Characterization of the unfolding of a weak focus and modulus of analytic classification

La thèse présente une description géométrique d’un germe de famille générique déployant un champ de vecteurs réel analytique avec un foyer faible à l’origine et son complexifié : le feuilletage holomorphe singulier associé. On montre que deux germes de telles familles sont orbitalement analytiquement équivalents si et seulement si les germes de familles de difféomorphismes déployant la complexification de leurs fonctions de retour de Poincaré sont conjuguées par une conjugaison analytique réelle. Le “caractère réel” de la famille correspond à sa Z2-équivariance dans R^4, et cela s’exprime comme l’invariance du plan réel sous le flot du système laquelle, à son tour, entraîne que l’expansion asymptotique de la fonction de Poincaré est réelle quand le paramètre est réel. Le pullback du plan réel après éclatement par la projection monoidal standard intersecte le feuilletage en une bande de Möbius réelle. La technique d’éclatement des singularités permet aussi de donner une réponse à la question de la “réalisation” d’un germe de famille déployant un germe de difféomorphisme avec un point fixe de multiplicateur égal à −1 et de codimension un comme application de semi-monodromie d’une famille générique déployant un foyer faible d’ordre un. Afin d’étudier l’espace des orbites de l’application de Poincaré, nous utilisons le point de vue de Glutsyuk, puisque la dynamique est linéarisable auprès des points singuliers : pour les valeurs réels du paramètre, notre démarche, classique, utilise une méthode géométrique, soit un changement de coordonée (coordonée “déroulante”) dans lequel la dynamique devient beaucoup plus simple. Mais le prix à payer est que la géométrie locale du plan complexe ambiante devient une surface de Riemann, sur laquelle deux notions de translation sont définies. Après avoir pris le quotient par le relèvement de la dynamique nous obtenons l’espace des orbites, ce qui s’avère être l’union de trois tores complexes plus les points singuliers (l’espace résultant est non-Hausdorff). Les translations, le caractère réel de l’application de Poincaré et le fait que cette application est un carré relient les différentes composantes du “module de Glutsyuk”. Cette propriété implique donc le fait qu’une seule composante de l’invariant Glutsyuk est indépendante.

Classification analytique de systèmes différentiels linéaires déployant une singularité irrégulière de rang de Poincaré 1

Cette thèse traite de la classification analytique du déploiement de systèmes différentiels linéaires ayant une singularité irrégulière. Elle est composée de deux articles sur le sujet: le premier présente des résultats obtenus lors de l'étude de la confluence de l'équation hypergéométrique et peut être considéré comme un cas particulier du second; le deuxième contient les théorèmes et résultats principaux. Dans les deux articles, nous considérons la confluence de deux points singuliers réguliers en un point singulier irrégulier et nous étudions les conséquences de la divergence des solutions au point singulier irrégulier sur le comportement des solutions du système déployé. Pour ce faire, nous recouvrons un voisinage de l'origine (de manière ramifiée) dans l'espace du paramètre de déploiement $\epsilon$. La monodromie d'une base de solutions bien choisie est directement reliée aux matrices de Stokes déployées. Ces dernières donnent une interprétation géométrique aux matrices de Stokes, incluant le lien (existant au moins pour les cas génériques) entre la divergence des solutions à $\epsilon=0$ et la présence de solutions logarithmiques autour des points singuliers réguliers lors de la résonance. La monodromie d'intégrales premières de systèmes de Riccati correspondants est aussi interprétée en fonction des éléments des matrices de Stokes déployées. De plus, dans le second article, nous donnons le système complet d'invariants analytiques pour le déploiement de systèmes différentiels linéaires $x^2y'=A(x)y$ ayant une singularité irrégulière de rang de Poincaré $1$ à l'origine au-dessus d'un voisinage fixé $\mathbb{D}_r$ dans la variable $x$. Ce système est constitué d'une partie formelle, donnée par des polynômes, et d'une partie analytique, donnée par une classe d'équivalence de matrices de Stokes déployées. Pour chaque valeur du paramètre $\epsilon$ dans un secteur pointé à l'origine d'ouverture plus grande que $2\pi$, nous recouvrons l'espace de la variable, $\mathbb{D}_r$, avec deux secteurs et, au-dessus de chacun, nous choisissons une base de solutions du système déployé. Cette base sert à définir les matrices de Stokes déployées. Finalement, nous prouvons un théorème de réalisation des invariants qui satisfont une condition nécessaire et suffisante, identifiant ainsi l'ensemble des modules.

