A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.

The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three modifications of these estimators are introduced and discussed. Numerical experiments for all estimators complement and confirm the theoretical results.

A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that the upper error bound depends on the alignment of the anisotropies of the mesh and of the solution. Hence reliable error estimation is possible for suitable anisotropic meshes. The lower error bound depends on the problem data via a local mesh Peclet number. Thus efficient error estimation is achieved for small mesh Peclet numbers. Altogether, error estimation approaches for isotropic meshes are successfully extended to anisotropic elements. Several numerical experiments support the analysis.

Die wissenschaftliche Auseinandersetzung mit schnellwachsenden Baumarten in Form der Kurzumtriebswirtschaft beschränkte sich lange Zeit fast ausschließlich auf die Arten der Sektion Pappel. Ertragswerte bzw. waldwachstumskundliche Untersuchungen an KUP aus Weide konnten im größeren Maßstab erst im vergangenen Jahrzehnt erhoben werden. Die Ertragswerte der Weiden auf den in dieser Arbeit untersuchten KUP bewegen sich zwischen 1,7 und 9,2 tatro∙ha-1∙a-1. In Folgerotationen kann sogar mit einem wesentlich höheren Biomasseertrag gerechnet werden. Eine eigene Untersuchung an einer bereits achtjährigen KUP in Krummenhennersdorf (Sachsen) auf einem mittleren Standort erbrachte eine durchschnittliche Gesamtwuchsleistung von ca. 14 tatro∙ha-1∙a- 1 in der dritten Rotation. Damit ist die Weide neben der Pappel eine sehr ertragreiche, schnellwachsende Baumart. Ihr Anbau kann demzufolge in Form von KUP uneingeschränkt empfohlen werden. Um den Biomasseertrag auf bestehenden KUP aus Weide zu ermitteln, wurden bisher vor allem destruktive Verfahren angewendet, die mit hohem Zeit- und Arbeitsaufwand verbunden sind. Das Hauptziel dieser Arbeit stellte daher die Entwicklung eines überregional einsetzbaren, praxistauglichen Ertragsermittlers zur schnellen und einfachen Ertragsbestimmung von KUP aus Weide der ersten Rotation dar. Die Modellentwicklung erfolgte auf zwei Wegen: Modellierung über eine Standardisierung von Biomassefunktionen (Modell I) und Modellierung über Biomasseverteilungsfunktionen (Modell II). Unterschiede in der Genauigkeit im Hinblick auf die Validierung der Modelle konnten explizit anhand des Bias und der Präzision nachgewiesen werden. Dabei ermittelt das Modell II den Biomasseertrag wesentlich genauer (Bias: 4.43%, Präzision: 12.11%), weshalb die Methode bereits für den Praktiker in Form eines einfach anzuwendenden Computerprogrammes (Ertragsschätzer für KUP aus Pappel und Weide) zur Verfügung gestellt wurde. Für die Anwendung des Ertragsschätzers sind von dem Nutzer die Eingangsgrößen Durchmesser des Grundflächenmittelstammes (dg), Alter und Pflanzverband erforderlich.

One of the main objectives of family policies in countries with low fertility levels is to stimulate birth rates and incentivize the citizens to have more children. Nevertheless, the research on whether this objective is being met remains inconclusive. In this thesis, we analyze two reforms which took place in the Czech Republic in 1995 and 2008, which adjusted the period of reception of the parental allowance. We use data from selected European OECD countries along with the synthetic control approach to construct a synthetic counterpart to the Czech Republic which gives us an idea about how fertility levels would have developed if the interventions did not take place. In both cases, 1995 reform and 2008 reform, we do not find any conclusive evidence that the interventions affected fertility levels in the Czech Republic. Moreover, we observe a change in the trend of total fertility rate about 2 years before each reform which suggests that these reforms were more likely reactions to changing fertility rates rather than remedies. JEL Classification J13, J17, J11, J12, E61, E65, F68 Keywords fertility, family policy, synthetic control estimator, parental allowance, parental leave Author's e-mail 31609261@fsv.cuni.cz Supervisor's e-mail barbara.pertold-gebicka@fsv.cuni.cz

Despite the potential benefits of larger datasets for crop insurance ratings, pooling yields with similar distributions is not a common practice. The current USDA-RMA county insurance ratings do not consider information across state lines, a politically driven assumption that ignores a wealth of climate and agronomic evidence suggesting that growing regions are not constrained by state boundaries. We test the appropriateness of this assumption, and provide empirical grounds for benefits of pooling datasets. We find evidence in favor of pooling across state lines, with poolable counties sometimes being as far as 2,500 miles apart. An out-of-sample performance exercise suggests our proposed pooling framework out-performs a no-pooling alternative, and supports the hypothesis that economic losses should be expected as a result of not adopting our pooling framework. Our findings have strong empirical and policy implications for accurate modeling of yield distributions and vis-à-vis the rating of crop insurance products.

