Stochastic regularization method for backward Cauchy problem in Banach spaces

We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

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.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

Expansion of support for first year law students : an overview from a first year coordinator

In the context of government funding and targets for increased participation in higher education and equity groups, as well as attrition rates, the literature on first year higher education highlights the importance of appropriate levels of support for students transitioning to higher education. In the law school context, support of first year students is also important in the response to the high levels of stress among law students. It is therefore necessary for universities to provide a variety of support to first year students from both a student perspective and a curriculum perspective. This paper explores the process of investigating the expansion of student support, including peer support programs, staff led programs, appointing a first year coordinator and developing a curriculum plan. These programs promote engagement and ensure a cohesive and integrated first year experience from both curriculum design and student experience perspectives. This paper will explain the process undertaken at QUT of expanding support for first year law students, overview the program details and will reflect on the feedback from students, peer facilitators and staff of expanding support for first year law students at QUT. The paper will conclude with recommendations for improvement to the program.

Query expansion using term relationships in language models for information retrieval

Language Modeling (LM) has been successfully applied to Information Retrieval (IR). However, most of the existing LM approaches only rely on term occurrences in documents, queries and document collections. In traditional unigram based models, terms (or words) are usually considered to be independent. In some recent studies, dependence models have been proposed to incorporate term relationships into LM, so that links can be created between words in the same sentence, and term relationships (e.g. synonymy) can be used to expand the document model. In this study, we further extend this family of dependence models in the following two ways: (1) Term relationships are used to expand query model instead of document model, so that query expansion process can be naturally implemented; (2) We exploit more sophisticated inferential relationships extracted with Information Flow (IF). Information flow relationships are not simply pairwise term relationships as those used in previous studies, but are between a set of terms and another term. They allow for context-dependent query expansion. Our experiments conducted on TREC collections show that we can obtain large and significant improvements with our approach. This study shows that LM is an appropriate framework to implement effective query expansion.

Tensor query expansion : a cognitively motivated relevance model

In information retrieval, a user's query is often not a complete representation of their real information need. The user's information need is a cognitive construction, however the use of cognitive models to perform query expansion have had little study. In this paper, we present a cognitively motivated query expansion technique that uses semantic features for use in ad hoc retrieval. This model is evaluated against a state-of-the-art query expansion technique. The results show our approach provides significant improvements in retrieval effectiveness for the TREC data sets tested.

An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

The growth and international expansion of an emerging market retailer in Latin America

This study contributes to the literature on international retailing by addressing a gap in the literature as to how retailers from emerging markets expand internationally. This historical case study analyzes the growth and internationalization process of Chilean retailer Falabella, one of the largest in Latin America and has been able to compete with multinationals from developed countries. The research is based upon primary and secondary data sources including 33 oral interviews with company managers and family executives, as well as industry data, corporate reports, and trade journals. Drawing on institutional theory, the findings show that by belonging to a family conglomerate, engaging in networks and partnerships, organizational learning, and having an experienced management team helped Falabella gain legitimacy in all international markets.

A brief history of haemotopoietic stem cell Ex vivo expansion

Haematopoiesis is the process by which a hierarchy of mature and progenitor blood cells are formed. These cell populations are all derived from multipotent haematopoietic stem cells (HSC), which reside in the bone marrow ‘niche’ of adult humans. Over the lifetime of a healthy individual, this HSC population replenishes between 1010-1011 blood cells on a daily basis. Dysregulation of this system can lead to a number of haematopoietic diseases, including aplastic anaemias and leukaemias, which result in, or require for disease resolution, bone marrow cell depletion. In 1956, E. Donnall Thomas demonstrated that haematopoiesis could be restored by transplanting bone marrow-derived cells from one man into his identical twin brother, who was suffering from advanced leukaemia. His success drew significant interest in academic research and medicine communities, and 12 years later, the first successful allogeneic transplant was performed. To this day, HSCs remain the most studied and characterised stem cell population. In fact, HSCs are the only stem cell population routinely utilised in the clinic. As such, HSCs function as a model system both for the biological investigation of stem cells, as well as for their clinical application. Herein, we briefly review HSC transplantation, strategies for the ex vivo cultivation of HSCs, recent clinical outcomes, and their impact on the future direction of HSC transplantation therapy.