Using spatially distributed parameters and multi-response objective functions to solve parameterization of complex applications of semi-distributed hydrological models

Application of semi-distributed hydrological models to large, heterogeneous watersheds deals with several problems. On one hand, the spatial and temporal variability in catchment features should be adequately represented in the model parameterization, while maintaining the model complexity in an acceptable level to take advantage of state-of-the-art calibration techniques. On the other hand, model complexity enhances uncertainty in adjusted model parameter values, therefore increasing uncertainty in the water routing across the watershed. This is critical for water quality applications, where not only streamflow, but also a reliable estimation of the surface versus subsurface contributions to the runoff is needed. In this study, we show how a regularized inversion procedure combined with a multiobjective function calibration strategy successfully solves the parameterization of a complex application of a water quality-oriented hydrological model. The final value of several optimized parameters showed significant and consistentdifferences across geological and landscape features. Although the number of optimized parameters was significantly increased by the spatial and temporal discretization of adjustable parameters, the uncertainty in water routing results remained at reasonable values. In addition, a stepwise numerical analysis showed that the effects on calibration performance due to inclusion of different data types in the objective function could be inextricably linked. Thus caution should be taken when adding or removing data from an aggregated objective function.

Does the physical disector method provide an accurate estimation of sensory neuron number in rat dorsal root ganglia?

The physical disector is a method of choice for estimating unbiased neuron numbers; nevertheless, calibration is needed to evaluate each counting method. The validity of this method can be assessed by comparing the estimated cell number with the true number determined by a direct counting method in serial sections. We reconstructed a 1/5 of rat lumbar dorsal root ganglia taken from two experimental conditions. From each ganglion, images of 200 adjacent semi-thin sections were used to reconstruct a volumetric dataset (stack of voxels). On these stacks the number of sensory neurons was estimated and counted respectively by physical disector and direct counting methods. Also, using the coordinates of nuclei from the direct counting, we simulate, by a Matlab program, disector pairs separated by increasing distances in a ganglion model. The comparison between the results of these approaches clearly demonstrates that the physical disector method provides a valid and reliable estimate of the number of sensory neurons only when the distance between the consecutive disector pairs is 60 microm or smaller. In these conditions the size of error between the results of physical disector and direct counting does not exceed 6%. In contrast when the distance between two pairs is larger than 60 microm (70-200 microm) the size of error increases rapidly to 27%. We conclude that the physical dissector method provides a reliable estimate of the number of rat sensory neurons only when the separating distance between the consecutive dissector pairs is no larger than 60 microm.

Parametric Approach to Blind Deconvolution of Nonlinear Channels

A parametric procedure for the blind inversion of nonlinear channels is proposed, based on a recent method of blind source separation in nonlinear mixtures. Experiments show that the proposed algorithms perform efficiently, even in the presence of hard distortion. The method, based on the minimization of the output mutual information, needs the knowledge of log-derivative of input distribution (the so-called score function). Each algorithm consists of three adaptive blocks: one devoted to adaptive estimation of the score function, and two other blocks estimating the inverses of the linear and nonlinear parts of the channel, (quasi-)optimally adapted using the estimated score functions. This paper is mainly concerned by the nonlinear part, for which we propose two parametric models, the first based on a polynomial model and the second on a neural network, while [14, 15] proposed non-parametric approaches.

Spatial filtering for pilot-aided WCDMA systems: a semi-blind subspace approach

This paper proposes a spatial filtering technique forthe reception of pilot-aided multirate multicode direct-sequencecode division multiple access (DS/CDMA) systems such as widebandCDMA (WCDMA). These systems introduce a code-multiplexedpilot sequence that can be used for the estimation of thefilter weights, but the presence of the traffic signal (transmittedat the same time as the pilot sequence) corrupts that estimationand degrades the performance of the filter significantly. This iscaused by the fact that although the traffic and pilot signals areusually designed to be orthogonal, the frequency selectivity of thechannel degrades this orthogonality at hte receiving end. Here,we propose a semi-blind technique that eliminates the self-noisecaused by the code-multiplexing of the pilot. We derive analyticallythe asymptotic performance of both the training-only andthe semi-blind techniques and compare them with the actual simulatedperformance. It is shown, both analytically and via simulation,that high gains can be achieved with respect to training-onlybasedtechniques.

