Robin K. S. Hankin

Auckland University of Technology | AUT · School of Computer and Mathematical Sciences

Discrete Lanchester-type attrition models describe many types of antagonistic situations; the preferred interpretation is two fleets of battleships, each trying to sink the other. Such models may be characterised by a bivariate recurrence relation. Here I consider a restricted case in which a fleet that finds itself two or three units behind its op...

In this short article I introduce the frab package which provides an alternative interpretation of named vectors in the R programming language; it is available on CRAN. The underlying mathematical object is the free Abelian group.

In this short article I introduce the "jordan" package which provides functionality for working with different types of Jordan algebra. I give some numerical verification of the Jordan identity for the five types of Jordan algebras. The package is available on CRAN at https://CRAN.R-project.org/package=stokes.

Here we analyse competitive surfing, specifically the 2019 Men’s World Surf League, using formal statistical methods. We use generalized Bradley-Terry likelihoods to assess a number of hypotheses of interest to the surfing community. We quantify the dominance of the top competitors using likelihood techniques, and go on to study the “Brazilian stor...

Weyl algebra is a simple noncommutative system used in quantum mechanics. Here I introduce the weyl package, written in the R computing language, which furnishes functionality for working with univariate and multivariate Weyl algebras. The package is available on CRAN at https://CRAN.R-project.org/package=weyl.

Here I present the lorentz package for working with relativistic physics. The package includes functionality for four-vector transformations, three-velocity addition, and other relativistic processes such as the behaviour of photons. It was designed to facilitate the search for a gyrodistributive law. In special relativity, three-velocities and sca...

Here I present the freegroup package for working with the free group on a finite set of symbols. The package is vectorised; internally it uses an efficient matrix-based representation for free group objects but uses a configurable print method. A range of R-centric functionality is provided. It is available on CRAN at https://CRAN.R-project.org/pac...

The free algebra is an interesting and useful algebraic object. Here I introduce "freealg", an R package which furnishes computational support for free algebras. The package uses the standard template library's "map" class for efficiency, which uses the fact that the order of the terms is algebraically immaterial. The package follows "disordR" disc...

In this short article I introduce the stokes package which provides functionality for working with tensors, alternating forms, wedge products, and related concepts from the exterior calculus. Notation and spirit follow Spivak. Stokes's generalized integral theorem, viz $\int_{\partial X}\phi=\int_Xd\phi$, is demonstrated here using the package; it...

In this short article I introduce the mvp package, which provides some functionality for handling multivariate polynomials. The package uses the C++ Standard Template Library's map class to store and retrieve elements; it conforms to disordR discipline for coefficients. The package is available on CRAN at https://CRAN.R-project.org/package=mvp.

In this short article I introduce the spray package, which provides some functionality for handling sparse arrays. The package uses the C++ Standard Template Library's map class to store and retrieve elements. One natural application for sparse arrays is multivariate polynomials and I give two examples of the package in use, one drawn from the fiel...

Objects in the {\tt stl map} class of {\tt C++} associate a value to each of a set of keys. Accessing values or keys of such an object is problematic in the R programming language because the value-key pairs are not stored in a well-defined order. This document motivates and discusses the concept of "disordered vector" as implemented by the {\tt di...

Here I present the 'clifford' package for working with Clifford algebras in the R programming language. The algebra is described and package idiom is given.

Light inextensible string under tension is a stalwart feature of elementary physics. Here I show how considering such a string in the vicinity of a black hole, with the help of computer algebra systems, can generate insight into the Schwarzschild geometry in the context of an undergraduate homework problem. Light taut strings minimize their proper...

In inference problems where the dataset comprises Bernoulli outcomes of paired comparisons, the Bradley–Terry model offers a simple and easily interpreted framework. However, it does not deal easily with chess because of the existence of draws, and the white player advantage. Here I present a new generalization of Bradley–Terry in which a chess gam...

Here I introduce the R package permutations, for manipulating permutations of a finite set. I show how the package has been used to investigate the megaminx puzzle and exhibit an 82-turn superflip that represents a new lower bound for this operation.

The following problem is considered. Two players are each required to allocate a quota of~$n$ counters among~$k$ boxes labelled~$1,2,\ldots,k$. At times $t=1,2,3,\ldots$ a random box is identified; the probability of choosing box~$i$ is~$p_i$. If a player has at least one counter in the chosen box, she removes one counter from it; otherwise she tak...

