A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

Estrutura a partir do Movimento em Sistemas Autónomos

Mestrado em Engenharia Electrotécnica e de Computadores - Ramo de Sistemas Autónomos

Estimation of infection rate in epidemic models with multiple populations

Dissertação para obtenção do Grau de Mestre em Matemática e Aplicações Especialização em Actuariado, Estatística e Investigação Operacional

Predisposition assessment modelling

Dissertation submitted for obtaining the degree of Master in Environmental Engineering

Analysis of output properties of the Peroxiredoxin/Thioredoxin/Thioredoxin reductase system

Dissertação de mestrado em Bioinformática

Modelling Amazonian forest eddy covariance data: a comparison of big leaf versus sun/shade models for the C-14 tower at Manaus I. Canopy photosynthesis

In this study, we concentrate on modelling gross primary productivity using two simple approaches to simulate canopy photosynthesis: "big leaf" and "sun/shade" models. Two approaches for calibration are used: scaling up of canopy photosynthetic parameters from the leaf to the canopy level and fitting canopy biochemistry to eddy covariance fluxes. Validation of the models is achieved by using eddy covariance data from the LBA site C14. Comparing the performance of both models we conclude that numerically (in terms of goodness of fit) and qualitatively, (in terms of residual response to different environmental variables) sun/shade does a better job. Compared to the sun/shade model, the big leaf model shows a lower goodness of fit and fails to respond to variations in the diffuse fraction, also having skewed responses to temperature and VPD. The separate treatment of sun and shade leaves in combination with the separation of the incoming light into direct beam and diffuse make sun/shade a strong modelling tool that catches more of the observed variability in canopy fluxes as measured by eddy covariance. In conclusion, the sun/shade approach is a relatively simple and effective tool for modelling photosynthetic carbon uptake that could be easily included in many terrestrial carbon models.

Desenvolupament d'interfícies HW per a FPGA des de Matlab

Aquest projecte consisteix en el desenvolupament d’estructures hardware digitals, sintetitzables sobre FPGA i realitzades des d’un entorn gràfic de disseny a nivell de sistema (alt nivell). S'ha escollit el Simulink (entorn gràfic que treballa sobre el software matemàtic Matlab de Mathworks) com a entorn de disseny, i que gràcies a la interfície proporcionada per Altera (DSPBuilder) és capaç de generar codi VHDL sintetitzable. Concretament ens centrarem en la gestió d’un sistema capturador d'imatges de comptadors del cabal d'aigua, en el qual volem fer la caracterització del comptador. Aquest capturador consta bàsicament d'un sensor d'imatge i una FPGA. En aquesta caracterització el que es pretén es ajustar els diferents paràmetres del sistema per fer que la lectura sigui òptima per a cada model de comptador que existeixen al mercat, com ara l'exposició del sensor, el guany d'un color, la realització d'un filtrat de la imatge, etc.

Understanding the low-temperature limitations to forest growth through calibration of a forest dynamics model with tree-ring data

The sensitivity of altitudinal and latitudinal tree-line ecotones to climate change, particularly that of temperature, has received much attention. To improve our understanding of the factors affecting tree-line position, we used the spatially explicit dynamic forest model TreeMig. Although well-suited because of its landscape dynamics functions, TreeMig features a parabolic temperature growth response curve, which has recently been questioned. and the species parameters are not specifically calibrated for cold temperatures. Our main goals were to improve the theoretical basis of the temperature growth response curve in the model and develop a method for deriving that curve's parameters from tree-ring data. We replaced the parabola with an asymptotic curve, calibrated for the main species at the subalpine (Swiss Alps: Pinus cembra, Larix decidua, Picea abies) and boreal (Fennoscandia: Pinus sylvestris, Betula pubescens, P. abies) tree-lines. After fitting new parameters, the growth curve matched observed tree-ring widths better. For the subalpine species, the minimum degree-day sum allowing, growth (kDDMin) was lowered by around 100 degree-days; in the case of Larix, the maximum potential ring-width was increased to 5.19 mm. At the boreal tree-line, the kDDMin for P. sylvestris was lowered by 210 degree-days and its maximum ring-width increased to 2.943 mm; for Betula (new in the model) kDDMin was set to 325 degree-days and the maximum ring-width to 2.51 mm; the values from the only boreal sample site for Picea were similar to the subalpine ones, so the same parameters were used. However, adjusting the growth response alone did not improve the model's output concerning species' distributions and their relative importance at tree-line. Minimum winter temperature (MinWiT, mean of the coldest winter month), which controls seedling establishment in TreeMig, proved more important for determining distribution. Picea, P. sylvestris and Betula did not previously have minimum winter temperature limits, so these values were set to the 95th percentile of each species' coldest MinWiT site (respectively -7, -11, -13). In a case study for the Alps, the original and newly calibrated versions of TreeMig were compared with biomass data from the National Forest Inventor), (NFI). Both models gave similar, reasonably realistic results. In conclusion, this method of deriving temperature responses from tree-rings works well. However, regeneration and its underlying factors seem more important for controlling species' distributions than previously thought. More research on regeneration ecology, especially at the upper limit of forests. is needed to improve predictions of tree-line responses to climate change further.

