Cette thèse porte sur l’étude du positionnement optimale des réseaux de capteurs pour la localisation de sources. Nous avons étudié deux approches: l’approche basée sur les performances de l’estimation en termes d’erreur quadratique moyenne et l’approche basée sur le seuil statistique de résolution (SSR).Pour le première approche, nous avons considéré les bornes inférieures de l’erreur quadratique moyenne qui sont utilisés généralement pour évaluer la performance d’estimation indépendamment du type d’estimateur considéré. Nous avons étudié deux types de bornes: la borne Cramér-Rao (BCR) pour le modèle où les paramètres sont supposés déterministes et la borne Weiss-Weinstein (BWW) pour le modèle où les paramètres sont supposés aléatoires. Nous avons dérivé les expressions analytiques de ces bornes pour développer des outils statistiques afin d’optimiser la géométrie des réseaux de capteurs. Par rapport à la BCR, la borne BWW peut capturer le décrochement de l’EQM des estimateurs dans la zone non-asymptotique. De plus, les expressions analytiques de la BWW pour un modèle Gaussien général à moyenne paramétré ou à covariance matrice paramétré sont donnés explicitement. Basé sur ces expressions analytiques, nous avons étudié l’impact de la géométrie des réseaux de capteurs sur les performances d’estimation en utilisant les réseaux de capteurs 3D et 2D pour deux modèles des observations concernant les signaux sources: (i) le modèle déterministe et (ii) le modèle stochastique. Nous en avons ensuite déduit des conditions concernant les propriétés d’isotropie et de découplage.Pour la deuxième approche, nous avons considéré le seuil statistique de résolution qui caractérise la séparation minimale entre les deux sources. Dans cette thèse, nous avons étudié le SSR pour le contexte Bayésien moins étudié dans la littérature. Nous avons introduit un modèle des observations linéarisé basé sur le critère de probabilité d’erreur minimale. Ensuite, nous avons présenté deux approches Bayésiennes pour le SSR, l’une basée sur la théorie de l’information et l’autre basée sur la théorie de la détection. Ces approches pourront être utilisée pour améliorer la capacité de résolution des systèmes. / This thesis deals with the array geometry optimization problem in the context of sources localization. We have considered two approaches for the array geometry optimization: the performance estimation in terms of mean square error approach and the statistical resolution limit (SRL) approach. In the first approach, the lower bounds on the mean square error which are usually used in array processing to evaluate the estimation performance independently of the considered estimator have been considered. We have investigated two kinds of lower bounds: the well-known Cramér-Rao bound (CRB) for the deterministic model in which the parameters are assumed to be deterministic, and the Weiss-Weinstein bound (WWB) which is less studied, for the Bayesian model, in which, the parameters are assumed to be random with some prior distributions. We have proposed closed-form expressions of these bounds, which can be used as a statistical tool for array geometry design. Compared to the CRB, the WWB can predict the threshold effect of the MSE in the non-asymptotic area. Moreover, the closed-form expressions of the WWB proposed for a general Gaussian model with parameterized mean or parameterized covariance matrix can also be useful for other problems. Based on these closed-form expressions, the 3D array geometry and the classical planar array geometry have been investigated under (i) the conditional observation model in which the source signal is modeled as a deterministic sequence and under (ii) the unconditional observation model in which the source signal is modeled as a Gaussian random process. Conditions concerning the isotropic and uncoupling properties were then derived.In the second approach, we have considered the statistical resolution limit which characterizes the minimal separation between the two closed spaced sources which still allows to determine correctly the number of sources. In this thesis, we are interested in the SRL in the Bayesian context which is less studied in the literature. Based on the linearized observation model with the minimum probability of error, we have introduced the two Bayesian approaches of the SRL based on the detection and information theories which could lead to some interesting tools for the system design.

