Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

Neural basis of route-planning and goal-coding during flexible navigation

Animals and humans are remarkable in their ability to flexibly adapt to changes in their surroundings. Navigational flexibility may take many forms and in this thesis we investigate its neural and behavioral underpinnings using a variety of methods and tasks tailored to each specific research aim. These methods include functional resonance magnetic imaging (fMRI), freely moving virtual reality, desktop virtual reality, large-scale online testing, and computational modelling. First, we reanalysed previously collected rodent data in the lab to better under- stand behavioural bias that may occur during goal-directed navigation tasks. Based on finding some biases we designed a new approach of simulating results on maze configurations prior to data collection to select the ideal mazes for our task. In a parallel line of methods development, we designed a freely moving navigation task using large-scale wireless virtual reality in a 10x10 space. We compared human behaviour to that of a select number of reinforcement learning agents to investigate the feasibility of computational modelling approaches to freely moving behaviour. Second, we further developed our new approach of simulating results on maze configuration to design a novel spatial navigation task used in a parallel experiment in both rats and humans. We report the human findings using desktop virtual reality and fMRI. We identified a network of regions including hippocampal, caudate nu- cleus, and lateral orbitofrontal cortex involvement in learning hidden goal locations. We also identified a positive correlation between Euclidean goal distance and brain activity in the caudate nucleus during ongoing navigation. Third, we developed a large online testing paradigm to investigate the role of home environment on wayfinding ability. We extended previous reports that street network complexity is beneficial in improving wayfinding ability as measured using a previously reported virtual navigation game, Sea Hero Quest, as well as in a novel virtual navigation game, City Hero Quest. We also report results of a navigational strategies questionnaire that highlights differences of growing up inside and outside cities in the United States and how this relates to wayfinding ability. Fourth, we investigate route planning in a group of expert navigators, licensed London taxi drivers. We designed a novel mental route planning task, probing 120 different routes throughout the extensive street network of London. We find hip- pocampal and retrosplenial involvement in route planning. We also identify the frontopolar cortex as one of several brain regions parametrically modulated by plan- ning demand. Lastly, I summarize the findings from these studies and how they all come to provide different insights into our remarkable ability to flexibly adapt to naviga- tional challenges in our environment

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..