In this thesis, we first propose a new scalar auxiliary variable (SAV) approach for general dissipative nonlinear systems. This new approach is half computational cost of the original SAV approach, can be extended to high order unconditionally energy stable backward differentiation formula (BDF) schemes and not restricted to the gradient flow structure. Rigorous error estimates for this new SAV approach are conducted for the Allen-Cahn and Cahn-Hilliard type equations from the BDF1 to the BDF5 schemes in a unified form. As an application of this new approach, we construct high order unconditionally stable, fully discrete schemes for the incompressible Navier-Stokes equation with periodic boundary condition. The corresponding error estimates for the fully discrete schemes are also reported. Secondly, by combining the new SAV approach with functional transformation, we propose a new method to construct high-order, linear, positivity/bound preserving and unconditionally energy stable schemes for general dissipative systems whose solutions are positivity/bound preserving. We apply this new method to second order equations: the Allen-Cahn equation with logarithm potential, the Poisson-Nernst-Planck equation and the Keller-Segel equations and fourth order equations: the thin film equation and the Cahn-Hilliard equation with logarithm potential. Ample numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.

Airborne angle-only geolocalization is the localization of objects on ground level from airborne vehicles (AV) using bearing measurements, namely azimuth and elevation. This thesis aims to introduce elevation data of the terrain to the airborne angle-only geolocalization problem and to demonstrate that it could be applicable for localization of jammers. Jammers are often used for deliberate interference with malicious intent which could interfere with the positioning system of a vehicle. It is important to locate the jammers to either avoid them or to remove them.    Three localization methods, i.e. the nonlinear least squares (NLS), the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are implemented and tested on simulated data. The methods are also compared to the theoretical lower bound, the Cramér-Rao Lower Bound (CRLB), to see if there is an efficient estimator. The simulated data are different scenarios where the number of AVs, the relative flight path of the AVs and the knowledge of the terrain can differ. Using the knowledge of the terrain elevation, the methods give more consistent localization than without it. Without elevation data, the localization relies on good geometry of the problem, i.e. the relative flight path of the AVs, while the geometry is not as critical when elevation data is available. However, the elevation data does not always improve the localization for certain geometries.    There is no method that is clearly better than the others when elevation data is used. The methods’ performances are very similar and they all converge to the CRLB but that could also be an advantage. This makes the usage of elevation data not restricted to a certain method and it leaves more up to the implementer which method they prefer.

La synchronisation temporelle est la première opération effectuée par le démodulateur. Elle permet d'assurer que les échantillons transmis aux processus de démodulation puissent réaliser un taux d'erreurs binaires le plus faible.Dans cette thèse, nous proposons l'étude d'algorithmes innovants de synchronisation temporelle à haute performance.D'abord, nous avons proposé des algorithmes exploitant l'information souple du décodeur en plus du signal reçu afin d'améliorer l'estimation aveugle d'un retard temporel supposé constant sur la durée d'observation.Ensuite, nous avons proposé un algorithme original basé sur la synchronisation par lissage à faible complexité.Cette étape a consisté à proposer une technique opérant dans un contexte hors ligne, permettant l'estimation d'un retard aléatoire variable dans le temps via les boucles d'aller-retour sur plusieurs itération. Les performances d'un tel estimateur dépassent celles des algorithmes traditionnels.Afin d'évaluer la pertinence de tous les estimateurs proposés, pour des retards déterministe et aléatoire, nous avons évalué et comparé leurs performances à des bornes de Cramèr-Rao que nous avons développées pour ce cadre. Enfin, nous avons évalué les algorithmes proposés sur des signaux WBAN. / Time synchronization is the first function performed by the demodulator. It ensures that the samples transmitted to the demodulation processes allow to achieve the lowest bit error rate.In this thesis we propose the study of innovative algorithms for high performance time synchronization.First, we propose algorithms exploiting the soft information from the decoder in addition to the received signal to improve the blind estimation of the time delay. Next, we develop an original algorithm based on low complexity smoothing synchronization techniques. This step consisted in proposing a technique operating in an off-line context, making it possible to estimate a random delay that varies over time on several iterations via Forward- Backward loops. The performance of such estimators exceeds that of traditional algorithms. In order to evaluate the relevance of all the proposed estimators, for deterministic and random delays, we evaluated and compared their performance to Cramer-Rao bounds that we developed within these frameworks. We, finally, evaluated the proposed algorithms on WBAN signals.

