Gaussian process framework for pervasive estimation of swimming velocity with body-worn IMU

Presented is an accurate swimming velocity estimation method using an inertial measurement unit (IMU) by employing a simple biomechanical constraint of motion along with Gaussian process regression to deal with sensor inherent errors. Experimental validation shows a velocity RMS error of 9.0 cm/s and high linear correlation when compared with a commercial tethered reference system. The results confirm the practicality of the presented method to estimate swimming velocity using a single low-cost, body-worn IMU.

Rate and processes of river network rearrangement during incipient faulting: The case of the Cahabon river, Guatemala

Deeply incised river networks are generally regarded as robust features that are not easily modified by erosion or tectonics. Although the reorganization of deeply incised drainage systems has been documented, the corresponding importance with regard to the overall landscape evolution of mountain ranges and the factors that permit such reorganizations are poorly understood. To address this problem, we have explored the rapid drainage reorganization that affected the Cahabon River in Guatemala during the Quaternary. Sediment-provenance analysis, field mapping, and electrical resistivity tomography (ERT) imaging are used to reconstruct the geometry of the valley before the river was captured. Dating of the abandoned valley sediments by the Be-10-Al-26 burial method and geomagnetic polarity analysis allow us to determine the age of the capture events and then to quantify several processes, such as the rate of tectonic deformation of the paleovalley, the rate of propagation of post-capture drainage reversal, and the rate at which canyons that formed at the capture sites have propagated along the paleovalley. Transtensional faulting started 1 to 3 million years ago, produced ground tilting and ground faulting along the Cahabon River, and thus generated differential uplift rate of 0.3 +/- 0.1 up to 0.7 +/- 0.4 mm . y(-1) along the river's course. The river responded to faulting by incising the areas of relative uplift and depositing a few tens of meters of sediment above the areas of relative subsidence. Then, the river experienced two captures and one avulsion between 700 ky and 100 ky. The captures breached high-standing ridges that separate the Cahabon River from its captors. Captures occurred at specific points where ridges are made permeable by fault damage zones and/or soluble rocks. Groundwater flow from the Cahabon River down to its captors likely increased the erosive power of the captors thus promoting focused erosion of the ridges. Valley-fill formation and capture occurred in close temporal succession, suggesting a genetic link between the two. We suggest that the aquifers accumulated within the valley-fills, increased the head along the subterraneous system connecting the Cahabon River to its captors, and promoted their development. Upon capture, the breached valley experienced widespread drainage reversal toward the capture sites. We attribute the generalized reversal to combined effects of groundwater sapping in the valley-fill, axial drainage obstruction by lateral fans, and tectonic tilting. Drainage reversal increased the size of the captured areas by a factor of 4 to 6. At the capture sites, 500 m deep canyons have been incised into the bedrock and are propagating upstream at a rate of 3 to 11 mm . y(-1) deepening at a rate of 0.7 to 1 5 mm . y(-1). At this rate, 1 to 2 million years will be necessary for headward erosion to completely erase the topographic expression of the paleovalley. It is concluded that the rapid reorganization of this drainage system was made possible by the way the river adjusted to the new tectonic strain field, which involved transient sedimentation along the river's course. If the river had escaped its early reorganization and had been given the time necessary to reach a new dynamic equilibrium, then the transient conditions that promoted capture would have vanished and its vulnerability to capture would have been strongly reduced.

