Parametric estimation of pulse arrival time: a robust approach to pulse wave velocity.

Pulse wave velocity (PWV) is a surrogate of arterial stiffness and represents a non-invasive marker of cardiovascular risk. The non-invasive measurement of PWV requires tracking the arrival time of pressure pulses recorded in vivo, commonly referred to as pulse arrival time (PAT). In the state of the art, PAT is estimated by identifying a characteristic point of the pressure pulse waveform. This paper demonstrates that for ambulatory scenarios, where signal-to-noise ratios are below 10 dB, the performance in terms of repeatability of PAT measurements through characteristic points identification degrades drastically. Hence, we introduce a novel family of PAT estimators based on the parametric modeling of the anacrotic phase of a pressure pulse. In particular, we propose a parametric PAT estimator (TANH) that depicts high correlation with the Complior(R) characteristic point D1 (CC = 0.99), increases noise robustness and reduces by a five-fold factor the number of heartbeats required to obtain reliable PAT measurements.

Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Dense deformation field estimation for atlas-based segmentation of pathological MR brain images.

Atlas registration is a recognized paradigm for the automatic segmentation of normal MR brain images. Unfortunately, atlas-based segmentation has been of limited use in presence of large space-occupying lesions. In fact, brain deformations induced by such lesions are added to normal anatomical variability and they may dramatically shift and deform anatomically or functionally important brain structures. In this work, we chose to focus on the problem of inter-subject registration of MR images with large tumors, inducing a significant shift of surrounding anatomical structures. First, a brief survey of the existing methods that have been proposed to deal with this problem is presented. This introduces the discussion about the requirements and desirable properties that we consider necessary to be fulfilled by a registration method in this context: To have a dense and smooth deformation field and a model of lesion growth, to model different deformability for some structures, to introduce more prior knowledge, and to use voxel-based features with a similarity measure robust to intensity differences. In a second part of this work, we propose a new approach that overcomes some of the main limitations of the existing techniques while complying with most of the desired requirements above. Our algorithm combines the mathematical framework for computing a variational flow proposed by Hermosillo et al. [G. Hermosillo, C. Chefd'Hotel, O. Faugeras, A variational approach to multi-modal image matching, Tech. Rep., INRIA (February 2001).] with the radial lesion growth pattern presented by Bach et al. [M. Bach Cuadra, C. Pollo, A. Bardera, O. Cuisenaire, J.-G. Villemure, J.-Ph. Thiran, Atlas-based segmentation of pathological MR brain images using a model of lesion growth, IEEE Trans. Med. Imag. 23 (10) (2004) 1301-1314.]. Results on patients with a meningioma are visually assessed and compared to those obtained with the most similar method from the state-of-the-art.

ROBETH: un logiciel pour les procédés statistiques robustes [ROBETH: a library for robust statistical procedures].

In the past 20 years the theory of robust estimation has become an important topic of mathematical statistics. We discuss here some basic concepts of this theory with the help of simple examples. Furthermore we describe a subroutine library for the application of robust statistical procedures, which was developed with the support of the Swiss National Science Foundation.

Source-wavelet estimation during full-waveform inversion of ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole ground-penetrating radar (GPR) data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a recently published time-domain inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity of both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little to no trade-off between the wavelet estimation and the tomographic imaging procedures.

The branch-site test of positive selection is surprisingly robust but lacks power under synonymous substitution saturation and variation in GC

Positive selection is widely estimated from protein coding sequence alignments by the nonsynonymous-to-synonymous ratio omega. Increasingly elaborate codon models are used in a likelihood framework for this estimation. Although there is widespread concern about the robustness of the estimation of the omega ratio, more efforts are needed to estimate this robustness, especially in the context of complex models. Here, we focused on the branch-site codon model. We investigated its robustness on a large set of simulated data. First, we investigated the impact of sequence divergence. We found evidence of underestimation of the synonymous substitution rate for values as small as 0.5, with a slight increase in false positives for the branch-site test. When dS increases further, underestimation of dS is worse, but false positives decrease. Interestingly, the detection of true positives follows a similar distribution, with a maximum for intermediary values of dS. Thus, high dS is more of a concern for a loss of power (false negatives) than for false positives of the test. Second, we investigated the impact of GC content. We showed that there is no significant difference of false positives between high GC (up to similar to 80%) and low GC (similar to 30%) genes. Moreover, neither shifts of GC content on a specific branch nor major shifts in GC along the gene sequence generate many false positives. Our results confirm that the branch-site is a very conservative test.

Effects of computing parameters and measurement locations on the estimation of 3D NPS in non-stationary MDCT images.

The goal of this study was to investigate the impact of computing parameters and the location of volumes of interest (VOI) on the calculation of 3D noise power spectrum (NPS) in order to determine an optimal set of computing parameters and propose a robust method for evaluating the noise properties of imaging systems. Noise stationarity in noise volumes acquired with a water phantom on a 128-MDCT and a 320-MDCT scanner were analyzed in the spatial domain in order to define locally stationary VOIs. The influence of the computing parameters in the 3D NPS measurement: the sampling distances bx,y,z and the VOI lengths Lx,y,z, the number of VOIs NVOI and the structured noise were investigated to minimize measurement errors. The effect of the VOI locations on the NPS was also investigated. Results showed that the noise (standard deviation) varies more in the r-direction (phantom radius) than z-direction plane. A 25 × 25 × 40 mm(3) VOI associated with DFOV = 200 mm (Lx,y,z = 64, bx,y = 0.391 mm with 512 × 512 matrix) and a first-order detrending method to reduce structured noise led to an accurate NPS estimation. NPS estimated from off centered small VOIs had a directional dependency contrary to NPS obtained from large VOIs located in the center of the volume or from small VOIs located on a concentric circle. This showed that the VOI size and location play a major role in the determination of NPS when images are not stationary. This study emphasizes the need for consistent measurement methods to assess and compare image quality in CT.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Is the formula of Traub still up to date in antemortem blood glucose level estimation?