The aim of the diploma thesis is based on a theoretical framework and with the help of typology to explain the importance of social tourism and its relationship to bound tourism and to find out, how social (bound) tourism displays itself as a specific form in the shape of summer children's camps. The work introduces and compares the definitions of social and bound tourism, there is performed the typology of social tourism and there are also mentioned current trends in social and bound tourism and the specifics of the development of bound and social tourism in the Czechia. After defining and characterizing the territory of the Jindřichův Hradec district, the search for information about children's camps and the methodology of my own research are explained in detail in the text, which consists in the content analysis of a structured interview with open questions. Within the analysis, keywords are selected, and a mix of quantitative and qualitative evaluation is performed, in which both the frequency of keywords and the content of individual statements are evaluated. Gradually, the geographical factors of camp location, their program factors, general characteristics and organizational factors of camps, their technical parameters and limitations of the coronavirus pandemic, social and demographic...

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Es sei Γ eine torsionsfreie arithmetische Untergruppe der symplektischen Gruppe Sp(n,R), die auf dem Siegelschen oberen Halbraum H_n vom Grad n wirkt. Wir betrachten den d-dimensionalen Raum der Siegelschen Spitzenformen vom Gewicht k zur Gruppe Γ, mit einer Orthonormalbasis {f_1,…,f_d}. In der vorliegenden Dissertation zeigen wir mit Hilfe des Wärmeleitungskerns, dass die Supremumsnorm von S_k(Z):=det(Y)^k (|f_1(Z)|^2+…+|f_d(Z)|^2) (Z∈H_n) für n=2 ohne zusätzliche Bedingungen und für n>2 unter Annahme einer vermuteten Determinanten-Ungleichung nach oben beschränkt ist. Wenn M:=Γ\H_n kompakt ist, dann ist die obere Schranke durch c_(n,Γ) k^{n(n+1)/2} gegeben. Wenn M nicht kompakt und von endlichem Volumen ist, dann ist die obere Schranke durch c_(n,Γ) k^{3n(n+1)/4} gegeben. In beiden Fällen ist c_(n,Γ) eine positive reelle Konstante, die nur vom Grad n und der Gruppe Γ abhängt. Wir zeigen weiter, dass die obere Schranke in dem Sinne gleichmäßig ist, dass bei fixierter Gruppe Γ_0 die Konstante c_(n,Γ) für Untergruppen Γ von endlichem Index nur vom Grad n und der Gruppe Γ_0 abhängt. / Let Γ be a torsion-free arithmetic subgroup of the symplectic group Sp(n,R) acting on the Siegel upper half-space H_n of degree n. Consider the d-dimensional space of Siegel cusp forms of weight k for Γ with an orthonormal basis {f_1,…,f_d}. In this thesis we show using the heat kernel method that for n=2 unconditionally and for n>2 subject to a conjectural determinant-inequality, the sup-norm of the quantity S_k(Z):=det(Y)^k (|f1(Z)|^2+…+|f_d(Z)|^2) (Z∈H_n) is bounded above by c_(n,Γ) k^{n(n+1)/2} when M:=Γ\H_n is compact and by c_(n,Γ) k^{3n(n+1)/4} when M is non-compact of finite volume, where c_(n,Γ) denotes a positive real constant depending only on the degree n and the group Γ. Furthermore, we show that this bound is uniform in the sense that if we fix a group Γ_0 and take Γ to be a subgroup of Γ_0 of finite index, then the constant c_(n,Γ) in these bounds depends only on the degree n and the fixed group Γ_0.

