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In this thesis, we examine whether the probability distribution given by the Brownian Motion on a semialgebraic set is definable in an o-minimal structure and we establish asymptotic expansions for the time evolution.
We study the probability distribution as an example for the occurrence of special parameterized integrals of a globally subanalytic function and the exponential function of a globally subanalytic function. This work is motivated by the work of Comte, Lion and Rolin, which considered parameterized integrals of globally subanalytic functions, of Cluckers and Miller, which examined parameterized integrals of constructible functions, and by the work of Cluckers, Comte, Miller, Rolin and Servi, which treated oscillatory integrals of globally subanalytic functions.
In the one dimensional case we show that the probability distribution on a family of sets, which are definable in an o-minimal structure, are definable in the Pfaffian closure.
In the two-dimensional case we investigate asymptotic expansions for the time evolution. As time t approaches zero, we show that the integrals behave like a Puiseux series, which is not necessarily convergent. As t tends towards infinity, we show that the probability distribution is definable in the expansion of the real ordered field by all restricted analytic functions if the semialgebraic set is bounded.
For this purpose, we apply results for parameterized integrals of globally subanalytic functions of Lion and Rolin. By establishing the asymptotic expansion of the integrals over an unbounded
set, we demonstrate that this expansion has the form of convergent Puiseux series with negative exponents and their logarithm. Subsequently, we get that the asymptotic expansion is definable in an o-minimal structure.
Finally, we study the three-dimensional case and give the proof that the probability distribution given by the Brownian Motion behaves like a Puiseux series as time t tends towards zero.
As t approaches infinity and the semialgebraic set is bounded, it can be ascertained that the probability distribution has the form of a constructible function by results of Cluckers and Miller and therefore it is definable in an o-minimal structure.
If the semialgebraic set is unbounded, we establish the asymptotic expansions and prove that the probability distribution given by the Brownian Motion on unbounded sets has an asymptotic expansion of the form of a constructible function. In consequence of that, the asymptotic expansion is definable in an o-minimal structure.
Inhaltsverzeichnis
I. Tabellenverzeichnis
II. Abbildungsverzeichnis
III. Projektbericht
1. Einleitung
2. Theoretische Einordnung
3. Anmerkungen zur Durchführung der Befragungsstudie
4. Wie attraktiv ist die Heimat? Ergebnispräsentation
4.1 Beschreibung der Stichprobe
4.2 Wie stellt sich die Situation für junge Leute im Landkreis dar?
4.3 Was sind die Ursachen für den Wunsch wegzugehen?
4.4 Begrenzte Reichweite der Studienergebnisse
4.5 Wünsche und Forderungen an Politik und Verwaltung
5. Zusammenfassung
IV. Literatur
V. Anhang
This work illustrates reform approaches in Africa using an international legal comparative approach. The research uses Tanzania and Senegal as the primary case studies and France, the United Kingdom and Germany as secondary case studies to illustrate how Europe reformed data protection regimes through the transposition of the EU Data Protection Directive of 1995.
Chapter one introduces the work; explaining the forces towards data protection regulations and their basis. Chapter two provides for a ‘back-to-back' comparison in three countries (France, Germany and United Kingdom) against the 1995 Data Protection Directive. The idea behind this chapter is to draw a picture on how the legal culture and the pre-existing notions of the right to privacy inform on data protection legal reforms and determines the nature, contents, context and interpretation of adopted regime for data protection. Eventually, all these aspects affect the nature and extent of protection offered regardless of the substance of the law adopted.
Chapter three gives a narrative explanation of nature and perceptions of the right to privacy in Africa and how this may affect data protection reforms in Africa. In the same disposition, African customary legal systems and practices are explained providing a reader with a picture of the overall nature of African systems that makes up an African legal culture. The overview of African privacy perception and legal system is necessary for assessing the workability of any data protection regime to be adopted in Africa which in effect answers the first research question. The chapter draws its rationale from chapter two. In understanding African perceptions of privacy and the African legal culture, one can be able to predict the content and context of the reforms and maybe how the judiciary might interpret the laws based on local perceptions and supporting systems.
