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

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

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

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

Recommender Systems for the Semantic Web

This paper presents a semantic approach to Recommender Systems (RS), to exploit available contextual information about both the items to be recommended and the recommendation process, in an attempt to overcome some of the shortcomings of traditional RS implementations. An ontology is used as a backbone to the system in the proposed architecture to represent the problem domain, while multiple web services are orchestrated to compose a suitable recommendation model, matching the current recommendation context at run-time. In order to allow for such dynamic behaviour, the proposed system tackles the recommendation problem by applying existing RS techniques on three different levels: the selection of appropriate sets of features, recommendation model and recommendable items

Rotation-Scale Equivariant Steerable Filters

Incorporating either rotation equivariance or scale equivariance into CNNs has proved to be effective in improving models' generalization performance. However, jointly integrating rotation and scale equivariance into CNNs has not been widely explored. Digital histology imaging of biopsy tissue can be captured at arbitrary orientation and magnification and stored at different resolutions, resulting in cells appearing in different scales. When conventional CNNs are applied to histopathology image analysis, the generalization performance of models is limited because 1) a part of the parameters of filters are trained to fit rotation transformation, thus decreasing the capability of learning other discriminative features; 2) fixed-size filters trained on images at a given scale fail to generalize to those at different scales. To deal with these issues, we propose the Rotation-Scale Equivariant Steerable Filter (RSESF), which incorporates steerable filters and scale-space theory. The RSESF contains copies of filters that are linear combinations of Gaussian filters, whose direction is controlled by directional derivatives and whose scale parameters are trainable but constrained to span disjoint scales in successive layers of the network. Extensive experiments on two gland segmentation datasets demonstrate that our method outperforms other approaches, with much fewer trainable parameters and fewer GPU resources required. The source code is available at: https://github.com/ynulonger/RSESF.Comment: Accepted by MIDL 202

Dynamical system approach for edge detection using coupled FitzHugh–Nagumo neurons

The prospect of emulating the impressive computational capabilities of biological systems has led to considerable interest in the design of analog circuits that are potentially implementable in very large scale integration CMOS technology and are guided by biologically motivated models. For example, simple image processing tasks, such as the detection of edges in binary and grayscale images, have been performed by networks of FitzHugh-Nagumo-type neurons using the reaction-diffusion models. However, in these studies, the one-to-one mapping of image pixels to component neurons makes the size of the network a critical factor in any such implementation. In this paper, we develop a simplified version of the employed reaction-diffusion model in three steps. In the first step, we perform a detailed study to locate this threshold using continuous Lyapunov exponents from dynamical system theory. Furthermore, we render the diffusion in the system to be anisotropic, with the degree of anisotropy being set by the gradients of grayscale values in each image. The final step involves a simplification of the model that is achieved by eliminating the terms that couple the membrane potentials of adjacent neurons. We apply our technique to detect edges in data sets of artificially generated and real images, and we demonstrate that the performance is as good if not better than that of the previous methods without increasing the size of the network

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

Scale-Equivariant UNet for Histopathology Image Segmentation

Digital histopathology slides are scanned and viewed under different magnifications and stored as images at different resolutions. Convolutional Neural Networks (CNNs) trained on such images at a given scale fail to generalise to those at different scales. This inability is often addressed by augmenting training data with re-scaled images, allowing a model with sufficient capacity to learn the requisite patterns. Alternatively, designing CNN filters to be scale-equivariant frees up model capacity to learn discriminative features. In this paper, we propose the Scale-Equivariant UNet (SEUNet) for image segmentation by building on scale-space theory. The SEUNet contains groups of filters that are linear combinations of Gaussian basis filters, whose scale parameters are trainable but constrained to span disjoint scales through the layers of the network. Extensive experiments on a nuclei segmentation dataset and a tissue type segmentation dataset demonstrate that our method outperforms other approaches, with much fewer trainable parameters.Comment: This paper was accepted by GeoMedIA 202