Unfolded singularities of analytic differential equations

La thèse est composée d’un chapitre de préliminaires et de deux articles sur le sujet du déploiement de singularités d’équations différentielles ordinaires analytiques dans le plan complexe. L’article Analytic classification of families of linear differential systems unfolding a resonant irregular singularity traite le problème de l’équivalence analytique de familles paramétriques de systèmes linéaires en dimension 2 qui déploient une singularité résonante générique de rang de Poincaré 1 dont la matrice principale est composée d’un seul bloc de Jordan. La question: quand deux telles familles sontelles équivalentes au moyen d’un changement analytique de coordonnées au voisinage d’une singularité? est complètement résolue et l’espace des modules des classes d’équivalence analytiques est décrit en termes d’un ensemble d’invariants formels et d’un invariant analytique, obtenu à partir de la trace de la monodromie. Des déploiements universels sont donnés pour toutes ces singularités. Dans l’article Confluence of singularities of non-linear differential equations via Borel–Laplace transformations on cherche des solutions bornées de systèmes paramétriques des équations non-linéaires de la variété centre de dimension 1 d’une singularité col-noeud déployée dans une famille de champs vectoriels complexes. En général, un système d’ÉDO analytiques avec une singularité double possède une unique solution formelle divergente au voisinage de la singularité, à laquelle on peut associer des vraies solutions sur certains secteurs dans le plan complexe en utilisant les transformations de Borel–Laplace. L’article montre comment généraliser cette méthode et déployer les solutions sectorielles. On construit des solutions de systèmes paramétriques, avec deux singularités régulières déployant une singularité irrégulière double, qui sont bornées sur des domaines «spirals» attachés aux deux points singuliers, et qui, à la limite, convergent vers une paire de solutions sectorielles couvrant un voisinage de la singularité confluente. La méthode apporte une description unifiée pour toutes les valeurs du paramètre.

Caractère intrinsèque des matrices de Stokes

Il est connu qu’une équation différentielle linéaire, x^(k+1)Y' = A(x)Y, au voisinage d’un point singulier irrégulier non-résonant est uniquement déterminée (à isomorphisme analytique près) par : (1) sa forme normale formelle, (2) sa collection de matrices de Stokes. La définition des matrices de Stokes fait appel à un ordre sur les parties réelles des valeurs propres du système, ordre qui peut être perturbé par une rotation en x. Dans ce mémoire, nous avons établi le caractère intrinsèque de cette relation : nous avons donc établi comment la nouvelle collection de matrices de Stokes obtenue après une rotation en x qui change l’ordre des parties réelles des valeurs propres dépend de la collection initiale. Pour ce faire, nous donnons un chapitre de préliminaires généraux sur la forme normale des équations différentielles ordinaires puis un chapitre sur le phénomène de Stokes pour les équations différentielles linéaires. Le troisième chapitre contient nos résultats.

The properties of the international classification of the external cause of injury when used as an instrument for injury prevention research