An overview of the African data protection architecture or rather human right architecture is provided in chapter four; ideally to provide a reader with a picture of the enforcement systems in Africa as a continent. This is followed by chapter five discussing the two major legal systems in Africa; the civil law and the common law system. The chapter also illustrates the position of African landscape in relation to legal harmonization/unification. This aspect is considered necessary because data protection regimes are more focused on legal harmonization and hence the question of how well or to what extent Africa as a continent can bring about harmonization in law became inevitable. Eventually, the chapter offers a comparative mirror analysis of the primary case studies, i.e. Senegal and Tanzania. The analysis is made on the reform approach taken, motivation behind the reforms and on the regime erected (this is done through textual analysis of the law and the draft bill respectively).
Chapter six concludes the work by answering research questions based on findings and scrutiny from each chapter. It is concluded that there is a very slim chance for the African States to cling on the cultural defence against the adoption of the Western frameworks for data protection. It is also concluded that, lest Africa becomes an active participant in the global process that informs on data protection challenges and regulations, it faces a danger of becoming a puppet of foreign data protection regulation, which may or may not fit African legal culture. The chapter also illustrates how Africa as a continent and the African States individually have taken up data protection reforms blindly. The motivations for the reforms are vaguely stated and unclear. In the majority of legal instruments, the reforms are not taken as a move towards securing and protecting individual rights rather a purely political move influenced by economic motivations. The reforms are to a large extent, a mere impression to align with global data protection regimes and hence lack the political will to enforce the laws.
Optical Graph Recognition
(2017)
Graphs are an important model for the representation of structural information between objects. One identifies objects and nodes as well as a binary relation between objects and edges. Graphs have many uses, e. g., in social sciences, life sciences and engineering. There are two primary representations: abstract and visual. The abstract representation is well suited for processing graphs by computers and is given by an adjacency list, an adjacency matrix or any abstract data structure. A visual representation is used by human users who prefer a picture. Common terms are diagram, scheme, plan, or network. The objective of Graph Drawing is to transform a graph into a visual representation called the drawing of a graph. The goal is a “nice” drawing.
In this thesis we introduce Optical Graph Recognition. Optical Graph Recognition (OGR) reverses Graph Drawing and transforms a digital image of a graph into an abstract representation. Our approach consists of four phases: Preprocessing where we determine which pixels of an image are part of the graph, Segmentation where we recognize the nodes, Topology Recognition where we detect the edges and Postprocessing where we enrich the recognized graph with additional information. We apply established digital image processing methods and make use of the special property that the image contains nodes that are connected by edges. We have focused on developing algorithms that need as little parameters as possible or to automatically calibrate the parameters. Most false recognition results are caused by crossing edges as this makes tracing the edges difficult and can lead to other recognition errors.
We have evaluated hand-drawn and computer-drawn graphs. Our algorithms have a very high recognition rate for computer-drawn graphs, e. g., from a set of 100000 computer-drawn graphs over 90% were correctly recognized. Most false recognition results where observed for hand-drawn graphs as they can include drawing errors and inaccuracies. For universal usability we have implemented a prototype called OGRup for mobile devices like smartphones or tablet computers. With our software it is possible to directly take a picture of a graph via a built in camera, recognize the graph, and then use the result for further processing. Furthermore, in order to gain more insight into the way a person draws a graph by hand, we have conducted a field study.
During the last few years, the technological progress in collecting, storing and processing a large quantity of data for a reasonable cost has raised serious privacy issues. Privacy concerns many areas, but is especially important in frequently used services like search engines (e.g., Google, Bing, Yahoo!). These services allow users to retrieve relevant content on the Internet by exploiting their personal data. In this context, developing solutions to enable users to use these services in a privacy-preserving way is becoming increasingly important.
In this thesis, we introduce SimAttack an attack against existing protection mechanism to query search engines in a privacy-preserving way. This attack aims at retrieving the original user query. We show with this attack that three representative state-of-the-art solutions do not protect the user privacy in a satisfactory manner.
