Completeness in Approximate Transduction

Symbolic finite automata (SFA) allow the representation of regular languages of strings over an infinite alphabet of symbols. Recently these automata have been studied in the context of abstract interpretation, showing their extreme flexibility in representing languages at different levels of abstraction. Therefore, SFAs can naturally approximate sets of strings by the language they recognise, providing a suitable abstract domain for the analysis of symbolic data structures. In this scenario, transducers model SFA transformations. We characterise the properties of transduction of SFAs that guarantee soundness and completeness of the abstract interpretation of operations manipulating strings. We apply our model to the derivation of sanitisers for preventing cross site scripting attacks in web application security. In this case we extract the code sanitiser directly from the backward (transduction) analysis of the program given the specification of the expected attack in terms of SFA

Short-term generation scheduling in a hydrothermal power system.

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Renormalization in tensor field theory and the melonic fixed point

This thesis focuses on renormalization of tensor field theories. Its first part considers a quartic tensor model with $O(N)^3$ symmetry and long-range propagator. The existence of a non-perturbative fixed point in any $d$ at large $N$ is established. We found four lines of fixed points parametrized by the so-called tetrahedral coupling. One of them is infrared attractive, strongly interacting and gives rise to a new kind of CFT, called melonic CFTs which are then studied in more details. We first compute dimensions of bilinears and OPE coefficients at the fixed point which are consistent with a unitary CFT at large $N$. We then compute $1/N$ corrections. At next-to-leading order, the line of fixed points collapses to one fixed point. However, the corrections are complex and unitarity is broken at NLO. Finally, we show that this model respects the $F$-theorem. The next part of the thesis investigates sextic tensor field theories in rank $3$ and $5$. In rank $3$, we found two IR stable real fixed points in short range and a line of IR stable real fixed points in long range. Surprisingly, the only fixed point in rank $5$ is the Gaussian one. For the rank $3$ model, in the short-range case, we still find two IR stable fixed points at NLO. However, in the long-range case, the corrections to the fixed points are non-perturbative and hence unreliable: we found no precursor of the large $N$ fixed point. The last part of the thesis investigates the class of model exhibiting a melonic large $N$ limit. We prove that models with tensors in an irreducible representation of $O(N)$ or $Sp(N)$ in rank $5$ indeed admit a large $N$ limit. This generalization relies on recursive bounds derived from a detailed combinatorial analysis of Feynman graphs involved in the perturbative expansion of our model.Comment: PhD thesis, 277 pages. Based on papers: arXiv:1903.03578, arXiv:1909.07767, arXiv:1912.06641, arXiv:2007.04603, arXiv:2011.11276, arXiv:2104.03665, arXiv:2109.08034, arXiv:2111.1179

A Sound Approach to Language Matters: In Honor of Ocke-Schwen Bohn

The contributions in this Festschrift were written by Ocke’s current and former PhD-students, colleagues and research collaborators. The Festschrift is divided into six sections, moving from the smallest building blocks of language, through gradually expanding objects of linguistic inquiry to the highest levels of description - all of which have formed a part of Ocke’s career, in connection with his teaching and/or his academic productions: “Segments”, “Perception of Accent”, “Between Sounds and Graphemes”, “Prosody”, “Morphology and Syntax” and “Second Language Acquisition”. Each one of these illustrates a sound approach to language matters

Nondifferentiable Optimization: Motivations and Applications

IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984. This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications