Alain Giron

Alain Giron
  • Sorbonne University

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123
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Current institution
Sorbonne University

Publications

Publications (123)
Article
The aim of this study was to compare CMR imaging biomarkers between SLE patients and matched controls. Electronic databases were systematically searched from inception until November 2023. All studies reporting CMR imaging data in SLE patients were included. PRISMA guidelines were followed, and risk of bias was assessed using the Newcastle-Ottawa Q...
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We propose to quantify dependence between two systems $X$ and $Y$ in a dataset $D$ based on the Bayesian comparison of two models: one, $H_0$, of statistical independence and another one, $H_1$, of dependence. In this framework, dependence between $X$ and $Y$ in $D$, denoted $B(X,Y|D)$, is quantified as $P(H_1|D)$, the posterior probability for the...
Preprint
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In functional MRI (fMRI), effective connectivity analysis aims at inferring the causal influences that brain regions exert on one another. A common method for this type of analysis is structural equation modeling (SEM). We here propose a novel method to test the validity of a given model of structural equation. Given a structural model in the form...
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Beside the well‐documented involvement of secondary somatosensory area, the cortical network underlying late somatosensory evoked potentials (P60/N60 and P100/N100) is still unknown. Electroencephalogram and magnetoencephalogram source imaging were performed to further investigate the origin of the brain cortical areas involved in late somatosensor...
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Background Ascending thoracic aortic aneurysm (ATAA) is a silent and threatening dilation of the ascending aorta (AscAo). Maximal aortic diameter which is currently used for ATAA patients management and surgery planning has been shown to inadequately characterize risk of dissection in a large proportion of patients. Our aim was to propose a compreh...
Article
We propose to quantify dependence between two systems $\mathcal{X}$ and $\mathcal{Y}$ in a dataset $D$ based on the Bayesian comparison of two models: one, $H_{0}$ , of statistical independence and another one, $H_{1}$ , of dependence. In this framework, dependence between $\mathcal{X}$ and $\mathcal{Y}$ in $D$ , denoted ${\mathfra...
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Background: Movement sonification, the use of real-time auditory feedback linked to movement parameters, have been proposed to support rehabilitation. Nevertheless, if promising results have been reported, the effect of the type of sound used has not been studied systematically. The aim of this study was to investigate in a single session the effe...
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For a random variable X, we are interested in the blind extraction of its finest mutual independence pattern μ(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu (X)...
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For a random variable $X$, we are interested in the blind extraction of its finest mutual independence pattern $\mu ( X )$. We introduce a specific kind of independence that we call dichotomic. If $\Delta ( X )$ stands for the set of all patterns of dichotomic independence that hold for $X$, we show that $\mu ( X )$ can be obtained as the intersect...
Article
Purpose: The purpose of this study was to investigate the benefit of aortic volumes compared to diameters or cross-sectional areas on three-dimensional (3D) magnetic resonance imaging (MRI) in discriminating between patients with dilated aorta and matched controls. Materials and methods: Sixty-two patients (47 men and 15 women; median age, 66 ye...
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Introduction: Autoimmune encephalitis (AE) diagnosis and follow-up remain challenging. Brain 18F-fluoro-deoxy-glucose positron emission tomography (FDG PET) has shown promising results in AE. Our aim was to investigate FDG PET alterations in AE, according to antibody subtype. Methods: We retrospectively included patients with available FDG PET a...
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Purpose: To evaluate a cardiac MRI feature tracking (FT)-derived parameter that combines right ventricular (RV) longitudinal and radial motions in detecting arrhythmogenic right ventricular cardiomyopathy (ARVC). Materials and methods: Patients with ARVC (n = 47; median age, 46 [IQR, 30-52] years; 31 men) were compared with controls (n = 39; med...
Preprint
Full-text available
Background: Movement sonification, the use of real-time auditory feedback linked to movement parameters, have been proposed to support rehabilitation. Nevertheless, if promising results have been reported, the effect of the type of sound used has not been studied systematically, and mechanisms involved during movement execution with sonification re...