Genetic differentiation in Silene dioica metapopulations: estimation of spatiotemporal effects in a successional plant species

Silene dioica is a diploid, dioecious, perennial, insect-pollinated herb and part of the deciduous phase of primary succession in Skeppsvik Archipelago, Gulf of Bothnia, Sweden. These islands are composed of material deposited and left underwater by melting ice at the end of the last ice age. A rapid and relatively constant rate of land uplift of 0.9 cm per year continually creates new islands available for colonization by plants. Because the higher deposits appear first, islands differ in age. Because it is possible to estimate the ages of islands and populations of plant species belonging to early stages of succession, the genetic dynamics occurring within an age-structured metapopulation can be investigated in this archipelago. Fifty-two island populations of S. dioica of known ages, sizes, and distances from each other were studied through electrophoretic data. A number of factors increase the degree of genetic differentiation among these island populations relative to an island model at equilibrium. Newly founded populations were more differentiated than those of intermediate age, which suggests that colonization dynamics increase genetic variance among populations. The very old populations, which decrease in size as they approach extinction, were more differentiated than intermediate-aged populations. Isolation by distance occurs in this system. Colonizers are likely to come from more than one source, and the migrant pool model best explains colonization events in the archipelago. Degree of environmental exposure also affects population differentiation.

Domain Adaptation in remote sensing: increasing the portability of land-cover classifiers

Among the types of remote sensing acquisitions, optical images are certainly one of the most widely relied upon data sources for Earth observation. They provide detailed measurements of the electromagnetic radiation reflected or emitted by each pixel in the scene. Through a process termed supervised land-cover classification, this allows to automatically yet accurately distinguish objects at the surface of our planet. In this respect, when producing a land-cover map of the surveyed area, the availability of training examples representative of each thematic class is crucial for the success of the classification procedure. However, in real applications, due to several constraints on the sample collection process, labeled pixels are usually scarce. When analyzing an image for which those key samples are unavailable, a viable solution consists in resorting to the ground truth data of other previously acquired images. This option is attractive but several factors such as atmospheric, ground and acquisition conditions can cause radiometric differences between the images, hindering therefore the transfer of knowledge from one image to another. The goal of this Thesis is to supply remote sensing image analysts with suitable processing techniques to ensure a robust portability of the classification models across different images. The ultimate purpose is to map the land-cover classes over large spatial and temporal extents with minimal ground information. To overcome, or simply quantify, the observed shifts in the statistical distribution of the spectra of the materials, we study four approaches issued from the field of machine learning. First, we propose a strategy to intelligently sample the image of interest to collect the labels only in correspondence of the most useful pixels. This iterative routine is based on a constant evaluation of the pertinence to the new image of the initial training data actually belonging to a different image. Second, an approach to reduce the radiometric differences among the images by projecting the respective pixels in a common new data space is presented. We analyze a kernel-based feature extraction framework suited for such problems, showing that, after this relative normalization, the cross-image generalization abilities of a classifier are highly increased. Third, we test a new data-driven measure of distance between probability distributions to assess the distortions caused by differences in the acquisition geometry affecting series of multi-angle images. Also, we gauge the portability of classification models through the sequences. In both exercises, the efficacy of classic physically- and statistically-based normalization methods is discussed. Finally, we explore a new family of approaches based on sparse representations of the samples to reciprocally convert the data space of two images. The projection function bridging the images allows a synthesis of new pixels with more similar characteristics ultimately facilitating the land-cover mapping across images.

Are the light-harvesting I complexes from Rhodospirillum rubrum arranged around the reaction centre in a square geometry?

The basic photosynthetic unit containing the reaction centre and the light-harvesting I complex (RC-LHI) of the purple non-sulphur bacterium Rhodospirillum rubrum was purified and reconstituted into two-dimensional (2D) membrane crystals. Transmission electron microscopy using conventional techniques and cryoelectron microscopy of the purified single particles and of 2D crystals yielded a projection of the RC-LHI complex at a resolution of at least 1.6 nm. In this projection the LHI ring appears to have a square symmetry and packs in a square crystal lattice. The square geometry of the LHI ring was observed also in images of single isolated particles of the RC-LHI complex. However, although the LHI units are packed identically within the crystal lattice, a new rotational analysis developed here showed that the reaction centres take up one of four possible orientations within the ring. This fourfold disorder supports our interpretation of a square ring symmetry and suggests that a hitherto undetected component may be present within the photosynthetic unit.

Cross-presenting human gammadelta T cells induce robust CD8+ alphabeta T cell responses.

Gammadelta T cells are implicated in host defense against microbes and tumors but their mode of function remains largely unresolved. Here, we have investigated the ability of activated human Vgamma9Vdelta2(+) T cells (termed gammadelta T-APCs) to cross-present microbial and tumor antigens to CD8(+) alphabeta T cells. Although this process is thought to be mediated best by DCs, adoptive transfer of ex vivo antigen-loaded, human DCs during immunotherapy of cancer patients has shown limited success. We report that gammadelta T-APCs take up and process soluble proteins and induce proliferation, target cell killing and cytokine production responses in antigen-experienced and naïve CD8(+) alphabeta T cells. Induction of APC functions in Vgamma9Vdelta2(+) T cells was accompanied by the up-regulation of costimulatory and MHC class I molecules. In contrast, the functional predominance of the immunoproteasome was a characteristic of gammadelta T cells irrespective of their state of activation. Gammadelta T-APCs were more efficient in antigen cross-presentation than monocyte-derived DCs, which is in contrast to the strong induction of CD4(+) alphabeta T cell responses by both types of APCs. Our study reveals unexpected properties of human gammadelta T-APCs in the induction of CD8(+) alphabeta T effector cells, and justifies their further exploration in immunotherapy research.

Automated DNA extraction using the QIAsymphony platform: Estimation of DNA recovery from simulated forensic stains

The aim of this study was to evaluate the forensic protocol recently developed by Qiagen for the QIAsymphony automated DNA extraction platform. Samples containing low amounts of DNA were specifically considered, since they represent the majority of samples processed in our laboratory. The analysis of simulated blood and saliva traces showed that the highest DNA yields were obtained with the maximal elution volume available for the forensic protocol, that is 200 ml. Resulting DNA extracts were too diluted for successful DNA profiling and required a concentration. This additional step is time consuming and potentially increases inversion and contamination risks. The 200 ml DNA extracts were concentrated to 25 ml, and the DNA recovery estimated with real-time PCR as well as with the percentage of SGM Plus alleles detected. Results using our manual protocol, based on the QIAamp DNA mini kit, and the automated protocol were comparable. Further tests will be conducted to determine more precisely DNA recovery, contamination risk and PCR inhibitors removal, once a definitive procedure, allowing the concentration of DNA extracts from low yield samples, will be available for the QIAsymphony.

Malaria haplotype frequency estimation.

We present a Bayesian approach for estimating the relative frequencies of multi-single nucleotide polymorphism (SNP) haplotypes in populations of the malaria parasite Plasmodium falciparum by using microarray SNP data from human blood samples. Each sample comes from a malaria patient and contains one or several parasite clones that may genetically differ. Samples containing multiple parasite clones with different genetic markers pose a special challenge. The situation is comparable with a polyploid organism. The data from each blood sample indicates whether the parasites in the blood carry a mutant or a wildtype allele at various selected genomic positions. If both mutant and wildtype alleles are detected at a given position in a multiply infected sample, the data indicates the presence of both alleles, but the ratio is unknown. Thus, the data only partially reveals which specific combinations of genetic markers (i.e. haplotypes across the examined SNPs) occur in distinct parasite clones. In addition, SNP data may contain errors at non-negligible rates. We use a multinomial mixture model with partially missing observations to represent this data and a Markov chain Monte Carlo method to estimate the haplotype frequencies in a population. Our approach addresses both challenges, multiple infections and data errors.

