Dynamic perceptual mapping

Perceptual maps have been used for decades by market researchers to illuminatethem about the similarity between brands in terms of a set of attributes, to position consumersrelative to brands in terms of their preferences, or to study how demographic and psychometricvariables relate to consumer choice. Invariably these maps are two-dimensional and static. Aswe enter the era of electronic publishing, the possibilities for dynamic graphics are opening up.We demonstrate the usefulness of introducing motion into perceptual maps through fourexamples. The first example shows how a perceptual map can be viewed in three dimensions,and the second one moves between two analyses of the data that were collected according todifferent protocols. In a third example we move from the best view of the data at the individuallevel to one which focuses on between-group differences in aggregated data. A final exampleconsiders the case when several demographic variables or market segments are available foreach respondent, showing an animation with increasingly detailed demographic comparisons.These examples of dynamic maps use several data sets from marketing and social scienceresearch.

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.

Amyloid and non-amyloid forms of 5q31-linked corneal dystrophy resulting from kerato-epithelin mutations at Arg-124 are associated with abnormal turnover of the protein.

Mutations in kerato-epithelin are responsible for a group of hereditary cornea-specific deposition diseases, 5q31-linked corneal dystrophies. These conditions are characterized by progressive accumulation of protein deposits of different ultrastructure. Herein, we studied the corneas with mutations at kerato-epithelin residue Arg-124 resulting in amyloid (R124C), non-amyloid (R124L), and a mixed pattern of deposition (R124H). We found that aggregated kerato-epithelin comprised all types of pathological deposits. Each mutation was associated with characteristic changes of protein turnover in corneal tissue. Amyloidogenesis in R124C corneas was accompanied by the accumulation of N-terminal kerato-epithelin fragments, whereby species of 44 kDa were the major constituents of amyloid fibrils. R124H corneas with prevailing non-amyloid inclusions showed accumulation of a new 66-kDa species altogether with the full-size 68-kDa form. Finally, in R124L cornea with non amyloid deposits, we found only the accumulation of the 68-kDa form. Two-dimensional gels revealed mutation-specific changes in the processing of the full-size protein in all affected corneas. It appears that substitutions at the same residue (Arg-124) result in cornea-specific deposition of kerato-epithelin via distinct aggregation pathways each involving altered turnover of the protein in corneal tissue.

Skin fibroblast model to study an impaired glutathione synthesis: consequences of a genetic polymorphism on the proteome.

An impaired glutathione (GSH) synthesis was observed in several multifactorial diseases, including schizophrenia and myocardial infarction. Genetic studies revealed an association between schizophrenia and a GAG trinucleotide repeat (TNR) polymorphism in the catalytic subunit (GCLC) of the glutamate cysteine ligase (GCL). Disease-associated genotypes of this polymorphism correlated with a decrease in GCLC protein expression, GCL activity and GSH content. To clarify consequences of a decreased GCL activity at the proteome level, three schizophrenia patients and three controls have been selected based on the GCLC GAG TNR polymorphism. Fibroblast cultures were obtained by skin biopsy and were challenged with tert-butylhydroquinone (t-BHQ), a substance known to induce oxidative stress. Proteome changes were analyzed by two dimensional gel electrophoresis (2-DE) and results revealed 10 spots that were upregulated in patients following t-BHQ treatment, but not in controls. Nine corresponding proteins could be identified by MALDI mass spectrometry and these proteins are involved in various cellular functions, including energy metabolism, oxidative stress response, and cytoskeletal reorganization. In conclusion, skin fibroblasts of subjects with an impaired GSH synthesis showed an altered proteome reaction in response to oxidative stress. Furthermore, the study corroborates the use of fibroblasts as an additional mean to study vulnerability factors of psychiatric diseases.

Topological locking restrains replication fork reversal.

Two-dimensional agarose gel electrophoresis, psoralen cross-linking, and electron microscopy were used to study the effects of positive supercoiling on fork reversal in isolated replication intermediates of bacterial DNA plasmids. The results obtained demonstrate that the formation of Holliday-like junctions at both forks of a replication bubble creates a topological constraint that prevents further regression of the forks. We propose that this topological locking of replication intermediates provides a biological safety mechanism that protects DNA molecules against extensive fork reversals.

Optimum Redundant Array Configurations for Earth Observation Aperture Synthesis Microwave Radiometers

Two-dimensional aperture synthesis radiometry is the technologyselected for ESA's SMOS mission to provide high resolution L-bandradiometric imagery. The array topology is a Y-shaped structure. Theposition and number of redundant elements to minimise instrumentdegradation in case of element failure(s) are studied.

Validation d'une version française de l'inventaire rationnel-experientiel (REI) et application au tabagisme

The Rational-Experiential Inventory REI (Pacini and Epstein, 1999) is a self-administered test comprising two scales measuring the attitude of respondents towards two thinking styles respectively referred to as the rational and the experiential thinking styles. Two validation studies were conducted using a new French-language version of the REI. The first study confirms the validity of the French translation. The second study, which is concerned with the REI's construct validity, assesses the questionnaire's capacity to discriminate between a group of smokers and a group of non-smokers. Both studies give generally satisfactory results. In particular, the advantages of using the two-dimensional REI rather than the better known Need For Cognition scale (Cacioppo & Petty, 1982) are made quite clear.

GalaxyDefenders: desenvolupament d'un side-scrolling shooter per iOS

Aquest projecte neix del interés personal de l’autor per a la indústria dels videojocs. El principal objectiu de l’aplicació és esdevenir un joc complet mitjançant l’ús de tècniques clàssicament empleades en el desenvolupament de jocs en dues dimensions de manera que la experiència i tècniques adquirides sigui el més reutilitzable possible.

Quantitative analysis of crystal/grain sizes and their distributions in 2D and 3D

We review methods to estimate the average crystal (grain) size and the crystal (grain) size distribution in solid rocks. Average grain sizes often provide the base for stress estimates or rheological calculations requiring the quantification of grain sizes in a rock's microstructure. The primary data for grain size data are either 1D (i.e. line intercept methods), 2D (area analysis) or 3D (e.g., computed tomography, serial sectioning). These data have been used for different data treatments over the years, whereas several studies assume a certain probability function (e.g., logarithm, square root) to calculate statistical parameters as the mean, median, mode or the skewness of a crystal size distribution. The finally calculated average grain sizes have to be compatible between the different grain size estimation approaches in order to be properly applied, for example, in paleo-piezometers or grain size sensitive flow laws. Such compatibility is tested for different data treatments using one- and two-dimensional measurements. We propose an empirical conversion matrix for different datasets. These conversion factors provide the option to make different datasets compatible with each other, although the primary calculations were obtained in different ways. In order to present an average grain size, we propose to use the area-weighted and volume-weighted mean in the case of unimodal grain size distributions, respectively, for 2D and 3D measurements. The shape of the crystal size distribution is important for studies of nucleation and growth of minerals. The shape of the crystal size distribution of garnet populations is compared between different 2D and 3D measurements, which are serial sectioning and computed tomography. The comparison of different direct measured 3D data; stereological data and direct presented 20 data show the problems of the quality of the smallest grain sizes and the overestimation of small grain sizes in stereological tools, depending on the type of CSD. (C) 2011 Published by Elsevier Ltd.

Anàlisi d'imatges estereoscòpiques utilitzant mètodes de baixa càrrega computacional

 Mitjançant imatges estereoscòpiques es poden detectar la posició respecte dela càmera dels objectes que apareixen en una escena. A partir de lesdiferències entre les imatges captades pels dos objectius es pot determinar laprofunditat dels objectes. Existeixen diversitat de tècniques de visió artificialque permeten calcular la localització dels objectes, habitualment amb l’objectiude reconstruir l’escena en 3D. Aquestes tècniques necessiten una gran càrregacomputacional, ja que utilitzen mètodes de comparació bidimensionals, i pertant, no es poden utilitzar per aplicacions en temps real.En aquest treball proposem un nou mètode d’anàlisi de les imatgesestereoscòpiques que ens permeti obtenir la profunditat dels objectes d’unaescena amb uns resultats acceptables. Aquest nou mètode es basa entransformar la informació bidimensional de la imatge en una informacióunidimensional per tal de poder fer la comparació de les imatges amb un baixcost computacional, i dels resultats de la comparació extreure’n la profunditatdels objectes dins l’escena. Això ha de permetre, per exemple, que aquestmètode es pugui implementar en un dispositiu autònom i li permeti realitzaroperacions de guiatge a través d’espais interiors i exteriors.

Comparative protein profiling identifies elongation factor-1beta and tryparedoxin peroxidase as factors associated with metastasis in Leishmania guyanensis.

Parasites of the Leishmania Viannia subgenus are major causative agents of mucocutaneous leishmaniasis (MCL), a disease characterised by parasite dissemination (metastasis) from the original cutaneous lesion to form debilitating secondary lesions in the nasopharyngeal mucosa. We employed a protein profiling approach to identify potential metastasis factors in laboratory clones of L. (V.) guyanensis with stable phenotypes ranging from highly metastatic (M+) through infrequently metastatic (M+/M-) to non-metastatic (M-). Comparison of the soluble proteomes of promastigotes by two-dimensional electrophoresis revealed two abundant protein spots specifically associated with M+ and M+/M- clones (Met2 and Met3) and two others exclusively expressed in M- parasites (Met1 and Met4). The association between clinical disease phenotype and differential expression of Met1-Met4 was less clear in L. Viannia strains from mucosal (M+) or cutaneous (M-) lesions of patients. Identification of Met1-Met4 by biological mass spectrometry (LC-ES-MS/MS) and bioinformatics revealed that M+ and M- clones express distinct acidic and neutral isoforms of both elongation factor-1 subunit beta (EF-1beta) and cytosolic tryparedoxin peroxidase (TXNPx). This interchange of isoforms may relate to the mechanisms by which the activities of EF-1beta and TXNPx are modulated, and/or differential post-translational modification of the gene product(s). The multiple metabolic functions of EF-1 and TXNPx support the plausibility of their participation in parasite survival and persistence and thereby, metastatic disease. Both polypeptides are active in resistance to chemical and oxidant stress, providing a basis for further elucidation of the importance of antioxidant defence in the pathogenesis underlying MCL.