Article
In directional statistics, the von Mises distribution is a key element in the analysis of circular data. While there is a general agreement regarding the estimation of its location parameter μ, several methods have been proposed to estimate the concentration parameter κ. We here provide a thorough evaluation of the behavior of 12 such estimators fo...
Article
Objective The role of ipsilateral motor cortex efferent pathways in the transmission of voluntary command to spinal motor nuclei remains controversial in humans. In healthy subjects, their implication in cortical control is hidden by predominant role of crossed corticospinal tract. However, evidence from electrophysiological and imaging studies sug...
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Background Familial Hypercholesterolemia (FH) is an underdiagnosed condition with an increased cardiovascular risk. It is unknown whether lipid accumulation plays a role in structural myocardial changes. Cardiovascular Magnetic Resonance (CMR) is the reference technique for the morpho-functional evaluation of heart chambers through cine sequences a...
Preprint
Full-text available
In directional statistics, the von Mises distribution is a key element in the analysis of circular data. While there is a general agreement regarding the estimation of its location parameter $\mu$, several methods have been proposed to estimate the concentration parameter $\kappa$. We here provide a thorough evaluation of the behavior of 12 such es...
Article
Full-text available
Purpose: There is a clinical need to better non-invasively characterize the tumor microenvironment in order to reveal evidence of early tumor response to therapy and to better understand therapeutic response. The goals of this work are first to compare the sensitivity to modifications occurring during tumor growth for measurements of tumor volume,...
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Background Ageing, hypertension and diabetes have an intricate effect on microvascular structure. In the retina, the respective contribution of remodeling and hypertrophy in such process is still unclear. We aimed at disentangling age, blood pressure and glycaemia effects on retinal microcirculation using the non-invasive adaptive optics ophthalmos...
Article
The diagnostic contribution of 2-D shear-wave elastography (SWE) in management of superficial lymph nodes (LNs) of any origin was evaluated in 222 patients referred for needle core biopsy. Each patient underwent conventional B-mode/Doppler ultrasound examinations (conventional ultrasound) and SWE. Quantitative SWE parameters and qualitative SWE map...
Article
Funding Acknowledgements Type of funding sources: Public Institution(s). Main funding source(s): INSERM Liliane Bettencourt doctoral grant Background Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC) is ass­­ociated with complex spatial and temporal right ventricular (RV) wall motion abnormalities. While cardiac magnetic resonance (CMR) is th...
Article
Funding Acknowledgements Type of funding sources: None. Background. Recent studies revealed the ability of MRI T1 mapping to characterize myocardial involvement in both idiopathic inflammatory myopathy (IIM) and acute viral myocarditis (AVM), as compared to healthy controls. However, neither myocardial T1 nor T2 maps were able to discriminate betwe...
Article
Funding Acknowledgements Type of funding sources: None. Background. Feature tracking (FT) is an emerging approach for the evaluation of both left atrium (LA) and left ventricular (LV) myocardial strain from the same cine MRI dataset. We hypothesized that the LA active contraction longitudinal strain, is a merge of an intrinsic LA booster contractio...
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Automated segmentation of three‐dimensional (3D) aortic magnetic resonance imaging (MRI) renders a possible retrospective selection of any location to perform quantification of aortic caliber perpendicular to its centerline and provides regional and global 3D biomarkers such as length, diameter, or volume. However, normative age‐related values of s...
Article
We consider Gaussian graphical models associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when the number of variables tend to infinity and quantify the difference between the finite and infinite cases.
Preprint
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We consider Gaussian graphical models associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when the number of variables tend to infinity and quantify the difference between the finite and infinite cases.
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Background and purpose: PET/MRI with 18F-FDG has demonstrated the advantages of simultaneous PET and MR imaging in head and neck cancer imaging, MRI allowing excellent soft-tissue contrast, while PET provides metabolic information. The aim of this study was to evaluate the added value of gadolinium contrast-enhanced sequences in the tumor delineat...
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IntroductionPrimary Central Nervous System Lymphoma (PCNSL) is a rare disease with different therapeutic implications than systemic lymphoma. In this study, we evaluated whole-body 18FDG-PET/CT for pre-chemotherapy imaging of suspected PCNSL.Methods One hundred and thirty consecutive immunocompetent patients were retrospectively included. The resul...