Analisi espacial del canvi climàtic al continent europeu. Incerteses i exposicions principals

El canvi climàtic del segle XXI és una realitat, hi ha moltes evidències científiques que indiquen que l’escalfament del sistema climàtic és inequívoc. Malgrat això, també hi ha moltes incerteses respecte els impactes que pot comportar aquest canvi climàtic global. L’objectiu d’aquest projecte és estudiar la possible evolució futura de tres variables climàtiques, que són el rang de la temperatura diürna a prop de la superfície (DTR), la temperatura mitjana a prop de la superfície (MT) i la precipitació mensual (PL_mes) i valorar l’exposició que poden experimentar diferents cobertes del sòl i diferents regions biogeogràfiques del continent europeu davant d’aquests possibles patrons de canvi. Per això s’han utilitzat Models Climàtics Globals que fan projeccions de variables climàtiques que permeten preveure el possible clima futur. Mitjançant l’aplicatiu informàtic Tetyn s’han extret els paràmetres climàtics dels conjunts de dades del Tyndall Centre for Climate Change Research, del futur (TYN SC) i del passat (CRU TS). Les variables obtingudes s’han processat amb eines de sistemes d’informació geogràfica (SIG) per obtenir els patrons de canvi de les variables a cada coberta del sòl. Els resultats obtinguts mostren que hi ha una gran variabilitat, que augmenta amb el temps, entre els diferents models climàtics i escenaris considerats, que posa de manifest la incertesa associada a la modelització climàtica, a la generació d’escenaris d’emissions i a la naturalesa dinàmica i no determinista del sistema climàtic. Però en general, mostren que les glaceres seran una de les cobertes més exposades al canvi climàtic, i la mediterrània, una de les regions més vulnerables

A gamma camera count rate saturation correction method for whole-body planar imaging.

Whole-body (WB) planar imaging has long been one of the staple methods of dosimetry, and its quantification has been formalized by the MIRD Committee in pamphlet no 16. One of the issues not specifically addressed in the formalism occurs when the count rates reaching the detector are sufficiently high to result in camera count saturation. Camera dead-time effects have been extensively studied, but all of the developed correction methods assume static acquisitions. However, during WB planar (sweep) imaging, a variable amount of imaged activity exists in the detector's field of view as a function of time and therefore the camera saturation is time dependent. A new time-dependent algorithm was developed to correct for dead-time effects during WB planar acquisitions that accounts for relative motion between detector heads and imaged object. Static camera dead-time parameters were acquired by imaging decaying activity in a phantom and obtaining a saturation curve. Using these parameters, an iterative algorithm akin to Newton's method was developed, which takes into account the variable count rate seen by the detector as a function of time. The algorithm was tested on simulated data as well as on a whole-body scan of high activity Samarium-153 in an ellipsoid phantom. A complete set of parameters from unsaturated phantom data necessary for count rate to activity conversion was also obtained, including build-up and attenuation coefficients, in order to convert corrected count rate values to activity. The algorithm proved successful in accounting for motion- and time-dependent saturation effects in both the simulated and measured data and converged to any desired degree of precision. The clearance half-life calculated from the ellipsoid phantom data was calculated to be 45.1 h after dead-time correction and 51.4 h with no correction; the physical decay half-life of Samarium-153 is 46.3 h. Accurate WB planar dosimetry of high activities relies on successfully compensating for camera saturation which takes into account the variable activity in the field of view, i.e. time-dependent dead-time effects. The algorithm presented here accomplishes this task.