Hintergrund. Exzessives Sorgen ist durch anhaltende, sich wiederholende negative Gedanken gekennzeichnet, die als aufdringlich und unkontrollierbar empfunden werden. Chronisches Sorgen kann zu einer schwer beeinträchtigenden mentalen Aktivität werden und es wird angenommen, dass es zur Entstehung, Aufrechterhaltung und Verschlechterung einer Reihe von somatischen Gesundheitsproblemen und psychischen Störungen beiträgt. Theoretische Modelle und empirische Befunde deuten darauf hin, dass exzessives Sorgen mit einer gestörten Bottom-up-Salienzverarbeitung, einer unzureichenden Top-down-Aufmerksamkeitssteuerung, Defiziten in der Emotionsregulation und abnormalen selbstreferenziellen mentalen Funktionen verbunden sind. Neuroimaging-Studien zu exzessivem Sorgen zeigen Veränderungen funktioneller Aktivierung und Konnektivität in limbischen und paralimbischen Hirnstrukturen, welche die Reaktivität auf emotionale Stimuli unterstützen, in präfrontalen Strukturen, die in Top-down-Prozesse involviert sind, welche der Aufmerksamkeitssteuerung und Emotionsregulation zugrunde liegen, und in medialen kortikalen Mittellinienstrukturen, die an selbstreferenziellen mentalen Aktivitäten beteiligt sind. Im Hinblick auf das Vorhandensein, die genaue Lokalisation der beteiligten Hirnareale und die Richtung der Effekte präsentieren diese Studien jedoch weitgehend heterogene Ergebnisse. Die hohe Variabilität der Befunde erschwert es, ein kohärentes Verständnis der neurobiologischen Mechanismen exzessiven Sorgens zu erlangen. Um dieses Verständnis zu erweitern und künftige Richtungen für die weitere Forschung auf diesem Gebiet aufzuzeigen, verfolgte die vorliegende Dissertationsschrift drei Ziele: (i) die emotionsbezogene, aufgabenbasierte fMRT-Literatur zu exzessivem Sorgen auf quantitative, datengesteuerte Weise zusammenzufassen, um konsistente funktionelle Störungen über Studien hinweg zu identifizieren; (ii) zu bestimmen, mit welchen psychologischen Prozessen die identifizierten Hirnregionen assoziiert sind, und in welchen funktionellen Hirnnetzwerken sie wirken; und (iii) Anomalien in der grundlegenden Hirnorganisation zu untersuchen, die mit exzessivem Sorgen assoziiert sind. Methoden. Eine State-of-the-Art koordinatenbasierte Meta-Analyse wurde unter Anwendung des Activation Likelihood Estimation (ALE) Algorithmus durchgeführt, um die Übereinstimmung zwischen 16 Neuroimaging-Experimenten zu bestimmen, die Veränderungen in der funktionellen Aktivität des Gehirns während der Verarbeitung emotionaler Inhalte zwischen Personen mit hoher und normaler Sorgenneigung berichten. Die identifizierten Regionen wurden mithilfe von Metadaten der funktionellen Magnetresonanztomographie (fMRT) hinsichtlich ihrer psychologischen Funktionen charakterisiert (Verhaltens-Charakterisierung). Zusätzlich wurde meta-analytic-connectivity modeling (MACM) verwendet, um ihre globalen funktionellen Konnektivitätsmuster zu bestimmen und so zugehörige Gehirnnetzwerke zu identifizieren. Schließlich wurde fMRT im Ruhezustand (resting-state) verwendet, um die funktionellen Konnektivitätsmuster zwischen 21 Personen mit hoher und 21 Personen mit normaler Sorgenneigung ohne einer aufgabenbezogenen Gehirnaktivierung zu vergleichen. Dispositionelle Sorgen wurden mit dem Penn State Worry Questionnaire als verlässliches Selbstauskunftsmaß für schwere Sorgen erhoben. Saatregion-basierte Analysen mit den meta-analytisch abgeleiteten Hirnregionen als Saatregionen und eine datengesteuerte Multi-Voxel-Pattern-Analyse (MVPA) wurden durchgeführt, um funktionelle Konnektivitätsunterschiede zwischen den beiden Gruppen zu detektieren. Darüber hinaus wurden gruppenüber-greifende