We prove that no stochastic domination exists between the effective resistance of a spherically symmetric random tree and that of a branching process in a varying environments tree if they grow according to the same law of distribution.

It is shown that on fairly weak conditions, the current solutions of a metaheuristic following the ant colony optimization paradigm, the graph-based ant system, converge with a probability that can be made arbitrarily close to unity to one element of the set of optimal solutions. The result generalizes a previous result by removing the very restrictive condition that both the optimal solution and its encoding are unique (this generalization makes the proof distinctly more difficult) and by allowing a wide class of implementation variants in the first phase of the algorithm. In this way, the range of application of the convergence result is considerably extended.

We consider a single-server queue with exponential service time and two types of arrivals: positive and negative. Positive customers are regular ones who form a queue and a negative arrival has the effect of removing a positive customer in the system. In many applications, it might be more appropriate to assume the dependence between positive arrival and negative arrival. In order to reflect the dependence, we assume that the positive arrivals and negative arrivals are governed by a finite-state Markov chain with two absorbing states, say 0 and 0′. The epoch of absorption to the states 0 and 0′ corresponds to an arrival of positive and negative customers, respectively. The Markov chain is then instantly restarted in a transient state, where the selection of the new state is allowed to depend on the state from which absorption occurred.

The Laplace–Stieltjes transforms (LSTs) of the sojourn time distribution of a customer, jointly with the probability that the customer completes his service without being removed, are derived under the combinations of service disciplines FCFS and LCFS and the removal strategies RCE and RCH. The service distribution of phase type is also considered.

It is proved that the total average waiting time is a convex function of the routing densities for regular routing to parallel queues.

We consider the problem of selecting a stopping time τ which determines when to exit an investment project when the project's cumulative profit up to time t is Xt, where {Xt : t ≥ 0} is a Brownian motion with drift μ and variance σ2. The profit rate μ never changes over time, but μ is not directly observable. Specifically, μ takes the value μH > 0 when in the high state and μL < 0 when in the low state, and the initial probability p0 that the project is in the high state is known. The decision-maker seeks to maximize the expected discounted profit up to time τ. Using the theory of stochastic differential equations, we show that it is optimal to exit only when the posterior probability Pt of being in the high state falls below a critical number p*, and we produce a simple, closed form for p*. Our most surprising comparative-statics result is that the expected discounted profit increases with |μL|, provided |μL| is large.

In the present article, we develop some efficient bounds for the distribution function of a two-dimensional scan statistic defined on a (double) sequence of independent and identically distributed (i.i.d.) binary trials. The methodology employed here takes advantage of the connection between the scan statistic problem and an equivalent reliability structure and exploits appropriate techniques of reliability theory to establish tractable bounds for the distribution of the statistic of interest. An asymptotic result is established and a numerical study is carried out to investigate the efficiency of the suggested bounds.

Biological Robotics covers the interface between robotics and behavioural biology. The first international conference in this area took place in Paris in 1990. This meeting led to the development of what is now called the Society for Adaptive Behaviour (SAB), which holds an international meeting every two years.

Two key aspects of most living organisms is their ability to detect and exploit natural sources of energy within their environment. We are currently developing a robotic system that will attempt to sustain itself by hunting and catching slugs on agricultural land. A microbial fuel cell will be used to convert the slug bio-mass to electricity thus providing the robot's energy supply. This paper outlines the requirements for such a predator and describes the entire robot. Data is also presented from trials of the robot hunting and catching slugs in a situation similar to that found in agricultural fields.

Thie first biologically inspired robots, the famous electromechanical tortoises, were designed and built in 1949 by W. Grey Walter. This paper reviews their origins in Walter's theories of the brain and the nature of life, and uses contemporary unpublished notes and photographs to assess their significance then and now.

The desert ant Cataglyphis is able to explore its desert habitat for hundreds of meters while foraging and return back to its nest precisely and in a straight line. With a body of less than 10 mm and a brain of less than one cubic millimeter they provide a challenge for hi-tech engineers. In this article, we give an overview of our attempts to model parts of its navigation behavior using robots and computer simulations. Inspired by the insect's navigation system we have developed mechanisms for path integration and visual piloting that were successfully employed on the mobile robot Sahabot 2.

This work introduces the concept of a brush-based tractor used for rescue in collapsed buildings or tunnels. The paper presents the bristle theory and traction experiments relating to a robot, which uses a sensor system for detecting the shapes of pipes or tunnel like voids within rubble. Traction experiments in the laboratory were used to investigate the characteristics of bristles and the performance of the brush units of different shapes. The experimental results are discussed in the paper and related to a single bristle theory with a view to giving guidance for the design of a future brush based rescue robot in debris.

This paper discusses robots that are operational within a human-inhabited environment. Specifically, we identify different roles that such robots can adopt, reflecting different human-robot relationships. We discuss three different roles of robots in a project where we develop a robot as a therapeutic tool for children with autism: the robot as a therapeutic playmate, the robot as a social mediator, and the robot as a model social agent. Implications of these roles that go beyond this particular project are discussed.

This paper demonstrates a new method in sampling environmental variables and underwater currents using special devices with a particular technique. The project involves developing a set of robots as the tools for data collection, and developing a system that can interpret the data collected. The ‘ocean' currents can be mapped using a flock of robots by dropping them into the ocean. As they descend, they record the desired sensory information such as salinity, temperature, pressure, the presence of specific chemicals, etc., along with other variables required for the system to function. Once at a predefined depth the robots start ascending and still continue collecting data until they reach the surface. Back on the surface, they communicate the collected data to a base computer in a ship or on land, through satellite or other means. The base computer collects the data from every recovered member of the flock and reconstructs the path they took underwater. Then using this path, it estimates the vectors of the oceanic currents. The environmental variables can be displayed in 3D for the sampled area.

In this paper we describe a prototype underwater robot capable of altering its density by heating oil. It is designed to gather information in the ocean, as a member of a flock of such robots. We also describe the forces acting on the robot, and suggest a preliminary control model.

This paper presents an investigation of odor localization by groups of autonomous mobile robots using principles of Swarm Intelligence. First, we describe a distributed algorithm by which groups of agents can solve the full odor localization task more efficiently than a single agent. Next, we demonstrate that a group of real robots under fully distributed control can successfully traverse a real odor plume, and that an embodied simulator can faithfully reproduce these real robots experiments. Finally, we use the embodied simulator combined with a reinforcement learning algorithm to optimize performance across group size, showing that it can be useful not only for improving real world odor localization, but also for quantitatively characterizing the influence of group size on task performance.

Pure Type Systems (PTS) come in two flavours: domain-free systems with untyped $\lambda$-abstractions (i.e. of the form $\lambda{x}.{M}$); and domain-free systems with typed $\lambda$-abstractions (i.e. of the form $\lambda{x}{A}{M}$). Both flavours of systems are related by an erasure function $\er{.}$ that removes types from $\lambda$-abstractions. Preservation of Equational Theory, which states the equational theories of both systems coincide through the erasure function, is a property of functional and normalizing PTSs. In this paper we establish that Preservation of Equational Theory fails for some non-normalizing PTSs, including the PTS with $\ast:\ast$. The gist of our argument is to exhibit a typable expression $Y_H$ whose erasure $\er{Y}$ is a fixpoint combinator, but which is not a fixpoint combinator itself.