All Outputs (26)

Neural fields with sigmoidal firing rates: Approximate solutions (2010)
Journal Article

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of... Read More about Neural fields with sigmoidal firing rates: Approximate solutions.

A hybrid approach to multi-scale modelling of cancer (2010)
Journal Article

In this paper, we review multi-scale models of solid tumour growth and discuss a middleout framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we comp... Read More about A hybrid approach to multi-scale modelling of cancer.

Household epidemic models with varying infection response (2010)
Journal Article

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different mode... Read More about Household epidemic models with varying infection response.

High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing (2010)
Journal Article

We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which -- in contrast to the well known Moyal-Weyl deformation -- lead to a theory with modified kinetic te... Read More about High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing.

Sloshing and slamming oscillations in a collapsible channel flow (2010)
Journal Article

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to a linear external pressure dist... Read More about Sloshing and slamming oscillations in a collapsible channel flow.

Canonical toric Fano threefolds (2010)
Journal Article

An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieti... Read More about Canonical toric Fano threefolds.

Modelling spatially regulated ?-catenin dynamics and invasion in intestinal crypts (2010)
Journal Article

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from... Read More about Modelling spatially regulated ?-catenin dynamics and invasion in intestinal crypts.

Field Theory on Curved Noncommutative Spacetimes (2010)
Journal Article

We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by us... Read More about Field Theory on Curved Noncommutative Spacetimes.

Spacetime Noncommutativity in Models with Warped Extradimensions (2010)
Journal Article

We construct consistent noncommutative (NC) deformations of the Randall-Sundrum spacetime that solve the NC Einstein equations with a non-trivial Poisson tensor depending on the fifth coordinate. In a class of these deformations where the Poisson ten... Read More about Spacetime Noncommutativity in Models with Warped Extradimensions.

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes (2010)
Journal Article

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compu... Read More about Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes.

Preferred foliation effects in Quantum General Relativity (2010)
Journal Article

We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators. The model we consider consists of pure quantum gravity coupled to a pr... Read More about Preferred foliation effects in Quantum General Relativity.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem (2010)
Journal Article

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, base... Read More about Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem.

The influence of bioreactor geometry and the mechanical environment on engineered tissues (2010)
Journal Article

A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium and porous scaffold are treated as distinct phases. The bioreactor system is... Read More about The influence of bioreactor geometry and the mechanical environment on engineered tissues.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry (2010)
Journal Article

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particula... Read More about Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry.

Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks (2010)
Journal Article

Ultraslow fluctuations (0.01-0.1 Hz) are a feature of intrinsic brain activity of as yet unclear origin. We propose a candidate mechanism based on retrograde endocannabinoid signaling in a synaptically coupled network of excitatory neurons. This is k... Read More about Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks.

A new method for conditioning stochastic groundwater flow models in fractured media (2010)
Journal Article

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposa... Read More about A new method for conditioning stochastic groundwater flow models in fractured media.

Normed algebras of differentiable functions on compact plane sets (2010)
Journal Article

We investigate the completeness and completions of the normed algebras (D(1)(X),∥•∥) for perfect, compact plane sets X. In particular, we construct a radially self-absorbing, compact plane set X such that the normed algebra (D(1)(X),∥•∥) is not compl... Read More about Normed algebras of differentiable functions on compact plane sets.

Large-scale neural dynamics: Simple and complex (2010)
Journal Article

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models... Read More about Large-scale neural dynamics: Simple and complex.

An SIR epidemic model on a population with random network and household structure and several types of individuals (2010)
Journal Article

We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random g... Read More about An SIR epidemic model on a population with random network and household structure and several types of individuals.

Analysis of a stochastic SIR epidemic on a random network incorporating household structure (2010)
Journal Article

This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour o... Read More about Analysis of a stochastic SIR epidemic on a random network incorporating household structure.