Korrelationen zwischen dem aktuellen Sorgenausmaß (State-Sorgen) und den funktionellen Konnektivitätsmustern der Saat-Regionen sowie den aus der MVPA abgeleiteten Komponenten-Werten analysiert. Ergebnisse. Die Meta-Analyse ergab konvergente Anomalien bei Individuen mit hoher im Vergleich mit normaler Sorgenneigung, hauptsächlich in einem linkshemisphärischen Cluster, welcher Teile des mittleren frontalen Gyrus, des inferioren frontalen Gyrus und der anterioren Insula umfasst. Die Verhaltens-Charakterisierung zeigte, dass der identifizierte Cluster mit der Sprachverarbeitung und dem Gedächtnis assoziiert ist. Darüber hinaus ergaben die meta-analytischen Konnektivitätskartierungen starke funktionelle Verbindungen zwischen den beobachteten konvergenten Regionen und frontalen, temporalen und parietalen Hirnregionen, die sich mit Teilen von zwei verhaltensrelevanten Hirnnetzwerken überschneiden, nämlich dem Salienznetzwerk (SN) und dem Default-Netzwerk (DN). Die resting-state funktionellen Konnektivitätsanalysen zeigten keine Unterschiede zwischen Individuen mit hoher und normaler Sorgenneigung und auch keine Korrelationen zwischen den resting-state funktionellen Konnektivitätsmustern und State-Sorgen, weder mit dem auf Saatregionen basierenden Ansatz noch mit dem MVPA-Ansatz. Schlussfolgerungen. Die Ergebnisse dieser Dissertationsschrift deuten darauf hin, dass exzessives Sorgen mit einer gestörten Funktion in Hirnarealen zusammenhängt, die mit bottom-up und top-down Aufmerksamkeitssteuerung sowie Emotionserzeugung und Emotionsregulation in Verbindung gebracht werden. Die Verhaltensanalyse deckte Assoziationen zwischen dem identifizierten Cluster und der Sprachverarbeitung auf, die mit dem übermäßigen inneren Sprechen bei zu Sorgen neigenden Personen zusammenhängen könnten. Diese Assoziation ist bisher eher unbeachtet geblieben und sollte weiter erforscht werden. Darüber hinaus stellen die identifizierten Hirnregionen Schlüsselknoten in interagierenden neuronalen Netzwerken dar, die endogen und exogen orientierte Kognition unterstützen und das dynamische Zusammenspiel zwischen diesen Prozessen steuern. Ihre veränderte netzwerkübergreifende Dynamik könnte die Ursache für die Unfähigkeit von zu schweren Sorgen neigen-den Personen sein, sich von intern orientierten Kognitionen zu lösen, wenn adaptives Reagieren einen externen Fokus der Aufmerksamkeit erfordern würde. Die Nullergebnisse der Ruhezustandsanalysen könnten auf das Studiendesign zurückzuführen sein oder durch Charakteristika des Sorgens selbst verursacht werden, werden aber nicht als Beleg dafür interpretiert, dass Anomalien in der intrinsischen Konnektivität des Gehirns in Verbindung mit exzessivem Sorgen nicht vorhanden sind. Die Ergebnisse dieser Arbeit können zukünftige Forschungen anleiten, die z.B. untersuchen könnten, ob und wie sich die dynamischen zeitlichen Interaktionen innerhalb und zwischen den hier identifizierten Netzwerken in Abhängigkeit vom Schweregrad des Sorgens unterscheiden. Die ALE-Ergebnisse liefern eine A-priori-Auswahl von Hirnregionen für solche Studien. Ein besseres Verständnis der Veränderungen in den Gehirnnetzwerken, die exzessivem Sorgen zugrunde liegen, und der psychologischen Funktionen, die dadurch beeinträchtigt werden, wird Ansatzpunkte für die Verbesserung therapeutischer Interventionen liefern.:Contents TABLES VIII FIGURES IX ABBREVIATIONS X ABSTRACT 1 1 THEORETICAL BACKGROUND 6 1.1 WORRY 6 1.1.1 DEFINITION, NATURE AND FUNCTION OF WORRY 6 1.1.2 THE WORRY CONTINUUM – NORMAL VERSUS MALADAPTIVE WORRY 7 1.1.3 THE DELETERIOUS EFFECTS OF EXCESSIVE WORRY 8 1.1.4 THEORETICAL MODELS OF EXCESSIVE WORRY 11 1.2 FUNCTIONAL BRAIN NETWORKS AND