Period-Luminosity-Colour distribution and classification of Galactic oxygen-rich LPVs I. Luminosity calibrations

The absolute K magnitudes and kinematic parameters of about 350 oxygen-rich Long-Period Variable stars are calibrated, by means of an up-to-date maximum-likelihood method, using HIPPARCOS parallaxes and proper motions together with radial velocities and, as additional data, periods and V-K colour indices. Four groups, differing by their kinematics and mean magnitudes, are found. For each of them, we also obtain the distributions of magnitude, period and de-reddened colour of the base population, as well as de-biased period-luminosity-colour relations and their two-dimensional projections. The SRa semiregulars do not seem to constitute a separate class of LPVs. The SRb appear to belong to two populations of different ages. In a PL diagram, they constitute two evolutionary sequences towards the Mira stage. The Miras of the disk appear to pulsate on a lower-order mode. The slopes of their de-biased PL and PC relations are found to be very different from the ones of the Oxygen Miras of the LMC. This suggests that a significant number of so-called Miras of the LMC are misclassified. This also suggests that the Miras of the LMC do not constitute a homogeneous group, but include a significant proportion of metal-deficient stars, suggesting a relatively smooth star formation history. As a consequence, one may not trivially transpose the LMC period-luminosity relation from one galaxy to the other.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Whole-body 3D T1-weighted MR imaging in patients with prostate cancer: feasibility and evaluation in screening for metastatic disease.

PURPOSE: To develop and assess the diagnostic performance of a three-dimensional (3D) whole-body T1-weighted magnetic resonance (MR) imaging pulse sequence at 3.0 T for bone and node staging in patients with prostate cancer. MATERIALS AND METHODS This prospective study was approved by the institutional ethics committee; informed consent was obtained from all patients. Thirty patients with prostate cancer at high risk for metastases underwent whole-body 3D T1-weighted imaging in addition to the routine MR imaging protocol for node and/or bone metastasis screening, which included coronal two-dimensional (2D) whole-body T1-weighted MR imaging, sagittal proton-density fat-saturated (PDFS) imaging of the spine, and whole-body diffusion-weighted MR imaging. Two observers read the 2D and 3D images separately in a blinded manner for bone and node screening. Images were read in random order. The consensus review of MR images and the findings at prospective clinical and MR imaging follow-up at 6 months were used as the standard of reference. The interobserver agreement and diagnostic performance of each sequence were assessed on per-patient and per-lesion bases. RESULTS: The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were significantly higher with whole-body 3D T1-weighted imaging than with whole-body 2D T1-weighted imaging regardless of the reference region (bone or fat) and lesion location (bone or node) (P < .003 for all). For node metastasis, diagnostic performance (area under the receiver operating characteristic curve) was higher for whole-body 3D T1-weighted imaging (per-patient analysis; observer 1: P < .001 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P = .006 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging; observer 2: P = .006 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P = .006 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging), as was sensitivity (per-lesion analysis; observer 1: P < .001 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P < .001 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging; observer 2: P < .001 for 2D T1-weighted imaging vs 3D T1-weighted imaging, P < .001 for 2D T1-weighted imaging + PDFS imaging vs 3D T1-weighted imaging). CONCLUSION: Whole-body MR imaging is feasible with a 3D T1-weighted sequence and provides better SNR and CNR compared with 2D sequences, with a diagnostic performance that is as good or better for the detection of bone metastases and better for the detection of lymph node metastases.

Dpp signaling activity requires Pentagone to scale with tissue size in the growing Drosophila wing imaginal disc.

The wing of the fruit fly, Drosophila melanogaster, with its simple, two-dimensional structure, is a model organ well suited for a systems biology approach. The wing arises from an epithelial sac referred to as the wing imaginal disc, which undergoes a phase of massive growth and concomitant patterning during larval stages. The Decapentaplegic (Dpp) morphogen plays a central role in wing formation with its ability to co-coordinately regulate patterning and growth. Here, we asked whether the Dpp signaling activity scales, i.e. expands proportionally, with the growing wing imaginal disc. Using new methods for spatial and temporal quantification of Dpp activity and its scaling properties, we found that the Dpp response scales with the size of the growing tissue. Notably, scaling is not perfect at all positions in the field and the scaling of target gene domains is ensured specifically where they define vein positions. We also found that the target gene domains are not defined at constant concentration thresholds of the downstream Dpp activity gradients P-Mad and Brinker. Most interestingly, Pentagone, an important secreted feedback regulator of the pathway, plays a central role in scaling and acts as an expander of the Dpp gradient during disc growth.