I assure that this thesis is the product of my own work and that it contains no plagiarism. I duly referenced all sources and marked all parts of this work that have been literally or analogously obtained from these sources. Finally, I assure that no work in this style or similar has previously been presented to any other board of examination.

First a few reformulations of Frankl’s conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to attack than Frankl’s. To this end we prove an inequality which might help in proving the stronger conjecture.

Human understanding of the physical world frequently derives from the narratives we construct about it. Analogously, we can incorporate narratives in virtual spaces to give visitors a sense of place and purpose. In this paper we describe two projects using interactive characters as a medium for story building and storytelling within and about the digital places they inhabit.

We demonstrate an algorithm for the retrieval of a qubit, encoded in spin angular momentum, that has been dropped into a no-firewall black hole. Retrieval is achieved analogously to quantum teleportation by collecting Hawking radiation and performing measurements on the black hole. Importantly, these methods require only the ability to perform measurements from outside the event horizon.

A non-empty set of vertices is called an even dominating set if each vertex in the graph is adjacent to an even number of vertices in the set (adjacency is reflexive). An odd dominating set is defined analogously. Results on parity dominating sets in grid graphs are surveyed and related results on “Lights Out!” games on grids and graphs are discussed.

Abstract We introduce the notions of ? -Baire property and -semiopen set using sets Lebesgue measure zero. For a family A subsets real line, we define ( ? )-property analogously as it was done in category case for )-property. The main result is that all line having has iff situated between Euclidean topology sets.

In this paper, we present a formulation of the slice balance approach using nonlinear closure relation derived analogously from adaptive-weighted diamond-difference form weighted method for Cartesian grids. The yields strictly positive solutions that reduce to standard diamond with fine-enough mesh granularity. It can be efficiently solved Newton-like iterative methods diffusion preconditioning.

In this paper, polynomial-predictive FIR (PPF) design is reviewed. Step-by-step instructions are given starting from the signal model, up to designing ideal fixed-point PPFs. This paper is a one-stop starting point for immediate application of PPFs. Also, a literature review is given, including examples of analogously designable filter types.

In Savage [41] a 'behavioral foundation' was given for subjective probabilities, to be used in the maximization of expected utility. This paper analogously gives a behavioral foundation for fuzzy measures, to be used in the maximization of 'Choquet-expected utility'. This opens the way to empirical verification or falsification of fuzzy measures, and frees them of their 'ad hoc' character.

There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded perimeter. Analogously, there exist tilings with triangles of equal perimeter, the areas of which are bounded from below by a positive constant. This solves a problem of Nandakumar.