http://www.researchonline.mq.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24770 The purpose of this paper is to quantify the efficiency with which Australian universities utilise their teaching resources. The study estimates the cost efficiency of 36 universities over the period 1995–2002 using stochastic frontier analysis. The present study differs from previous cost and efficiency studies of Australian universities in two respects. First, it employs stochastic frontier analysis for the specification of a cost function for Australian universities which allows for the estimation of cost efficiency for each university under study. Second, a panel data set is utilised in the estimation of the cost function which enables not only comparisons of cost efficiency between universities but also an econometric testing of the assumption of an identical cost function for every university. The main finding is that universities are not operating efficiently as measured by cost efficiency and in relative terms. An efficiency ranking is derived and policy inferences are discussed. 2013-03-13T09:50:51.076Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24669 We study stochastic scheduling on m parallel identical machines with random processing times. The cost involved in the problem is discounted to the present value and the objective is to minimize the expected discounted holding cost, which covers in a unified framework many performance measures discussed in the literature as special cases, including discounted rewards, flowtime, and makespan. We prove that the SEPT rule is optimal, on a fairly general ground, in the class of preemptive dynamic policies, the class of nonpreemptive dynamic policies, and the class of nonpreemptive static list policies. The LEPT rule, on the other hand, is optimal to minimize the expected discounted makespan only under certain restrictive conditions. Without such conditions, the LEPT rule is found no longer optimal for discounted makespan by a counterexample, in contrast to the case without discounting. 2013-03-11T21:10:34.403Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14949 This paper develops a valuation model for options under the class of self-exciting threshold autoregressive (SETAR) models and their variants for the price dynamics of the underlying asset using the self-exciting threshold autoregressive Esscher transform (SETARET). In particular, we focus on the first generation SETAR models first proposed by Tong (1977, 1978) and later developed in Tong (1980, 1983) and Tong and Lim (1980), and the second generation models, including the SETAR-GARCH model proposed in Tong (1990) and the double-threshold autoregressive heteroskedastic time series model (DTARCH) proposed by Li and Li (1996). The class of SETAR-GARCH models has the advantage of modelling the non-linearity of the conditional first moment and the varying conditional second moment of the financial time series. We adopt the SETARET to identify an equivalent martingale measure for option valuation in the incomplete market described by the discrete-time SETAR models. We are able to justify our choice of probability measure by the SETARET by considering the self-exciting threshold dynamic utility maximization. Simulation studies will be conducted to investigate the impacts of the threshold effect in the conditional mean described by the first generation model and that in the conditional variance described by the second generation model on the qualitative behaviors of the option prices as the strike price varies. 2012-06-21T02:50:14.401Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:18300 Monoidal objects (or pseudomonoids) in monoidal bicategories share many of the properties of the paradigmatic example: monoidal categories. The existence of (say, left) duals in a monoidal category leads to a dualization operation which was abstracted to the context of monoidal objects by Day et al. (Appl Categ Struct 11:229–260, 2003). We define a relative version of this called exact pairing for two arrows in a monoidal bicategory; when one of the arrows is an identity, the other is a dualization. In this context we supplement results of Day et al. (Appl Categ Struct 11:229–260, 2003) (and even correct one of them) and only assume the existence of biduals in the bicategory where necessary. We also abstract recent work of Day and Pastro (New York J Math 14:733–742, 2008) on Frobenius monoidal functors to the monoidal bicategory context. Our work began by focusing on the invertibility of components at dual objects of monoidal natural transformations between Frobenius monoidal functors. As an application of the abstraction, we recover a theorem of Walters and Wood (Theory Appl Categ 3:25–47, 2008) asserting that, for objects A and X in a cartesian bicategory C , if A is Frobenius then the category MapC (X, A) of left adjoint arrows is a groupoid. Also, the characterization in Walters and Wood (Theory Appl Categ 3:25–47, 2008) of left adjoint arrows between Frobenius objects of a cartesian bicategory is put into our current setting. In the same spirit, we show that when a monoidal object admits a dualization, its lax centre coincides with the centre defined in Street (Theory Appl Categ 13:184–190, 2004). Finally we look at the relationship between lax duals for objects and adjoints for arrows in a monoidal bicategory. 2012-03-26T16:01:12.239Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16252 Large scale optimisation problems are frequently solved using stochastic methods. Such methods often generate points randomly in a search region in a neighbourhood of the current point, backtrack to get past barriers and employ a local optimiser. The aim of this paper is to explore how these algorithmic components should be used, given a particular objective function landscape. In a nutshell, we begin to provide rules for efficient travel, if we have some knowledge of the large or small scale geometry. 2011-12-09T21:17:14.966Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16253 The purposes of this discussion paper are twofold. First, features of an objective function landscape which provide barriers to rapid finding of the global optimum are described. Second, stochastic algorithms are discussed and their performance examined, both theoretically and computationally, as the features change. The paper lays a foundation for the later findings paper. 