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

S-system parameter estimation for noisy metabolic profiles using newton-flow analysis.

Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.

Música i fotografia

La relació entre la música i les arts plàstiques s'ha donat des de diverses perspectives al llarg de la història. Després d'analitzar en quins aspectes i amb quina finalitat s'han basat aquestes relacions, proposo una nova aproximació entre la música i la fotografia, basada en els paràmetres morfològics i formals d'aquesta per buscar una relació el més objectiva possible. A partir d'aquesta equivalència defenso la idea de que el coneixement del llenguatge d'una altra forma artística ens pot permetre enriquir el nostre propi llenguatge, aplicant en aquest cas a la música, aquells elements característics de la fotografia. Finalment poso en pràctica aquesta equivalència, per experimentar fins a quin punt ens pot ajudar a enriquir el nostre llenguatge.

Changing landscapes of Switzerland: assessing effects of historic and future land uses and land covers on the occurrence of selected butterfly species

Summary Landscapes are continuously changing. Natural forces of change such as heavy rainfall and fires can exert lasting influences on their physical form. However, changes related to human activities have often shaped landscapes more distinctly. In Western Europe, especially modern agricultural practices and the expanse of overbuilt land have left their marks in the landscapes since the middle of the 20th century. In the recent years men realised that mare and more changes that were formerly attributed to natural forces might indirectly be the result of their own action. Perhaps the most striking landscape change indirectly driven by human activity we can witness in these days is the large withdrawal of Alpine glaciers. Together with the landscapes also habitats of animal and plant species have undergone vast and sometimes rapid changes that have been hold responsible for the ongoing loss of biodiversity. Thereby, still little knowledge is available about probable effects of the rate of landscape change on species persistence and disappearance. Therefore, the development and speed of land use/land cover in the Swiss communes between the 1950s and 1990s were reconstructed using 10 parameters from agriculture and housing censuses, and were further correlated with changes in butterfly species occurrences. Cluster analyses were used to detect spatial patterns of change on broad spatial scales. Thereby, clusters of communes showing similar changes or transformation rates were identified for single decades and put into a temporally dynamic sequence. The obtained picture on the changes showed a prevalent replacement of non-intensive agriculture by intensive practices, a strong spreading of urban communes around city centres, and transitions towards larger farm sizes in the mountainous areas. Increasing transformation rates toward more intensive agricultural managements were especially found until the 1970s, whereas afterwards the trends were commonly negative. However, transformation rates representing the development of residential buildings showed positive courses at any time. The analyses concerning the butterfly species showed that grassland species reacted sensitively to the density of livestock in the communes. This might indicate the augmented use of dry grasslands as cattle pastures that show altered plant species compositions. Furthermore, these species also decreased in communes where farms with an agricultural area >5ha have disappeared. The species of the wetland habitats were favoured in communes with smaller fractions of agricultural areas and lower densities of large farms (>10ha) but did not show any correlation to transformation rates. It was concluded from these analyses that transformation rates might influence species disappearance to a certain extent but that states of the environmental predictors might generally outweigh the importance of the corresponding rates. Information on the current distribution of species is evident for nature conservation. Planning authorities that define priority areas for species protection or examine and authorise construction projects need to know about the spatial distribution of species. Hence, models that simulate the potential spatial distribution of species have become important decision tools. The underlying statistical analyses such as the widely used generalised linear models (GLM) often rely on binary species presence-absence data. However, often only species presence data have been colleted, especially for vagrant, rare or cryptic species such as butterflies or reptiles. Modellers have thus introduced randomly selected absence data to design distribution models. Yet, selecting false absence data might bias the model results. Therefore, we investigated several strategies to select more reliable absence data to model the distribution of butterfly species based on historical distribution data. The results showed that better models were obtained when historical data from longer time periods were considered. Furthermore, model performance was additionally increased when long-term data of