We therefore develop PEAS a new protection mechanism that better protects the user privacy. This solution leverages two types of protection: hiding the user identity (with a succession of two nodes) and masking users' queries (by combining them with several fake queries). To generate realistic fake queries, PEAS exploits previous queries sent by the users in the system.
Finally, we present mechanisms to identify sensitive queries. Our goal is to adapt existing protection mechanisms to protect sensitive queries only, and thus save user resources (e.g., CPU, RAM). We design two modules to identify sensitive queries. By deploying these modules on real protection mechanisms, we establish empirically that they dramatically improve the performance of the protection mechanisms.
Border Basis Schemes
(2017)
The basic idea of border basis theory is to describe a zero-dimensional ring P/I by an order ideal of terms whose residue classes form a K-vector space basis of P/I. The O-border basis scheme is a scheme that parametrizes all zero-dimensional ideals that have an O-border basis. In general, the O-border basis scheme is not an affine space. Subsequently, in [Huib09] it is proved that if an order ideal with "d" elements is defined in a two-dimensional polynomial ring and it is of some special shapes, then the O-border basis scheme is isomorphic to the affine space of dimension 2d. This thesis is dedicated to find a more general condition for an O-border basis scheme to be isomorphic to an affine space of dimension "nd" that is independent of the shape of the order ideal with "d" elements and "n" is the dimension of the polynomial ring that the order ideal is defined in.
We accomplish this in 6 Chapters. In Chapters 2 and 3 we develop the concepts and properties of border basis schemes. In Chapter 4 we transfer the smoothness criterion (see [Huib05]) for the point (0,...,0) in a Hilbert scheme of points to the monomial point of the border basis scheme by employing the tools from border basis theory. In Chapter 5 we explain trace and Jacobi identity syzygies of the defining equations of a O-border basis scheme and characterize them by the arrow grading. In Chapter 6 we give a criterion for the isomorphism between 2d dimensional affine space and O-border basis scheme by using the results from Chapters 3 and Chapter 4. The techniques from other chapters are applied in Chapter 6.1 to segment border basis schemes and in Chapter 6.2 to O-border basis schemes for which O is of the sawtooth form.
The increasing scale and complexity of computer networks imposes a need for highly flexible management mechanisms. The concept of network virtualization promises to provide this flexibility. Multiple arbitrary virtual networks can be constructed on top of a single substrate network. This allows network operators and service providers to tailor their network topologies to the specific needs of any offered service.
However, the assignment of resources proves to be a problem. Each newly defined virtual network must be realized by assigning appropriate physical resources. For a given set of virtual networks, two questions arise: Can all virtual networks be accommodated in the given substrate network? And how should the respective resources be assigned? The underlying problem is commonly known as the Virtual Network Embedding problem. A multitude of algorithms has already been proposed, aiming to provide solutions to that problem under various constraints. For the evaluation of these algorithms typically an empirical approach is adopted, using artificially created random problem instances. However, due to complex effects of random problem generation the obtained results can be hard to interpret correctly. A structured evaluation methodology that can avoid these effects is currently missing.
This thesis aims to fill that gap. Based on a thorough understanding of the problem itself, the effects of random problem generation are highlighted. A new simulation architecture is defined, increasing the flexibility for experimentation with embedding algorithms. A novel way of generating embedding problems is presented which migitates the effects of conventional problem generation approaches. An evaluation using these newly defined concepts demonstrates how new insights on algorithm behavior can be gained. The proposed concepts support experimenters in obtaining more precise and tangible evaluation data for embedding algorithms.
Ausgehend von den theoretischen Überlegungen zu einem Mikro-Meso-Makromodell kollektiver Erinnerung (Heinrich/Weyland 2016) wurde im Rahmen eines Pilotprojekts eine Inhaltsanalyse von Diskussionsseiten der Wikipedia durchgeführt. Ziel war es, in Erfahrung zu bringen, inwieweit auf dieser Plattform die durch den Enzyklopädieeintrag präsentierte Geschichtsversion ausgehandelt wird. Darüber hinaus will diese Studie die Grundlagen für eine automatisierte Datenanalyse legen, mit deren Hilfe es zu einem späteren Zeitpunkt möglich sein soll, Erkenntnisse zu gewinnen, die über den Einzelfall hinausgehen.