2011-12-09T21:17:13.613Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16254 This discussion paper considers the use of stochastic algorithms for solving global optimisation problems in which function evaluations are subject to random noise. An idea is outlined for discussion at the forthcoming Stochastic Global Optimisation 2001 workshop in Hanmer in June; we propose that a noisy version of pure random search be studied. 2011-12-09T21:17:11.658Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16265 For many decades linear programming has been used to find minimum cost diets, notably in the chicken and pig meat industries. More recently, animal growth models together with nonlinear optimisation methods have been used to find feeding schedules which simultaneously minimise feed costs and maximise market return, so maximising gross margin. Genetic algorithms can handle these problems, albeit slowly. In this paper we study the particular nature of the objective function (for pig meat production) and develop a global optimisation algorithm tailored to its discontinuous structure. We also demonstrate the use of stochastic programming to cope with changing feed costs and changing price at slaughter. 2011-12-09T21:16:41.687Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16268 This study employs the classical and modified rescaled adjusted range statistic (R/S statistic) to investigate the sensitivity of the long-term return anomaly observed on the Dow Jones Industrial Average (DJIA) to sample and method bias. Daily data from 1/1/1970 to 17/3/2004 is used with sub-periods identified based on sign shifts in the mean returns as well as the October 1987 crash. The return series are also filtered to accommodate autoregressive conditional heteroskedastic (ARCH) innovations and short-term dependencies. Hurst exponent and V-statistic values for each of the filtered series for the whole sample and sub-periods are estimated, while polynomial regression techniques are applied to plot the V-statistics. These plots show oscillating cycles of varying lengths. Overall, we find the null hypothesis of no long-term dependence is accepted for the whole sample and every sub-period using the modified rescaled range test, but not necessarily using the classical rescaled adjusted range test. The later test does, however, reveal episodes of both positive and negative dependence over the various sample periods, which have been reported by other researchers. 2011-12-09T21:16:35.950Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16299 Two common questions when one uses a stochastic global optimization algorithm, e.g., simulated annealing, are when to stop a single run of the algorithm, and whether to restart with a new run or terminate the entire algorithm. In this paper, we develop a stopping and restarting strategy that considers tradeoffs between the computational effort and the probability of obtaining the global optimum. The analysis is based on a stochastic process called Hesitant Adaptive Search with Power-Law Improvement Distribution (HASPLID). HASPLID models the behavior of stochastic optimization algorithms, and motivates an implementable framework, Dynamic Multistart Sequential Search (DMSS). We demonstrate here the practicality of DMSS by using it to govern the application of a simple local search heuristic on three test problems from the global optimization literature. 2011-12-09T21:15:25.353Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16303 It is shown that the discriminant of the discriminant of a multivariate polynomial has the same irreducible factors as the product of seven polynomials each of which is defined as the GCD of the generators of an elimination ideal. Under relatively mild conditions of genericity, three of these polynomials are irreducible and generate the corresponding elimination ideals, while the other four are equal to one. Moreover the irreducible factors of two of these polynomials have multiplicity at least two in the iterated discriminant and the irreducible factors of two others of the seven polynomials have multiplicity at least three. The proof involves an extended use of the notion of generic point of an algebraic variety and a careful study of the singularities of the hypersurface defined by a discriminant, which may be interesting by themselves. 2011-12-09T21:15:16.043Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16329 Motivated by the search for a body of mathematical theory to support the semantics of computational effects, we first recall the relationship between Lawvere theories and monads on Set. We generalise that relationship from Set to an arbitrary locally presentable category such as Poset and ωCpo or functor categories such as [Inj, Set] and [Inj, ωCpo]. That involves allowing the arities of Lawvere theories to be extended to being size-restricted objects of the locally presentable category. We develop a body of theory at this level of generality, in particular explaining how the relationship between generalised Lawvere theories and monads extends Gabriel–Ulmer duality. 2011-12-09T21:14:19.219Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15222 In this paper, we introduce a High-order Markov-Switching (HMS) model for measuring the risk of a portfolio. We suppose that the rate of return from a risky portfolio follows an HMS model with the drift and the volatility modulated by a discrete-time weak Markov chain. The states of the weak Markov chain are interpreted as observable states of an economy. We adopt the Value-at-Risk (VaR) as a metric for market risk quantification and examine the high-order effect of the underlying Markov chain on the risk measures via backtesting. 2011-10-05T13:11:20.541Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15223 We investigate an optimal portfolio selection problem in a continuous-time Markov-modulated financial market when an economic agent faces model uncertainty and seeks a robust optimal portfolio strategy. The key market parameters are assumed to be modulated by a continuous-time, finite-state Markov chain whose states are interpreted as different states of an economy. The goal of the agent is to maximize the minimal expected utility of terminal wealth over a family of probability measures in a finite time horizon. The problem is then formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game between the agent and the market. We solve the problem by the Hamilton-Jacobi-Bellman approach. 