EXCESSIVE WORRY 18 1.2.1 A SYSTEMS NEUROSCIENCE VIEW OF EXCESSIVE WORRY 18 1.2.2 EMPIRICAL EVIDENCE: FMRI STUDIES ON EXCESSIVE WORRY 20 1.3 RESEARCH QUESTION 32 2 STUDY I: A QUANTITATIVE META-ANALYSIS OF FMRI STUDIES INVESTIGATING EMOTIONAL PROCESSING IN EXCESSIVE WORRIERS: APPLICATION OF ACTIVATION LIKELIHOOD ESTIMATION ANALYSIS 35 2.1 ABSTRACT 36 2.2 INTRODUCTION 37 2.3 METHODS 40 2.3.1 LITERATURE SEARCH AND STUDY SELECTION 40 2.3.2 ACTIVATION LIKELIHOOD ESTIMATION 46 2.3.3 META-ANALYTIC CONNECTIVITY MODELING 47 2.3.4 ANALYSIS OF BEHAVIORAL DOMAIN PROFILES 47 2.4 RESULTS 48 2.4.1 SIGNIFICANT ALE CLUSTERS 48 2.4.2 FUNCTIONAL CONNECTIVITY OF THE DERIVED ALE-CLUSTER – MACM-ANALYSIS 51 2.4.3 FUNCTIONAL CHARACTERIZATION OF THE DERIVED ALE-CLUSTER – BEHAVIORAL ANALYSIS 54 2.5 DISCUSSION 55 2.6 CONCLUSION 59 2.7 SUPPLEMENTARY MATERIAL STUDY I: LISTING OF ALE CLUSTERS SIGNIFICANT AT P < 0.001 UNCORRECTED, CLUSTER SIZE > 100MM3 60 3 STUDY II: HIGH AND LOW WORRIERS DO NOT DIFFER IN UNSTIMULATED RESTING-STATE BRAIN CONNECTIVITY 61 3.1 ABSTRACT 62 3.2 INTRODUCTION 63 3.3 MATERIALS AND METHODS 65 3.3.1 PARTICIPANTS AND PROCEDURE 65 3.3.2 FMRI DATA ACQUISITION 66 3.3.3 SELF-REPORT ASSESSMENTS AND STATE WORRY ASSESSMENT 66 3.3.4 STATISTICAL ANALYSES 67 3.4 RESULTS 69 3.4.1 SELF-REPORT MEASURES 69 3.4.2 FMRI RESULTS 72 3.5 DISCUSSION 72 3.6 CONCLUSION 75 3.7 SUPPLEMENTARY MATERIAL STUDY II: STATE WORRY ASSESSMENT 75 4 GENERAL DISCUSSION 76 4.1 CONVERGENT ABERRANT FUNCTION IN THE MFG-IFG-INSULA-CLUSTER 76 4.2 META-ANALYTIC FUNCTIONAL CHARACTERIZATION AND CONNECTIVITY MAPPING OF THE MFG-IFG-INSULA CLUSTER 82 4.3 NO RESTING-STATE FUNCTIONAL CONNECTIVITY DIFFERENCES BETWEEN HW AND LW 84 4.4 STRENGTHS AND LIMITATIONS 87 4.5 FUTURE DIRECTIONS 90 4.6 CONCLUSION 91 REFERENCES 92 APPENDIX: DECLARATION OF HONOUR / EIGENSTÄNDIGKEITSERKLÄRUNG 131 / Background. Excessive worry is characterized by persistent, repetitive negative thoughts that are perceived as intrusive and uncontrollable. Chronic worrying can become a severely debilitating mental activity and is thought to contribute to the development, maintenance and deterioration of a range of somatic health problems and mental disorders. Theoretical accounts and empirical findings suggest that excessive worry is associated with impaired bottom-up salience-processing, insufficient top-down attentional control, deficits in emotion regulation and abnormal self-referential mental functions. Neuroimaging studies of excessive worry indicate functional activation and connectivity alterations in limbic and paralimbic brain structures that support reactivity to emotional stimuli, in prefrontal structures implicated in top-down processes underlying attentional control and emotion regulation, and in cortical midline structures involved in self-referential mental activity. However, with regard to the presence, the exact localization of the brain areas involved and the directionality of the effects, these studies have presented largely heterogenous results. The high variability of findings makes it difficult to achieve a coherent understanding of the neurobiological mechanisms of excessive worry. To extend this understanding and provide future directions for continued research in this area, the aim of this thesis was threefold: (i) to synthesize the emotional task-based fMRI literature on excessive worry in a quantitative, data-driven manner for the purpose of identifying consistent functional perturbations across studies; (ii) to determine the psychological processes with which the identified brain regions are associated and the functional brain networks in which they operate; and (iii) to examine