species that show similar habitat requirements as the modelled species were used. This successful methodological approach was further applied to assess consequences of future landscape changes on the occurrence of butterfly species inhabiting dry grasslands or wetlands. These habitat types have been subjected to strong deterioration in the recent decades, what makes their protection a future mission. Four spatially explicit scenarios that described (i) ongoing land use changes as observed between 1985 and 1997, (ii) liberalised agricultural markets, and (iii) slightly and (iv) strongly lowered agricultural production provided probable directions of landscape change. Current species-environment relationships were derived from a statistical model and used to predict future occurrence probabilities in six major biogeographical regions in Switzerland, comprising the Jura Mountains, the Plateau, the Northern and Southern Alps, as well as the Western and Eastern Central Alps. The main results were that dry grasslands species profited from lowered agricultural production, whereas overgrowth of open areas in the liberalisation scenario might impair species occurrence. The wetland species mostly responded with decreases in their occurrence probabilities in the scenarios, due to a loss of their preferred habitat. Further analyses about factors currently influencing species occurrences confirmed anthropogenic causes such as urbanisation, abandonment of open land, and agricultural intensification. Hence, landscape planning should pay more attention to these forces in areas currently inhabited by these butterfly species to enable sustainable species persistence. In this thesis historical data were intensively used to reconstruct past developments and to make them useful for current investigations. Yet, the availability of historical data and the analyses on broader spatial scales has often limited the explanatory power of the conducted analyses. Meaningful descriptors of former habitat characteristics and abundant species distribution data are generally sparse, especially for fine scale analyses. However, this situation can be ameliorated by broadening the extent of the study site and the used grain size, as was done in this thesis by considering the whole of Switzerland with its communes. Nevertheless, current monitoring projects and data recording techniques are promising data sources that might allow more detailed analyses about effects of long-term species reactions on landscape changes in the near future. This work, however, also showed the value of historical species distribution data as for example their potential to locate still unknown species occurrences. The results might therefore contribute to further research activities that investigate current and future species distributions considering the immense richness of historical distribution data. Résumé Les paysages changent continuellement. Des farces naturelles comme des pluies violentes ou des feux peuvent avoir une influence durable sur la forme du paysage. Cependant, les changements attribués aux activités humaines ont souvent modelé les paysages plus profondément. Depuis les années 1950 surtout, les pratiques agricoles modernes ou l'expansion des surfaces d'habitat et d'infrastructure ont caractérisé le développement du paysage en Europe de l'Ouest. Ces dernières années, l'homme a commencé à réaliser que beaucoup de changements «naturels » pourraient indirectement résulter de ses propres activités. Le changement de paysage le plus apparent dont nous sommes témoins de nos jours est probablement l'immense retraite des glaciers alpins. Avec les paysages, les habitats des animaux et des plantes ont aussi été exposés à des changements vastes et quelquefois rapides, tenus pour coresponsable de la continuelle diminution de la biodiversité. Cependant, nous savons peu des effets probables de la rapidité des changements du paysage sur la persistance et la disparition des espèces. Le développement et la rapidité du changement de l'utilisation et de la couverture du sol dans les communes suisses entre les années 50 et 90 ont donc été reconstruits au moyen de 10 variables issues des recensements agricoles et résidentiels et ont été corrélés avec des changements de présence des papillons diurnes. Des analyses de groupes (Cluster analyses) ont été utilisées pour détecter des arrangements spatiaux de changements à l'échelle de la Suisse. Des communes avec des changements ou rapidités comparables ont été délimitées pour des décennies séparées et ont été placées en séquence temporelle, en rendrent une certaine dynamique du changement. Les résultats ont montré un remplacement répandu d'une agriculture extensive des pratiques intensives, une forte expansion des faubourgs urbains autour des grandes cités et des transitions vers de plus grandes surfaces d'exploitation dans les Alpes. Dans le cas des exploitations agricoles, des taux de changement croissants ont été observés jusqu'aux années 70, alors que la tendance a généralement été inversée dans les années suivantes. Par contre, la vitesse de construction des nouvelles maisons a montré des courbes positives pendant les 50 années. Les analyses sur la réaction des