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    ABSTRACT: The work presented in this papers is directed at mechanisms where by 3D surfaces can be represented to support the generation and application of classification techniques. Three different mechanisms are presented to allow for the representation of 3D surfaces in such a way that key features are retained while at the same time ensuring compatibility with prediction (classification) techniques. The three representation techniques are: (i) Local Geometry Matrices (LGMs) founded on the concept of local binary patterns, (ii) Local Distance Measure (LDM) founded on the idea that distances from edges (critical points) may be significant, and (iii) Point Series (PS) whereby local geometries are represented in terms of a linearisation of space. The representations are designed to capture the nature of 3D surfaces in terms of their local geometry and predict class labels associated with such local geometries. To act as a focus for the work the prediction of “springback” within the context of sheet metal forming is considered, where springback is a form of deformation that occurs (in a non-uniform manner) across a manufactured 3D surface as a result of the application of some sheet metal forming process. The evaluation of each of the techniques, and variations thereof, using sheet metal parts that have been manufactured especially for the purpose, is fully described. The paper also reports on a statistical significance test concerning the results.
    No preview · Article · Jan 2015 · Expert Systems with Applications
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    ABSTRACT: Model checking is a well-established technique for the formal verification of concurrent and distributed systems. In recent years, model checking has been extended and adapted for multi-agent systems, primarily to enable the formal analysis of belief–desire–intention systems. While this has been successful, there is a need for more complex logical frameworks in order to verify realistic multi-agent systems. In particular, probabilistic and real-time aspects, as well as knowledge, belief, goals, etc., are required. However, the development of new model checking tools for complex combinations of logics is both difficult and time consuming. In this article, we show how model checkers for the constituent temporal, probabilistic, and real-time logics can be re-used in a modular way when we consider combined logics involving different dimensions. This avoids the re-implementation of model checking procedures. We define a modular approach, prove its correctness, establish its complexity, and show how it can be used to describe existing combined approaches and define yet-unimplemented combinations. We also demonstrate the feasibility of our approach on a case study.
    Full-text · Article · Sep 2013 · Theoretical Computer Science
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    ABSTRACT: We investigate the computational complexity of the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly $r > 1$ countries each. We prove that the problem can be solved in polynomial time using $s$ colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than $s/r$. However, if $s \geq 3$, the problem is NP-hard even if the graph is a forest of paths of arbitrary lengths (for any $r \geq 2$, provided $s < 2r - \sqrt{2r + 1/4+ 3/2). Furthermore we obtain a complete characterization of the problem's complexity for the case when the input graph is a tree, whereas our result for arbitrary planar graphs fall just short of a similar dichotomy. Specifically, we prove that the empire colouring problem is NP-hard for trees, for any $r \geq 2$, if $3 \leq s \leq 2r-1$ (and polynomial time solvable otherwise). For arbitrary planar graphs we prove NP-hardness if $s<7$ for $r=2$, and $s < 6r-3$, for $r \geq 3$. The result for planar graphs also proves the NP-hardness of colouring with less than 7 colours graphs of thickness two and less than $6r-3$ colours graphs of thickness $r \geq 3$.
    Preview · Article · Jun 2013 · Discrete Mathematics
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