The Category of Mereotopology and Its Ontological Consequences

We introduce the category of mereotopology Mtop as an alternative category to that of topology Top, stating ontological consequences throughout. We consider entities such as boundaries utilizing Brentano’s thesis and holes utilizing homotopy theory with a rigorous proof of Hausdorff Spaces satisfying [GEM]TC axioms. Lastly, we mention further areas of study in this category

Towards a Semantic-based Approach for Modeling Regulatory Documents in Building Industry

Regulations in the Building Industry are becoming increasingly complex and involve more than one technical area. They cover products, components and project implementation. They also play an important role to ensure the quality of a building, and to minimize its environmental impact. In this paper, we are particularly interested in the modeling of the regulatory constraints derived from the Technical Guides issued by CSTB and used to validate Technical Assessments. We first describe our approach for modeling regulatory constraints in the SBVR language, and formalizing them in the SPARQL language. Second, we describe how we model the processes of compliance checking described in the CSTB Technical Guides. Third, we show how we implement these processes to assist industrials in drafting Technical Documents in order to acquire a Technical Assessment; a compliance report is automatically generated to explain the compliance or noncompliance of this Technical Documents

Attack-Resilient Sensor Fusion

This work considers the problem of attack-resilient sensor fusion in an autonomous system where multiple sensors measure the same physical variable. A malicious attacker may corrupt a subset of these sensors and send wrong measurements to the controller on their behalf, potentially compromising the safety of the system. We formalize the goals and constraints of such an attacker who also wants to avoid detection by the system. We argue that the attacker’s capabilities depend on the amount of information she has about the correct sensors’ measurements. In the presence of a shared bus where messages are broadcast to all components connected to the network, the attacker may consider all other measurements before sending her own in order to achieve maximal impact. Consequently, we investigate effects of communication schedules on sensor fusion performance. We provide worst- and average-case results in support of the Ascending schedule, where sensors send their measurements in a fixed succession based on their precision, starting from the most precise sensors. Finally, we provide a case study to illustrate the use of this approach

Protected gates for topological quantum field theories

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons; in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.Comment: 50 pages, many figures, v3: updated to match published versio