Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N₀), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H², is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N₀, M, and n. Asymptotic approximations of H² are deduced and tested for both one‐dimensional (1‐D) and 2‐D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power‐law relationship, , with the CPU cost index, b, indicating the weighting of N₀ in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N₀ determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015     

Australia,uranium and nuclear power

The nuclear debate in Australia is shaped by the nation's substantial base of energy resources, including its large reserves of uranium and recent rises in the market price of uranium. But the debate also echoes Australia's past in the development of programs for nuclear weapons. The proposals include uranium enrichment, the storage of nuclear waste in Australia, and the introduction of nuclear reactors. A national inquiry has been instituted by the government. These developments, stemming from a range of factors, have revived the opposition to uranium mining and nuclear power which has for two decades held a dominant role in Australian politics. The issue of what should be Australia's energy path in a time of climate change is beginning to be examined. The importance of the decisions, whether to be a player in the nuclear club with its attendant multiple hazards, or to play a quite different leadership role in the development and adoption of sustainable energy strategies and technologies, cannot be exaggerated.     

Long-Run Trends in Victorian Housing Affordability and First Transition into Homeownership

Over the past two decades housing pathways have become increasingly differentiated between generations, particularly in advanced societies dominated by owner-occupied tenure systems. Demographic transformations caused by aging and falling fertility rates, along with a more volatile economy and a neo-liberal reorientation of governance have combined to restructure housing conditions. Drawing on empirical research in Japan, this paper illustrates the social origins and impact of generation-based differentiations in housing patterns in that country. It considers the housing experiences of three cohorts: baby-boomers, baby-busters and the ‘lost generation’. The contrast of housing pathways between these generations in Japan illustrates the contemporary dynamics of housing and social processes in homeowner societies.     

A multi-objective model for seasonal personnel reassignment

The focus of this research was the development of a model to address the problem of reassigning summer construction workers to winter snow and ice removal teams in an efficient and cost-effective manner. The model is a multi-objective integer program that can generate the complete and precise trade-off curve between the objectives of minimizing total distance that the reassigned workforce must travel from their respective homes to one of many site locations, and minimizing the maximum distance that any one worker must travel. System constraints include demand requirements for workers at each site and the limited availability of state-owned vehicles that may be issued to workers assigned to remote sites. Details of the model structure and solution procedure are presented together with the results of an actual application.     

Hadamard tensors and lower bounds on multiparty communication complexity

We develop a new method for estimating the discrepancy of tensors associated with multiparty communication problems in the “Number on the Forehead” model of Chandra, Furst, and Lipton. We define an analog of the Hadamard property of matrices for tensors in multiple dimensions and show that any k-party communication problem represented by a Hadamard tensor must have Ω(n/2 ^k ) multiparty communication complexity. We also exhibit constructions of Hadamard tensors. This allows us to obtain Ω(n/2 ^k ) lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.     

Self Organising Maps for variable selection: Application to human saliva analysed by nuclear magnetic resonance spectroscopy to investigate the effect of an oral healthcare product

SOMs (Self Organising Maps) are derived from the machine learning literature and serve as a valuable method for representing data. In this paper, the use of SOMs as a technique for determining the most significant variables (or markers) in a dataset is described. The method is applied to the NMR spectra of 96 human saliva samples, half of which have been treated with an oral rinse formulation and half of which are controls, and 49 variables consisting of bucketed intensities. In addition, three simulations, two of which consist of the same number of samples and variables as the experimental dataset and a third that contains a much larger number of variables, are described. Two of the simulations contain known discriminatory variables, and the remaining is treated as a null dataset without any specific discriminatory variables added. The described SOM method is contrasted to Partial Least Squares Discriminant Analysis, and a list of the markers determined to be most significant using both approaches was obtained and the differences arising are discussed. A SOM Discrimination Index (SOMDI) is defined, whose magnitude relates to how strongly a variable is considered to be a discriminator. In order to ensure that the model is stable and not dependent on the random starting point of the SOM, one hundred iterations were performed and variables that were consistently of high rank were selected. A variety of approaches for data representation are illustrated, and the main theoretical principles of employing SOMs for determining which variables are most significant are outlined. Software used in this paper was written in-house, allowing greater flexibility over existing packages, and tailored for the specific application in hand.