Here I present the hyper2 package for generalized Bradley-Terry models and give examples from two competitive situations: single scull rowing, and the competitive cooking game show MasterChef Australia. A number of natural statistical hypotheses may be tested straightforwardly using the software.

This chapter presents a new model for developing and assessing the decision competencies of executive decision-makers. Prior models consider individual and group decision-making but neglect to consider the impact of group-interactive decision-making on real-world problem-solving and sense-making activities. In the present study experimental protoco...

In this short article, I discuss the æsthetics of knot projections and introduce software that creates two-dimensional knot diagrams optimized for visual appearance. The software is in the form of a documented and self-contained suite of functionality written in the R programming language (that is, a ‘package’): knotR. The package leverages the gra...

In this short article I introduce the knotR package, which creates two dimensional knot diagrams optimized for visual appearance using the R programming language. The knotR package is a systematic R-centric suite of software for the creation of production-quality artwork of knot diagrams, released under GPL2.

The nasal cycle, through variation in nasal airflow partitioning, allows the upper airway to accommodate the contrasting demands of air conditioning and removal of entrapped air contaminants. The purpose of this study was to investigate the influence of nasal continuous positive airway pressure (nCPAP) breathing has on both nasal airflow partitioni...

A screencast is a video recording of a computer monitor display, together with voice-over. This teaching technique has multiple advantages including the ability to model the thought processes of a mathematician in a context in which content may be repeated at will. Anecdotal evidence suggests that screencasts can be a very effective teaching tool,...

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Microbial biofilms cause a number of problems in the dairy industry. Understanding the interactions of bacteria with the environment – the physical properties of the substratum, the characteristics of the fluid, such as pH, temperature and availability of nutrients, and the intrinsic properties of bacteria, yeasts and moulds – is the first step in...

Here I introduce package cmvnorm, a complex generalization of the mvtnorm package. A complex generalization of the Gaussian process is suggested and numerical results presented using the package. An application in the context of approximating the Weierstrass σ-function using a complex Gaussian process is given.

This paper introduces the hypergeo package of R routines for numerical calculation of hypergeometric functions. The package is focussed on efficient and accurate evaluation of the Gauss hypergeometric function over the whole of the complex plane within the constraints of fixed-precision arithmetic. The hypergeometric series is convergent only withi...

Extreme weather/climate events have significant environmental and societal impacts, and anthropogenic climate change has and will continue to alter their characteristics (IPCC, 2011). Drought is one of the most damaging natural hazards through its effects on agricultural, hydrological, ecological and socio-economic systems. Climate change is stimul...

We present two natural generalizations of the multinomial and multivariate binomial distributions, which arise from the multiplicative binomial distribution of Altham (1978). The resulting two distributions are discussed and we introduce an R package, MM, which includes associated functionality.

A multivariate generalization of the emulator technique described by Hankin (2005) is presented in which random multivariate functions may be assessed. In the standard univariate case (Oakley'99), a Gaussian process, a finite number of observations is made; here, observations of different types are considered. The technique has the property that ma...

Exotic plant invasions are a key threat to New Zealand biodiversity. Alligator weed (Alternanthera philoxeroides; Amaranthaceae) is an invasive, herbaceous weed native to South America. Little is known about its dynamics in natural ecosystems in its introduced range, despite known agricultural impacts. We quantified alligator weed infestation at La...

The need to fuse beliefs from different sources occurs in many situations. For example, multiple agents can fuse their preferences about alternatives in order to make a single choice, or the output of multiple sensors can be fused to determine which of multiple possible events is most likely to have taken place. These situations are different and m...

Air delivered under augmented pressure during breathing therapy normally requires external humidification in order to avoid upper airways dryness and discomfort. Nasal heat and water flux between air and mucosa is dynamically regulated through changes in the erectile tissue volume. This investigation utilizes magnetic resonance imaging to investiga...

Bayesian theory of model calibration provides a coherent framework for distinguishing and encoding multiple sources of uncertainty in probabilistic predictions of flooding. This paper demonstrates the use of a Bayesian approach to computer model calibration, where the calibration data are in the form of spatial observations of flood extent. The Bay...

The parable of Daisyworld places biological homeostasis on a non-teleological basis. However, one feature of Daisyworld is that, at equilibrium, the system appears to require habitable but bare ground. The presence of bare ground is an unavoidable consequence of the death rate parameter γ. Here, we simplify Watson and Lovelock's original formulatio...