In den folgenden Kapiteln wird die Vorgehensweise bei der Inhaltsanalyse mit den einzelnen Arbeitsschritten dokumentiert. Damit ist die Intersubjektivität des Forschungsprozesses gewährleistet. Entsprechend ist die Dokumentation in Ergänzung zur Publikation der Studienergebnisse (Heinrich & Gilowsky 2018) zu lesen.
Nachfolgend werden kurz der theoretische Rahmen skizziert und das methodische Vorgehen geschildert. Kernstück der Dokumentation sind dann die Präsentation des Textkorpus, wie er zum Stichdatum im Internet präsentiert wurde, das Kategorienschema, das auf die Diskussionsbeiträge in der Wikipedia angewendet wurde, sowie die konkreten Textstellen mit ihren Kodierungen. Eine weitere Tabelle demonstriert, inwieweit die Äußerungen auf der Diskussionsplattform zu Änderungen am Lexikoneintrag gefunden haben.
This thesis presents various techniques that aim at enabling more effective and more
efficient approaches for automatic software verification.
After a brief motivation why automatic software verification is getting ever more
relevant, we continue with detailing the formalism used in this thesis and on the
concepts it is built on.
We then describe the design and implementation of the value analysis, an analysis
for automatic software verification that tracks state information concretely. From
a thorough evaluation based on well over 4 000 verification tasks from the latest
edition of the International Competition on Software Verification (SV-COMP), we
learn that this plain value analysis leads to an efficient verification process for many
verification tasks, but at the same time, fails to solve other verification tasks due
to state-space explosion. From this insight we infer that some form of abstraction
technique must be added to the value analysis in order to also allow the successful
verification of large and complex verification tasks.
As a solution, we propose to incorporate counterexample-guided abstraction refinement (CEGAR) and interpolation into the value domain. To this end, we design
a novel interpolation procedure, that extracts from infeasible counterexamples interpolants for the value domain, allowing to form a precision strong enough to exclude
these infeasible counterexamples, and to make progress in the CEGAR loop. We
then describe several optimizations and extensions to these concepts, such that the
value analysis with CEGAR becomes competitive for automatic software verification.
As the next step, we combine the value analysis with CEGAR with a predicate
analysis, to obtain a more precise and efficient composite analysis based on CEGAR.
This composite analysis is indeed on a par with the world’s leading software verification tools, as witnessed by the results of SV-COMP’13 where this approach achieved
the 2 nd place in the overall ranking.
After having available competitive CEGAR-based analyses for the value domain,
the predicate domain, and the combination thereof, we then turn our attention to
techniques that have the goal to make all these CEGAR-based approaches more
successful. Our first novel idea in this regard is based on the concept of infeasible
sliced prefixes, which allow the computation of different precisions from a single
infeasible counterexample. This adds choice to the CEGAR loop, while without this
enhancement, no choice for a specific precision, i. e., a specific refinement, is possible.
In our evaluation we show, for both the value analysis and the predicate analysis,
that choosing different infeasible sliced prefixes during the refinement step leads to
major differences in verification effectiveness and verification efficiency.
Extending on the concept of infeasible sliced prefixes, we define several heuristics
in order to precisely select a single refinement from a set of possible refinements. We
make this new concept, which we refer to as guided refinement selection, available
to both the value and predicate analysis, and in a large-scale evaluation we try to
answer the question which selection technique leads to well suited abstractions and
thus, to a more effective verification process. Additionally, we present the idea of
inter-analysis refinement selection, where the refinement component of a composite
analysis may decide which of its component analyses is best to be refined, and in yet
another evaluation we highlight the positive effects of this technique.
Finally, we present the results of SV-COMP’16, where the verifier we contributed
and which is based on the concepts and ideas presented in this thesis achieved the
1 st place in the category DeviceDriversLinux64.