Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Bwembya Chikolwa quoted by Mike Taylor for Money Management 7th September 2009, Thaw for listed property

Australian property bond markets are starting to improve, but don’t expect a return to the buoyant days of the past any time soon.

David Hicks and Cathie Holden (eds.) (2007). Teaching The Global Dimension. London: Routledge, Taylor & Francis Group, 212 pages.

Teaching The Global Dimension (2007) is intended for primary and secondary teachers, pre-service teachers and educators interested in fostering global concerns in the education system. It aims at linking theory and practice and is structured as follows. Part 1, the global dimension, proposes an educational framework for understanding global concerns. Individual chapters in this section deal with some educational responses to global issues and the ways in which young people might become, in Hick’s terms, more “world-minded”. In the first two chapters, Hicks presents first, some educational responses to global issues that have emerged in recent decades, and second, an outline of the evolution of global education as a specific field. As with all the chapters in this book, most of the examples are drawn from the United Kingdom. Young people’s concerns, student teachers’ views and the teaching of controversial issues, comprise the other chapters in this section. Taken collectively, the chapters in Part 2 articulate the conceptual framework for developing, teaching and evaluating a global dimension across the curriculum. Individual chapters in this section, written by a range of authors, explore eight key concepts considered necessary to underpin appropriate learning experiences in the classroom. These are conflict, social justice, values and perceptions, sustainability, interdependence, human rights, diversity and citizenship. These chapters are engaging and well structured. Their common format consists of a succinct introduction, reference to positive action for change, and examples of recent effective classroom practice. Two chapters comprise the final section of this book and suggest different ways in which the global dimension can be achieved in the primary and the secondary classroom.

Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Economic development and construction productivity in Malaysia

The productivity of the construction industry has a significant effect on national economic growth. Gains from higher construction productivity flow through the economy, as all industries rely on construction to some extent as part of their business investment. Contractions and expansions of economic activity are common phenomena in an economy. Three construction cycles occurred between the years 1970 and 2011 in Malaysia. The relationships between construction productivity and economic development are examined by the partial correlation method to establish the underlying factors driving the change in construction productivity. Construction productivity is statistically significantly correlated with gross domestic product (GDP) per capita in a positive direction for the 1985–98 and 1998–2009 cycles, but not the 1970–85 cycle. Fluctuations in construction activities and the influx of foreign workers underlie the changes of construction productivity in the 1985–98 cycle. There was less fluctuation in construction activities in the 1998–2009 cycle, with changes being mainly due to the fiscal stimulation policies of the government in attempting to stabilize the economy. The intensive construction of mega-projects resulted in resource constraints and cost pressures during the 1980s and 1990s. A better management of the ‘boom-bust’ nature of the construction business cycle is required to maintain the capability and capacity of the industry.

Saffman-Taylor fingers with kinetic undercooling

The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularisation on the interface is not provided by surface tension, but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, which acts to penalise high velocities and prevent blow-up of the unregularised solution. Previous asymptotic results for the Hele-Shaw finger problem with kinetic undercooling suggest that for a given value of the kinetic undercooling parameter, there is a discrete set of possible finger shapes, each analytic at the nose and occupying a different fraction of the channel width. In the limit in which the kinetic undercooling parameter vanishes, the fraction for each family approaches 1/2, suggesting that this selection of 1/2 by kinetic undercooling is qualitatively similar to the well-known analogue with surface tension. We treat the numerical problem of computing these Saffman-Taylor fingers with kinetic undercooling, which turns out to be more subtle than the analogue with surface tension, since kinetic undercooling permits finger shapes which are corner-free but not analytic. We provide numerical evidence for the selection mechanism by setting up a problem with both kinetic undercooling and surface tension, and numerically taking the limit that the surface tension vanishes.

Changes in CO2 emissions over business cycle recessions and expansions in the United States: A decomposition analysis

This paper examines the asymmetry of changes in CO2 emissions over business cycle recessions and expansions using yearly data from 1949 and monthly data from 1973 for the United States (US). In addition, decomposition analysis is applied to investigate the relative roles of various proximate contributing factors to observed changes in total and per capita CO2 emissions and emissions intensity, over business cycle phases. The results suggest, inter alia, that aggregate emissions and emissions intensity reduce much faster in contractions than they increase in expansions. In addition, unlike the three previous expansions, in the most recent post-GFC US expansion, emissions per capita have continued to decline, and at a rate very similar to the rate of reduction in preceding contractions. This suggests the real possibility that the most recent contraction may have had an ongoing impact on the path of per capita emissions well beyond the immediate impact experienced during the contraction itself.

Disorderly categories in picture postcards from colonial Papua and New Guinea

At the turn of the century in Melbourne, a notice typed on the verso of a postcard stated that the South Yarra Baptist Young Men's class was meeting on the following Sunday at 2.45 p.m. The card, published in the United Kingdom, was numbered 51828 in the Valentine series of Papuan postcards.1 The image, a photograph of Hanuabada village taken in the early 1880s, and the text, written early in 1900, are contradictory and constitute separate realms of evidence that invite a renegotiation of meaning, analysis, and interpretation of the relationships between images, tourism, colonial rule, and ethnographic knowing. The visual evidence suggests the postcard may have played an ethnographic, educative role in the public understanding of Papua, which had just become an Australian Territory and was not yet well known. It is also suggestive of educative roles related to mission endeavours, subimperialist ambitions and the new tourist traffic through the ports of Port Moresby, Samarai, and Rabaul.