This vignette is based on Hankin (2007a). This short paper introduces a code snippet in the form of an R function that enumerates all possible partitions of a finite set given the sizes of the equivalence classes. Three combinatorial problems are solved using the software: one from bioinformatics, one from scheduling theory, and one from forensic s...

This vignette shows how to use S4 methods to create a simple package. The other vignette shows how to use the package for solving problems involving very large numbers; it is based on Hankin (2007c).

This vignette is based on Hankin (2006) and corrects an algebraic error therein. This vignette introduces the onion package of R routines, for manipulation of quater-nions and octonions. A simple application of the quaternions in use is given, using the package.

This paper discusses a generalization of the Dirichlet distribution, the âÂÂhyperdirichletâÂÂ, in which various types of incomplete observations may be incorporated. It is conjugate to the multinomial distribution when some observations are censored or grouped. The hyperdirichlet R package is introduced and examples given. A number of statistical...

The distribution of abundance amongst species with similar ways of life is a classical problem in ecology. The unified neutral theory of biodiversity, due to Hubbell, states that observed population dynamics may be explained on the assumption of per capita equivalence amongst individuals. One can thus dispense with differences between species, and...

There is compelling evidence for massive discharge of volatiles, including toxic species, into the atmosphere at the end of the Permian. It has been argued that most of the gases were produced during thermal metamorphism of coal and evaporite deposits in the East Siberia Tunguska basin following sill intrusion (Retallack and Jahren, 2008; Svensen e...

Recent work by Lin, Lipsitz, Sinha, Gawande, Regenbogen, and Greenberg proposed a Bayesian analysis of a 2 × 2 table including incompletely classified data. Here, we subject the same dataset to further analysis using recently developed techniques and software written in the R programming language. This vignette is based on a manuscript submitted to...

TWODEE-2 is a FORTRAN 90 code based on previous code (TWODEE). It is designed to solve the shallow water equations for fluid depth, depth-averaged horizontal velocities and depth-averaged fluid density. The shallow layer approach used by TWODEE-2 is a compromise between the complexity of CFD models and the simpler integral models. It can be used fo...

This article was submitted without an abstract, please refer to the full-text PDF file.

This article was submitted without an abstract, please refer to the full-text PDF file.

This report provides a review of the most relevant recent literature in the areas of climate science, impacts of climate change and climate change economics, with a focus on post IPCC Fourth Assessment report work. It also provides information on the key research gaps which might have a major impact on mitigation decisions. CLIMATE SCIENCE: The AR...

Interpreting paleoclimate data is often ambiguous as the proxies involved usually depend on more than one environmental variable, i.e. not just temperature. One method used regularly to overcome this problem is paired analysis of two proxies (mostly, delta18O and Mg/Ca), however, to produce a more robust statistical analysis and reduce error in the...

Fisher's exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher's exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial d...

Within coupled hydrological simulation systems, taking socio-economic processes into account is still a challenging task. In particular, systems that aim at evaluating impacts of climatic change on large spatial and temporal scales cannot be based on ...

An individual’s h-index corresponds to the number h of his/her papers that each has at least h citations. When the citation count of an article exceeds h, however, as is the case for the hundreds or even thousands of citations that accompany the most highly cited papers, no additional credit is given (these citations falling outside the so-called “...

This paper describes the development and first results of the “Community Integrated Assessment System” (CIAS), a unique multi-institutional modular and flexible integrated assessment system for modelling climate change. Key to this development is the supporting software infrastructure, SoftIAM. Through it, CIAS is distributed between the communitie...

1] Several nonvolcanic sources in central Italy emit a large amount of carbon dioxide (CO 2). Under stable atmospheric conditions and/or in the presence of topographic depressions, the concentration of CO 2 , which has a molecular mass greater than that of air, can reach high values that are lethal to humans or animals. Several episodes of this phe...

The distribution of abundance amongst species with similar ways of life is a classical problem in ecology. The unified neutral theory of biodiversity, due to Hubbell, states that observed population dynamics may be explained on the assumption of per capita equivalence amongst individuals. One can thus dispense with differences between species, and...

This short paper introduces a code snippet in the form of an R function that enumerates all possible partitions of a nite set given the sizes of the equivalence classes. Three combinatorial problems are solved using the software: one from bioinformatics, one from scheduling theory, and one from forensic science.

