Reply to comment on `Integrable Kondo impurity in one-dimensional q-deformed t - J models

This is a reply to the comment by P Schlottmann and A A Zvyagin.

Reliability factors in business software: volatility, requirements and end-users

Many business-oriented software applications are subject to frequent changes in requirements. This paper shows that, ceteris paribus, increases in the volatility of system requirements decrease the reliability of software. Further, systems that exhibit high volatility during the development phase are likely to have lower reliability during their operational phase. In addition to the typically higher volatility of requirements, end-users who specify the requirements of business-oriented systems are usually less technically oriented than people who specify the requirements of compilers, radar tracking systems or medical equipment. Hence, the characteristics of software reliability problems for business-oriented systems are likely to differ significantly from those of more technically oriented systems.

Estimating Two-Stage Models for Genetic Influences on Alcohol, Tobacco or Drug Use Initiation and Dependence Vulnerability in Twin and Family Data

Genetic research on risk of alcohol, tobacco or drug dependence must make allowance for the partial overlap of risk-factors for initiation of use, and risk-factors for dependence or other outcomes in users. Except in the extreme cases where genetic and environmental risk-factors for initiation and dependence overlap completely or are uncorrelated, there is no consensus about how best to estimate the magnitude of genetic or environmental correlations between Initiation and Dependence in twin and family data. We explore by computer simulation the biases to estimates of genetic and environmental parameters caused by model misspecification when Initiation can only be defined as a binary variable. For plausible simulated parameter values, the two-stage genetic models that we consider yield estimates of genetic and environmental variances for Dependence that, although biased, are not very discrepant from the true values. However, estimates of genetic (or environmental) correlations between Initiation and Dependence may be seriously biased, and may differ markedly under different two-stage models. Such estimates may have little credibility unless external data favor selection of one particular model. These problems can be avoided if Initiation can be assessed as a multiple-category variable (e.g. never versus early-onset versus later onset user), with at least two categories measurable in users at risk for dependence. Under these conditions, under certain distributional assumptions., recovery of simulated genetic and environmental correlations becomes possible, Illustrative application of the model to Australian twin data on smoking confirmed substantial heritability of smoking persistence (42%) with minimal overlap with genetic influences on initiation.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.

Reconciling paleodistribution models and comparative phylogeography in the Wet Tropics rainforest land snail Gnarosophia bellendenkerensis (Brazier 1875)

Comparative phylogeography has proved useful for investigating biological responses to past climate change and is strongest when combined with extrinsic hypotheses derived from the fossil record or geology. However, the rarity of species with sufficient, spatially explicit fossil evidence restricts the application of this method. Here, we develop an alternative approach in which spatial models of predicted species distributions under serial paleoclimates are compared with a molecular phylogeography, in this case for a snail endemic to the rainforests of North Queensland, Australia. We also compare the phylogeography of the snail to those from several endemic vertebrates and use consilience across all of these approaches to enhance biogeographical inference for this rainforest fauna. The snail mtDNA phylogeography is consistent with predictions from paleoclimate modeling in relation to the location and size of climatic refugia through the late Pleistocene-Holocene and broad patterns of extinction and recolonization. There is general agreement between quantitative estimates of population expansion from sequence data (using likelihood and coalescent methods) vs. distributional modeling. The snail phylogeography represents a composite of both common and idiosyncratic patterns seen among vertebrates, reflecting the geographically finer scale of persistence and subdivision in the snail. In general, this multifaceted approach, combining spatially explicit paleoclimatological models and comparative phylogeography, provides a powerful approach to locating historical refugia and understanding species' responses to them.

Supersymmetric t-J Gaudin models and KZ equations

Supersymmetric t-J Gaudin models with open boundary conditions are investigated by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the boundary Gaudin systems are derived, and used to construct and solve the KZ equations associated with sl (2\1)((1)) superalgebra.

A review of animal models for the study of arsenic carcinogenesis

As inorganic arsenic is a proven human carcinogen, significant effort has been made in recent decades in an attempt to understand arsenic carcinogenesis using animal models, including rodents (rats and mice) and larger mammals such as beagles and monkeys. Transgenic animals were also used to test the carcinogenic effect of arsenicals, but until recently all models had failed to mimic satisfactorily the actual mechanism of arsenic carcinogenicity. However, within the past decade successful animal models have been developed using the most common strains of mice or rats. Thus dimethylarsinic acid (DMA), an organic arsenic compound which is the major metabolite of inorganic arsenicals in mammals, has been proven to be tumorigenic in such animals. Reports of successful cancer induction in animals by inorganic arsenic (arsenite and arsenate) have been rare, and most carcinogenetic studies have used organic arsenicals such as DMA combined with other tumor initiators. Although such experiments used high concentrations. of arsenicals for the promotion of tumors, animal models using doses of arsenicals species closed to the exposure level of humans in endemic areas are obviously the most significant. Almost all researchers have used drinking water or food as the pathway for the development of animal model test systems in order to mimic chronic arsenic poisoning in humans; such pathways seem more likely to achieve desirable results. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Partial automation of database processing of simulation outputs from L-systems models of plant morphogenesis

Models of plant architecture allow us to explore how genotype environment interactions effect the development of plant phenotypes. Such models generate masses of data organised in complex hierarchies. This paper presents a generic system for creating and automatically populating a relational database from data generated by the widely used L-system approach to modelling plant morphogenesis. Techniques from compiler technology are applied to generate attributes (new fields) in the database, to simplify query development for the recursively-structured branching relationship. Use of biological terminology in an interactive query builder contributes towards making the system biologist-friendly. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Coordination and movement pathology: models of structure and function

Here we consider the role of abstract models in advancing our understanding of movement pathology. Models of movement coordination and control provide the frameworks necessary for the design and interpretation of studies of acquired and developmental disorders. These models do not however provide the resolution necessary to reveal the nature of the functional impairments that characterise specific movement pathologies. In addition, they do not provide a mapping between the structural bases of various pathologies and the associated disorders of movement. Current and prospective approaches to the study and treatment of movement disorders are discussed. It is argued that the appreciation of structure-function relationships, to which these approaches give rise, represents a challenge to current models of interlimb coordination, and a stimulus for their continued development. (C) 2002 Elsevier Science B.V. All rights reserved.

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.