Coverage and Vacuity in Network Formation Games

The frameworks of coverage and vacuity in formal verification analyze the effect of mutations applied to systems or their specifications. We adopt these notions to network formation games, analyzing the effect of a change in the cost of a resource. We consider two measures to be affected: the cost of the Social Optimum and extremums of costs of Nash Equilibria. Our results offer a formal framework to the effect of mutations in network formation games and include a complexity analysis of related decision problems. They also tighten the relation between algorithmic game theory and formal verification, suggesting refined definitions of coverage and vacuity for the latter

The local structure of n-Poisson and n-Jacobi manifolds

N-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied. Necessary and sufficient conditions for the sum and the wedge product of two $n$-Poisson sructures to be again a multi-Poisson are found. It is proven that the canonical $n$-vector on the dual of an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The problem of compatibility of two n-Lie algebra structures is analyzed and the compatibility relations connecting hereditary structures of a given n-Lie algebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their "elementary particle-like" structure is discovered. Some simple applications to dynamics are discussed.Comment: 45 pages, latex, no figure

A General Framework for Representing, Reasoning and Querying with Annotated Semantic Web Data

We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the web. We formalise the annotated language, the corresponding deductive system and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g. temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language -- AnQL -- that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions

Trust networks for recommender systems

Recommender systems use information about their user’s profiles and relationships to suggest items that might be of interest to them. Recommenders that incorporate a social trust network among their users have the potential to make more personalized recommendations compared to traditional systems, provided they succeed in utilizing the additional (dis)trust information to their advantage. Such trust-enhanced recommenders consist of two main components: recommendation technologies and trust metrics (techniques which aim to estimate the trust between two unknown users.) We introduce a new bilattice-based model that considers trust and distrust as two different but dependent components, and study the accompanying trust metrics. Two of their key building blocks are trust propagation and aggregation. If user a wants to form an opinion about an unknown user x, a can contact one of his acquaintances, who can contact another one, etc., until a user is reached who is connected with x (propagation). Since a will often contact several persons, one also needs a mechanism to combine the trust scores that result from several propagation paths (aggregation). We introduce new fuzzy logic propagation operators and focus on the potential of OWA strategies and the effect of knowledge defects. Our experiments demonstrate that propagators that actively incorporate distrust are more accurate than standard approaches, and that new aggregators result in better predictions than purely bilattice-based operators. In the second part of the dissertation, we focus on the application of trust networks in recommender systems. After the introduction of a new detection measure for controversial items, we show that trust-based approaches are more effective than baselines. We also propose a new algorithm that achieves an immediate high coverage while the accuracy remains adequate. Furthermore, we also provide the first experimental study on the potential of distrust in a memory-based collaborative filtering recommendation process. Finally, we also study the user cold start problem; we propose to identify key figures in the network, and to suggest them as possible connection points for newcomers. Our experiments show that it is much more beneficial for a new user to connect to an identified key figure instead of making random connections