Querying and efficiently analyzing complex data is required to gain valuable business insights, to support machine learning applications, and to make up-to-date information available. Therefore, this thesis investigates opportunities and challenges of selecting the most efficient execution strategy for analytical queries. These challenges include hard-to-capture data characteristics such as skew and correlation, the support of arbitrary data types, and the optimization time overhead of complex queries. Existing approaches often rely on optimistic assumptions about the data distribution, which can result in significant response time delays when these assumptions are not met. On the contrary, we focus on robust query optimization, emphasizing consistent query performance and applicability. Our presentation follows the general select-project-join query pattern, representing the fundamental stages of analytical query processing. To support arbitrary data types and complex filter expressions in the select stage, a novel sampling-based selectivity estimator is developed. Our approach exploits information from filter subexpressions and estimates correlations that are not captured by existing sampling-based methods. We demonstrate improved estimation accuracy and query execution time. Further, to minimize the runtime overhead of sampling, we propose new techniques that exploit access patterns and auxiliary database objects such as indices. For the join stage, we introduce a robust optimization approach by developing an upper-bound join enumeration strategy that connects accurate filter selectivity estimates –e.g., using our sampling-based approach– to join ordering. We demonstrate that join orders based on our upper-bound join ordering strategy achieve more consistent performance and faster workload execution on state-of-the-art database systems. However, besides identifying good logical join orders, it is crucial to determine appropriate physical join operators before query plan execution. To understand the importance of fine-grained physical operator selections, we exhaustively execute fixed join orders with all possible operator combinations. This analysis reveals that none of the investigated query optimizers fully reaches the potential of optimal operator decisions. Based on these insights and to achieve fine-grained operator selections for the previously determined join orders, the thesis presents a lightweight learning-based physical execution plan refinement component called. We show that this refinement component consistently outperforms existing approaches for physical operator selection while enabling a novel two-stage optimizer design. We conclude the thesis by providing a framework for the two-stage optimizer design that allows users to modify, replicate, and further analyze the concepts discussed throughout this thesis.:1 INTRODUCTION 1.1 Analytical Query Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Select-Project-Join Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Basics of SPJ Query Optimization . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.1 Plan Enumeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.2 Cost Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.3 Cardinality Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Robust SPJ Query Optimization . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.1 Tail Latency Root Cause Analysis . . . . . . . . . . . . . . . . . . . 17 1.4.2 Tenets of Robust Query Optimization . . . . . . . . . . . . . . . . . 19 1.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 SELECT (-PROJECT) STAGE 2.1 Sampling for Selectivity Estimation . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.1 Combined Selectivity Estimation (CSE) . . . . . . . . . . . . . . . . 29 2.2.2 Kernel Density Estimator . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.3 Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Beta Estimator for 0-Tuple-Situations . . . . . . . . . . . . . . . . . . . . . 33 2.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.2 Beta Distribution in Non-0-TS . . . . . . . . . . . . . . . . . . . . . . 35 2.3.3 Parameter Estimation in 0-TS . . . . . . . . . . . . . . . . . . . . . . 37 2.3.4 Selectivity Estimation and Predicate Ordering . . . . . . . . . . . 39 2.3.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4 Customized Sampling Techniques . . . . . . . . . . . . . . . . . . . . . . 53 2.4.1 Focused Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.4.2 Conditional Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4.3 Zone Pruning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3 JOIN STAGE: LOGICAL ENUMERATION 3.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1.1 Point Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.2 Join Cardinality Upper Bound . . . . . . . . . . . . . . . . . . . . . 64 3.2 Upper Bound Join Enumeration with Synopsis (UES) . . . . . . . . . . . . 66 3.2.1 U-Block: Simple Upper Bound for Joins . . . . . . . . . . . . . . . . 67 3.2.2 E-Block: Customized Enumeration Scheme . . . . . . . . . . . . . 68 3.2.3 UES Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.1 General Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4 JOIN STAGE: PHYSICAL OPERATOR SELECTION 4.1 Operator Selection vs Join Ordering . . . . . . . . . . . . . . . . . . . . . 77 4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1 Adaptive Query Processing . . . . . . . . . . . . . . . . . . . . . . 80 4.2.2 Bandit Optimizer (Bao) . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.3 TONIC: Learned Physical Join Operator Selection . . . . . . . . . . . . . 82 4.3.1 Query Execution Plan Synopsis (QEP-S) . . . . . . . . . . . . . . . 83 4.3.2 QEP-S Life-Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.3 QEP-S Design Considerations . . . . . . . . . . . . . . . . . . . . . . 87 4.4 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4.1 Performance Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.4.2 Rate of Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.4.3 Data Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4.4 TONIC - Runtime Traits . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5 TWO-STAGE OPTIMIZER FRAMEWORK 5.1 Upper-Bound-Driven Join Ordering Component . . . . . . . . . . . . . 101 5.2 Physical Operator Selection Component . . . . . . . . . . . . . . . . . . 103 5.3 Example Query Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 103 6 CONCLUSION 107 BIBLIOGRAPHY 109 LIST OF FIGURES 117 LIST OF TABLES 121 A APPENDIX A.1 Basics of Query Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 A.2 Why Q? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 A.3 0-TS Proof of Unbiased Estimate . . . . . . . . . . . . . . . . . . . . . . . . 125 A.4 UES Upper Bound Property . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A.5 TONIC – Selectivity-Aware Branching . . . . . . . . . . . . . . . . . . . . . 128 A.6 TONIC – Sequences of Query Execution . . . . . . . . . . . . . . . . . . . 129