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Information retrieval is much more challenging than traditional small document collection retrieval. The main difference is the importance of correlations between related concepts in complex data structures. These structures have been studied by several information retrieval systems. This research began by performing a comprehensive review and comparison of several techniques of matrix dimensionality estimation and their respective effects on enhancing retrieval performance using singular value decomposition and latent semantic analysis. Two novel techniques have been introduced in this research to enhance intrinsic dimensionality estimation, the Multi-criteria Decision Weighted model to estimate matrix intrinsic dimensionality for large document collections and the Average Standard Estimator (ASE) for estimating data intrinsic dimensionality based on the singular value decomposition (SVD). ASE estimates the level of significance for singular values resulting from the singular value decomposition. ASE assumes that those variables with deep relations have sufficient correlation and that only those relationships with high singular values are significant and should be maintained. Experimental results over all possible dimensions indicated that ASE improved matrix intrinsic dimensionality estimation by including the effect of both singular values magnitude of decrease and random noise distracters. Analysis based on selected performance measures indicates that for each document collection there is a region of lower dimensionalities associated with improved retrieval performance. However, there was clear disagreement between the various performance measures on the model associated with best performance. The introduction of the multi-weighted model and Analytical Hierarchy Processing (AHP) analysis helped in ranking dimensionality estimation techniques and facilitates satisfying overall model goals by leveraging contradicting constrains and satisfying information retrieval priorities. ASE provided the best estimate for MEDLINE intrinsic dimensionality among all other dimensionality estimation techniques, and further, ASE improved precision and relative relevance by 10.2% and 7.4% respectively. AHP analysis indicates that ASE and the weighted model ranked the best among other methods with 30.3% and 20.3% in satisfying overall model goals in MEDLINE and 22.6% and 25.1% for CRANFIELD. The weighted model improved MEDLINE relative relevance by 4.4%, while the scree plot, weighted model, and ASE provided better estimation of data intrinsic dimensionality for CRANFIELD collection than Kaiser-Guttman and Percentage of variance. ASE dimensionality estimation technique provided a better estimation of CISI intrinsic dimensionality than all other tested methods since all methods except ASE tend to underestimate CISI document collection intrinsic dimensionality. ASE improved CISI average relative relevance and average search length by 28.4% and 22.0% respectively. This research provided evidence supporting a system using a weighted multi-criteria performance evaluation technique resulting in better overall performance than a single criteria ranking model. Thus, the weighted multi-criteria model with dimensionality reduction provides a more efficient implementation for information retrieval than using a full rank model.

Underwater communication within underwater sensor network is crucial for surveillance of coast and ocean areas. The aim of this report was to examine whether it is realistic to use the communication signal which is sent from one node to another as a sonar pulse, and in such case at what distances. To examine the problem, a system consisting of two nodes and one approaching target was simulated in Matlab. At first, the system tries to detect the target by using a generalized likelihood ratio test, which calculates the probability of a present target from the surrounding sounds. When a target is detected by a node, it estimates the bearing to the target by using beamforming and sends out a communication signal to the other node. The communication signal spreads out in the water, and bounces on the target before it is received by the second node. To calculate the distance, the second node decodes the signal to get the time difference, from which the distance is calculated. In the end, the target's position was estimated with a weighted least square estimator with measurements of the bearing and distance. The result shows that the distance to the target could be estimated with high precision in the given scenario, and that the width of the Cramér-Rao lower bound depends mainly on the variance of the beamforming algorithm. The maximum distance reached up to two kilometers but was mainly restricted by the detection algorithm. In conclusion, the result shows that the communication pulse can be used as a sonar pulse at the tested distances. However, the simulated scenario is a simplified version of the real world so more testing should be performed before a final conclusion can be made. / För övervakning av kust- och havsområden, vid exempelvis militära operationer eller för oceanografska observationer, används ofta ett undervattenssystem som är uppbyggt av flera noder som finns utplacerade på botten. Noderna lyssnar efter mål såsom ubåtar, fartyg etc, med syftet att kunna detektera och lokalisera dessa. Om en nod lyckas detektera ett mål så skickar den ut en akustisk kommunikationssignal till övriga noder i systemet. Målet med detta examensarbete var att undersöka om den kommunikationssignal som skickas mellan noderna också kan användas som en sonarpuls för att bestämma avståndet till målet, och därmed förbättra lokaliseringen av målets position. Under antagandet att kommunikationssignalen kan användas som sonarpuls, så undersöktes dessutom vid vilka avstånd mellan noden och målet som det var möjligt att använda signalen som sonarpuls. Resultatet visar att det är möjligt att använda kommunikationssignalen som en sonarpuls. Bäst funkar det på nära avstånd, då är den estimerade positionen i stort sett lika med det riktiga positionen. I takt med att avståndet till målet ökar så ökar även osäkerheten i vilken rikting målet befinner sig, estimeringen av avståndet höll sig däremot väldigt nära den faktiska distansen i alla simuleringar som gjordes. Simuleringen som gjordes var dock en förenkling av verkligheten, och flera av de störningsmoment som finns ute i naturen har inte tagits med i beräkningarna. För att undersöka detta så simulerades ett sensorsystem bestående av två noder tillsammans med ett mål som närmade sig noderna. Noderna försöker detektera målet genom att lyssna efter ljud som tillhör målet. Genom att mäta energinivåer i de ljudsignaler som noderna hör, så kan man utifrån sannolikhetslära bestämma hur troligt det är att det finns ett mål i närheten. När sannolikheten är tillräckligt hög säger man att ett mål detekterats. För att bestämma positionen så uppskattades målets riktning och avstånd i förhållande till noderna, som i sin tur användes för att beräkna målets position.

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