Conventional emulation considers a random field as a function of position in parameter space. This document shows how that framework may be generalized naturally to accommodate multivariate output. In the univariate case, a correlation matrix A is defined and the corresponding variance matrix is 2A, where 2 is a scalar. In the multivariate generali...

This vignette is based on Hankin (2007). This short paper introduces a code snippet in the form of two new R functions that enumerate possible draws from an urn without replacement; these functions call C code, written by the author. Some simple combinatorial problems are solved using the software. For reasons of performance, this vignette uses pre...

This document constructs a minimal working example of a simple application of the approximator package, step by step. Datasets and functions have a .vig sux, repre-

This document constructs a minimal working example of a simple application of the calibrator package, step by step. Datasets and functions have a .vig sux, representing \vignette".

This vignette shows how to use the Brobdingnag package to manipulate very large numbers; it is based on Hankin (2007c). The other vignette shows how to use S4 methods in the context of a simple package.

Many volcanic and non-volcanic areas in Italy emit a very large amount of gas into the atmosphere. Several non-volcanic sources in Central Italy emit a huge amount of cold carbon dioxide (CO2). These degassing areas are generally fed by buried carbonate reservoirs, covered by low permeability formations, where the gas produced at depth accumulates...

This vignette is based on Hankin (2005). This vignette introduces the partitions package of R routines, for numerical calcula- tion of integer partititions. Functionality for unrestricted partitions, unequal partitions, and restricted partitions is provided in a small package that accompanies this note; the emphasis is on terse, ecient C code. A si...

We introduce a new, flexible family of distributions for non-negative data, defined by means of a quantile function. We describe some properties of this family, and discuss several methods for estimating the parameters. The distribution is applied to an example from environmental engineering.

This paper introduces the elliptic package of R routines, for numerical calculation of elliptic and related functions. Elliptic functions furnish interesting and instructive examples of many ideas of complex analysis, and the package illustrates these numerically and visually. A statistical application in fluid mechanics is presented.

Many volcanic and non-volcanic areas in Italy emit a huge amount of gas into the atmosphere. Non-volcanic sources in central Italy emit a huge amount of carbon dioxide (CO2) which has a molecular mass greater than that of air. Under stable atmospheric conditions and/or in presence of topographic depressions, its concentration can reach high values...

This vignette introduces the gsl package of R utilities for accessing the functions of the GSL package. An earlier version of this document was published as Hankin (2006).

If the thermohaline circulation were to collapse we could see very rapid climate changes, with North West Europe becoming much cooler and widespread impacts across the globe. The risk of such an event has two aspects: the first is the impact of a collapse in the circulation and the second is the probability that it will happen. In this paper we loo...

This paper introduces the BACCO bundle of R routines for carrying out Bayesian analysis of computer code output. The bundle comprises packages emulator and calibrator, computerized implementations of the ideas of Oakley and O'Hagan (2002) and Kennedy and O'Hagan (2001a) respectively. The bundle is self-contained and fully documented R code, and inc...

The R computer language (R Development Core Team 2004) has been applied with a great deal of success to a wide variety of statistical, physical, and medical applica- tions. Here, I show that R is an equally superb research tool in the eld of recreational mathematics. An earlier version of this vignette was published as Hankin (2005).

Planning for sustainable land management and the development of land classification systems has become a very complex process with the increasing sophistication of GIS techniques. This has resulted in the emphasis moving to detailed micro-scale description and planning, with a loss of perception of the physical processes and hierarchy of constraint...

Liquefied gases, such as chlorine or ammonia, are stored in large quantities on industrial sites. If released accidentally, they can form a heavy gas cloud that has the potential to kill or injure large numbers of people. The dispersion of such a cloud is thus of interest to the risk assessment community.This is the first of a two-part paper. Here,...

This is the second part of a two-part paper which considers the risk of being exposed to accidentally released toxic gas; part one considered continuous releases and this part considers instantaneous releases. The risk estimated is RI, the probability at any point of receiving a non-zero dose given an instantaneous release (probability language is...

Western Europe's climate is warmer than would be expected because of heat transported by the thermohaline circulation in the North Atlantic Ocean. Model simulations and paleoclimate data show that it is possible for this circulation to shut down leading to rapid cooling in European climate. We investigate the probability of this occurring using the...

