Okasaki introduced the canonical formulation of functional red-black trees when he gave a concise, elegant method of persistent element insertion. Persistent element deletion, on the other hand, has not enjoyed the same treatment. For this reason, many functional implementations simply omit persistent deletion. Those that include deletion typically take one of two approaches. The more-common approach is a superficial translation of the standard imperative algorithm. The resulting algorithm has functional airs but remains clumsy and verbose, characteristic of its imperative heritage. (Indeed, even the term insertion is a holdover from imperative origins, but is now established in functional contexts. Accordingly, we use the term deletion which has the same connotation.) The less-common approach leverages the features of advanced type systems, which obscures the essence of the algorithm. Nevertheless, foreign-language implementors reference such implementations and, apparently unable to tease apart the algorithm and its type specification, transliterate the entirety unnecessarily. Our goal is to provide for persistent deletion what Okasaki did for insertion: a succinct, comprehensible method that will liberate implementors. We conceptually simplify deletion by temporarily introducing a “double-black” color into Okasaki's tree type. This third color, with its natural interpretation, significantly simplifies the preservation of invariants during deletion.

In this paper the control of flexible-joint manipulators while explicitly avoiding actuator saturation is considered. The controllers investigated are composed of a bounded proportional control term and a Hammerstein strictly positive real angular rate control term. This control structure ensures that the total torque demanded of each actuator is bounded by a value that is less than the maximum torque that each actuator is able to provide, thereby disallowing actuator saturation. The proposed controllers are shown to render the closed-loop system asymptotically stable, even in the presence of modeling uncertainties. The performance of the controllers is demonstrated experimentally and in simulation.

Particle swarm optimization (PSO) is a heuristic optimization algorithm and is commonly used for the tuning of PD/PID-type controllers. In this paper, PSO is applied for control gain tuning of a position domain PID controller in order to improve contour tracking performances of linear and nonlinear contours for a serial multi-DOF robotic manipulator. A new fitness function is proposed for gain tuning based on the statistics of the contour error, and pre-existed fitness functions are also applied for the optimization process, followed by some comparison studies. The PSO tuning technique demonstrated the same effectiveness in position domain controllers as in time domain controllers with the results being quite satisfying with low contour errors for both linear and nonlinear contours, and the proposed fitness function is proved to be on par with the pre-existed fitness functions.

Recently, small-sized compact electric vehicles have been in demand for short-distance travel in urban areas, although battery charging in electric vehicles present in the market is still problematic. Borrowing from the concept of a mobile inverted pendulum system, in this paper, a two-wheel robotic vehicle system is implemented and controlled as the future personal transportation device called the TransBOT. The TransBOT has two driving modes: a regular vehicle mode, where stable contact on the ground is maintained by two wheels and two casters, and the balancing mode, which maintains the stable posture with two wheels on the ground. The two-wheel balancing mechanism can be used as a transportation vehicle in narrow and busy urban areas. Gain scheduling control methods based on linear controllers are used for different drivers. In addition, desired balancing angles are specified for the different sizes of drivers in order to have a stable balancing control performance. These desired balancing angle values have been found by empirical studies. Experimental studies with drivers of different weights, as well as indoor and outdoor driving tasks, were conducted to ensure the feasibility of TransBOT.

Although proprioceptive impairment is likely to affect in a significant manner the capacity of stroke patients to recover functionality of upper limb, clinical assessment methods currently in use are rather crude, with a low level of reliability and a limited capacity to discriminate the relevant features of this severe deficit. In the present paper, we describe a new technique based on robot technology, with the goal of providing a reliable, accurate, and quantitative evaluation of kinesthetic acuity, which can be integrated in robot therapy. The proposed technique, based on a pulsed assistance paradigm, has been evaluated on a group of healthy subjects.

This paper presents a probabilist paraconsistent theory of belief revision. This theory is based on a very general theory of probability, that fits with a wide range of classical and nonclassical logics. The theory incorporates a version of Jeffrey conditionalisation as its method of updating. A Dutch book argument is given, and the theory is applied to the problem of choosing a logical system.

We have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we identify three distinct forms of measurement process and three types of measurement algorithm. We give axiomatic specifications of three forms of interfaces that enable the three types of experiment to be used as oracles to Turing machines, and lemmas that help certify an experiment satisfies the axiomatic specifications. For experiments that satisfy our axiomatic specifications, we give lower bounds on the computational power of Turing machines in polynomial time using nonuniform complexity classes. These lower bounds break the barrier defined by the Church-Turing Thesis.

We consider statistical properties of random integer partitions. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form P(x)F(x), where P(x) is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of F(x) around x = 1, which parallels the classical singularity analysis of Flajolet and Odlyzko in many ways. Numerous examples from the literature, as well as some new statistics, are treated via this methodology. In addition, we show how to compute further terms in the asymptotic expansions of previously studied partition statistics.

Compound Poisson population models are particular conditional branching process models. A formula for the transition probabilities of the backward process for general compound Poisson models is verified. Symmetric compound Poisson models are defined in terms of a parameter θ ∈ (0, ∞) and a power series φ with positive radius r of convergence. It is shown that the asymptotic behaviour of symmetric compound Poisson models is mainly determined by the characteristic value θrφ′(r−). If θrφ′(r−)≥1, then the model is in the domain of attraction of the Kingman coalescent. If θrφ′(r−) < 1, then under mild regularity conditions a condensation phenomenon occurs which forces the model to be in the domain of attraction of a discrete-time Dirac coalescent. The proofs are partly based on the analytic saddle point method. They draw heavily from local limit theorems and from results of S. Janson on simply generated trees, conditioned Galton-Watson trees, random allocations and condensation. Several examples of compound Poisson models are provided and analysed.