abnormalities in basic brain organization associated with excessive worry. Methods. A state-of-the-art coordinate-based meta-analysis was conducted applying the activation likelihood estimation (ALE) algorithm to determine concordance among 16 neuroimaging experiments reporting alterations in brain functional activity during emotional processing between individuals experiencing high versus normal levels of worry. The identified regions were behaviorally characterized using functional magnetic resonance imaging (fMRI) metadata. Additionally, meta-analytic-connectivity modeling (MACM) was used to determine their global functional connectivity (FC) patterns and thus identify related brain networks. Finally, resting-state fMRI was used to compare FC patterns between 21 high and 21 low worriers in the absence of task-related brain activation. Dispositional worry was assessed using the Penn State Worry Questionnaire as a reliable self-report measure of severe worry. Seed-based analyses with the meta-analytically derived brain regions as seeds and a data-driven multi-voxel pattern analysis (MVPA) were performed to detect FC differences between the two groups. In addition, cross-group correlations between state worry levels and the FC patterns of the seed regions as well as the MVPA-derived component scores were analyzed. Results. The meta-analysis revealed convergent aberrations in high compared to normal worriers mainly in a left-hemispheric cluster comprising parts of the middle frontal gyrus, inferior frontal gyrus and anterior insula. Behavioral characterization indicated the identified cluster to be associated with language processing and memory. Furthermore, meta-analytic connectivity mapping yielded strong functional connections between the observed convergent regions and frontal, temporal, and parietal brain regions that overlap with parts of two behaviorally relevant brain networks, specifically the salience network (SN) and the default network (DN). The resting-state FC (rsFC) analyses revealed no differences between high and normal worriers and also no correlations between rsFC patterns and state worry, neither using the seed-based nor the MVPA approach. Conclusions. The results of this thesis indicate that excessive worry is related to disturbed functioning in brain areas that have been related to bottom-up and top-down attentional control as well as emotion generation and regulation. Behavioral analysis uncovered associations between the identified cluster and language processing that might be related to the exaggerated inner speech processes in worry prone individuals. This association has so far remained rather unnoticed and requires further exploration. Moreover, the identified brain regions constitute key nodes within interacting neural networks that support internally and externally oriented cognition and control the dynamic interplay among these processes. Their altered cross-network dynamics may underlie the inability of worry-prone individuals to disengage from internally oriented cognitions when adaptive responding would require an external focus of attention. The null-findings of the resting-state analyses might be due to the study design or caused by characteristics of worry itself, but are not interpreted as evidence that abnormalities in the brain's intrinsic connectivity associated with excessive worrying are absent. The results of this thesis may guide future research that could, for example, investigate whether and how the dynamic temporal interactions within and between the networks identified here differ depending on the severity of worry. The ALE results provide an a priori selection of brain regions