We analyse classes of planar graphs with respect to various properties such as polynomial-time solvability of the dominating set problem or boundedness of the tree-width. A helpful tool to address this question is the notion of boundary classes. The main result of the paper is that for many important properties there are exactly two boundary classes of planar graphs.

In order to widen the potentialities of manipulation of the Laboratoire de Mécanique des solides (LMS) mechanical hand, we developed a new planning approach based on the use of a specific exoskeleton. This one has kinematics architecture and dimensions identical to the mechanical hand. This feature allows us to obtain manipulation trajectories for the mechanical hand, very easily and very quickly, by using the exoskeleton, without complex calibration. Manipulation's trajectories are replayed offline with an autonomous control, and, consequently, the exoskeleton is not used with any feedback strategy for telemanipulation. This paper presents the characteristics of this exoskeleton and the graphic interface that we developed. This one uses a method to determine the object's evolution during the manipulation with the exoskeleton, without using exteroceptive sensors. This new approach was tested for standard trajectories by simulation on a Computer-aided design (CAD) robotics system and by using the mechanical hand. Thus, we validate the use concept of an isomorphic exoskeleton to mechanical hand for manipulation planning with the LMS mechanical hand.

This paper reports the design of sliding-mode control laws for controlling multiple small-sized autonomous helicopters in arbitrary formations. Two control schemes, which are required for defining arbitrary three-dimensional formation meshes, are discussed. In the presented leader–follower formation control schemes, each helicopter only needs to receive motion information from at most two neighboring helicopters. A nonlinear six-degree-of-freedom dynamic model has been used for each helicopter. Four control inputs, the main and the tail rotor thrusts, and the roll and pitch moments, are assumed. Parameter uncertainty in the dynamic model and wind disturbance are considered in designing the controllers. The effectiveness and robustness of these control laws in the presence of parameter uncertainty in the dynamic model and wind disturbances are demonstrated by computer simulations.

Let G be a graph with n vertices, and let k be an integer dividing n. G is said to be strongly k-colourable if, for every partition of V(G) into disjoint sets V1 ∪ ··· ∪ Vr, all of size exactly k, there exists a proper vertex k-colouring of G with each colour appearing exactly once in each Vi. In the case when k does not divide n, G is defined to be strongly k-colourable if the graph obtained by adding isolated vertices is strongly k-colourable. The strong chromatic number of G is the minimum k for which G is strongly k-colourable. In this paper, we study the behaviour of this parameter for the random graph Gn,p. In the dense case when p ≫ n−1/3, we prove that the strong chromatic number is a.s. concentrated on one value Δ + 1, where Δ is the maximum degree of the graph. We also obtain several weaker results for sparse random graphs.

In this paper, a novel algorithm is formulated and implemented for optimum path planning of parallel manipulators. A multi-objective optimisation problem has been formulated for an efficient numerical solution procedure through kinematic and dynamic features of manipulator operation. Computational economy has been obtained by properly using a genetic algorithm to search an optimal solution for path spline-functions. Numerical characteristics of the numerical solving procedure have been outlined through a numerical example applied to Cassino Parallel Manipulator (CaPaMan) both for path planning and design purposes.

The state-of-the-art FastSLAM algorithm has been shown to cause a particle depletion problem while performing simultaneous localization and mapping for mobile robots. As a result, it always produces over-confident estimates of uncertainty as time progresses. This particle depletion problem is mainly due to the resampling process in FastSLAM, which tends to eliminate particles with low weights. Therefore, the number of particles to conduct loop-closure decreases, which makes the performance of FastSLAM degenerate. The resampling process has not been thoroughly analyzed even though it is the main reason for the particle depletion problem. In this paper, standard resampling algorithms (systematic residual and partial resampling), a rank-based resampling adopting genetic algorithms are analyzed using computer simulations. Several performance measures such as the effective sample size, the number of distinct particles, estimation errors, and complexity are used for the thorough analysis of the resampling algorithms. Moreover, a new compensation technique is proposed instead of resampling to resolve the particle depletion problem in FastSLAM. In estimation errors, the compensation technique outperformed other resampling algorithms though its run-time was longer than those of others. The most appropriate time to instigate compensation to reduce the run-time was also analyzed with the diminishing number of particles.

This paper suggests a generalized approach to the mathematical modeling of biped locomotion systems (humans or humanoid robots) with special attention paid to impact and contact dynamics. Instead of the usual inductive approach that starts from the analysis of different situations of real motion (walking, running, jumping, climbing the stairs, etc.) and tries to make a generalization, a deductive approach is pursued, whereby an entirely general problem is considered. Impact dynamics is modeled applying the linear complementarity problem (LCP) formulation. General methodology is explained and demonstrated via the synthesis of a spatial biped model. The validity of the modeling approach is proved by experimental measurements on a human subject in the laboratory conditions. Plenty of graphic presentations illustrating experimental results, as well as the results of the corresponding simulation tests are shown.

Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q provide the same output, that is, they have the same answer sets. Notions in between strong and ordinary equivalence have been introduced as theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programs R or by bounding the set of atoms allowed to occur in R (relativized equivalence). For the latter approach, different yield properly different equivalence notions, in general. For the former approach, however, it turned out that any “reasonable” syntactic restriction to R coincides with either ordinary, strong, or uniform equivalence (for uniform equivalence, the context ranges over arbitrary sets of facts, rather than program rules). In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by bounding, on the one hand, the atoms which are allowed to occur in the rule heads of the context and, on the other hand, the atoms which are allowed to occur in the rule bodies of the context. We introduce a general semantical characterization which includes known ones as SE-models (for strong equivalence) or UE-models (for uniform equivalence) as special cases. Moreover, we provide complexity bounds for the problem in question and sketch a possible implementation method making use of dedicated systems for checking ordinary equivalence.

