethyl acetate and n-butanol partitions showed MIC 187.5 mg L-1 and 93.7 mg L-1, respectively, arousing interest for isolation studies. The antioxidant activity was evaluated by the DPPH free radical method. The ethanolic extract, ethyl acetate and n-butanol partitions were active, since they showed EC50 values (4.53 ug mL-1, 4.07 and 8.39 ug mL-1, respectively), values equivalent to the BHT (7.3 mg L-1). The analysis by HPLC-MS/MS of the most active fractions (ethyl acetate and n-butanol) identified phenolic compounds (flavonols and phenolic acids) which exert recognized biological activity. The GC-MS analysis of the essential oils from leaves collected in two periods studied (dry and wet), showed a small variation in the number of compounds. The major classes identified for the oil collected in the dry period were aliphatic alcohols (23,4%), terpenoids (18.7%), sterols (10.4%) and long-chain alkanes (9.2%) compounds. Terpenoids (26.8%) were the major class for the rain season. The major compounds (3Z) -hexenol, phytol and untriacontano are present in the two seasons but in different amounts (19.4%, 9.8% and 7.5% during the dry season, and 17.0 %, 14.9% and 15.3% in the rainy season, respectively). The essential oil from rainy season was not effective against to the oral bacteria Gram positive and Gram negative tested. However, showed significant antifungal activity with MIC 1000 mg L-1 against Candidas. Thus, the promising results with respect to biological assays of ethanolic extract and partitions from B. laevifolia contributed to the chemical and biological knowledge of the species B. laevifolia.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

Size-partitioned phytoplankton carbon concentrations retrieved from ocean color data, links to data in netCDF format

Owing to their important roles in biogeochemical cycles, phytoplankton functional types (PFTs) have been the aim of an increasing number of ocean color algorithms. Yet, none of the existing methods are based on phytoplankton carbon (C) biomass, which is a fundamental biogeochemical and ecological variable and the "unit of accounting" in Earth system models. We present a novel bio-optical algorithm to retrieve size-partitioned phytoplankton carbon from ocean color satellite data. The algorithm is based on existing methods to estimate particle volume from a power-law particle size distribution (PSD). Volume is converted to carbon concentrations using a compilation of allometric relationships. We quantify absolute and fractional biomass in three PFTs based on size - picophytoplankton (0.5-2 µm in diameter), nanophytoplankton (2-20 µm) and microphytoplankton (20-50 µm). The mean spatial distributions of total phytoplankton C biomass and individual PFTs, derived from global SeaWiFS monthly ocean color data, are consistent with current understanding of oceanic ecosystems, i.e., oligotrophic regions are characterized by low biomass and dominance of picoplankton, whereas eutrophic regions have high biomass to which nanoplankton and microplankton contribute relatively larger fractions. Global climatological, spatially integrated phytoplankton carbon biomass standing stock estimates using our PSD-based approach yield - 0.25 Gt of C, consistent with analogous estimates from two other ocean color algorithms and several state-of-the-art Earth system models. Satisfactory in situ closure observed between PSD and POC measurements lends support to the theoretical basis of the PSD-based algorithm. Uncertainty budget analyses indicate that absolute carbon concentration uncertainties are driven by the PSD parameter No which determines particle number concentration to first order, while uncertainties in PFTs' fractional contributions to total C biomass are mostly due to the allometric coefficients. The C algorithm presented here, which is not empirically constrained a priori, partitions biomass in size classes and introduces improvement over the assumptions of the other approaches. However, the range of phytoplankton C biomass spatial variability globally is larger than estimated by any other models considered here, which suggests an empirical correction to the No parameter is needed, based on PSD validation statistics. These corrected absolute carbon biomass concentrations validate well against in situ POC observations.

Seawater carbonate chemistry and Emiliania huxleyi mass and size, 2011

About one-third of the carbon dioxide (CO2) released into the atmosphere as a result of human activity has been absorbed by the oceans, where it partitions into the constituent ions of carbonic acid. This leads to ocean acidification, one of the major threats to marine ecosystems and particularly to calcifying organisms such as corals, foraminifera and coccolithophores. Coccolithophores are abundant phytoplankton that are responsible for a large part of modern oceanic carbonate production. Culture experiments investigating the physiological response of coccolithophore calcification to increased CO2 have yielded contradictory results between and even within species. Here we quantified the calcite mass of dominant coccolithophores in the present ocean and over the past forty thousand years, and found a marked pattern of decreasing calcification with increasing partial pressure of CO2 and concomitant decreasing concentrations of CO3. Our analyses revealed that differentially calcified species and morphotypes are distributed in the ocean according to carbonate chemistry. A substantial impact on the marine carbon cycle might be expected upon extrapolation of this correlation to predicted ocean acidification in the future. However, our discovery of a heavily calcified Emiliania huxleyi morphotype in modern waters with low pH highlights the complexity of assemblage-level responses to environmental forcing factors.