2011-10-05T13:11:17.462Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:13494 In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates than in the general case and thus can be of use for pseudorandom number generation. 2011-06-07T08:31:21.656Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:13497 Recently, multisequences have gained increasing interest for applications in cryptography and quasi-Monte Carlo methods. We study the (generalized) joint linear complexity of a class of nonlinear pseudorandom multisequences introduced by the first two authors as well as the linear complexity of its coordinate sequences. We prove lower bounds which are much stronger than in the case of single sequences since the multidimensional case brings in new and favourable effects. 2011-06-07T08:31:18.331Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12740 This paper is to study nonparametric Bayesian estimation for a proportional hazards model with "long-term survivors". The cumulative hazards function is modeled by a beta process, and the priors of the cure rate and coefficient of covariates can be improper distributions under the proposed model. The posterior estimators of the cure rate, the coefficient for covariates and the survival function are estimated from the cases of discrete-time, continuous-time and grouped survival data. A set of leukemia data are re-analyzed to illustrate the proposed model and statistical inference via a Markov chain Monte Carlo (MCMC) algorithm with Gibbs sampling. 2011-05-25T22:03:02.655Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12844 19 page(s) 2011-05-25T21:58:45.221Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12861 We use lattice reduction to obtain a polynomial time algorithm for recovering an integer (up to a small interval) from its residues modulo sufficiently many primes, when the residues are corrupted by a small additive noise bounded in the Lee norm. Our results are similar to those obtained for Hamming norm, but based on rather different arguments. 2011-05-25T21:58:08.091Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:13188 8 page(s) 2011-05-25T21:44:36.030Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:11257 The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an “algebraic” refinement of the small object argument, cast in terms of Grandis and Tholen’s natural weak factorisation systems, which rectifies each of these three deficiencies. 2011-01-13T12:11:56.427Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8859 What do our students think of mathematics and how do we help prepare them for the workplace? This article reports results from an open-ended questionnaire with engineering students in five countries. We investigate how they conceive of mathematics and how they perceive their university study has prepared them for the workforce. The results show that students have different ideas of mathematics itself and how they will use it. Some view mathematics as a tool to be used in their professional lives, others think they will use the analytical and problem solving skills. There were also those who do not believe they will use mathematics at all---that computers will do it all for them. Since notions about future utility can influence engagement with learning, we as teachers need to proactively expand students' perceptions of the fundamental importance of mathematics to working as an engineer. I provide an example of an assessment task that will help students expand their ideas of how they will use mathematics in their careers 2010-07-06T07:40:24.267Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8688 We investigate the problem of scheduling n jobs on a single machine with the following features. The cost functions are general stochastic processes, which can be used to model the effects of stochastic price fluctuations, stochastic due times, etc., and the stochastic processing times follow a class of distributions, which includes exponential, geometric, and other families of distributions. Such a class of distributions is characterized by its characteristic functions. The optimal policies for these scheduling problems, both without precedence constraints, or with precedence in the form of nonpreemptive chains, are discussed, respectively. 2010-06-21T10:11:50.058Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8689 We study the problem of scheduling a set of jobs on a single machine, to minimize the maximum lateness ML or the maximum weighted lateness MWL under stochastic order. The processing time P i, the due date D i, and the weight W i of each job i may all be random variables. We obtain the optimal sequences in the following situations: (i) For ML, the {P i} can be likelihood-ratio ordered, the {D i} can be hazard-rate ordered, and the orders are agreeable; (ii) For MWL, {D i} are exponentially distributed, {P i} and {W i} can be likelihood-ratio ordered and the orders are agreeable with the rates of {D i}; and (iii) For ML, P i and D i are exponentially distributed with rates μ i and ν i, respectively, and the sequence {ν i(ν i+μ i)} has the same order as {ν i(ν i + μ i + A ₀)} for some sufficiently large A ₀. Some related results are also discussed. 2010-06-21T10:11:48.112Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8409 In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set Gn = {(a, b) : a, b ∈ ℤ, ab ≡ 1 (mod n) , 1 ≤ a, b ≤ n - 1} . The heuristic is based on an asymptotic formula of Renyi and Sulanke. After describing two algorithms to determine the convex closure, we compare the numeric results with the heuristic estimate, and find that they do not agree—there are some interesting peculiarities, for which we provide a heuristic explanation. We then describe some numerical work on the convex closure of the graph of random quadratic and cubic polynomials over ℤn. In this case the numeric results are in much closer agreement with the heuristic, which strongly suggests that the curve xy = 1(mod n) is "atypical." 2010-06-04T14:20:23.641Z ]]>