Article
OBJECTIVE. The purpose of this study was to test the hypothesis that patients with idiopathic dilated cardiomyopathy (IDCM) and heart failure have increased liver T1 relaxation times at MRI owing to congestion compared with the T1 relaxation times in patients with IDCM without heart failure and healthy control subjects. MATERIALS AND METHODS. For t...
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Purpose: Understanding and prediction of ascending thoracic aortic aneurysms (ATAA) progression are not well established yet and aortic dissection is frequently occurring on normally sized and mildly dilated aortas. Despite known theoretical associations between pressures and blood flow patterns there are no studies focusing on their simultaneous e...
Article
We investigated the in vitro ultrasound-triggered release of paclitaxel, a well known anti-cancerous drug, encapsulated in an emulsion and in the presence of CT26 tumor cells. The emulsion was made of nanodroplets, which volume comprised 95% of perfluoro-octyl bromide and 5% of tributyl O-acetylcitrate, where paclitaxel was solubilized. These nanod...
Article
Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into the other and used to generate a null distribution for a statistic of interest, usually under the asymptotic a...
Preprint
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Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into the other and used to generate a null distribution for a statistic of interest, usually under the asymptotic a...
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Abstract Background Arterial pulse wave velocity (PWV) is associated with increased mortality in aging and disease. Several studies have shown the accuracy of applanation tonometry carotid-femoral PWV (Cf-PWV) and the relevance of evaluating central aorta stiffness using 2D cardiovascular magnetic resonance (CMR) to estimate PWV, and aortic distens...
Article
Objective One of the main challenges of integrated PET/MR is to achieve an accurate PET attenuation correction (AC), especially in brain acquisition. Here, we evaluated an AC method based on zero echo time (ZTE) MRI, comparing it with the single-atlas AC method and CT-based AC, set as reference. Methods Fifty patients (70 ± 11 years old, 28 men) u...
Preprint
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We consider a generalization of information density to a partitioning into $N \geq 2$ subvectors. We calculate its cumulant-generating function and its cumulants, showing that these quantities are only a function of all the regression coefficients associated with the partitioning.
Article
Background: Endobronchial ultrasound transbronchial needle aspiration (EBUS-TBNA) is a reliable technique providing high diagnostic yield in mediastinal lymphadenopathy. However, mediastinoscopy is sometimes necessary to eliminate false-negative results. Elastography is a recent technique that can be combined with EBUS to evaluate the elasticity a...
Article
We consider a generalization of information density to a partitioning into N≥2 subvectors. We calculate its cumulant-generating function and its cumulants in the particular case of a multivariate normal distribution, showing that these quantities are only a function of all the regression coefficients associated with the partitioning.
Article
Purpose Integrated positron emission tomography (PET)/magnetic resonance imaging (MRI) offers promising tools for evaluating brain disorders, including the minimization of exposure to ionizing radiation. Considering the length of scanning time with PET/MRI systems and their high sensitivity, we assumed that the activity could be reduced by one half...
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Background Aging‐related arterial stiffness is associated with substantial changes in global and local arterial pressures. The subsequent early return of reflected pressure waves leads to an elevated left ventricular (LV) afterload and ultimately to a deleterious concentric LV remodeling. Purpose To compute aortic time‐resolved pressure fields of...
Article
Spasticity after spinal cord injury has considerable quality of life implications, impacts on rehabilitation efforts and requires long-term multidisciplinary pharmacological and non-pharmacological management. The potassium chloride co-transporter (KCC2) plays a central role in intracellular chloride homeostasis and the inhibitory function of matur...
Article
Background: Clinically, aortic geometry assessment is mainly based on the measurement of maximal diameters at different anatomic locations, which are subsequently used to indicate prophylactic aortic surgery. However, 3D evaluation of aortic morphology could provide volumetric quantification, which integrates both aortic dilatation and elongation...
Article
Introduction/Background Transcranial direct current stimulation is used to modify noninvasively cortical brain excitability in humans. It consists in delivering a weak current trough two electrodes: one applied over the motor cortex and a second in supra-orbital position. Recently we showed in healthy subjects that anodal tDCS applied over the moto...
