A Low Dimensional Approximation For Competence In Bacillus Subtilis

The behaviour of a high dimensional stochastic system described by a Chemical Master Equation (CME) depends on many parameters, rendering explicit simulation an inefficient method for exploring the properties of such models. Capturing their behaviour by low-dimensional models makes analysis of system behaviour tractable. In this paper, we present low dimensional models for the noise-induced excitable dynamics in Bacillus subtilis, whereby a key protein ComK, which drives a complex chain of reactions leading to bacterial competence, gets expressed rapidly in large quantities (competent state) before subsiding to low levels of expression (vegetative state). These rapid reactions suggest the application of an adiabatic approximation of the dynamics of the regulatory model that, however, lead to competence durations that are incorrect by a factor of 2. We apply a modified version of an iterative functional procedure that faithfully approximates the time-course of the trajectories in terms of a 2-dimensional model involving proteins ComK and ComS. Furthermore, in order to describe the bimodal bivariate marginal probability distribution obtained from the Gillespie simulations of the CME, we introduce a tunable multiplicative noise term in a 2-dimensional Langevin model whose stationary state is described by the time-independent solution of the corresponding Fokker-Planck equation.Comment: 12 pages, to be published in IEEE/ACM Transactions on Computational Biology and Bioinformatic

Decentralised Clinical Guidelines Modelling with Lightweight Coordination Calculus

Background: Clinical protocols and guidelines have been considered as a major means to ensure that cost-effective services are provided at the point of care. Recently, the computerisation of clinical guidelines has attracted extensive research interest. Many languages and frameworks have been developed. Thus far, however,an enactment mechanism to facilitate decentralised guideline execution has been a largely neglected line of research. It is our contention that decentralisation is essential to maintain a high-performance system in pervasive health care scenarios. In this paper, we propose the use of Lightweight Coordination Calculus (LCC) as a feasible solution. LCC is a light-weight and executable process calculus that has been used successfully in multi-agent systems, peer-to-peer (p2p) computer networks, etc. In light of an envisaged pervasive health care scenario, LCC, which represents clinical protocols and guidelines as message-based interaction models, allows information exchange among software agents distributed across different departments and/or hospitals. Results: We outlined the syntax and semantics of LCC; proposed a list of refined criteria against which the appropriateness of candidate clinical guideline modelling languages are evaluated; and presented two LCC interaction models of real life clinical guidelines. Conclusions: We demonstrated that LCC is particularly useful in modelling clinical guidelines. It specifies the exact partition of a workflow of events or tasks that should be observed by multiple "players" as well as the interactions among these "players". LCC presents the strength of both process calculi and Horn clauses pair of which can provide a close resemblance of logic programming and the flexibility of practical implementation

A phenomenological cluster-based model of Ca2+ waves and oscillations for Inositol 1,4,5-trisphosphate receptor (IP3R) channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release -- puffs, waves, and oscillations respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. We connect the termination of large-scale Ca2+ release events to IP3 unbinding or stochasticity.Comment: 18 pages, 10 figure

Living with the Semantic Gap: Experiences and remedies in the context of medical imaging

Semantic annotation of images is a key concern for the newly emerged applications of semantic multimedia. Machine processable descriptions of images make it possible to automate a variety of tasks from search and discovery to composition and collage of image data bases. However, the ever occurring problem of the semantic gap between the low level descriptors and the high level interpretation of an image poses new challenges and needs to be addressed before the full potential of semantic multimedia can be realised. We explore the possibilities and lessons learnt with applied semantic multimedia from our engagement with medical imaging where we deployed ontologies and a novel distributed architecture to provide semantic annotation, decision support and methods for tackling the semantic gap problem

Data driven ontology evaluation

The evaluation of ontologies is vital for the growth of the Semantic Web. We consider a number of problems in evaluating a knowledge artifact like an ontology. We propose in this paper that one approach to ontology evaluation should be corpus or data driven. A corpus is the most accessible form of knowledge and its use allows a measure to be derived of the 'fit' between an ontology and a domain of knowledge. We consider a number of methods for measuring this 'fit' and propose a measure to evaluate structural fit, and a probabilistic approach to identifying the best ontology

Quasi-Particles, Conformal Field Theory, and qq-Series

We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain. These fermionic representations are q-series which are generalizations of the sums occurring in the Rogers-Ramanujan identities

Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields

We consider sl(2) minimal conformal field theories and the dual parafermion models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS) models and its Virasoro modules expressed in terms of paths, we propose a general level-by-level algorithm to build matrix representations of the Virasoro generators and chiral vertex operators (CVOs). We implement our scheme for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories on a cylinder and confirm that it is consistent with the known two-point functions for the CVOs and energy-momentum tensor. Our algorithm employs a distinguished basis which we call the L_1-basis. We relate the states of this canonical basis level-by-level to orthonormalized Virasoro states