The home-range size and location of reef-associated snapper Pagrus auratus: Sparidae were investigated by use of a radio acoustic-positioning telemetry (RAPT) system. Tags were surgically implanted in 5 snapper that were subsequently monitored every minute for a period of 5 mo, and then intermittently over another 7 mo. Site fidelity was high among...

This paper considers the risk to major hazard plant from terrorists deliberately causing catastrophic industrial accidents. The United States of America Department of Justice [Assessment of the increased risk of terrorist or other criminal activity associated with posting off-site consequence analysis information on the internet, 2000] reports that...

This paper assesses the value of shallow layer modelling for instantaneous releases of heavy gas over a slope using the established computer model TWODEE [R.K.S. Hankin, Heavy gas dispersion over complex terrain, Ph.D. thesis, Cambridge University, 1997; J. Hazard. Mater. 66 (1999) 211; J. Hazard. Mater. 66 (1999) 227; J. Hazard. Mater. 66 (1999) 2...

Although much research considers heavy gas dispersion over flat ground, less is known about the physics of dense gas dispersion on a slope. Here, the appropriateness of shallow layer models for the simple case of releases over a slope in a calm ambient is assessed. This two-part paper assesses the value of shallow layer modelling using the establis...

Although much research considers heavy gas dispersion over flat ground, less is known about the physics of dense gas dispersion on a slope. Here, the appropriateness of shallow layer models for the simple case of releases over a slope in a calm ambient is assessed. This two-part paper assesses the value of shallow layer modelling using the establis...

Integral models for heavy gas dispersion approximate a dispersing cloud in terms of a small number of variables; each of these is ultimately a function of an independent variable which is usually time (instantaneous releases) or downwind distance (continuous releases). This type of model is used almost exclusively in risk assessment [HSE's risk ass...

Liquefied gases, such as chlorine and ammonia, are stored in large quantities at industrial sites. If released accidentally, they form a heavy gas cloud that has the potential to kill or injure large numbers of people. The dispersion of such a cloud is thus of interest to the risk assessment community [Nussey, Pantony, & Smallwood, 1992. HSE’s risk...

The Euler equations, together with an equation of state, govern the motion of an inviscid compressible fluid. Here, a new equation of state for volumes containing both gas and liquid is derived; this allows the Euler equations for two substances, here air and water, to be expressed in pure conservation form. This in turn allows simulation of shocks...

Natal dispersal can have important effects on mammal population structure and dynamics following a local population crash. Such dispersal is of practical importance when applied to the control of pest species because dispersal may significantly, and undesirably, reduce the population recovery time following a control operation. The relative dispers...

The Major Hazard Assessment Unit of the Health and Safety Executive (HSE) provides advice to local planning authorities on land use planning in the vicinity of major hazard sites. For sites with the potential for large scale releases of toxic heavy gases such as chlorine this advice is based on risk levels and is informed by use of the computerised...

Part 1 of this three part paper described the mathematical and physical basis of TWODEE, the Health and Safety Laboratory's shallow layer model for heavy gas dispersion. In this part, the numerical solution method used to simulate the TWODEE mathematical model is developed. The boundary conditions for the leading edge, discussed in part 1, make dem...

Part 1 of this three-part paper described the mathematical and physical basis of TWODEE, the Health and Safety Laboratory's shallow layer model for heavy gas dispersion. In part 2, the numerical solution method used to simulate the TWODEE mathematical model was developed; the flux correction scheme of Zalesak [S.T. Zalesak, Fully multidimensional f...

This paper describes the background research, development and application within the UK Health and Safety Executive (HSE) of an audit technique for assessing the effectiveness of safety management systems at onshore major hazard sites. The work is driven by HSE's use of quantified risk assessment for formulating advice to local planning authorities...

Recent work by Lin, Lipsitz, Sinha, Gawande, Regenbogen, and Greenberg proposed a Bayesian analysis of a 2 2 table including incompletely classied data. Here, we subject the same dataset to further analysis using recently developed techniques and software written in the R programming language. This vignette is based on a manuscript submitted to the...

In this short article I introduce the multipol package, which provides some functionality for handling multivariate polynomials; the package is discussed here from a programming perspective. An example from the eld of enumerative combinatorics is presented. This vignette is based on Hankin (2008).

This vignette shows how the multivator package may be used to analyze computer model systems such as CIAS, which comprise interchangeable modules. If the different modules require different input parameters, then it is possible to use specify a reasonable mean and covariance structure using the package, and a short example, using synthetic data, is...