High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Complexity, evolution, and the structure of demand

This chapter argues that evolutionary economics should be founded upon complex systems theory rather than neo-Darwinian analogies concerning natural selection, which focus on supply side considerations and competition amongst firms and technologies. It suggests that conceptions such as production and consumption functions should be replaced by network representations, in which the preferences or, more correctly, the aspirations of consumers are fundamental and, as such, the primary drivers of economic growth. Technological innovation is viewed as a process that is intermediate between these aspirational networks, and the organizational networks in which goods and services are produced. Consumer knowledge becomes at least as important as producer knowledge in determining how economic value is generated. It becomes clear that the stability afforded by connective systems of rules is essential for economic flexibility to exist, but that too many rules result in inert and structurally unstable states. In contrast, too few rules result in a more stable state, but at a low level of ordered complexity. Economic evolution from this perspective is explored using random and scale free network representations of complex systems.

Digital complementary assets

Google, Facebook, Twitter, LinkedIn, etc. are some of the prominent large-scale digital service providers that are having tremendous impact on societies, corporations and individuals. However, despite the rapid uptake and their obvious influence on the behavior of individuals and the business models and networks of organizations, we still lack a deeper, theory-guided understanding of the related phenomenon. We use Teece’s notion of complementary assets and extend it towards ‘digital complementary assets’ (DCA) in an attempt to provide such a theory-guided understanding of these digital services. Building on Teece’s theory, we make three contributions. First, we offer a new conceptualization of digital complementary assets in the form of digital public goods and digital public assets. Second, we differentiate three models for how organizations can engage with such digital complementary assets. Third, user-base is found to be a critical factor when considering appropriability.

Timing of births and endometrial cancer risk in Swedish women

While a protective long-term effect of parity on endometrial cancer risk is well established, the impact of timing of births is not fully understood. We examined the relationship between endometrial cancer risk and reproductive characteristics in a population-based cohort of 2,674,465 Swedish women, 20–72 years of age. During follow-up from 1973 through 2004, 7,386 endometrial cancers were observed. Compared to uniparous women, nulliparous women had a significantly elevated endometrial cancer risk (hazard ratio [HR] = 1.32, 95% confidence interval [CI], 1.22–1.42). Endometrial cancer risk decreased with increasing parity; compared to uniparous women, women with ≥4 births had a HR=0.66 (95% CI, 0.59–0.74); p-trend < 0.001. Among multiparous women, we observed no relationship of risk with age at first birth after adjustment for other reproductive factors. While we initially observed a decreased risk with later ages at last birth, this appeared to reflect a stronger relationship with time since last birth, with women with shorter times being at lowest risk. In models for multiparous women that included number of births, age at first and last birth, and time since last birth, age at last birth was not associated with endometrial cancer risk, while shorter time since last birth and increased parity were associated with statistically significantly reduced endometrial cancer risks. The HR was 3.95 (95%CI; 2.17–7.20; p-trend=<0.0001) for women with ≥25 years since a last birth compared to women having given birth within 4 years. Our findings support that clearance of initiated cells during delivery may be important in endometrial carcinogenesis. Keywords: endometrial carcinoma, parity, registry, reproductive factors

Gene transfer vectors targeted to human prostate cancer : do we need better preclinical testing systems?

Destruction of cancer cells by genetically modified viral and nonviral vectors has been the aim of many research programs. The ability to target cytotoxic gene therapies to the cells of interest is an essential prerequisite, and the treatment has always had the potential to provide better and more long-lasting therapy than existing chemotherapies. However, the potency of these infectious agents requires effective testing systems, in which hypotheses can be explored both in vitro and in vivo before the establishment of clinical trials in humans. The real prospect of off-target effects should be eliminated in the preclinical stage, if current prejudices against such therapies are to be overcome. In this review we have set out, using adenoviral vectors as a commonly used example, to discuss some of the key parameters required to develop more effective testing, and to critically assess the current cellular models for the development and testing of prostate cancer biotherapy. Only by developing models that more closely mirror human tissues will we be able to translate literature publications into clinical trials and hence into acceptable alternative treatments for the most commonly diagnosed cancer in humans.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

