In this paper we are concerned with the following conjecture.

Conjecture. For any positive integers n and k satisfying k < n, and any sequence a1, a2, … ak of not necessarily distinct elements of Zn, there exists a permutation π ∈ Sk such that the elements aπ(i)+i are all distinct modulo n.

We prove this conjecture when 2k [les ] n+1. We then apply this result to tree embeddings. Specifically, we show that, if T is a tree with n edges and radius r, then T decomposes Kt for some t [les ] 32(2r+4)n2+1.

Häggkvist and Scott asked whether one can find a quadratic function q(k) such that, if G is a graph of minimum degree at least q(k), then G contains vertex-disjoint cycles of k consecutive even lengths. In this paper, it is shown that if G is a graph of average degree at least k2+19k+10 with sufficiently many vertices, then G contains vertex-disjoint cycles of k consecutive even lengths, answering the above question in the affirmative. The coefficient of k2 cannot be decreased and, in this sense, this result is best possible.

In this paper, we take a detailed look at the performance of components of an idealized question answering system on two different tasks: the TREC Question Answering task and a set of reading comprehension exams. We carry out three types of analysis: inherent properties of the data, feature analysis, and performance bounds. Based on these analyses we explain some of the performance results of the current generation of Q/A systems and make predictions on future work. In particular, we present four findings: (1) Q/A system performance is correlated with answer repetition; (2) relative overlap scores are more effective than absolute overlap scores; (3) equivalence classes on scoring functions can be used to quantify performance bounds; and (4) perfect answer typing still leaves a great deal of ambiguity for a Q/A system because sentences often contain several items of the same type.

We consider the problem of sampling ‘unlabelled structures’, i.e., sampling combinatorial structures modulo a group of symmetries. The main tool which has been used for this sampling problem is Burnside’s lemma. In situations where a significant proportion of the structures have no nontrivial symmetries, it is already fairly well understood how to apply this tool. More generally, it is possible to obtain nearly uniform samples by simulating a Markov chain that we call the Burnside process: this is a random walk on a bipartite graph which essentially implements Burnside’s lemma. For this approach to be feasible, the Markov chain ought to be ‘rapidly mixing’, i.e., converge rapidly to equilibrium. The Burnside process was known to be rapidly mixing for some special groups, and it has even been implemented in some computational group theory algorithms. In this paper, we show that the Burnside process is not rapidly mixing in general. In particular, we construct an infinite family of permutation groups for which we show that the mixing time is exponential in the degree of the group.

For a stochastic approximation-type recursion with finitely many possible limit points, we find a lower bound on the probability of converging to a prescribed point in its ‘domain of attraction’. This has implications for the lock-in phenomena in the stochastic models of increasing return economics and the sample complexity of stochastic approximation algorithms in engineering.

Suppose that G is a graph with maximum degree d(G) such that, for every vertex v in G, the neighbourhood of v contains at most d(G)2/f (f > 1) edges. We show that the list chromatic number of G is at most Kd(G)/log f, for some positive constant K. This result is sharp up to the multiplicative constant K and strengthens previous results by Kim [9], Johansson [7], Alon, Krivelevich and Sudakov [3], and the present author [18]. This also motivates several interesting questions.

As an application, we derive several upper bounds for the strong (list) chromatic index of a graph, under various assumptions. These bounds extend earlier results by Faudree, Gyárfás, Schelp and Tuza [6] and Mahdian [13] and determine, up to a constant factor, the strong (list) chromatic index of a random graph. Another application is an extension of a result of Kostochka and Steibitz [10] concerning the structure of list critical graphs.

This paper presents an investigation into the development of parametric and non-parametric approaches for dynamic modelling of a flexible manipulator system. The least mean squares, recursive least squares and genetic algorithms are used to obtain linear parametric models of the system. Moreover, non-parametric models of the system are developed using a non-linear AutoRegressive process with eXogeneous input model structure with multi-layered perceptron and radial basis function neural networks. The system is in each case modelled from the input torque to hub-angle, hub-velocity and end-point acceleration outputs. The models are validated using several validation tests. Finally, a comparative assessment of the approaches used is presented and discussed in terms of accuracy, efficiency and estimation of the vibration modes of the system.

This paper rechecks the relative degree of the end-point tracking control system of a flexible manipulator.New added insights into the ill-defined behavior of the relative degree are presented by constructing a perturbed truncation model. The implications for the inverse dynamics motivate us to reformulate the inverse dynamics based on the perturbed truncation model in the extreme case of truncating all of the flexible modes. New potential advantages arising from this novel formulation are investigated for the inverse dynamics control design as well.

In this paper we propose an analytical formulation for simulation and design of a one d.o.f. articulated finger mechanism with three phalanges. The formulation is based on a study of the design and operation of an index human finger. In particular, we have proposed a suitable mechanical design for an anthropomorphic finger as both an approximation of human architecture and an easy practical design. Kinematic characteristics are illustrated with numerical examples.

This paper discusses the problem of stable grasping and object manipulation by a pair of robot fingers when fingertips are covered with soft compressible material and fingers are allowed to incline their last link against the object surface. The area contact between the fingertips and the rigid object surface leads to nonholonomic constraints even for the planar case; however, the variational principle can be applied and the equation of motion is derived as a set of nonlinear differential equations with extra terms of Langrange multipliers incorporating the constraints. The proposed feedback controller is a linear combination of simple feedback control signals each designed for realizing grasp stabilization, regulation of object rotation and regulation of object position respectively. The controller is shown to achieve asymptotic convergence to the desired state at a stable grasping configuration. Simulation results are presented confirming the theoretical findings.