We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the generalization involves nondeterminism. Our main results demonstrate that our formalism is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with weight atoms lparse programs) with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.

Semi-graphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group Sn. In this paper we resolve two problems on semi-graphoids posed in Studený's book (2005), and we answer a related question of Postnikov, Reiner and Williams on generalized permutohedra. We also study the semigroup and the toric ideal associated with semi-graphoids.

A proper vertex colouring of a graph is equitable if the sizes of colour classes differ by at most one. We present a new shorter proof of the celebrated Hajnal–Szemerédi theorem: for every positive integer r, every graph with maximum degree at most r has an equitable colouring with r+1 colours. The proof yields a polynomial time algorithm for such colourings.

This investigation describes the mechanical configuration and control environment for a novel cart-seesaw system. This mechanism is called a super articulated mechanical system (SAMS). The system comprises a cart that slides on the pneumatic rodless cylinder. The rodless cylinder is double-acting with the carrier bracket, on which a cart is a pinion mechanism for the tracks. The cart-seesaw system brings the cart from any initial position to a desired position on the seesaw by applying an appropriate force to the cart and thus adjusting the angle of the seesaw. The position of a cart denotes the first degree of freedom, which is activated by a pneumatic proportional valve, and the angle of the seesaw indicates the second degree of freedom that is not actuated. Consequently, the proposed new pneumatic cart-seesaw system is straightforward to construct and direct to operate in different scenarios of performance. A state feedback controller is applied for stabilization of the equilibrium point of the system. Moreover, this study adds a supervisory controller that takes control action in extreme situations. Test results reveal excellent properties in control performance. The proposed product can be extensively applied in SAMS and pneumatic control for robotics control laboratory.

We prove tail estimates for variables of the form ∑if(Xi), where (Xi)i is a sequence of states drawn from a reversible Markov chain, or, equivalently, from a random walk on an undirected graph. The estimates are in terms of the range of the function f, its variance, and the spectrum of the graph. The purpose of our estimates is to determine the number of chain/walk samples which are required for approximating the expectation of a distribution on vertices of a graph, especially an expander. The estimates must therefore provide information for fixed number of samples (as in Gillman's [4]) rather than just asymptotic information. Our proofs are more elementary than other proofs in the literature, and our results are sharper. We obtain Bernstein- and Bennett-type inequalities, as well as an inequality for sub-Gaussian variables.

We prove that the chromatic polynomial of a finite graph of maximal degree Δ is free of zeros for |q| ≥ C*(Δ) withThis improves results by Sokal and Borgs. Furthermore, we present a strengthening of this condition for graphs with no triangle-free vertices.

This paper shows how type effect systems can be combined with model-checking techniques to produce powerful, automatically verifiable program logics for higher order programs. The properties verified are based on the ordered sequence of events that occur during program execution, so-called event traces. Our type and effect systems infer conservative approximations of the event traces arising at run-time, and model-checking techniques are used to verify logical properties of these histories. Our language model is based on the λ-calculus. Technical results include a type inference algorithm for a polymorphic type effect system, and a method for applying known model-checking techniques to the trace effects inferred by the type inference algorithm, allowing static enforcement of history- and stack-based security mechanisms. A type safety result is proven for both unification and subtyping constraint versions of the type system, ensuring that statically well-typed programs do not contain trace event checks that can fail at run-time.

We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph have no component with more than k vertices. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n → ∞, then the number in question is essentially the same for all values of k that satisfy both k → ∞ and k =o(n).

Context modeling has long been acknowledged as a key aspect in a wide variety of problem domains. In this paper we focus on the combination of contextualization and personalization methods to improve the performance of personalized information retrieval. The key aspects in our proposed approach are (1) the explicit distinction between historic user context and live user context, (2) the use of ontology-driven representations of the domain of discourse, as a common, enriched representational ground for content meaning, user interests, and contextual conditions, enabling the definition of effective means to relate the three of them, and (3) the introduction of fuzzy representations as an instrument to properly handle the uncertainty and imprecision involved in the automatic interpretation of meanings, user attention, and user wishes. Based on a formal grounding at the representational level, we propose methods for the automatic extraction of persistent semantic user preferences, and live, ad-hoc user interests, which are combined in order to improve the accuracy and reliability of personalization for retrieval.

Human categorization is neither a binary nor a context-free process. Rather, the criteria that govern the use and recognition of certain concepts may be satisfied to different degrees in different contexts. In light of this reality, the idealized, static structure of a lexical-ontology like WordNet appears both excessively rigid and unduly fragile when faced with real texts that draw upon different contexts to communicate different world-views. In this paper we describe a syntagmatic, corpus-based approach to redefining the concepts of a lexical-ontology like WordNet in a functional, gradable and context-sensitive fashion. We describe how the most diagnostic properties of concepts, on which these functional definitions are based, can be automatically acquired from the Web, and demonstrate how these properties are more predictive of how concepts are actually used and perceived than properties derived from other sources (such as WordNet itself).