The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

Architectural issues related to the optical implementation of an EGS network based on embedded control

Free-space optical implementations of switching networks have been proposed to circumvent many of the system-level problems that may be encountered in systems that require many high-density, high-bandwidth connections. The details of a new class of switching network (the EGS network), that is well-suited to free-space implementations, is described. The common control injection problem that plagues most free-space photonic networks, i.e. how can control information from an electronic source be injected into the network for applications that require relatively high network reconfiguration rates, is examined. A new technique for control injection, called embedded control, which permits network operation even with relatively high network reconfiguration rates is also proposed.     

Three chiral vinyldioxaza­borocanes

The structures of three chiral vinyldioxaza­borocanes are reported, namely (2E)‐ and (2Z)‐6‐benzyl‐2‐buten‐2‐yl‐1,3,6,2‐dioxaza­borocane, C₂₇H₃₀BNO₂, (II) and (III), respectively, and (2Z)‐2‐buten‐2‐yl‐6‐isobutyl‐1,3,6,2‐dioxaza­boro­cane, C₂₄H₃₂BNO₂, (IV). These compounds may be useful in asymmetric reactions. In the structures reported here, the N—B donor–acceptor bond is longer than in any previously reported analogous compounds.     

Continuous approximation schemes for stochastic programs

One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation.His work is supported by Office of Naval Research Grant N0014-86-K-0628 and the National Science Foundation under Grant ECS-8815101 and DDM-9215921.His work is supported by the Australian Research Council.     

Cost–benefit modelling for reliability growth

Decisions during the reliability growth development process of engineering equipment involve trade-offs between cost and risk. However slight, there exists a chance an item of equipment will not function as planned during its specified life. Consequently the producer can incur a financial penalty. To date, reliability growth research has focussed on the development of models to estimate the rate of failure from test data. Such models are used to support decisions about the effectiveness of options to improve reliability. The extension of reliability growth models to incorporate financial costs associated with ‘unreliability’ is much neglected. In this paper, we extend a Bayesian reliability growth model to include cost analysis. The rationale of the stochastic process underpinning the growth model and the cost structures are described. The ways in which this model can be used to support cost–benefit analysis during product development are discussed and illustrated through a simple case.     

Light Modulates Electric Phenomena in Hornet Cuticle¶

In the cuticle of live social hornets, such as Vespa orientalis (Hymenoptera, Vespinae), endogenous electric effects are encountered, i.e. voltages of 100–200 mV under illumination and currents amounting to several microamperes on its subjection to darkness—clearly a process of charging and discharging. Of the various wavelengths of sunlight, UV was found to be the most contributory to the active cuticular voltage generation. Throughout the warm season of the yearthe–the active period in colonies of social hornets and wasps—colony members exit from the dark nest during the daytime and fly to the field under the hot sun for various foraging purposes, ultimately returning to the nest. Thus, each hornet, be it queen, worker or drone, probably undergoes daily cyclical process of electric charge and discharge in the exterior part of their integument, cuticle, which lasts up to 30–40 min. Such photoelectric phenomenon was detected in both live, ether‐anaesthetized hornets and dead hornets, albeit in the latter the electric values recorded were lower. The present study addresses the possible impact of the phenomenon on vespan daily life and also compares it with a parallel occurrence in electric fish.     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).