ML approaches to channel estimation for pilot-aided multi-rate DS/CDMA systems

This paper analyzes the asymptotic performance of maximum likelihood (ML) channel estimation algorithms in wideband code division multiple access (WCDMA) scenarios. We concentrate on systems with periodic spreading sequences (period larger than or equal to the symbol span) where the transmitted signal contains a code division multiplexed pilot for channel estimation purposes. First, the asymptotic covariances of the training-only, semi-blind conditional maximum likelihood (CML) and semi-blind Gaussian maximum likelihood (GML) channelestimators are derived. Then, these formulas are further simplified assuming randomized spreading and training sequences under the approximation of high spreading factors and high number of codes. The results provide a useful tool to describe the performance of the channel estimators as a function of basicsystem parameters such as number of codes, spreading factors, or traffic to training power ratio.

On the inclusion of channel's time dependence in a hidden Markov model for blind channel estimation

In this paper, the theory of hidden Markov models (HMM) isapplied to the problem of blind (without training sequences) channel estimationand data detection. Within a HMM framework, the Baum–Welch(BW) identification algorithm is frequently used to find out maximum-likelihood (ML) estimates of the corresponding model. However, such a procedureassumes the model (i.e., the channel response) to be static throughoutthe observation sequence. By means of introducing a parametric model fortime-varying channel responses, a version of the algorithm, which is moreappropriate for mobile channels [time-dependent Baum-Welch (TDBW)] isderived. Aiming to compare algorithm behavior, a set of computer simulationsfor a GSM scenario is provided. Results indicate that, in comparisonto other Baum–Welch (BW) versions of the algorithm, the TDBW approachattains a remarkable enhancement in performance. For that purpose, onlya moderate increase in computational complexity is needed.

Estimation utilisant les polynômes de Bernstein

Ce mémoire porte sur la présentation des estimateurs de Bernstein qui sont des alternatives récentes aux différents estimateurs classiques de fonctions de répartition et de densité. Plus précisément, nous étudions leurs différentes propriétés et les comparons à celles de la fonction de répartition empirique et à celles de l'estimateur par la méthode du noyau. Nous déterminons une expression asymptotique des deux premiers moments de l'estimateur de Bernstein pour la fonction de répartition. Comme pour les estimateurs classiques, nous montrons que cet estimateur vérifie la propriété de Chung-Smirnov sous certaines conditions. Nous montrons ensuite que l'estimateur de Bernstein est meilleur que la fonction de répartition empirique en terme d'erreur quadratique moyenne. En s'intéressant au comportement asymptotique des estimateurs de Bernstein, pour un choix convenable du degré du polynôme, nous montrons que ces estimateurs sont asymptotiquement normaux. Des études numériques sur quelques distributions classiques nous permettent de confirmer que les estimateurs de Bernstein peuvent être préférables aux estimateurs classiques.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Improving cropping systems of semi-arid south-western Madagascar under multiple ecological and socio-economic constraints