On the impact of the "linguistic turn" on research in information systems

The linguistic turn within philosophy has recently gained increased attention within social sciences. It can be seen as an attempt to investigate traditional philosophical problems by analysing the linguistic expressions used for these investigations. More generally, the phenomenon of language itself must be considered because of its (constitutional) impact on the investigation of phenomena in social sciences. In order to understand the consequences of the linguistic turn, its origins in philosophy are important and will be discussed. Within social sciences the linguistic turn already had significant impact. As an example, we will therefore discuss what directions the linguistic turn enabled for organizational analysis. Information Systems as a discipline must face the consequences of the linguistic turn as well. We will discuss how the linguistic framework introduced impacts the development of knowledge management and that of managerial and organizational support systems. This example shows what different perspectives the linguistic turn can provide for investigations within Information Systems. In addition, we will briefly outline the impact of the linguistic turn with respect to methodologies in Information Systems research.

Reputation and Legitimacy : accreditation and rankings to assess organizations

A key perspective on reputation is that of assessment. Much of the communication literature focuses on the influence organizations have on impression formation. This chapter however suggests that in order to understand reputation assessment, it is also important to understand the related concept of legitimacy. It addresses two approaches to understanding reputation namely accreditation and ranking. Accreditation alludes to concepts of legitimacy in which firms may acquire credibility by meeting formalized standards of certification. Ranking deals with categorizing and rating organizational reputations so that they may be assessed relative to one another. The chapter explores the various ways in which the mechanisms of accreditation and ranking operate and the role of social actors in developing and applying them. Ranking systems that provide the mechanism for comparing organizations and assessing their relative value are also explored.

Integrating the impact of climate into event based failure models for water pipes

This paper presents an event-based failure model to predict the number of failures that occur in water distribution assets. Often, such models have been based on analysis of historical failure data combined with pipe characteristics and environmental conditions. In this paper weather data have been added to the model to take into account the commonly observed seasonal variation of the failure rate. The theoretical basis of existing logistic regression models is briefly described in this paper, along with the refinements made to the model for inclusion of seasonal variation of weather. The performance of these refinements is tested using data from two Australian water authorities.

Sewer performance reporting : factors that influence blockages

Managing sewer blockages represents a significant operational challenge for water utilities. In Australia, company-level blockage rates are used to compare the effectiveness of the management strategies of different utilities. Anecdotal evidence suggests this may not be a fair basis for comparison because blockages are influenced by a range of factors beyond management control and that vary from company to company. This issue was investigated as part of a broader research effort on sewer blockage management undertaken in conjunction with the Water Services Association of Australia (WSAA) and its members. A Web-based survey was used to collate expert opinion on factors that influence blockage rate. The identified factors were then investigated in an exploratory analysis of blockage-related data provided by two participating utilities, supported by literature reviews. The results indicate that blockage rate is influenced by a range of factors, including asset attributes, climatic conditions, water consumption, and soil type. Since these factors vary from utility to utility, this research supports the assertion that company-level blockage rate is not in itself an appropriate metric for comparing management effectiveness.

Conjugation of carcinogens by 6 class glutathione S-transferases : mechanisms and relevance to variations in human risk

Conjugation of chemicals with glutathione (GSH) can lead to decreased or increased toxicity. A genetic deficiency in the GSH S-transferase μ class gene M1 has been hypothesized to lead to greater risk of lung cancer in smokers. Recently a gene deletion polymorphism involving the human θ enzyme T1 has been described; the enzyme is present in erythrocytes and can be readily assayed. A rat θ class enzyme, 5-5, has structural and catalytic similarity and the protein was expressed in the Salmonella typhimurium tester strain TA1535. Expression of the cDNA vector increased the mutagenicity of ethylene dibromide and several methylene dihalides. Mutations resulting from the known GSH S-transferase substrate 1,2-epoxy-3-(4′nitrophenoxy)propane were decreased in the presence of the transferase. Expression of transferase 5-5 increased mutations when 1,2,3,4-diepoxybutane (butadiene diepoxide), 4-bromo-1,2-epoxybutane, or 1,3-dichloracetone were added. The latter compound is a model for the putative 1,2-dibromo-3-chloropropane oxidation product 1-bromo-3-chloroacetone. These genotoxicity and genotyping assays may be of use in further studies of the roles of GSH S-transferase θ enzymes in bioactivation and detoxication and any changes in risk due to polymorphism.