Les objets logiques et l'invariance : le statut du programme d'Erlangen dans les approches contemporaines

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

QTLs mapping for primary metabolites responsible of the organoleptic and nutritional characteristics of strawberry (Fragaria x ananassa)

The cultivated strawberry (Fragaria x ananassa) is the berry fruit most consumed worldwide and is well-known for its delicate flavour and nutritional properties. However, fruit quality attributes have been lost or reduced after years of traditional breeding focusing mainly on agronomical traits. To face the obstacles encountered in the improvement of cultivated crops, new technological tools, such as genomics and high throughput metabolomics, are becoming essential for the identification of genetic factors responsible of organoleptic and nutritive traits. Integration of “omics” data will allow a better understanding of the molecular and genetic mechanisms underlying the accumulation of metabolites involved in the flavour and nutritional value of the fruit. To identify genetic components affecting/controlling? fruit metabolic composition, here we present a quantitative trait loci (QTL) analysis using a 95 F1 segregating population derived from genotypes ‘1392’, selected for its superior flavour, and ‘232’ selected based in high yield (Zorrilla-Fontanesi et al., 2011; Zorrilla-Fontanesi et al., 2012). Metabolite profiling was performed on red stage strawberry fruits using gas chromatography hyphenated to time-of-flight mass spectrometry, which is a rapid and highly sensitive approach, allowing a good coverage of the central pathways of primary metabolism. Around 50 primary metabolites, including sugars, sugars derivatives, amino and organic acids, were detected and quantified after analysis in each individual of the population. QTL mapping was performed on the ‘232’ x ‘1392’ population separately over two successive years, based on the integrated linkage map (Sánchez-Sevilla et al., 2015). First, significant associations between metabolite content and molecular markers were identified by the non-parametric test of Kruskal-Wallis. Then, interval mapping (IM), as well as the multiple QTL method (MQM) allowed the identification of QTLs in octoploid strawberry. A permutation test established LOD thresholds for each metabolite and year. A total of 132 QTLs were detected in all the linkage groups over the two years for 42 metabolites out of 50. Among them, 4 (9.8%) QTLs for sugars, 9 (25%) for acids and 7 (12.7%) for amino acids were stable and detected in the two successive years. We are now studying the QTLs regions in order to find candidate genes to explain differences in metabolite content in the different individuals of the population, and we expect to identify associations between genes and metabolites which will help us to understand their role in quality traits of strawberry fruit.

Spectral-based mesh segmentation

In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (BRep), which in turn is central for featurebased design, machining, parametric CAD and reverse engineering, among others -- Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited -- We preprocess the mesh to obtain a edgelength homogeneous triangle set and its Graph Laplacian is calculated -- We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature submeshes -- Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh -- We present tests of our method on large complex meshes, which show results which mostly adjust to BRep FACE partition -- The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation -- Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous submesh removals

Distribution entropy analysis of epileptic EEG signals

It is an open-ended challenge to accurately detect the epileptic seizures through electroencephalogram (EEG) signals. Recently published studies have made elaborate attempts to distinguish between the normal and epileptic EEG signals by advanced nonlinear entropy methods, such as the approximate entropy, sample entropy, fuzzy entropy, and permutation entropy, etc. Most recently, a novel distribution entropy (DistEn) has been reported to have superior performance compared with the conventional entropy methods for especially short length data. We thus aimed, in the present study, to show the potential of DistEn in the analysis of epileptic EEG signals. The publicly-accessible Bonn database which consisted of normal, interictal, and ictal EEG signals was used in this study. Three different measurement protocols were set for better understanding the performance of DistEn, which are: i) calculate the DistEn of a specific EEG signal using the full recording; ii) calculate the DistEn by averaging the results for all its possible non-overlapped 5 second segments; and iii) calculate it by averaging the DistEn values for all the possible non-overlapped segments of 1 second length, respectively. Results for all three protocols indicated a statistically significantly increased DistEn for the ictal class compared with both the normal and interictal classes. Besides, the results obtained under the third protocol, which only used very short segments (1 s) of EEG recordings showed a significantly (p <; 0.05) increased DistEn for the interictal class in compassion with the normal class, whereas both analyses using relatively long EEG signals failed in tracking this difference between them, which may be due to a nonstationarity effect on entropy algorithm. The capability of discriminating between the normal and interictal EEG signals is of great clinical relevance since it may provide helpful tools for the detection of a seizure onset. Therefore, our study suggests that the DistEn analysis of EEG signals is very promising for clinical and even portable EEG monitoring.

Étude de la médiane de permutations sous la distance de Kendall-Tau

La distance de Kendall-τ compte le nombre de paires en désaccord entre deux permuta- tions. La distance d’une permutation à un ensemble est simplement la somme des dis- tances entre cette permutation et les permutations de l’ensemble. À partir d’un ensemble donné de permutations, notre but est de trouver la permutation, appelée médiane, qui minimise cette distance à l’ensemble. Le problème de la médiane de permutations sous la distance de Kendall-τ, trouve son application en bio-informatique, en science politique, en télécommunication et en optimisation. Ce problème d’apparence simple est prouvé difficile à résoudre. Dans ce mémoire, nous présentons plusieurs approches pour résoudre le problème, pour trouver une bonne solution approximative, pour le séparer en classes caractéristiques, pour mieux com- prendre sa compléxité, pour réduire l’espace de recheche et pour accélérer les calculs. Nous présentons aussi, vers la fin du mémoire, une généralisation de ce problème et nous l’étudions avec ces mêmes approches. La majorité du travail de ce mémoire se situe dans les trois articles qui le composent et est complémenté par deux chapitres servant à les lier.