Budgeting rockfall and modeling sedimentary delivery in torrent systems

This thesis is a compilation of projects to study sediment processes recharging debris flow channels. These works, conducted during my stay at the University of Lausanne, focus in the geological and morphological implications of torrent catchments to characterize debris supply, a fundamental element to predict debris flows. Other aspects of sediment dynamics are considered, e.g. the coupling headwaters - torrent, as well as the development of a modeling software that simulates sediment transfer in torrent systems. The sediment activity at Manival, an active torrent system of the northern French Alps, was investigated using terrestrial laser scanning and supplemented with geostructural investigations and a survey of sediment transferred in the main torrent. A full year of sediment flux could be observed, which coincided with two debris flows and several bedload transport events. This study revealed that both debris flows generated in the torrent and were preceded in time by recharge of material from the headwaters. Debris production occurred mostly during winter - early spring time and was caused by large slope failures. Sediment transfers were more puzzling, occurring almost exclusively in early spring subordinated to runoffconditions and in autumn during long rainfall. Intense rainstorms in summer did not affect debris storage that seems to rely on the stability of debris deposits. The morpho-geological implication in debris supply was evaluated using DEM and field surveys. A slope angle-based classification of topography could characterize the mode of debris production and transfer. A slope stability analysis derived from the structures in rock mass could assess susceptibility to failure. The modeled rockfall source areas included more than 97% of the recorded events and the sediment budgets appeared to be correlated to the density of potential slope failure. This work showed that the analysis of process-related terrain morphology and of susceptibility to slope failure document the sediment dynamics to quantitatively assess erosion zones leading to debris flow activity. The development of erosional landforms was evaluated by analyzing their geometry with the orientations of potential rock slope failure and with the direction of the maximum joint frequency. Structure in rock mass, but in particular wedge failure and the dominant discontinuities, appear as a first-order control of erosional mechanisms affecting bedrock- dominated catchment. They represent some weaknesses that are exploited primarily by mass wasting processes and erosion, promoting not only the initiation of rock couloirs and gullies, but also their propagation. Incorporating the geological control in geomorphic processes contributes to better understand the landscape evolution of active catchments. A sediment flux algorithm was implemented in a sediment cascade model that discretizes the torrent catchment in channel reaches and individual process-response systems. Each conceptual element includes in simple manner geomorphological and sediment flux information derived from GIS complemented with field mapping. This tool enables to simulate sediment transfers in channels considering evolving debris supply and conveyance, and helps reducing the uncertainty inherent to sediment budget prediction in torrent systems. Cette thèse est un recueil de projets d'études des processus de recharges sédimentaires des chenaux torrentiels. Ces travaux, réalisés lorsque j'étais employé à l'Université de Lausanne, se concentrent sur les implications géologiques et morphologiques des bassins dans l'apport de sédiments, élément fondamental dans la prédiction de laves torrentielles. D'autres aspects de dynamique sédimentaire ont été abordés, p. ex. le couplage torrent - bassin, ainsi qu'un modèle de simulation du transfert sédimentaire en milieu torrentiel. L'activité sédimentaire du Manival, un système torrentiel actif des Alpes françaises, a été étudiée par relevés au laser scanner terrestre et complétée par une étude géostructurale ainsi qu'un suivi du transfert en sédiments du torrent. Une année de flux sédimentaire a pu être observée, coïncidant avec deux laves torrentielles et plusieurs phénomènes de charriages. Cette étude a révélé que les laves s'étaient générées dans le torrent et étaient précédées par une recharge de débris depuis les versants. La production de débris s'est passée principalement en l'hiver - début du printemps, causée par de grandes ruptures de pentes. Le transfert était plus étrange, se produisant presque exclusivement au début du printemps subordonné aux conditions d'écoulement et en automne lors de longues pluies. Les orages d'été n'affectèrent guère les dépôts, qui semblent dépendre de leur stabilité. Les implications morpho-géologiques dans l'apport sédimentaire ont été évaluées à l'aide de MNT et études de terrain. Une classification de la topographie basée sur la pente a permis de charactériser le mode de production et transfert. Une analyse de stabilité de pente à partir des structures de roches a permis d'estimer la susceptibilité à la rupture. Les zones sources modélisées comprennent plus de 97% des chutes de blocs observées et les bilans sédimentaires sont corrélés à la densité de ruptures potentielles. Ce travail d'analyses des morphologies du terrain et de susceptibilité à la rupture documente la dynamique sédimentaire pour l'estimation quantitative des zones érosives induisant l'activité torrentielle. Le développement des formes d'érosion a été évalué par l'analyse de leur géométrie avec celle des ruptures potentielles et avec la direction de la fréquence maximale des joints. Les structures de roches, mais en particulier les dièdres et les discontinuités dominantes, semblent être très influents dans les mécanismes d'érosion affectant les bassins rocheux. Ils représentent des zones de faiblesse exploitées en priorité par les processus de démantèlement et d'érosion, encourageant l'initiation de ravines et couloirs, mais aussi leur propagation. L'incorporation du control géologique dans les processus de surface contribue à une meilleure compréhension de l'évolution topographique de bassins actifs. Un algorithme de flux sédimentaire a été implémenté dans un modèle en cascade, lequel divise le bassin en biefs et en systèmes individuels répondant aux processus. Chaque unité inclut de façon simple les informations géomorpologiques et celles du flux sédimentaire dérivées à partir de SIG et de cartographie de terrain. Cet outil permet la simulation des transferts de masse dans les chenaux, considérants la variabilité de l'apport et son transport, et aide à réduire l'incertitude liée à la prédiction de bilans sédimentaires torrentiels. Ce travail vise très humblement d'éclairer quelques aspects de la dynamique sédimentaire en milieu torrentiel.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Detection and Characterization of Preferential Flow Paths in the Downstream Area of a Hazardous Landfill

