Applying Mean-Field Approximation to Continuous Time Markov Chains

The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agent populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally, we illustrate the application of existing model checking analysis techniques

Gene Regulation in the Pi Calculus: Simulating Cooperativity at the Lambda Switch

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4230).Also part of the Lecture Notes in Bioinformatics book sub series (volume 4230).International audienceWe propose to model the dynamics of gene regulatory networks as concurrent processes in the stochastic pi calculus. As a first case study, we show how to express the control of transcription initiation at the lambda switch, a prototypical example where cooperative enhancement is crucial. This requires concurrent programming techniques that are new to systems biology, and necessitates stochastic parameters that we derive from the literature. We test all components of our model by exhaustive stochastic simulations. A comparison with previous results reported in the literature, experimental and simulation based, confirms the appropriateness of our modeling approach

Phase Behavior of Aqueous Na-K-Mg-Ca-CI-NO3 Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na{sup +}, K{sup +}, Mg{sup 2+}, Ca{sup 2+}, Cl{sup -}, and NO{sub 3}{sup -} ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 C. The measurements have been performed using Oak Ridge National Laboratory's (ORNL) previously designed gravimetric isopiestic apparatus, which makes it possible to detect solid phase precipitation. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid-liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor-liquid and solid-liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems

The evolution of a single-paired immigration death process

The general question of whether it is possible to determine the fundamental structure of a hidden stochastic process purely from counts of escaping individuals is of immense importance in fields such as quantum optics, where externally based radiation elucidates the nature of the electromagnetic radiation process. Although the general probability structure has been derived in an earlier paper in terms of the joint probability generating function of the (hidden) population size and (known) counts, its complex nature hides some particularly intriguing features of the underlying process. Our current objective is therefore to examine specific immigration regimes in order to highlight the underlying saw-tooth behaviour of the underlying probability and moment structures. The paper first explores paired- and triple-immigration schemes, and then introduces birth in order to showthat the technique is equally successful in exposing hidden multiplicative effects. These analyses uncover novel and highly illuminating features, and emphasize the potential of this population-counting construct for expanding into more complex multi-type situations

Parameter inference for a stochastic kinetic model of expanded polyglutamine proteins

The presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutaime (PolyQ) proteins in cells have been used to gain a better understanding of the biological system. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly, and so they are estimated within the inference algorithm by repeatedly simulating realizations from the model. In general such an approach is computationally very expensive, and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by highlighting appropriate values of the model parameters leading to new insights into the underlying biological processes

Using resources: conceptualizing the mediation and reflective use of tools and signs

The idea that culture comprises resources that are used has become a popular means to re-conceptualize the culture—agency antinomy. However, the theorization of using resources is fragmented. The present article reviews several attempts to theorize resources, arguing that there has been too much focus upon the resources themselves, while the notion of use has been neglected. Focusing upon mode of use, as opposed to the resources used, the article underscores the importance of distinguishing between tools, which are used to act upon the world, and signs, which are used to act upon the mind. The article also argues for a distinction between non-reflective use, or mediation, and reflective use of resources. Future research should focus upon the transformation of tools into signs and the transformation of mediation into reflective use. The article concludes by discussing problematic issues that remain in conceptualizing the use of resources

A pragmatist approach to the problem of knowledge in health psychology

The multiplicity of forms of health-related knowledge, including biomedical knowledge, lay knowledge and critical constructionist knowledge, raises challenges for health researchers. On one hand, there is a demand for a pluralist acceptance of the variety of health-related knowledge. On the other, the need to improve health calls for action, and thus for choices between opposing forms of knowledge. The present article proposes a pragmatist approach to this epistemological problem. According to pragmatism, knowledge is a tool for action and as such it should be evaluated according to whether it serves our desired interests. We identify implications for research methodology and the choice of research goals