Paleoecology, Diagenesis and Biological Affinity of Tetradiids in the Upper Ordovician (Sandbian) Black River Group of the Kingston Area, Ontario, Canada

Tetradiids are a group of colonial, tubular fossils that occur globally in Middle to Upper Ordovician strata. Tetradiids were first described as a type of tabulate coral; however, based on their four-fold symmetry, division, and presence of a central-sparry canal, they were recently reinterpreted as a florideophyte rhodophyte algae, a reinterpretation that is tested in this thesis. This study focused on understanding the affinity and taphonomy of this order of fossil. Research was conducted by stratigraphic and petrographic analyses of the Black River Group in the Kingston, Ontario region. Tetradiid occurrences were divided into fragment or colonial, with three morphologies of tetradiids described (Tetradium, Phytopsis and Paratetradium). Morphology is specific to depositional environment, with compact Tetradium consistently within ooid grainstones and open branching Phytopsis and chained Paratetradium consistently within mudstones. Two types of patch reefs were recognized: a Paratetradium bioherm, and a Paratetradium, Phytopsis, stromatolite bioherm. The presence of bioherms implies that tetradiids were capable of hypercalcifying. Preservation styles of tetradiids were investigated, and were compared to brachiopods, echinoderms, mollusks, and ooids. Tetradiids were preferentially preserved as molds and demonstrated complete dissolution of skeletal material. Rare specimens, however, demonstrated preserved horizontal partitions, central plates, and a double wall. Skeletal molds were filled with either calcite spar, mud or encrusted by a cryptomicrobial colony. Both calcitic and aragonitic ooids were discovered. The co-occurrence of aragonitic ooids, aragonitic crytodontids, and the evolution of aragonitic, hypercalcifying tetradiids is interpreted as representing the geochemical favoring of aragonite and HMC in a time of global calcite seas. The geochemical favoring of aragonite is interpreted to be independent to global Mg: Ca ratios, but was the result of increased saturation levels and temperature driven by high atmospheric pCO2. Based on the presence of epitheca, tabulae, septa, and the commonality of growth forms, tetradiids are interpreted as an order of Cnidaria. The evolution of an aragonitic skeleton in tetradiids is interpreted to be the result of de novo acquisition of a skeleton from an unmineralized clade.

Un répertoire de musique brésilienne adapté à l’enseignement collectif du trombone

Cette thèse, complémentaire à deux récitals donnés dans le cadre de la réalisation d’un doctorat en études pédagogiques et pratiques musicales instrumentales, a comme fil conducteur l’enseignement collectif du trombone au Brésil et examine le trombone sous trois angles : historique, pédagogique et dans une perspective d’interprétation musicale. Bien que le sujet ne soit pas nouveau, le projet présente une réflexion, sur le trombone et son enseignement, encore inexplorée en raison principalement du répertoire sélectionné pour la présente étude. En effet, à notre connaissance, le répertoire populaire brésilien n’a jusqu’à maintenant pas fait l’objet d’arrangements musicaux écrits, en vue d’une exploitation non seulement en contexte de représentation publique, mais aussi avec des visées pédagogiques. Les morceaux choisis ont été retenus en raison de leur contenu, qui présente un vocabulaire musical lié à la culture régionale de quatre des cinq régions géographiques du Brésil. Dans le processus de réalisation du projet, les morceaux choisis ont fait l’objet d’arrangements dans la perspective qu’ils servent comme outil pédagogique pour la formation en trombone, en contexte de musique brésilienne. Les arrangements ont été conçus pour des ensembles réduits, où le trombone tient fréquemment le rôle de soliste. Ainsi, au-delà des concepts et techniques issus de la formation traditionnelle reçue, l’interprétation des arrangements a été une occasion pour le doctorant et soliste de présenter, à travers l’improvisation dans le langage de la musique populaire brésilienne, les résultats de processus développés au cours des deux dernières années. Les partitions sont annexées au texte de la thèse, afin d’illustrer certains propos et avec l’objectif de soutenir les recherches futures dans ce domaine. La thèse est divisée en quatre chapitres lesquels, bien que présentés séparément, possèdent entre eux d’étroites relations. Le premier chapitre donne un aperçu général de l’histoire de l’instrument, à travers les cinq siècles de son existence. Le deuxième chapitre s’articule autour de l’histoire de la musique brésilienne et de la présence du trombone au Brésil. Le troisième chapitre présente d’abord un aperçu de l’enseignement artistique et musical au Brésil au 20e et 21e siècle, poursuit en abordant la situation de l’enseignement du trombone au Brésil et aboutit à une proposition favorisant l’apprentissage du trombone en contexte d’enseignement musical collectif. Finalement, le quatrième chapitre fait un retour sur l’expérience musicale vécue dans le premier volet du projet, celui se rapportant à la pratique musicale instrumentale, établit des liens et trace des pistes dans une perspective d’enseignement et d’apprentissage du trombone.

Mesh partitioning: A multilevel balancing and refinement algorithm

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan-Lin partition optimisation algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of the-art partitioner and shown to provide improved results.

Load-balancing for parallel adaptive unstructured grids

A parallel method for the dynamic partitioning of unstructured meshes is outlined. The method includes diffusive load-balancing techniques and an iterative optimisation technique known as relative gain optimisationwhich both balances theworkload and attempts to minimise the interprocessor communications overhead. It can also optionally include amultilevel strategy. Experiments on a series of adaptively refined meshes indicate that the algorithmprovides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.