for such studies. Increasing our understanding of the aberrations in brain networks that underlie excessive worry and the psychological functions that are impaired as a result will provide targets for improving therapeutic interventions.:Contents TABLES VIII FIGURES IX ABBREVIATIONS X ABSTRACT 1 1 THEORETICAL BACKGROUND 6 1.1 WORRY 6 1.1.1 DEFINITION, NATURE AND FUNCTION OF WORRY 6 1.1.2 THE WORRY CONTINUUM – NORMAL VERSUS MALADAPTIVE WORRY 7 1.1.3 THE DELETERIOUS EFFECTS OF EXCESSIVE WORRY 8 1.1.4 THEORETICAL MODELS OF EXCESSIVE WORRY 11 1.2 FUNCTIONAL BRAIN NETWORKS AND EXCESSIVE WORRY 18 1.2.1 A SYSTEMS NEUROSCIENCE VIEW OF EXCESSIVE WORRY 18 1.2.2 EMPIRICAL EVIDENCE: FMRI STUDIES ON EXCESSIVE WORRY 20 1.3 RESEARCH QUESTION 32 2 STUDY I: A QUANTITATIVE META-ANALYSIS OF FMRI STUDIES INVESTIGATING EMOTIONAL PROCESSING IN EXCESSIVE WORRIERS: APPLICATION OF ACTIVATION LIKELIHOOD ESTIMATION ANALYSIS 35 2.1 ABSTRACT 36 2.2 INTRODUCTION 37 2.3 METHODS 40 2.3.1 LITERATURE SEARCH AND STUDY SELECTION 40 2.3.2 ACTIVATION LIKELIHOOD ESTIMATION 46 2.3.3 META-ANALYTIC CONNECTIVITY MODELING 47 2.3.4 ANALYSIS OF BEHAVIORAL DOMAIN PROFILES 47 2.4 RESULTS 48 2.4.1 SIGNIFICANT ALE CLUSTERS 48 2.4.2 FUNCTIONAL CONNECTIVITY OF THE DERIVED ALE-CLUSTER – MACM-ANALYSIS 51 2.4.3 FUNCTIONAL CHARACTERIZATION OF THE DERIVED ALE-CLUSTER – BEHAVIORAL ANALYSIS 54 2.5 DISCUSSION 55 2.6 CONCLUSION 59 2.7 SUPPLEMENTARY MATERIAL STUDY I: LISTING OF ALE CLUSTERS SIGNIFICANT AT P < 0.001 UNCORRECTED, CLUSTER SIZE > 100MM3 60 3 STUDY II: HIGH AND LOW WORRIERS DO NOT DIFFER IN UNSTIMULATED RESTING-STATE BRAIN CONNECTIVITY 61 3.1 ABSTRACT 62 3.2 INTRODUCTION 63 3.3 MATERIALS AND METHODS 65 3.3.1 PARTICIPANTS AND PROCEDURE 65 3.3.2 FMRI DATA ACQUISITION 66 3.3.3 SELF-REPORT ASSESSMENTS AND STATE WORRY ASSESSMENT 66 3.3.4 STATISTICAL ANALYSES 67 3.4 RESULTS 69 3.4.1 SELF-REPORT MEASURES 69 3.4.2 FMRI RESULTS 72 3.5 DISCUSSION 72 3.6 CONCLUSION 75 3.7 SUPPLEMENTARY MATERIAL STUDY II: STATE WORRY ASSESSMENT 75 4 GENERAL DISCUSSION 76 4.1 CONVERGENT ABERRANT FUNCTION IN THE MFG-IFG-INSULA-CLUSTER 76 4.2 META-ANALYTIC FUNCTIONAL CHARACTERIZATION AND CONNECTIVITY MAPPING OF THE MFG-IFG-INSULA CLUSTER 82 4.3 NO RESTING-STATE FUNCTIONAL CONNECTIVITY DIFFERENCES BETWEEN HW AND LW 84 4.4 STRENGTHS AND LIMITATIONS 87 4.5 FUTURE DIRECTIONS 90 4.6 CONCLUSION 91 REFERENCES 92 APPENDIX: DECLARATION OF HONOUR / EIGENSTÄNDIGKEITSERKLÄRUNG 131

Cognitive radio is a technology that aims to maximize the current usage of the licensed frequency spectrum. Cognitive radio aims to provide services for license-exempt users by making use of dynamic spectrum access (DSA) and opportunistic spectrum sharing strategies (OSS). Cognitive radios are defined as intelligent wireless devices capable of adapting their communication parameters in order to operate within underutilized bands while avoiding causing interference to licensed users. An underused band of frequencies in a specific location or time is known as a spectrum hole. Therefore, in order to locate spectrum holes, reliable spectrum sensing algorithms are crucial to facilitate the evolution of cognitive radio networks. Since a large and growing body of literature has mainly focused into the conventional time domain (TD) energy detector, throughout this thesis the problem of spectrum sensing is investigated within the context of a frequency domain (FD) approach. The purpose of this study is to investigate detection based on methods of nonparametric power spectrum estimation. The considered methods are the periodogram, Bartlett's method, Welch overlapped segments averaging (WOSA) and the Multitaper estimator (MTE). Another major