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Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider Λπ(Δx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λπ(Δx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δx,Δy ∈ (Z/qZ)m - 0. We give a proof of this theorem using the Stein-Chen method: As qm approaches infinity, the distribution of Λπ(Δx, Δy) is approximately Poisson with parameter ½. Error bounds for this approximation are provided.

Sverige har länge varit ledande inom tillgänglighet. Genom införandet av begreppen ”tillgänglighet” och ”användbarhet” har man genom Plan- och bygglagen och Boverkets riktlinjer ställt krav på den fysiska miljön. Ca 7 000 barn i Sverige är rörelsehindrade. Ungefär hälften av dessa barn använder en rullstol. Trots att alla barn har rätt till lek, är det intressant att undersöka huruvida alla barn ges möjlighet att utnyttja denna rättighet. Efter att ha uppmärksammat Helsingborgs stads kreativa lekplatsbyggen, dök frågan kring huruvida alla barn har möjlighet att leka på dessa lekplatser, upp. Syftet med arbetet är att belysa vikten av tillgängliga lekplatser, samt att undersöka hur tillgängligheten på lekplatser kan förbättras och vilka anpassningar som krävs för att förbättra tillgängligheten för rullstolsburna barn. I detta arbete görs en litteraturstudie, med fokus på regelverk och litteratur kopplad till tillgänglighet. En fallstudie görs i form av platsbesök på 8 lekplatser i Helsingborg, som underlag för en jämförelse. En intervju görs med Johanna Elgström, landskapsarkitekt på Helsingborgs stad. Slutsatsen av detta arbete är att lekplatser där man fokuserat mer på tillgänglighet ofta är mer tillgängliga och användbara för barn i rullstol. Dock krävs incitament för att säkerställa en tillgänglig och användbar lekplatsmiljö, samt tydligare definition av dessa begrepp. Genom att ha en lekplats som är tillgänglig och användbar för de flesta, gynnas den sociala hållbarheten. Slutsatsen av detta arbete blir således att säkerställandet av tillgängliga och användbara lekplatser gynnar rullstolsburna barns möjlighet till socialt samspel. / Sweden is one of the leading countries when it comes to availability in the physical environment. Approximately 7 000 children in Sweden are disabled. Half of these children use a wheelchair. It is every child’s right to play, and it’s thereby interesting to know whether every child is given the opportunity to use a playground. In the county of Helsingborg there are playgrounds appealing to many children, although the question is whether every child is given the chance to play at these playgrounds. The aim of this study is to highlight the importance of availability at playgrounds and outline ways to improve the availability. The method used in this thesis is a literature study, focusing on legal framework and literature about availability, usability and playgrounds. The case study provides information about eight playgrounds in Helsingborg. There is also an interview with landscape architect Johanna Elgström. Playgrounds where availability has been prioritized are often more available and useable for wheelchair-bound children. Still, the legal framework is in need of a more precise definition of availability and usability to ensure that playgrounds are suitable for children using a wheelchair. The playgrounds that are more available and useable can favor children using a wheelchair and give them the opportunity to socially interact with other children.