The purpose of this note is to give a methodologically simple proof of the undecidability of strong normalisation in the pure lambda calculus. For this we show how to represent an arbitrary partial recursive function by a term whose application to any Church numeral is either strongly normalizable or has no normal form. Intersection types are used for the strong normalization argument.

The intersection-types discipline for λ-calculus was introduced in Coppo and Dezani-Ciancaglini (1980) as an extension of Curry's type assignment system. The motivation was essentially to increase the class of terms possessing types. Indeed, it turned out that this discipline can assign types to all and only the strongly normalising terms. This is largely a folklore result; the first published proof appears in Pottinger (1980). Subsequently, the intersection-types discipline was used in Barendregt et al. (1983) as a tool for proving Scott's conjecture concerning the completeness of the set-theoretic semantics for simple types.

We consider a continuously monitored system that gradually and stochastically deteriorates. An alarm threshold is set on the system deterioration level for triggering a delayed preventive maintenance operation. A mathematical model is developed to find the value of the alarm threshold that minimizes the asymptotic unavailability. Approximations are derived to improve the numerical optimization.

In this article, we consider a discrete-time insurance risk model. An autoregressive model is used to model both the claim process and the premium process. The probability of ruin is examined in a model with a constant interest rate. Both exponential and nonexponential upper bounds are obtained for the ruin probability of an infinite time horizon.

In general, finite mixtures of distributions with increasing failure rates are not increasing. However, conditions have been given by Lynch [8] so that a mixture of distributions with increasing failure rates has increasing failure rate. We establish similar results for other standard classes and also give examples which show that although the assumptions are stringent, continuous mixtures of standard families of lifetime distributions do have increasing failure rates. We also show that the result of Lynch follows from Savits [12] and the techniques of the last-cited paper can be applied to other classes as well.

We describe a stochastic dynamic programming approach for “real option”-based valuation of electricity generation capacity incorporating operational constraints and start-up costs. Stochastic prices of electricity and fuel are represented by recombining multinomial trees. Generators are modeled as a strip of cross-commodity call options with a delay and a cost imposed on each option exercise. We illustrate implications of operational characteristics on the valuation of generation assets under different modeling assumptions about the energy commodity prices. We find that the impacts of operational constraints on real asset valuation are dependent on both the model specification and the nature of operating characteristics.

Stochastic discretization is a technique of representing a continuous random variable as a random sum of i.i.d. exponential random variables. In this article, we apply this technique to study the limiting behavior of a stochastic fluid model. Specifically, we consider an infinite-capacity fluid buffer, where the net input of fluid is regulated by a finite-state irreducible continuous-time Markov chain. Most long-run performance characteristics for such a fluid system can be expressed as the long-run average reward for a suitably chosen reward structure. In this article, we use stochastic discretization of the fluid content process to efficiently determine the long-run average reward. This method transforms the continuous-state Markov process describing the fluid model into a discrete-state quasi-birth–death process. Hence, standard tools, such as the matrix-geometric approach, become available for the analysis of the fluid buffer. To demonstrate this approach, we analyze the output of a buffer processing fluid from K sources on a first-come first-served basis.

We give a new characterization of the ruin probability of the classical insurance risk model and use it to obtain bounds on and a computational approach for evaluating this probability.

Simulation-based policy iteration (SBPI) is a modification of the policy iteration algorithm for computing optimal policies for Markov decision processes. At each iteration, rather than solving the average evaluation equations, SBPI employs simulation to estimate a solution to these equations. For recurrent average-reward Markov decision processes with finite state and action spaces, we provide easily verifiable conditions that ensure that simulation-based policy iteration almost-surely eventually never leaves the set of optimal decision rules. We analyze three simulation estimators for solutions to the average evaluation equations. Using our general results, we derive simple conditions on the simulation run lengths that guarantee the almost-sure convergence of the algorithm.

Inactivity time is a reliability conception dual to the residual life. In this article, we establish some stochastic comparisons on inactivity time and the residual life of series and parallel systems, respectively. Some applications are presented as well.

