Dual positive and negative regulation of GPCR signaling by GTP hydrolysis (2009)
Smith, Benjamin, Hill, Claire, Godfrey, Emma L., Rand, D. A. (David A.), Van Den Berg, Hugo, Thornton, Steve, ...
G protein-coupled receptors (GPCRs) regulate a variety of intracellular pathways through their ability to promote the binding of GTP to heterotrimeric G proteins. Regulator of G protein signaling...
-conjugacy classes of f and various classes of C (2007)
Laminated Surface Dynamics, A. A. Pinto, D. A. Rand
Abstract. We consider surface homeomorphisms f: M! M which leave invariant a set ae M and satisfy conditions which generalise the situation where is a hyperbolic invariant set or where f is Anosov or...
The purpose of this note is to point out two substantial errors in the papers [6] and [7] which are henceforth referred to respectively as I and II and to correct the first.
RENORMALISATION GIVES ALL SURFACE ANOSOV DIFFEOMORPHISMS WITH A SMOOTH INVARIANT MEASURE. (2007)
Abstract. We prove that there is a natural one-to-one correspondence between fixed points of the renormalisation transformation on C 1+ conjugacy classes of C 1+ diffeomorphisms of the circle and...
Existence, Uniqueness And Ratio Decomposition For Gibbs States Via Duality. (2007)
Gibbs States, Via Duality, A. A. Pinto, D. A. Rand
this paper we give a novel and elementary proof of existence and uniqueness of Gibbs states for Holder weight systems. A bonus of this approach is that it leads directly to a decomposition of the...
Sullivan's scaling function provides a complete description of the smooth conjugacy classes of cookie-cutters. However, for smooth conjugacy classes of Markov maps on a train track, such as...
Spatila Heterogeneity and the Maintenance of Sex (2007)
. The persistence of sexual reproduction is one of the outstanding problems in evolution. Two main explanations have arisen: mutation clearance and the enhanced spread of advantageous traits,...
V. M. Gundlach, D. A. Rand, Coventry Cv Al
In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are infinite-dimensional analogues of Axiom A systems....
Spatio-Temporal Chaos. 2. Unique Gibbs States for Higher-Dimensional Symbolic Systems (2007)
V. M. Gundlach, D. A. Rand, Coventry Cv Al
In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are infinite-dimensional analogues of Axiom A systems....
Spatio-Temporal Chaos. 3. Natural Spatio-Temporal Measures for Coupled Circle Map Lattices (2007)
V. M. Gundlach, D. A. Rand, Coventry Cv Al
In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are infinite-dimensional analogues of Axiom A systems....
Spatio-temporal chaos. Errors and correction. (2007)
This paper contains a treatment of the structure theory for non-compact systems in
M. J. Keeling, J. Mcglade, D. A. Rand
Running head: Characteristic length scales in ecology
Geometric measures for hyperbolic sets on surfaces (2006)
We present a moduli space for all hyperbolic basic sets of diffeomorphisms on surfaces that have an invariant measure that is absolutely continuous with respect to Hausdorff measure. To do this we...
Rigidity of hyperbolic sets on surfaces (2005)
Pinto, A. A., Rand, D. A. (David A.)
Given a hyperbolic invariant set of a diffeomorphism on a surface, it is proved that, if the holonomies are sufficiently smooth, then the diffeomorphism on the hyperbolic invariant set is rigid in...
Teichmüller spaces and HR structures for hyperbolic surface dynamics (2002)
Pinto, A. A., Rand, D. A. (David A.)
We construct a Teichmüller space for the C^{1+}-conjugacy classes of hyperbolic dynamical systems on surfaces. After introducing the notion of an HR structure which associates an affine structure...
Smoothness of holonomies for codimension 1 hyperbolic dynamics (2002)
Pinto, A. A., Rand, D. A. (David A.)
Hyperbolic invariant sets {Lambda} of C1+{gamma} diffeomorphisms where either the stable or unstable leaves are 1-dimensional are considered in this paper. Under the assumption that the {Lambda} has...
Existence uniqueness and ratio decomposition for Gibbs states via duality (2001)
Pinto, A. A., Rand, D. A. (David A.)
We give an elementary proof of existence and uniqueness of Gibbs states for Hölder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of...
Structural Stability of Coupled Hyperbolic Invariant Manifolds (1997)
this paper we consider an infinite dimensional non-compact manifold which is invariant under a hyperbolic map F and find conditions for it to be structurally stable. That is, we consider small...
A Spatial Mechanism for the Evolution and Maintenance of Sexual Reproduction. (1995)
In this paper we discuss a spatial mechanism for the evolution and maintenance of sexual reproduction. We consider three related models in which sexual reproduction is maintained by parasitism...
D.A. Rand, M. Keeling, H.B. Wilson
We consider an individual-based spatial model of a generic host-pathogen system and explore the differences between such models and mean-field systems. We find a range of new dynamical and...
Classifying C¹+ structures on dynamical fractals: 2 Embedded trees. (1995)
We classify the C 1+ff structures on embedded trees. This extends the results of Sullivan [9] on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded...
Gibbs States for Bundle Systems with an Application to Spatio-Temporal Chaos (1994)
this paper we prove a bundle version of the Ruelle-Perron-Frobenius Theorem and discuss an application to spatio-temporal chaos. In subsequent papers we will apply this result to a range of problems...
Gibbs States for Bundle Systems with an Application to Spatio-Temporal Chaos (1994)
this paper we prove a bundle version of the Ruelle-Perron-Frobenius Theorem and discuss an application to spatio-temporal chaos. In subsequent papers we will apply this result to a range of problems...
NON-UNITARY VALUATION SUBALGEBRAS (1973)
Let U be a commutative ring with identity. The approach of this paper is to consider U as an algebra over another commutative ring R with identity and then to study the structure of U in terms of its...
Reconstructing the dynamics of unobserved variables in spatially extended systems
Attractor reconstruction using embedding techniques is a widely used tool when analysing data from real systems. It allows reconstruction of the system dynamics from only one observable and is thus...
Correlation models for childhood epidemics.
Keeling, M J, Rand, D A, Morris, A J
One of the simplest set of equations for the description of epidemics (the SEIR equations) has been much studied, and produces reasonable approximations to the dynamics of communicable disease....
Dynamics of T-cell antagonism: enhanced viral diversity and survival.
In rapidly evolving viruses the detection of virally infected cells can possibly be subverted by the production of altered peptides. There are peptides with single amino acid changes that can...
A moment closure model of sexually transmitted disease spread through a concurrent partnership network is developed. The model employs pair approximations of higher-order correlations to derive...
Characteristic length scales of spatial models in ecology via fluctuation analysis
Keeling, M. J., Mezić, I., Hendry, R. J., McGlade, J., Rand, D. A.
A technique of fluctuation analysis is introduced for the identification of characteristic length scales in spatial models, with similarities to the recently introduced methods using correlations....
Design principles underlying circadian clocks.
Rand, D. A., Shulgin, B. V., Salazar, D., Millar, A. J.
A fundamental problem for regulatory networks is to understand the relation between form and function: to uncover the underlying design principles of the network. Circadian clocks present a...
The dynamical systems arising from gene regulatory, signalling and metabolic networks are strongly nonlinear, have high-dimensional state spaces and depend on large numbers of parameters....