Das Mahafaly Plateau im südwestlichen Madagaskar ist gekennzeichnet durch raue klimatische Bedingungen, vor allem regelmäßige Dürren und Trockenperioden, geringe Infrastruktur, steigende Unsicherheit, hohe Analphabetenrate und regelmäßige Zerstörung der Ernte durch Heuschreckenplagen. Da 97% der Bevölkerung von der Landwirtschaft abhängen, ist eine Steigerung der Produktivität von Anbausystemen die Grundlage für eine Verbesserung der Lebensbedingungen und Ernährungssicherheit in der Mahafaly Region. Da wenig über die Produktivität von traditionellen extensiven und neu eingeführten Anbaumethoden in diesem Gebiet bekannt ist, waren die Zielsetzungen der vorliegenden Arbeit, die limitierenden Faktoren und vielversprechende alternative Anbaumethoden zu identifizieren und diese unter Feldbedingungen zu testen. Wir untersuchten die Auswirkungen von lokalem Viehmist und Holzkohle auf die Erträge von Maniok, der Hauptanbaufrucht der Region, sowie die Beiträge von weiteren Faktoren, die im Untersuchungsgebiet ertragslimitierend sind. Darüber hinaus wurde in der Küstenregion das Potenzial für bewässerten Gemüseanbau mit Mist und Holzkohle untersucht, um zu einer Diversifizierung von Einkommen und Ernährung beizutragen. Ein weiterer Schwerpunkt dieser Arbeit war die Schätzung von Taubildung und deren Beitrag in der Jahreswasserbilanz durch Testen eines neu entworfenen Taumessgerätes. Maniok wurde über drei Jahre und in drei Versuchsfeldern in zwei Dörfern auf dem Plateau angebaut, mit applizierten Zeburindermistraten von 5 und 10 t ha-1, Holzkohleraten von 0,5 und 2 t ha-1 und Maniokpflanzdichten von 4500 Pflanzen ha-1. Maniokknollenerträge auf Kontrollflächen erreichten 1 bis 1,8 t Trockenmasse (TM) ha-1. Mist führte zu einer Knollenertragssteigerung um 30 - 40% nach drei Jahren in einem kontinuierlich bewirtschafteten Feld mit geringer Bodenfruchtbarkeit, hatte aber keinen Effekt auf den anderen Versuchsfeldern. Holzkohle hatte keinen Einfluss auf Erträge über den gesamten Testzeitraum, während die Infektion mit Cassava-Mosaikvirus zu Ertragseinbußen um bis zu 30% führte. Pflanzenbestände wurden felder-und jahresübergreifend um 4-54% des vollen Bestandes reduziert, was vermutlich auf das Auftreten von Trockenperioden und geringe Vitalität von Pflanzmaterial zurückzuführen ist. Karotten (Daucus carota L. var. Nantaise) und Zwiebeln (Allium cepa L. var. Red Créole) wurden über zwei Trockenzeiten mit lokal erhältlichem Saatgut angebaut. Wir testeten die Auswirkungen von lokalem Rindermist mit einer Rate von 40 t ha-1, Holzkohle mit einer Rate von 10 t ha-1, sowie Beschattung auf die Gemüseernteerträge. Lokale Bewässerungswasser hatte einen Salzgehalt von 7,65 mS cm-1. Karotten- und Zwiebelerträge über Behandlungen und Jahre erreichten 0,24 bis 2,56 t TM ha-1 beziehungsweise 0,30 bis 4,07 DM t ha-1. Mist und Holzkohle hatten keinen Einfluss auf die Erträge beider Kulturen. Beschattung verringerte Karottenerträge um 33% im ersten Jahr, während sich die Erträge im zweiten Jahr um 65% erhöhten. Zwiebelerträge wurden unter Beschattung um 148% und 208% im ersten und zweiten Jahr erhöht. Salines Bewässerungswasser sowie Qualität des lokal verfügbaren Saatgutes reduzierten die Keimungsraten deutlich. Taubildung im Küstendorf Efoetsy betrug 58,4 mm und repräsentierte damit 19% der Niederschlagsmenge innerhalb des gesamten Beobachtungszeitraum von 18 Monaten. Dies weist darauf hin, dass Tau in der Tat einen wichtigen Beitrag zur jährlichen Wasserbilanz darstellt. Tageshöchstwerte erreichten 0,48 mm. Die getestete Tauwaage-Vorrichtung war in der Lage, die nächtliche Taubildung auf der metallischen Kondensationsplatte zuverlässig zu bestimmen. Im abschließenden Kapitel werden die limitierenden Faktoren für eine nachhaltige Intensivierung der Landwirtschaft in der Untersuchungsregion diskutiert.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

Parametric pension reform and the intensive margin of labor supply, evidence from Colombia

We analyze the effect of a parametric reform of the fully-funded pension regime in Colombia on the intensive margin of the labor supply. We take advantage of a threshold defined by law in order to identify the causal effect using a regression discontinuity design. We find that a pension system that increases retirement age and the minimum weeks during which workers must contribute to claim pension benefits causes an increase of around 2 hours on the number of weekly worked hours; this corresponds to 4% of the average number of weekly worked hours or around 14% of a standard deviation of weekly worked hours. The effect is robust to different specifications, polynomial orders and sample sizes.

The crime kuznets curve

We document the existence of a Crime Kuznets Curve in US states since the 1970s. As income levels have risen, crime has followed an inverted U-shaped pattern, first increasing and then dropping. The Crime Kuznets Curve is not explained by income inequality. In fact, we show that during the sample period inequality has risen monotonically with income, ruling out the traditional Kuznets Curve. Our finding is robust to adding a large set of controls that are used in the literature to explain the incidence of crime, as well as to controlling for state and year fixed effects. The Curve is also revealed in nonparametric specifications. The Crime Kuznets Curve exists for property crime and for some categories of violent crime.

An empirical study of process-related attributes in segmented software cost-estimation relationships

Parametric software effort estimation models consisting on a single mathematical relationship suffer from poor adjustment and predictive characteristics in cases in which the historical database considered contains data coming from projects of a heterogeneous nature. The segmentation of the input domain according to clusters obtained from the database of historical projects serves as a tool for more realistic models that use several local estimation relationships. Nonetheless, it may be hypothesized that using clustering algorithms without previous consideration of the influence of well-known project attributes misses the opportunity to obtain more realistic segments. In this paper, we describe the results of an empirical study using the ISBSG-8 database and the EM clustering algorithm that studies the influence of the consideration of two process-related attributes as drivers of the clustering process: the use of engineering methodologies and the use of CASE tools. The results provide evidence that such consideration conditions significantly the final model obtained, even though the resulting predictive quality is of a similar magnitude.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.