On q-summation and confluence

This paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent solution of a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of such a q-difference equation. In the second part, we work under the assumption q\in ]1,+\infty[. In this case, at least four different q-Borel sums of a divergent solution of an irregular singular analytic q-difference equations are spread in the literature: under convenient assumptions we clarify the relations among them.Comment: 36 pages. Following the referee's comments, we have clarified the exposition of some proofs and corrected some misprint

Requirements traceability in model-driven development: Applying model and transformation conformance

The variety of design artifacts (models) produced in a model-driven design process results in an intricate relationship between requirements and the various models. This paper proposes a methodological framework that simplifies management of this relationship, which helps in assessing the quality of models, realizations and transformation specifications. Our framework is a basis for understanding requirements traceability in model-driven development, as well as for the design of tools that support requirements traceability in model-driven development processes. We propose a notion of conformance between application models which reduces the effort needed for assessment activities. We discuss how this notion of conformance can be integrated with model transformations

Multi-layer syntactical model transformation for model based systems engineering

This dissertation develops a new model transformation approach that supports engineering model integration, which is essential to support contemporary interdisciplinary system design processes. We extend traditional model transformation, which has been primarily used for software engineering, to enable model-based systems engineering (MBSE) so that the model transformation can handle more general engineering models. We identify two issues that arise when applying the traditional model transformation to general engineering modeling domains. The first is instance data integration: the traditional model transformation theory does not deal with instance data, which is essential for executing engineering models in engineering tools. The second is syntactical inconsistency: various engineering tools represent engineering models in a proprietary syntax. However, the traditional model transformation cannot handle this syntactic diversity. In order to address these two issues, we propose a new multi-layer syntactical model transformation approach. For the instance integration issue, this approach generates model transformation rules for instance data from the result of a model transformation that is developed for user model integration, which is the normal purpose of traditional model transformation. For the syntactical inconsistency issue, we introduce the concept of the complete meta-model for defining how to represent a model syntactically as well as semantically. Our approach addresses the syntactical inconsistency issue by generating necessary complete meta-models using a special type of model transformation.PhDCommittee Chair: Leon F. McGinnis; Committee Member: Charles Eastman; Committee Member: Chris Paredis; Committee Member: Joel Sokol; Committee Member: Marc Goetschalck

Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion

Quasinormal modes are characteristic oscillatory modes that control the relaxation of a perturbed physical system back to its equilibrium state. In this work, we calculate QNM frequencies and angular eigenvalues of Kerr--de Sitter black holes using a novel method based on conformal field theory. The spin-field perturbation equations of this background spacetime essentially reduce to two Heun's equations, one for the radial part and one for the angular part. We use the accessory parameter expansion of Heun's equation, obtained via the isomonodromic $\tau$-function, in order to find analytic expansions for the QNM frequencies and angular eigenvalues. The expansion for the frequencies is given as a double series in the rotation parameter $a$ and the extremality parameter $\epsilon=(r_{C}-r_{+})/L$, where $L$ is the de Sitter radius and $r_{C}$ and $r_{+}$ are the radii of, respectively, the cosmological and event horizons. Specifically, we give the frequency expansion up to order $\epsilon^2$ for general $a$, and up to order $\epsilon^{3}$ with the coefficients expanded up to $(a/L)^{3}$. Similarly, the expansion for the angular eigenvalues is given as a series up to $(a\omega)^{3}$ with coefficients expanded for small $a/L$. We verify the new expansion for the frequencies via a numerical analysis and that the expansion for the angular eigenvalues agrees with results in the literature.Comment: 38+19 pages, 8 figures. v3: minor changes, matches published versio

Partial Evaluation for Java Malware Detection

The fact that Java is platform independent gives hackers the opportunity to write exploits that can target users on any platform, which has a JVM implementation. Metasploit is a well-known source of Java exploits and to circumvent detection by Anti Virus (AV) software, obfuscation techniques are routinely applied to make an exploit more difficult to recognise. Popular obfuscation techniques for Java include string obfuscation and applying reflection to hide method calls; two techniques that can either be used together or independently. This paper shows how to apply partial evaluation to remove these obfuscations and thereby improve AV matching. The paper presents a partial evaluator for Jimple, which is a typed three-address code suitable for optimisation and program analysis, and also demonstrates how the residual Jimple code, when transformed back into Java, improves the detection rates of a number of commercial AV products

Galois theory of fuchsian q-difference equations

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups. Then we describe \emph{fundamental subgroups} that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger's type.Comment: Prepublication du Laboratoire Emile Picard n.246. See also http://picard.ups-tlse.f