The objective of the paper is to present a method of designing geometrical parameters of 3-dof orientation mechanisms. The parameters are to be determined for a given workspace, which in this case is described as a set of angles of orientation. An algorithm is presented, based on the equations of constraints which makes it possible to obtain the parameters of a manipulator. whose workspace involves the specified taskspace.

ADVANCED NEURO-ROBOTICS

1. ‘Robo Rat' project

United States scientists from SUNY Downstate Medical Centre have reported on a Robo Rat project that they have initiated. In a research paper published in Nature (May, 2002) they describe some of their remarkable results. It may soon be possible, we are told, that because of their researches, a remote-controlled living ‘Robo Rat' could be involved in numerous and varied applications. Their work is a spin-off from research to give paralysed people the ability to move and feel artificial limbs. The report of the project presents their findings and described how five rats carrying a special backpack, which contained a battery, radio receiver and brain stimulator, were controlled by a human operator sitting up to 500 yards away. The human operator was able to make them weave in and out of obstacles and navigated them over a course. Instead of using the traditional methods ofanimal training which associated behaviour with rewards, the researchers directly stimulated the parts of the animals' brains that responded to the movements of their whiskers and to receiving rewards of food. Electrical signals were sent to parts of the brain and provided a virtual contact to the animal's whiskers, showing them which way the operator wished them to go. In their research paper it is shown how by stimulaling these ‘whisker centres' the rats could be steered and by stimulating the brain's reward centre, they could reinforce the correct behaviour.

The paper is aimed at generating optimal gait cycles in the sagittal plane of a biped, the locomotion system of which has anthropomorphic characteristics. Both single and double support phases are globally optimised, considering incompletely specified transition postural configurations from one phase to the other. An impactless heel-touch is prescribed. Full dynamic models are developed for both gait phases. They are completed by specific constraints attached to the unilaterality of contact with the supporting ground.

A parametric optimisation method is implemented. The biped joint coordinates are approximated by cubic splines functions connected at uniformly distributed knots along the motion time. The finite set of unknowns consists of the joint coordinate values at knots, some gait pattern parameters at phase transitions, and the motion time of each phase. The step length is adjusted to the prescribed gait speed by the optimisation process. Numerical simulations concerning slow and fast optimal gaits are presented and discussed.

A method for the time suboptimal control of an industrial manipulator that moves along a specified path while keeping its end-effector orientation unchanged is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in a case study to verify the method developed.

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.

This paper describes an adaptive S-curve used to recover a tool path upon a system crash in the Windows operating system (OS). For a mechanism such as a robot or machine tool, the joint values, being delivered as setpoints to the servo-controller, are dynamically recorded by the real-time operating system also residing on the computer. The real-time OS can control the abort and record pertinent motion data after Windows OS crash.

Upon system recovery, the recovery trajectory generator examines the setpoints intervals to determine the current slow joint. At every trajectory step, and for the current slow joint, the S-curve velocity profile applies the joint entry state (position, speed, acceleration, and jerk) to interpolate the motion between the setpoints in a reverse direction. The other joints are proportionally interpolated (slowed) so that they pass through each setpoint simultaneously with the slow joint, but in a reverse direction.

The trajectory algorithm is optimal since the slow joint always uses the maximum allowable jerk to change the profile speed and acceleration for each trajectory step.

The influence of ground irregularities on the behavior of a wheeled mobile robot (WMR) navigating on uneven surfaces is addressed. The paper studies the vibratory movements induced on the body of the WMR, in order to analyze its ability for carrying out on-board tasks, and on the accuracy of the data collected by its external sensorial systems. The adhesion capability of the wheels of the WMR on this uneven terrain is also studied, since it conditions the braking, traction and steering performance. The method is applied to the WMR RAM.

The purpose of the present study is to assess the influence of auditory and haptic signals on the manipulation performance in a virtual reality-based hand rehabilitation system. A personal computer, a tracker, and a data glove were included in this system. Three-dimensional virtual environments were developed. Forty volunteers were recruited to participate in a pick-and-place procedure, with three levels of difficulty and four feedback modes. Task time and collision frequency were the parameters used to evaluate their manipulation performance. It can be concluded that the haptics is a significant signal for improving a subject's performance at the high difficulty level.