ANALYSIS OF POPULUS TREMULOIDES CLONAL VARIATION AND DELINEATION IN THE OTTAWA NATIONAL FOREST

The technique of delineating Populus tremuloides (Michx.) clonal colonies based on morphology and phenology has been utilized in many studies and forestry applications since the 1950s. Recently, the availability and robustness of molecular markers has challenged the validity of such approaches for accurate clonal identification. However, genetically sampling an entire stand is largely impractical or impossible. For that reason, it is often necessary to delineate putative genet boundaries for a more selective approach when genetically analyzing a clonal population. Here I re-evaluated the usefulness of phenotypic delineation by: (1) genetically identifying clonal colonies using nuclear microsatellite markers, (2) assessing phenotypic inter- and intraclonal agreement, and (3) determining the accuracy of visible characters to correctly assign ramets to their respective genets. The long-term soil productivity study plot 28 was chosen for analysis and is located in the Ottawa National Forest, MI (46° 37'60.0" N, 89° 12'42.7" W). In total, 32 genets were identified from 181 stems using seven microsatellite markers. The average genet size was 5.5 ramets and six of the largest were selected for phenotypic analyses. Phenotypic analyses included budbreak timing, DBH, bark thickness, bark color or brightness, leaf senescence, leaf serrations, and leaf length ratio. All phenotypic characters, except for DBH, were useful for the analysis of inter- and intraclonal variation and phenotypic delineation. Generally, phenotypic expression was related to genotype with multiple response permutation procedure (MRPP) intraclonal distance values ranging from 0.148 and 0.427 and an observed MRPP delta value=0.221 when the expected delta=0.5. The phenotypic traits, though, overlapped significantly among some clones. When stems were assigned into phenotypic groups, six phenotypic groups were identified with each group containing a dominant genotype or clonal colony. All phenotypic groups contained stems from at least two clonal colonies and no clonal colony was entirely contained within one phenotypic group. These results demonstrate that phenotype varies with genotype and stand clonality can be determined using phenotypic characters, but phenotypic delineation is less precise. I therefore recommend that some genetic identification follow any phenotypic delineation. The amount of genetic identification required for clonal confirmation is likely to vary based on stand and environmental conditions. Further analysis, however, is needed to test these findings in other forest stands and populations.

USING MOSSES TO ASSESS CONDITIONS IN NORTHERN WHITE CEDAR SWAMPS

Northern white cedar (Thuja occidentalis L.) (NWC) swamps are valuable both commercially and ecologically. Unfortunately, many NWC swamps are degraded and information about them is not abundant. Especially there have been no definitive studies about mosses in northern white cedar swamps and how they react to disturbances. Mosses are sensitive to changes in their environment and thus they could be used to assess ecosystem conditions of NWC swamps. The objective of this study was to determine if mosses could be used to asses conditions in NWC swamps and if there are differences between moss communities in disturbed and undisturbed sites. Seventeen sample plots were taken from 12 disturbed and undisturbed sites around upper Michigan and northern Minnesota in the summer of 2012. All mosses occurring on the plots were identified and several associated environmental parameters were measured. The main environmental conditions affecting moss communities were identified with non-metric multidimensional scaling (NMS). Multiple response permutation procedures (MRPP) were run to ascertain if there were significant differences in community composition between disturbances. Indicator species analysis was then done to identify species that are related to different types of disturbances. A one-way ANOVA was used to check for significant differences between species richness and moss cover of undisturbed and disturbed sites. Over all sixty-two moss species were identified. The results indicate that there was no significant difference in species richness or moss cover between disturbed and undisturbed sites. However, moss community composition was affected by disturbance and strongly divided by a wetness gradient. Dicranum fuscescens was found to indicate undisturbed conditions. Calliergon cordifolium and Climacium dendroides indicated disturbed sites with wet conditions. Brotherella recurvans and Eurhynchium pulchellum indicated swamps with other disturbances.

Inferences about Parameters of Trivariate Normal Distribution with Missing Data

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.

Étude de la médiane de permutations sous la distance de Kendall-Tau

La distance de Kendall-τ compte le nombre de paires en désaccord entre deux permuta- tions. La distance d’une permutation à un ensemble est simplement la somme des dis- tances entre cette permutation et les permutations de l’ensemble. À partir d’un ensemble donné de permutations, notre but est de trouver la permutation, appelée médiane, qui minimise cette distance à l’ensemble. Le problème de la médiane de permutations sous la distance de Kendall-τ, trouve son application en bio-informatique, en science politique, en télécommunication et en optimisation. Ce problème d’apparence simple est prouvé difficile à résoudre. Dans ce mémoire, nous présentons plusieurs approches pour résoudre le problème, pour trouver une bonne solution approximative, pour le séparer en classes caractéristiques, pour mieux com- prendre sa compléxité, pour réduire l’espace de recheche et pour accélérer les calculs. Nous présentons aussi, vers la fin du mémoire, une généralisation de ce problème et nous l’étudions avec ces mêmes approches. La majorité du travail de ce mémoire se situe dans les trois articles qui le composent et est complémenté par deux chapitres servant à les lier.