Objective: To demonstrate properties of the International Classification of the External Cause of Injury (ICECI) as a tool for use in injury prevention research. Methods: The Childhood Injury Prevention Study (CHIPS) is a prospective longitudinal follow up study of a cohort of 871 children 5–12 years of age, with a nested case crossover component. The ICECI is the latest tool in the International Classification of Diseases (ICD) family and has been designed to improve the precision of coding injury events. The details of all injury events recorded in the study, as well as all measured injury related exposures, were coded using the ICECI. This paper reports a substudy on the utility and practicability of using the ICECI in the CHIPS to record exposures. Interrater reliability was quantified for a sample of injured participants using the Kappa statistic to measure concordance between codes independently coded by two research staff. Results: There were 767 diaries collected at baseline and event details from 563 injuries and exposure details from injury crossover periods. There were no event, location, or activity details which could not be coded using the ICECI. Kappa statistics for concordance between raters within each of the dimensions ranged from 0.31 to 0.93 for the injury events and 0.94 and 0.97 for activity and location in the control periods. Discussion: This study represents the first detailed account of the properties of the ICECI revealed by its use in a primary analytic epidemiological study of injury prevention. The results of this study provide considerable support for the ICECI and its further use.

Spatially-explicit modelling of grassland classes - an improved method of integrating a climate-based classification model with interpolated climate surfaces

Spatially-explicit modelling of grassland classes is important to site-specific planning for improving grassland and environmental management over large areas. In this study, a climate-based grassland classification model, the Comprehensive and Sequential Classification System (CSCS) was integrated with spatially interpolated climate data to classify grassland in Gansu province, China. The study area is characterized by complex topographic features imposed by plateaus, high mountains, basins and deserts. To improve the quality of the interpolated climate data and the quality of the spatial classification over this complex topography, three linear regression methods, namely an analytic method based on multiple regression and residues (AMMRR), a modification of the AMMRR method through adding the effect of slope and aspect to the interpolation analysis (M-AMMRR) and a method which replaces the IDW approach for residue interpolation in M-AMMRR with an ordinary kriging approach (I-AMMRR), for interpolating climate variables were evaluated. The interpolation outcomes from the best interpolation method were then used in the CSCS model to classify the grassland in the study area. Climate variables interpolated included the annual cumulative temperature and annual total precipitation. The results indicated that the AMMRR and M-AMMRR methods generated acceptable climate surfaces but the best model fit and cross validation result were achieved by the I-AMMRR method. Twenty-six grassland classes were classified for the study area. The four grassland vegetation classes that covered more than half of the total study area were "cool temperate-arid temperate zonal semi-desert", "cool temperate-humid forest steppe and deciduous broad-leaved forest", "temperate-extra-arid temperate zonal desert", and "frigid per-humid rain tundra and alpine meadow". The vegetation classification map generated in this study provides spatial information on the locations and extents of the different grassland classes. This information can be used to facilitate government agencies' decision-making in land-use planning and environmental management, and for vegetation and biodiversity conservation. The information can also be used to assist land managers in the estimation of safe carrying capacities which will help to prevent overgrazing and land degradation.

Analysis of Bayesian classification-based approaches for Android malware detection

Mobile malware has been growing in scale and complexity spurred by the unabated uptake of smartphones worldwide. Android is fast becoming the most popular mobile platform resulting in sharp increase in malware targeting the platform. Additionally, Android malware is evolving rapidly to evade detection by traditional signature-based scanning. Despite current detection measures in place, timely discovery of new malware is still a critical issue. This calls for novel approaches to mitigate the growing threat of zero-day Android malware. Hence, the authors develop and analyse proactive machine-learning approaches based on Bayesian classification aimed at uncovering unknown Android malware via static analysis. The study, which is based on a large malware sample set of majority of the existing families, demonstrates detection capabilities with high accuracy. Empirical results and comparative analysis are presented offering useful insight towards development of effective static-analytic Bayesian classification-based solutions for detecting unknown Android malware.