papillons diurnes ont montré que les espèces des prairies sèches supportaient une grande densité de bétail. Il est possible que dans ces communes beaucoup des prairies sèches aient été fertilisées et utilisées comme pâturages, qui ont une autre composition floristique. De plus, les espèces ont diminué dans les communes caractérisées par une rapide perte des fermes avec une surface cultivable supérieure à 5 ha. Les espèces des marais ont été favorisées dans des communes avec peu de surface cultivable et peu de grandes fermes, mais n'ont pas réagi aux taux de changement. Il en a donc été conclu que la rapidité des changements pourrait expliquer les disparitions d'espèces dans certains cas, mais que les variables prédictives qui expriment des états pourraient être des descripteurs plus importants. Des informations sur la distribution récente des espèces sont importantes par rapport aux mesures pour la conservation de la nature. Pour des autorités occupées à définir des zones de protection prioritaires ou à autoriser des projets de construction, ces informations sont indispensables. Les modèles de distribution spatiale d'espèces sont donc devenus des moyens de décision importants. Les méthodes statistiques courantes comme les modèles linéaires généralisés (GLM) demandent des données de présence et d'absence des espèces. Cependant, souvent seules les données de présence sont disponibles, surtout pour les animaux migrants, rares ou cryptiques comme des papillons ou des reptiles. C'est pourquoi certains modélisateurs ont choisi des absences au hasard, avec le risque d'influencer le résultat en choisissant des fausses absences. Nous avons établi plusieurs stratégies, basées sur des données de distribution historique des papillons diurnes, pour sélectionner des absences plus fiables. Les résultats ont démontré que de meilleurs modèles pouvaient être obtenus lorsque les données proviennent des périodes de temps plus longues. En plus, la performance des modèles a pu être augmentée en considérant des données de distribution à long terme d'espèces qui occupent des habitats similaires à ceux de l'espèce cible. Vu le succès de cette stratégie, elle a été utilisée pour évaluer les effets potentiels des changements de paysage futurs sur la distribution des papillons des prairies sèches et marais, deux habitats qui ont souffert de graves détériorations. Quatre scénarios spatialement explicites, décrivant (i) l'extrapolation des changements de l'utilisation de sol tels qu'observés entre 1985 et 1997, (ii) la libéralisation des marchés agricoles, et une production agricole (iii) légèrement amoindrie et (iv) fortement diminuée, ont été utilisés pour générer des directions de changement probables. Les relations actuelles entre la distribution des espèces et l'environnement ont été déterminées par le biais des modèles statistiques et ont été utilisées pour calculer des probabilités de présence selon les scénarios dans six régions biogéographiques majeures de la Suisse, comportant le Jura, le Plateau, les Alpes du Nord, du Sud, centrales orientales et centrales occidentales. Les résultats principaux ont montré que les espèces des prairies sèches pourraient profiter d'une diminution de la production agricole, mais qu'elles pourraient aussi disparaître à cause de l'embroussaillement des terres ouvertes dû à la libéralisation des marchés agricoles. La probabilité de présence des espèces de marais a décrû à cause d'une perte générale des habitats favorables. De plus, les analyses ont confirmé que des causes humaines comme l'urbanisation, l'abandon des terres ouvertes et l'intensification de l'agriculture affectent actuellement ces espèces. Ainsi ces forces devraient être mieux prises en compte lors de planifications paysagères, pour que ces papillons diurnes puissent survivre dans leurs habitats actuels. Dans ce travail de thèse, des données historiques ont été intensivement utilisées pour reconstruire des développements anciens et pour les rendre utiles à des recherches contemporaines. Cependant, la disponibilité des données historiques et les analyses à grande échelle ont souvent limité le pouvoir explicatif des analyses. Des descripteurs pertinents pour caractériser les habitats anciens et des données suffisantes sur la distribution des espèces sont généralement rares, spécialement pour des analyses à des échelles fores. Cette situation peut être améliorée en augmentant l'étendue du site d'étude et la résolution, comme il a été fait dans cette thèse en considérant toute la Suisse avec ses communes. Cependant, les récents projets de surveillance et les techniques de collecte de données sont des sources prometteuses, qui pourraient permettre des analyses plus détaillés sur les réactions à long terme des espèces aux changements de paysage dans le futur. Ce travail a aussi montré la valeur des anciennes données de distribution, par exemple leur potentiel pour aider à localiser des' présences d'espèces encore inconnues. Les résultats peuvent contribuer à des activités de recherche à venir, qui étudieraient les distributions récentes ou futures d'espèces en considérant l'immense richesse des données de distribution historiques.

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.