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Objectives: Infraclinical sensory alterations have been reported at early stages of amyotrophic lateral sclerosis (ALS). While previous studies mainly focused on early somatosensory evoked potentials (SEPs), late SEPs, which reflect on cortical pathways involved in cognitive-motor functions, are relatively underinvestigated. Early and late SEPs we...
Article
Introduction: ¹⁸F-fluorodeoxyglucose PET/CT (FDG-PET/CT) is an imaging modality routinely used in oncology, hematology, as well as in infectious and inflammatory diseases. Frequently, patients and their accompanying persons may be apprehensive concerning risks of radiation exposure after performing this examination, particularly when it concerns ne...
Article
Background: A feature tracking (FT) was designed to simultaneously extract myocardial strains in main cardiac chambers from cine MRI images. Its inter-observer and scan-rescan reproducibility was assessed and sample sizes required to detect predefined longitudinal changes in strain values were provided. Method: FT was applied on left (LV) and ri...
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In the study of mechanical properties of human bone, specimens may be defatted before experiments to prevent contamination and the risk of infections. High energy synchrotron radiation micro-computed tomography (SR-μCT) is a popular technique to study bone microstructure. However, little is known about the effects of defatting or irradiation during...
Article
Objectifs Le TEP/IRM permet une reduction de l’exposition aux rayonnements ionisants due a l’absence de TDM. Compte tenu de la sensibilite elevee des cameras TEP/IRM et, considerant qu’une duree d’acquisition minimale de 20 minutes est necessaire dans les indications neurologiques du fait de l’IRM, nous supposons que l’activite injectee habituellem...
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Objectif Les carcinomes adénoïdes kystiques des glandes salivaires (CAK-GS) sont des cancers rares d’évolution lente. Les extensions périneurales sont fréquentes et exposent au risque de récidive locale. L’envahissement ganglionnaire cervical est inhabituel. En revanche, les métastases à distance sont retrouvées dans 35–50 % des cas. Notre objectif...
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Brain computation relies on effective interactions between ensembles of neurons. In neuroimaging, measures of functional connectivity (FC) aim at statistically quantifying such interactions, often to study normal or pathological cognition. Their capacity to reflect a meaningful variety of patterns as expected from neural computation in relation to...
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Full-text available
Objectifs Les carcinomes adénoïdes kystiques (CAK) sont des cancers rares des glandes salivaires de métabolisme variable et de croissance lente, comportant néanmoins un risque élevé de récidive loco-régionale (en raison d’engainements périnerveux) et de métastases à distance. Le diagnostic histologique préopératoire repose sur la cytologie (compte...
Article
Aims Importance of left atrial (LA) phasic function evaluation is increasingly recognized for its incremental value in terms of prognosis and risk stratification. LA phasic deformation in the pathway of normal aging have been characterized using echocardiographic speckle tracking. However no data are available regarding age-related variations using...
Article
Compare seven previous methods for the estimation of aortic characteristic impedance, which contributes to left ventricle pulsatile load, from phase-contrast cardiovascular magnetic resonance (CMR) and applanation tonometry data. We studied 77 healthy (43 ± 16 years) individuals and 16 hypertensive (61 ± 9 years) patients, who consecutively underwe...
Article
Our objectives were to assess the ability of phasecontrast MRI (PC-MRI) to detect sub-clinical age-related variations of left ventricular (LV) diastolic parameters and thus to provide age-related reference ranges currently available for echocardiography but not for MRI-PC, and to identify independent associates of such variations. We studied 100 he...
Article
PurposeWe sought to noninvasively estimate aortic impedance indices from MR and tonometric data. Materials and MethodsMR aortic velocity-encoded and carotid applanation tonometry pressure data of 70 healthy subjects (19–79 years) were used to calculate the following indices from impedance spectrum: (i) characteristic impedance (Zc) reflecting pulsa...
Article
We examined the influence of the AGTR1 A1166C genotype on the 16-year evolution of pulse wave velocity (PWV) in a middle-aged population. In a cross-sectional study, we reported that the presence of the AGTR1 1166C allele was associated with higher aortic stiffness compared with the AGTR1 1166AA genotype. The study was conducted in 259 subjects who...