An analytic knowledge network process for construction entrepreneurship education

Purpose - The purpose of this paper is to provide a quantitative multicriteria decision-making approach to knowledge management in construction entrepreneurship education by means of an analytic knowledge network process (KANP) Design/methodology/approach- The KANP approach in the study integrates a standard industrial classification with the analytic network process (ANP). For the construction entrepreneurship education, a decision-making model named KANP.CEEM is built to apply the KANP method in the evaluation of teaching cases to facilitate the case method, which is widely adopted in entrepreneurship education at business schools. Findings- The study finds that there are eight clusters and 178 nodes in the KANP.CEEM model, and experimental research on the evaluation of teaching cases discloses that the KANP method is effective in conducting knowledge management to the entrepreneurship education. Research limitations/implications- As an experimental research, this paper ignores the concordance between a selected standard classification and others, which perhaps limits the usefulness of KANP.CEEM model elsewhere. Practical implications- As the KANP.CEEM model is built based on the standard classification codes and the embedded ANP, it is thus expected that the model has a wide potential in evaluating knowledge-based teaching materials for any education purpose with a background from the construction industry, and can be used by both faculty and students. Originality/value- This paper fulfils a knowledge management need and offers a practical tool for an academic starting out on the development of knowledge-based teaching cases and other teaching materials or for a student going through the case studies and other learning materials.

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

How Twitter is studied in the medical professions: a classification of Twitter papers indexed in PubMed

Background: Since their inception, Twitter and related microblogging systems have provided a rich source of information for researchers and have attracted interest in their affordances and use. Since 2009 PubMed has included 123 journal articles on medicine and Twitter, but no overview exists as to how the field uses Twitter in research. // Objective: This paper aims to identify published work relating to Twitter indexed by PubMed, and then to classify it. This classification will provide a framework in which future researchers will be able to position their work, and to provide an understanding of the current reach of research using Twitter in medical disciplines. Limiting the study to papers indexed by PubMed ensures the work provides a reproducible benchmark. // Methods: Papers, indexed by PubMed, on Twitter and related topics were identified and reviewed. The papers were then qualitatively classified based on the paper’s title and abstract to determine their focus. The work that was Twitter focused was studied in detail to determine what data, if any, it was based on, and from this a categorization of the data set size used in the studies was developed. Using open coded content analysis additional important categories were also identified, relating to the primary methodology, domain and aspect. // Results: As of 2012, PubMed comprises more than 21 million citations from biomedical literature, and from these a corpus of 134 potentially Twitter related papers were identified, eleven of which were subsequently found not to be relevant. There were no papers prior to 2009 relating to microblogging, a term first used in 2006. Of the remaining 123 papers which mentioned Twitter, thirty were focussed on Twitter (the others referring to it tangentially). The early Twitter focussed papers introduced the topic and highlighted the potential, not carrying out any form of data analysis. The majority of published papers used analytic techniques to sort through thousands, if not millions, of individual tweets, often depending on automated tools to do so. Our analysis demonstrates that researchers are starting to use knowledge discovery methods and data mining techniques to understand vast quantities of tweets: the study of Twitter is becoming quantitative research. // Conclusions: This work is to the best of our knowledge the first overview study of medical related research based on Twitter and related microblogging. We have used five dimensions to categorise published medical related research on Twitter. This classification provides a framework within which researchers studying development and use of Twitter within medical related research, and those undertaking comparative studies of research relating to Twitter in the area of medicine and beyond, can position and ground their work.

Classification of cortical microcircuits based on micro-electrode-array data from slices of rat barrel cortex

The bewildering complexity of cortical microcircuits at the single cell level gives rise to surprisingly robust emergent activity patterns at the level of laminar and columnar local field potentials (LFPs) in response to targeted local stimuli. Here we report the results of our multivariate data-analytic approach based on simultaneous multi-site recordings using micro-electrode-array chips for investigation of the microcircuitary of rat somatosensory (barrel) cortex. We find high repeatability of stimulus-induced responses, and typical spatial distributions of LFP responses to stimuli in supragranular, granular, and infragranular layers, where the last form a particularly distinct class. Population spikes appear to travel with about 33 cm/s from granular to infragranular layers. Responses within barrel related columns have different profiles than those in neighbouring columns to the left or interchangeably to the right. Variations between slices occur, but can be minimized by strictly obeying controlled experimental protocols. Cluster analysis on normalized recordings indicates specific spatial distributions of time series reflecting the location of sources and sinks independent of the stimulus layer. Although the precise correspondences between single cell activity and LFPs are still far from clear, a sophisticated neuroinformatics approach in combination with multi-site LFP recordings in the standardized slice preparation is suitable for comparing normal conditions to genetically or pharmacologically altered situations based on real cortical microcircuitry.

