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.

Complementary use of modeling grammars

Conceptual modeling continues to be an important means for graphically capturing the requirements of an information system. Observations of modeling practice suggest that modelers often use multiple modeling grammars in combination to articulate various aspects of real-world domains. We extend an ontological theory of representation to suggest why and how users employ multiple conceptual modeling grammars in combination. We provide an empirical test of the extended theory using survey data and structured interviews about the use of traditional and structured analysis grammars within an automated tool environment. We find that users of the analyzed tool combine grammars to overcome the ontological incompleteness that exists in each grammar. Users further selected their starting grammar from a predicted subset of grammars only. The qualitative data provides insights as to why some of the predicted deficiencies manifest in practice differently than predicted.

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.

Modeling of a magneto-rheological (MR) fluid damper using a self tuning fuzzy mechanism

A magneto-rheological (MR) fluid damper is a semi-active control device that has recently begun to receive more attention in the vibration control community. However, the inherent nonlinear nature of the MR fluid damper makes it challenging to use this device to achieve high damping control system performance. Therefore the development of an accurate modeling method for a MR fluid damper is necessary to take advantage of its unique characteristics. Our goal was to develop an alternative method for modeling a MR fluid damper by using a self tuning fuzzy (STF) method based on neural technique. The behavior of the researched damper is directly estimated through a fuzzy mapping system. In order to improve the accuracy of the STF model, a back propagation and a gradient descent method are used to train online the fuzzy parameters to minimize the model error function. A series of simulations had been done to validate the effectiveness of the suggested modeling method when compared with the data measured from experiments on a test rig with a researched MR fluid damper. Finally, modeling results show that the proposed STF interference system trained online by using neural technique could describe well the behavior of the MR fluid damper without need of calculation time for generating the model parameters.

Data modeling in elementary and middle school classes : a shared experience

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown’s Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children’s predictions for missing data in Baxter Brown’s Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels’ sharing of their products for Planning a Picnic.

Four facets of a process modeling facilitator

Business process modeling as a practice and research field has received great attention in recent years. However, while related artifacts such as models, tools or grammars have substantially matured, comparatively little is known about the activities that are conducted as part of the actual act of process modeling. Especially the key role of the modeling facilitator has not been researched to date. In this paper, we propose a new theory-grounded, conceptual framework describing four facets (the driving engineer, the driving artist, the catalyzing engineer, and the catalyzing artist) that can be used by a facilitator. These facets with behavioral styles have been empirically explored via in-depth interviews and additional questionnaires with experienced process analysts. We develop a proposal for an emerging theory for describing, investigating, and explaining different behaviors associated with Business Process Modeling Facilitation. This theory is an important sensitizing vehicle for examining processes and outcomes from process modeling endeavors.

Building information modeling in the Australian architecture engineering and construction industry

Building Information Modeling (BIM) is a modern approach to the design, documentation, delivery, and life cycle management of buildings through the use of project information databases coupled with object-based parametric modeling. BIM has the potential to revolutionize the Architecture, Engineering and Construction (AEC) industry in terms of the positive impact it may have on information flows, working relationships between project participants from different disciplines and the resulting benefits it may achieve through improvements to conventional methods. This chapter reviews the development of BIM, the extent to which BIM has been implemented in Australia, and the factors which have affected the up-take of BIM. More specifically, the objectives of this chapter are to investigate the adoption of BIM in the Australian AEC industry and factors that contribute towards the uptake (or non uptake) of BIM. These objectives are met by a review of the related literature in the first instance, followed by the presentation of the results of a 2007 postal questionnaire survey and telephone interviews of a random sample of professionals in the Australian AEC industry. The responses suggest that less than 25 percent of the sample had been involved in BIM – rather less than might be expected from reading the literature. Also, of those who have been involved with BIM, there has been very little interdisciplinary collaboration. The main barriers impeding the implementation of BIM widely across the Australian AEC industry are also identified. These were found to be primarily a lack of BIM expertise, lack of awareness and resistance to change. The benefits experienced as a result of using BIM are also discussed. These include improved design consistency, better coordination, cost savings, higher quality work, greater productivity and increased speed of delivery. In terms of conclusion, some suggestions are made concerning the underlying practical reasons for the slow up-take of BIM and the successes for those early adopters. Prospects for future improvement are discussed and proposals are also made for a large scale worldwide comparative study covering industry-wide participants

“Modeling with tools is easier, believe me” : the effects of tool functionality on modeling grammar usage beliefs

Increasingly, studies are reported that examine how conceptual modeling is conducted in practice. Yet, typically the studies to date have examined in isolation how modeling grammars can be, or are, used to develop models of information systems or organizational processes, without considering that such modeling is typically done by means of a modeling tool that extends the modeling functionality offered by a grammar through complementary features. This paper extends the literature by examining how the use of seven different features of modeling tools affects usage beliefs users develop when using modeling grammars for process modeling. We show that five distinct tool features positively affect usefulness, ease of use and satisfaction beliefs of users. We offer a number of interpretations about the findings. We also describe how the results inform decisions of relevance to developers of modeling tools as well as managers in charge for making modeling-related investment decisions.

Modeling key compromise impersonation attacks on group key exchange protocols

Two-party key exchange (2PKE) protocols have been rigorously analyzed under various models considering different adversarial actions. However, the analysis of group key exchange (GKE) protocols has not been as extensive as that of 2PKE protocols. Particularly, an important security attribute called key compromise impersonation (KCI) resilience has been completely ignored for the case of GKE protocols. Informally, a protocol is said to provide KCI resilience if the compromise of the long-term secret key of a protocol participant A does not allow the adversary to impersonate an honest participant B to A. In this paper, we argue that KCI resilience for GKE protocols is at least as important as it is for 2PKE protocols. Our first contribution is revised definitions of security for GKE protocols considering KCI attacks by both outsider and insider adversaries. We also give a new proof of security for an existing two-round GKE protocol under the revised security definitions assuming random oracles. We then show how to achieve insider KCIR in a generic way using a known compiler in the literature. As one may expect, this additional security assurance comes at the cost of an extra round of communication. Finally, we show that a few existing protocols are not secure against outsider KCI attacks. The attacks on these protocols illustrate the necessity of considering KCI resilience for GKE protocols.