Since a slave manipulator with a high reduction ratio joint generally has slow dynamics in comparison with a master manipulator in telemanipulation systems, its control input is likely to be saturated resulting in poor position tracking performance and deteriorated stability. This paper proposes a force reflecting control scheme for telemanipulators with a high reduction ratio joint, which can effectively compensate the control input saturation caused by the high ratio gear reducer at its joint. The proposed scheme is also shown to guarantee the stability and provides an excellent position tracking performance regardless of the saturation.

This paper concerns the issue of mechanism design of a simplified 6-DOF 6-RUS parallel manipulator. The design of robotic mechanisms, especially for 6-DOF parallel manipulators, is an important and challenging problem in the field of robotics. This paper presents a design method for robotic mechanisms, which is based on the physical model of the solution space. The physical model of the solution space, which can transfer a multi-dimensional problem to a two or three-dimensional one, is a useful tool to obtain all kinds of performance atlases. In this paper, the physical model of the solution space for spatial 6-RUS (R stands for revolute joint, U universal joint and S spherical joint) parallel manipulators is established. The atlases of performances, such as workspace and global conditioning index, are plotted in the physical model of the solution space. The atlases are useful for the mechanism design of the 6-RUS parallel manipulators. The technique used in this paper can be applied to the design of other robots.

In this paper, two algorithms for solving the Inverse Dynamic Problem based on the Gibbs-Appell equations are proposed and verified. Both are developed using mainly vectorial variables, and the equations are expressed in a recursive form. The first algorithm has a computational complexity of O(n2)and is the least efficient of the two; the second algorithm has a computational complexity of O(n). This algorithm will be compared with one based on Newton-Euler equations of motion, formulated in a similar way, and using mainly vectors in its recursive formulation. The O(n) proposed algorithm will be used to solve the Inverse Dynamic Problem in a PUMA industrial robot.

This paper presents a neural model to solve the visual-tactile-motor coordination problem in robotic applications. The proposed neural controller is based on the VAMC (Vector Associative Map) model. This algorithm is based on the human biological system and has the ability of learning the mapping that establishes the relationship between the spatial and the motor coordinates. These spatial inputs are composed of visual and force parameters. The LINCE stereohead carries out a visual detection process, detecting the positions of the object and of the manipulator. The artificial tactile skins placed over the two fingers of the gripper measure the force distribution when an object is touched. The neural controller has been implemented for robotic operations of reaching and object grasping. The reaching process is fed back in order to minimize the Difference Vector (DV) between the visual projections of the object and the manipulator. The stable grasping task processes the force distribution maps detected in the contact with the two surfaces of the gripper, in order to direct the object into the robotic fingers. Experimental results have demonstrated the robustness of the model and the accuracy of the final pick-and-place process.

This paper addresses the problem of finding a nonholonomic path subject to a curvature restriction, to be tracked by a wheeled autonomous navigation vehicle. This robot is able to navigate in a structured environment, with obstacles modeled as polygons, thus constituting a model based system. The path planning methodology begins with the conditioning of the polygonal environment by offsetting each polygon in order to avoid the possibility of collision with the mobile. Next, the modified polygonal environment is used to compute a preliminary shortest path (PA) between the two extreme positions of the trajectory in the plane (x, y). This preliminary path (PA) does not yet consider the restrictions on the curvature and is formed only by straight line segments. A smoothing process follows in order to obtain a path (PS) that satisfies curvature restrictions which consist basically of joining the straight line segments by circular arcs of minimum radius R (filleting). Finally, the initial and final orientation of the vehicle are accounted for. This is done using a technique we have called the Star Algorithm, because of the geometric shape of the resulting maneuvers. A final complete path (PC) is thus obtained.

Modern industry is concerned about extending the lifetime of its critical processes and maintaining them only when required. Significant aspects of these trends include the ability to diagnose impending failures, prognosticate the remaining useful lifetime of the process and schedule maintenance operations so that uptime is maximized. Prognosis is probably the most difficult of the three issues leading to condition-based maintenance (CBM). This paper attempts to address this challenging problem with intelligence-oriented techniques, specifically dynamic wavelet neural networks (DWNNs). DWNNs incorporate temporal information and storage capacity into their functionality so that they can predict into the future, carrying out fault prognostic tasks. Such fundamental issues as the network structure, learning algorithms, stability analysis, uncertainty management, and performance assessment are studied in a theoretical framework. An example is presented in which a trained DWNN successfully prognoses a defective bearing with a crack in its inner race.

We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules (i.e., the driving direction on the infrastructure is switched between two directions according to a fixed time schedule). We analyze both symmetric and asymmetric systems (i.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random setup times and periodic (nonexhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1–2% for Poisson arrivals. Also, we indicate how our approximations can be generalized to compound Poisson arrivals.

This article studies the geometric convergence rate of a discrete renewal sequence with decreasing hazard rate or, more generally, new worse than used lifetimes. Several variants of these structural orderings are considered. The results are derived from power series methods; roots of generating functions are the prominent issue. Optimality of the rates are considered. Examples demonstrating the utility of the results, as well as applications to Markov chains, are presented.