On redundant topological constraints

© 2015 Elsevier B.V. All rights reserved. Redundancy checking is an important task in the research of knowledge representation and reasoning. In this paper, we consider redundant qualitative constraints. For a set Γ of qualitative constraints, we say a constraint (xRy) in Γ is redundant if it is entailed by the rest of Γ. A prime subnetwork of Γ is a subset of Γ which contains no redundant constraints and has the same solution set as Γ. It is natural to ask how to compute such a prime subnetwork, and when it is unique. We show that this problem is in general intractable, but becomes tractable if Γ is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of the Region Connection Calculus RCC8 in which weak composition distributes over nonempty intersections, then Γ has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from Γ. As a by-product, we show that any path-consistent network over such a distributive subalgebra is minimal and globally consistent in a qualitative sense. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms, especially in constraint networks with larger proportions of partial overlap relations

Irreducible Hamiltonian BRST approach to topologically coupled abelian forms

An irreducible Hamiltonian BRST approach to topologically coupled p- and (p+1)-forms is developed. The irreducible setting is enforced by means of constructing an irreducible Hamiltonian first-class model that is equivalent from the BRST point of view to the original redundant theory. The irreducible path integral can be brought to a manifestly Lorentz covariant form.Comment: 29 pages, LaTeX 2.0

Efficient Contact State Graph Generation for Assembly Applications

An important aspect in the design of many automated assembly strategies is the ability to automatically generate the set of contact states that may occur during an assembly task. In this paper, we present an efficient means of constructing the set of all geometrically feasible contact states that may occur within a bounded set of misalignments (bounds determined by robot inaccuracy). This set is stored as a graph, referred to as an Assembly Contact State Graph (ACSG), which indicates neighbor relationships between feasible states. An ACSG is constructed without user intervention in two stages. In the first stage, all hypothetical primitive principle contacts (PPCs; all contact states allowing 5 degrees of freedom) are evaluated for geometric feasibility with respect to part-imposed and robot-imposed restrictions on relative positioning (evaluated using optimization). In the second stage, the feasibility of each of the various combinations of PPCs is efficiently evaluated, first using topological existence and uniqueness criteria, then using part-imposed and robot-imposed geometric criteria

Foundations of Relational Particle Dynamics

Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as discussion of conceptual issues connected with the problem of time in quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces of shapes are n-spheres and complex projective spaces, from which knowledge I construct natural mechanics on these spaces. I also show that these coincide with Barbour's indirectly-constructed relational dynamics by performing a full reduction on the latter. Then the identification of the configuration spaces as n-spheres and complex projective spaces, for which spaces much mathematics is available, significantly advances the understanding of Barbour's relational theory in spatial dimensions 1 and 2. I also provide the parallel study of a new theory for which positon and scale are purely relative but orientation is absolute. The configuration space for this is an n-sphere regardless of the spatial dimension, which renders this theory a more tractable arena for investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update

Evolutionary constraints on the complexity of genetic regulatory networks allow predictions of the total number of genetic interactions

Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete. In this study, we analyzed the distribution of GRN structural properties across a large set of distinct prokaryotic organisms and found a set of constrained characteristics such as network density and number of regulators. Our results allowed us to estimate the number of interactions that complete networks would have, a valuable insight that could aid in the daunting task of network curation, prediction, and validation. Using state-of-the-art statistical approaches, we also provided new evidence to settle a previously stated controversy that raised the possibility of complete biological networks being random and therefore attributing the observed scale-free properties to an artifact emerging from the sampling process during network discovery. Furthermore, we identified a set of properties that enabled us to assess the consistency of the connectivity distribution for various GRNs against different alternative statistical distributions. Our results favor the hypothesis that highly connected nodes (hubs) are not a consequence of network incompleteness. Finally, an interaction coverage computed for the GRNs as a proxy for completeness revealed that high-throughput based reconstructions of GRNs could yield biased networks with a low average clustering coefficient, showing that classical targeted discovery of interactions is still needed.Comment: 28 pages, 5 figures, 12 pages supplementary informatio

Efficiently characterizing non-redundant constraints in large real world qualitative spatial networks

RCC8 is a constraint language that serves for qualitative spatial representation and reasoning by encoding the topological relations between spatial entities. We focus on efficiently characterizing non-redundant constraints in large real world RCC8 networks and obtaining their prime networks. For a RCC8 network N a constraint is redundant, if removing that constraint from N does not change the solution set of N. A prime network of N is a network which contains no redundant constraints, but has the same solution set as N. We make use of a particular partial consistency, namely, G⋄-consistency, and obtain new complexity results for various cases of RCC8 networks, while we also show that given a maximal distributive subclass for RCC8 and a network N defined on that subclass, the prunning capacity of G⋄-consistency and ⋄-consistency is identical on the common edges of G and the complete graph of N, when G is a triangulation of the constraint graph of N. Finally, we devise an algorithm based on G⋄-consistency to compute the unique prime network of a RCC8 network, and show that it significantly progresses the state-of-the-art for practical reasoning with real RCC8 networks scaling up to millions of nodes