Supervised variational relevance learning, an analytic geometric feature selection with applications to omic datasets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Data-Analytic Strategy for Protein-Biomarker Discovery: Profiling of High-Dimensional Proteomic Data for Cancer Detection

With recent advances in mass spectrometry techniques, it is now possible to investigate proteins over a wide range of molecular weights in small biological specimens. This advance has generated data-analytic challenges in proteomics, similar to those created by microarray technologies in genetics, namely, discovery of "signature" protein profiles specific to each pathologic state (e.g., normal vs. cancer) or differential profiles between experimental conditions (e.g., treated by a drug of interest vs. untreated) from high-dimensional data. We propose a data analytic strategy for discovering protein biomarkers based on such high-dimensional mass-spectrometry data. A real biomarker-discovery project on prostate cancer is taken as a concrete example throughout the paper: the project aims to identify proteins in serum that distinguish cancer, benign hyperplasia, and normal states of prostate using the Surface Enhanced Laser Desorption/Ionization (SELDI) technology, a recently developed mass spectrometry technique. Our data analytic strategy takes properties of the SELDI mass-spectrometer into account: the SELDI output of a specimen contains about 48,000 (x, y) points where x is the protein mass divided by the number of charges introduced by ionization and y is the protein intensity of the corresponding mass per charge value, x, in that specimen. Given high coefficients of variation and other characteristics of protein intensity measures (y values), we reduce the measures of protein intensities to a set of binary variables that indicate peaks in the y-axis direction in the nearest neighborhoods of each mass per charge point in the x-axis direction. We then account for a shifting (measurement error) problem of the x-axis in SELDI output. After these pre-analysis processing of data, we combine the binary predictors to generate classification rules for cancer, benign hyperplasia, and normal states of prostate. Our approach is to apply the boosting algorithm to select binary predictors and construct a summary classifier. We empirically evaluate sensitivity and specificity of the resulting summary classifiers with a test dataset that is independent from the training dataset used to construct the summary classifiers. The proposed method performed nearly perfectly in distinguishing cancer and benign hyperplasia from normal. In the classification of cancer vs. benign hyperplasia, however, an appreciable proportion of the benign specimens were classified incorrectly as cancer. We discuss practical issues associated with our proposed approach to the analysis of SELDI output and its application in cancer biomarker discovery.

The properties of the International Classification of the External Cause of Injury when used as an instrument for injury prevention research

Objective: To demonstrate properties of the International Classification of the External Cause of Injury (ICECI) as a tool for use in injury prevention research. Methods: The Childhood Injury Prevention Study (CHIPS) is a prospective longitudinal follow up study of a cohort of 871 children 5 - 12 years of age, with a nested case crossover component. The ICECI is the latest tool in the International Classification of Diseases (ICD) family and has been designed to improve the precision of coding injury events. The details of all injury events recorded in the study, as well as all measured injury related exposures, were coded using the ICECI. This paper reports a substudy on the utility and practicability of using the ICECI in the CHIPS to record exposures. Interrater reliability was quantified for a sample of injured participants using the Kappa statistic to measure concordance between codes independently coded by two research staff. Results: There were 767 diaries collected at baseline and event details from 563 injuries and exposure details from injury crossover periods. There were no event, location, or activity details which could not be coded using the ICECI. Kappa statistics for concordance between raters within each of the dimensions ranged from 0.31 to 0.93 for the injury events and 0.94 and 0.97 for activity and location in the control periods. Discussion: This study represents the first detailed account of the properties of the ICECI revealed by its use in a primary analytic epidemiological study of injury prevention. The results of this study provide considerable support for the ICECI and its further use.

Inclusion Properties for Certain Classes of Analytic Functions Involving a Family of Fractional Integral Operators

2000 Math. Subject Classification: 30C45