Article
Several systems for the diagnosis of melanoma from images of naevi obtained under controlled conditions have demonstrated comparable efficiency with dermatologists. However, their robustness to analyze daily routine images was sometimes questionable. The purpose of this work is to investigate to what extent the automatic melanoma diagnosis may be a...
Article
To assess regional ventricular function via an accurate and automated definition of functional parameters. An automated method is proposed that estimates reliable regional normalized mean transition times (F(mc)) and mean radial velocities (V(m)) from cine images. This approach combines a quantitative parametric imaging method and an automated dete...
Article
Alzheimer's disease (AD) and frontotemporal dementia (FTD) are among the most frequent neurodegenerative cognitive disorders, but their differential diagnosis is difficult. The aim of this study was to evaluate an automatic method returning the probability that a patient suffers from AD or FTD from the analysis of brain perfusion single photon emis...
Article
To improve diagnosis of early Alzheimer's disease (AD), i.e., prodromal AD, by an automated quantitative tool combining brain perfusion single-photon emission computed tomography (SPECT) images and memory tests scores in order to be applied in clinical practice. In this prospective, longitudinal, multi-centric study, a baseline (99m)Tc-ECD perfusio...
Article
Ability at social skills in daily life was examined in a group of normal children. The aim was to establish standard values for the EASE scale. 327 normal children of different age groups were tested. The results revealed the significant influence of age in the development of mentalisation and confirmed that this capacity is acquired between 3 and...
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The facial appearance of a person does not always reflect the chronological age; some people look younger or older than they really are. Many studies have described the changes in skin properties (colour, wrinkles, sagging, micro relief, etc.) with age, but few of them have analysed their influence on the perceived age. The primary objective of thi...
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Performances in social abilities of everyday life were studied in children with specific language impairment or PDD (pervasive developmental disorders). Comparison was made with normal children, children with intellectual deficiencies and dyslexic children. Results concerning children with language impairment confirm a relationship exists between l...
Article
Assessment of social intelligence in children Ability at social skills in daily life was examined in a group of normal children. The aim was to establish standard values for the EASE scale. 327 normal children of different age groups were tested. The results revealed the significant influence of age in the development of mentalisation and confirmed...
Article
Mapping high-dimensional data in a low-dimensional space, for example, for visualization, is a problem of increasingly major concern in data analysis. This paper presents data-driven high-dimensional scaling (DD-HDS), a nonlinear mapping method that follows the line of multidimensional scaling (MDS) approach, based on the preservation of distances...
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To determine the value of IL-10 measurement in aqueous humor (AH) for screening in primary intraocular lymphoma (PIOL). One hundred consecutive diagnostic or therapeutic vitrectomies were performed in patients with uveitis. During surgery, 100 microL of both AH and pure vitreous was taken. IL-10 levels were determined with a standard quantitative s...
Conference Paper
Alzheimer's disease (AD) and frontotemporal dementia (FTD) are the most frequent neurodegenerative cognitive disorders, but their differential diagnosis is difficult. The aim of this study is to evaluate an automatic method that returns the probability that a patient suffers from AD or FTD from the analysis of brain SPECT (single photon emission co...
Article
This study was designed to investigate the influence of aortic arch geometry on vascular remodeling after anatomically successful repair of coarctation of the aorta (CoA). Abnormalities of the precoarctation vasculature are known to occur after CoA repair and appear related to adverse outcomes. The influence of aortic arch geometry on such abnormal...
Article
“Kernel logistic PLS” (KL-PLS) is a new tool for supervised nonlinear dimensionality reduction and binary classification. The principles of KL-PLS are based on both PLS latent variables construction and learning with kernels. The KL-PLS algorithm can be seen as a supervised dimensionality reduction (complexity control step) followed by a classifica...
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GENSTYLE (http://Genstyle.imed.jussieu.fr) is a workspace designed for the characterization and classification of nucleotide sequences. Based on the genomic signature paradigm, GENSTYLE focuses on oligonucleotide frequencies in DNA sequences. Users can select sequences of interest in the GENSTYLE companion database, where the whole set of GenBank s...
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Molecular phylogenetic methods are based on alignments of nucleic or peptidic sequences. The tremendous increase in molecular data permits phylogenetic analyses of very long sequences and of many species, but also requires methods to help manage large datasets. Here we explore the phylogenetic signal present in molecular data by genomic signatures,...
Article
Horizontal DNA transfer is an important factor of evolution and participates in biological diversity. Unfortunately, the location and length of horizontal transfers (HTs) are known for very few species. The usage of short oligonucleotides in a sequence (the so-called genomic signature) has been shown to be species-specific even in DNA fragments as...
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est un ensemble d'outils disponible sur le web destiné à la caractérisation et la classification de séquences d'ADN à partir de leur signature génomique (l'ensemble des fréquences d'oligonucléotides). Les signatures génomiques caractérisent le « style d'écriture » des espèces. Leur comparaison permet, par exemple, de détecter des segments originaux...
Article
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Kernel Logistic PLS” (KL-PLS), a new tool for classification with performances similar to the most powerful statistical methods is described in this paper. KL-PLS is based on the principles of PLS generalized regression and learning via kernel. The successions of simple regressions, simple logistic regression and multiple logistic regressions on a...
Article
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Résumé. De nombreuses « propriétés » intuitives des données de faible dimension (1-3) ne sont pas vérifiées quand le nombre de dimensions augmente. La comparaison entre les signatures génomiques se heurte à cette « malédiction de la dimension ». En se basant sur des travaux qui tentent de répondre à ce problème, nous étudions l'influence de la métr...
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Introduction The usage of short oligonucleotides in sequences (the so-called genomic signature) has been shown to be species-specific. Since the genomic signature can be observed in DNA sequences as short as 1Kb, it appears to result from a "style" that characterizes the organization of DNA all over each genome. As a consequence, given a short DNA...
Article
Introduction Genomes, from a functional point of view, can be split in three groups of sequences, DNA coding for protein genes, non coding DNA and DNA coding for structural RNAs (rRNA, tRNA, snRNA ...). Many bioinformatic methods are designed for detecting a priori the function of a DNA sequence. Hidden Markov Models are widely used for this purpos...
Article
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The molecular systematics of vertebrates has been based entirely on alignments of primary structures of macromolecules; however, higher order features of DNA sequences not used in traditional studies also contain valuable phylogenetic information. Recent molecular data sets conflict over the phylogenetic placement of flightless birds (ratites - pal...
Article
Visualization techniques are very useful when exploring large amounts of information especially when dealing with data flow. A pixel-oriented visualization technique based on the CGR algorithm has been designed to help recognize type of flowing data on the fly. The CGR method-originally developed for the analysis of genomic sequences- and modified...
Article
In this paper, the architecture of an all-round pattern recognition system is described together with some of the results obtained when dealing with the characterization of infected areas in retinal angiograms. Several tricky aspects of the implementation are discussed. In particular, special attention is given to the feature-extraction scheme and...
Article
Melanoma diagnosis greatly relies on the observation of some characteristic features on skin tumors. Similarly, a computer- based diagnostic system has been designed to detect these features. However, specificity and sensitivity of features often rely on their location within the tumor. Locating the border of lesions is therefore of utmost importan...
Article
Medical images provide experienced physicians with meaningful visual stimuli but their features are frequently hard to decipher. The development of a computational model to mimic physicians' expertise is a demanding task, especially if a significant and sophisticated preprocessing of images is required. Learning from well-expertised images may be a...
Conference Paper
A operational system devoted to the segmentation of virus-infected areas in the retina is described. It uses a 3-stage approach which involves image sampling, unsupervised coding and supervised classification. Unsupervised coding is provided by principal component analysis whereas supervised classification is performed by a multilayer perceptron. S...
Conference Paper
The “chaos game representation” (CGR) paradigm has been implemented to display the use of short oligonucleotides in genomes in the form of fractal images. These images can be considered as a genomic signature. Using an unsupervised classification approach, it is shown that short fragments of genomic sequences retain most of the characteristics of t...
Chapter
The detection of specific features in medical images is often a key support for diagnosis. Taking advantage of large bases of images where features of interest have been localized by clinicians, a modular system has been developed to spot similar features on new images. Images are scanned through a window, the size of which being previously fitted...

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