motivation is that the MTE is strongly recommended for the application of cognitive radios. This study aims to derive the detector performance measures for each case. Another aim is to investigate and highlight the main differences between the TD and the FD approaches. The performance is addressed for independent and identically distributed (i.i.d.) Rayleigh channels and the general Rician and Nakagami fading channels. For each of the investigated detectors, the analytical models are obtained by studying the characteristics of the Hermitian quadratic form representation of the decision statistic and the matrix of the Hermitian form is identified. The results of the study have revealed the high accuracy of the derived mathematical models. Moreover, it is found that the TD detector differs from the FD detector in a number of aspects. One principal and generalized conclusion is that all the investigated FD methods provide a reduced probability of false alarm when compared with the TD detector. Also, for the case of periodogram, the probability of sensing errors is independent of the length of observations, whereas in time domain the probability of false alarm is increased when the sample size increases. The probability of false alarm is further reduced when diversity reception is employed. Furthermore, compared to the periodogram, both Bartlett method and Welch method provide better performance in terms of lower probability of false alarm but an increased probability of detection for a given probability of false alarm. Also, the performance of both Bartlett's method and WOSA is sensitive to the number of segments, whereas WOSA is also sensitive to the overlapping factor. Finally, the performance of the MTE is dependent on the number of employed discrete prolate spheroidal (Slepian) sequences, and the MTE outperforms the periodogram, Bartlett's method and WOSA, as it provides the minimal probability of false alarm.

This thesis aims to estimate the value of the company Vodovody a kanalizace Havlíčkův Brod with appraisal methods. The first step is the strategic analysis and the financial analysis of the company. The financial plan, required for the actual appraisal, is processed as the final task of the preparatory part before the appraisal. The final part contains estimated costs of capital, long-term growth rate and the actual value of the company, including the evaluation of the appraisal.

Indiana University-Purdue University Indianapolis (IUPUI) / Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects, as well as their functional forms is essential for practical data analysis. However, no existing methods have been developed to meet this need in a joint model setting. In this dissertation, I describe a penalized likelihood-based method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for model selection. By reparameterizing variance components through a Cholesky decomposition, I introduce a penalty function of group shrinkage; the penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. The functional forms of the independent effects are determined through a procedure for structural discovery. Specifically, I first construct the model by penalized cubic B-spline and then decompose the B-spline to linear and nonlinear elements by spectral decomposition. The decomposition represents the model in a mixed-effects model format, and I then use the mixed-effects variable selection method to perform structural discovery. Simulation studies show excellent performance. A clinical application is described to illustrate the use of the proposed methods, and the analytical results demonstrate the usefulness of the methods.