On linear, fractional, and submodular optimization

In this thesis, we study four fundamental problems in the theory of optimization. 1. In fractional optimization, we are interested in minimizing a ratio of two functions over some domain. A well-known technique for solving this problem is the Newton– Dinkelbach method. We propose an accelerated version of this classical method and give a new analysis using the Bregman divergence. We show how it leads to improved or simplified results in three application areas. 2. The diameter of a polyhedron is the maximum length of a shortest path between any two vertices. The circuit diameter is a relaxation of this notion, whereby shortest paths are not restricted to edges of the polyhedron. For a polyhedron in standard equality form with constraint matrix A, we prove an upper bound on the circuit diameter that is quadratic in the rank of A and logarithmic in the circuit imbalance measure of A. We also give circuit augmentation algorithms for linear programming with similar iteration complexity. 3. The correlation gap of a set function is the ratio between its multilinear and concave extensions. We present improved lower bounds on the correlation gap of a matroid rank function, parametrized by the rank and girth of the matroid. We also prove that for a weighted matroid rank function, the worst correlation gap is achieved with uniform weights. Such improved lower bounds have direct applications in submodular maximization and mechanism design. 4. The last part of this thesis concerns parity games, a problem intimately related to linear programming. A parity game is an infinite-duration game between two players on a graph. The problem of deciding the winner lies in NP and co-NP, with no known polynomial algorithm to date. Many of the fastest (quasi-polynomial) algorithms have been unified via the concept of a universal tree. We propose a strategy iteration framework which can be applied on any universal tree

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Singular systems with time-varying delays

Preliminaries on time-delay singular systems -- Stability of time-delay singular systems -- State feedback controller for time-delay singular systems -- Static output feedback controller for time-delay singular systems with saturating actuators

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

H. P. Blavatsky's Theosophy in Context: The Construction of Meaning in Modern Western Esotericism

To contact the author for further details go to www.h-e-r-m-e-s.orgAbstract of PhD Thesis by Tim Rudbøg, 15 December 2012 H. P. Blavatsky’s Theosophy in Context: The Construction of Meaning in Modern Western Esotericism H. P. Blavatsky’s (1831-1891) Theosophy has been defined as central to the history of modern Western spirituality and esotericism, yet to this date no major study has mapped and analysed the major themes of Blavatsky’s writings, how Blavatsky used the concept ‘Theosophy’ or to what extent she was engaged with the intellectual contexts of her time. Thus the purpose of this thesis is to fill this gap. The proposed theoretical framework is based on the centrality of language in the production of intellectual products, such as texts—but contrary to the dominant focus on strategies, rhetoric and power this thesis will focus on the construction of meaning coupled with a set of methodological tools based on contextual analysis, intellectual history and intertextuality. In addition to an overview of Blavatsky research this thesis will map and analyse Blavatsky’s use of the concept ‘Theosophy’ as well as Blavatsky’s primary discourses, identified as: (1) discourse for ancient knowledge, (2) discourse against Christian dogmatism, (3) discourse against the modern natural sciences and materialism, (4) discourse against modern spiritualism, (5) discourse for system and (7) discourse for universal brotherhood. In mapping and analysing Blavatsky’s discourses, it was found that her construction of meaning was significantly interconnected with broader intellectual contexts, such as ‘modern historical consciousness’, ‘critical enlightenment ideas’, studies in religion, studies in mythology, the modern sciences, spiritualism, systemic philosophy, reform movements and practical ethics. It, for example, becomes clear that Blavatsky’s search for an ancient ‘Wisdom Religion’ was actually a part of a common intellectual occupation during the eighteenth and nineteenth centuries and that her critique of the Christian dogmas was equally a common intellectual trend. To read Blavatsky’s discourses as the idiosyncratic strategies of an esotericist, isolated from their larger contexts or only engaged with them in order to legitimise minority views would therefore largely fail to account for the result of this thesis: that in historical actuality, they were a part of the larger cultural web of meaning