According to the hypothesis of Traub, also known as the 'formula of Traub', postmortem values of glucose and lactate found in the cerebrospinal fluid or vitreous humor are considered indicators of antemortem blood glucose levels. However, because the lactate concentration increases in the vitreous and cerebrospinal fluid after death, some authors postulated that using the sum value to estimate antemortem blood glucose levels could lead to an overestimation of the cases of glucose metabolic disorders with fatal outcomes, such as diabetic ketoacidosis. The aim of our study, performed on 470 consecutive forensic cases, was to ascertain the advantages of the sum value to estimate antemortem blood glucose concentrations and, consequently, to rule out fatal diabetic ketoacidosis as the cause of death. Other biochemical parameters, such as blood 3-beta-hydroxybutyrate, acetoacetate, acetone, glycated haemoglobin and urine glucose levels, were also determined. In addition, postmortem native CT scan, autopsy, histology, neuropathology and toxicology were performed to confirm diabetic ketoacidosis as the cause of death. According to our results, the sum value does not add any further information for the estimation of antemortem blood glucose concentration. The vitreous glucose concentration appears to be the most reliable marker to estimate antemortem hyperglycaemia and, along with the determination of other biochemical markers (such as blood acetone and 3-beta-hydroxybutyrate, urine glucose and glycated haemoglobin), to confirm diabetic ketoacidosis as the cause of death.

Molecular estimation of dispersal for ecology and population genetics

The dispersal process, by which individuals or other dispersing agents such as gametes or seeds move from birthplace to a new settlement locality, has important consequences for the dynamics of genes, individuals, and species. Many of the questions addressed by ecology and evolutionary biology require a good understanding of species' dispersal patterns. Much effort has thus been devoted to overcoming the difficulties associated with dispersal measurement. In this context, genetic tools have long been the focus of intensive research, providing a great variety of potential solutions to measuring dispersal. This methodological diversity is reviewed here to help (molecular) ecologists find their way toward dispersal inference and interpretation and to stimulate further developments.

Multifractal portrayal of the Swiss population

Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. These analyses were carried out using fractal and multifractal measures for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). The fractal characterization was performed by means of the box-counting dimension and the multifractal analysis was conducted through the Renyi's generalized dimensions and the multifractal spectrum. Results showed that the four population patterns are all multifractals and present different clustering behaviours. Applying multifractal and fractal methods at different geographical regions and at different scales allowed us to quantify and describe the dissimilarities between the four structures and their underlying processes. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

Cardiovascular risk estimation and eligibility for statin therapy using different scoring systems in Europe: a population-based study in Switzerland

BACKGROUND: Recommendations for statin use for primary prevention of coronary heart disease (CHD) are based on estimation of the 10- year CHD risk. We compared the 10-year CHD risk assessments and eligibility percentages for statin therapy using three scoring algorithms currently used in Europe. METHODS: We studied 5683 women and men, aged 35-75, without overt cardiovascular disease (CVD), in a population-based study in Switzerland. We compared the 10-year CHD risk using three scoring schemes, i.e., the Framingham risk score (FRS) from the U.S. National Cholesterol Education Program's Adult Treatment Panel III (ATP III), the PROCAM scoring scheme from the International Atherosclerosis Society (IAS), and the European risk SCORE for low-risk countries, without and with extrapolation to 60 years as recommended by the European Society of Cardiology guidelines (ESC). With FRS and PROCAM, high-risk was defined as a 10- year risk of fatal or non-fatal CHD>20% and a 10-year risk of fatal CVD≥5% with SCORE. We compared the proportions of high-risk participants and eligibility for statin use according to these three schemes. For each guideline, we estimated the impact of increased statin use from current partial compliance to full compliance on potential CHD deaths averted over 10 years, using a success proportion of 27% for statins. RESULTS: Participants classified at high-risk (both genders) were 5.8% according to FRS and 3.0% to the PROCAM, whereas the European risk SCORE classified 12.5% at high-risk (15.4% with extrapolation to 60 years). For the primary prevention of CHD, 18.5% of participants were eligible for statin therapy using ATP III, 16.6% using IAS, and 10.3% using ESC (13.0% with extrapolation) because ESC guidelines recommend statin therapy only in high-risk subjects. In comparison with IAS, agreement to identify eligible adults for statins was good with ATP III, but moderate with ESC. Using a population perspective, a full compliance with ATP III guidelines would reduce up to 17.9% of the 24′ 310 CHD deaths expected over 10 years in Switzerland, 17.3% with IAS and 10.8% with ESC (11.5% with extrapolation). CONCLUSIONS: Full compliance with guidelines for statin therapy would result in substantial health benefits, but proportions of high-risk adults and eligible adults for statin use varied substantially depending on the scoring systems and corresponding guidelines used for estimating CHD risk in Europe.