We have used surface-based electrical resistivity tomography to detect and characterize preferential hydraulic pathways in the immediate downstream area of an abandoned, hazardous landfill. The landfill occupies the void left by a former gravel pit and its base is close to the groundwater table and lacking an engineered barrier. As such, this site is remarkably typical of many small- to medium-sized waste deposits throughout the densely populated and heavily industrialized foreland on both sides of the Alpine arc. Outflows of pollutants lastingly contaminated local drinking water supplies and necessitated a partial remediation in the form of a synthetic cover barrier, which is meant to prevent meteoric water from percolating through the waste before reaching the groundwater table. Any future additional isolation of the landfill in the form of lateral barriers thus requires adequate knowledge of potential preferential hydraulic pathways for outflowing contaminants. Our results, inferred from a suite of tomographically inverted surfaced-based electrical resistivity profiles oriented roughly perpendicular to the local hydraulic gradient, indicate that potential contaminant outflows would predominantly occur along an unexploited lateral extension of the original gravel deposit. This finds its expression as a distinct and laterally continuous high-resistivity anomaly in the resistivity tomograms. This interpretation is ground-truthed through a litholog from a nearby well. Since the probed glacio-fluvial deposits are largely devoid of mineralogical clay, the geometry of hydraulic and electrical pathways across the pore space of a given lithological unit can be assumed to be identical, which allows for an order-of-magnitude estimation of the overall permeability structure. These estimates indicate that the permeability of the imaged extension of the gravel body is at least two to three orders-of-magnitude higher than that of its finer-grained embedding matrix. This corroborates the preeminent role of the high-resistivity anomaly as a potential preferential flow path.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

Bio-electrical impedance analysis for estimation of fat-free mass and muscle mass in cystic fibrosis patients.

The nutritional status of cystic fibrosis (CF) patients has to be regularly evaluated and alimentary support instituted when indicated. Bio-electrical impedance analysis (BIA) is a recent method for determining body composition. The present study evaluates its use in CF patients without any clinical sign of malnutrition. Thirty-nine patients with CF and 39 healthy subjects aged 6-24 years were studied. Body density and mid-arm muscle circumference were determined by anthropometry and skinfold measurements. Fat-free mass was calculated taking into account the body density. Muscle mass was obtained from the urinary creatinine excretion rate. The resistance index was calculated by dividing the square of the subject's height by the body impedance. We show that fat-free mass, mid-arm muscle circumference and muscle mass are each linearly correlated to the resistance index and that the regression equations are similar for both CF patients and healthy subjects.