Oscillations in a maturation model of blood cell production.

We present a mathematical model of blood cell production which describes both the development of cells through the cell cycle, and the maturation of these cells as they differentiate to form the various mature blood cell types. The model differs from earlier similar ones by considering primitive stem cells as a separate population from the differentiating cells, and this formulation removes an apparent inconsistency in these earlier models. Three different controls are included in the model: proliferative control of stem cells, proliferative control of differentiating cells, and peripheral control of stem cell committal rate. It is shown that an increase in sensitivity of these controls can cause oscillations to occur through their interaction with time delays associated with proliferation and differentiation, respectively. We show that the characters of these oscillations are quite distinct and suggest that the model may explain an apparent superposition of fast and slow oscillations which can occur in cyclical neutropenia. © 2006 Society for Industrial and Applied Mathematics

On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

Chemical evolution of star clusters

I discuss the chemical evolution of star clusters, with emphasis on old globular clusters, in relation to their formation histories. Globular clusters clearly formed in a complex fashion, under markedly different conditions from any younger clusters presently known. Those special conditions must be linked to the early formation epoch of the Galaxy and must not have occurred since. While a link to the formation of globular clusters in dwarf galaxies has been suggested, present-day dwarf galaxies are not representative of the gravitational potential wells within which the globular clusters formed. Instead, a formation deep within the proto-Galaxy or within dark-matter minihaloes might be favoured. Not all globular clusters may have formed and evolved similarly. In particular, we may need to distinguish Galactic halo from Galactic bulge clusters.Comment: 27 pages, 2 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 6 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. LaTeX, requires rspublic.cls style fil

Quantising on a category

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose `configuration space' (or history-theory analogue) is the set of objects \Ob\Q in a category \Q. We develop a scheme based on constructing an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold $Q\simeq G/H$, where $G$ and $H$ are Lie groups. In particular, we choose as the analogue of $G$ the monoid of `arrow fields' on \Q. Physically, this means that an arrow between two objects in the category is viewed as an analogue of momentum. After finding the `category quantisation monoid', we show how suitable representations can be constructed using a bundle (or, more precisely, presheaf) of Hilbert spaces over \Ob\Q. For the example of a category of finite sets, we construct an explicit representation structure of this type.Comment: To appear in a volume dedicated to the memory of James Cushin

On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure

Particle Impact Analysis of Bulk Powder During Pneumatic Conveyance

Fragmentation of powders during transportation is a common problem for manufacturers of food and pharmaceutical products. We illustrate that the primary cause of breakage is due to inter-particle collisions, rather than particle-wall impacts, and provide a statistical mechanics model giving the number of collisions resulting in fragmentation

The adrenocortical response to synthetic ACTH following a trek to high altitude

Background: Gradual ascent to high altitude is typically associated with reduced resting aldosterone and unchanged cortisol, features that may facilitate acclimatization but are poorly understood. Aims: To investigate the cortisol and aldosterone response to adrenocorticotrophic hormone at altitude. Methods: Eleven subjects underwent a 250 µg short synacthen test at sea-level and again after trekking to 3600 m in Nepal. Cortisol and aldosterone were measured by conventional assay from blood samples taken immediately prior to the administration of synacthen (T0) and then 30 (T30) and 60 (T60) minutes later. Results: At 3600 m resting basal cortisol and aldosterone levels were both significantly lower than they were at sea-level (p=0.004, p=0.003 respectively). Cortisol values at T30 and T60 were no different between sea-level and 3600 m but the increment after synacthen was significantly (p=0.041) greater at 3600 m due to a lower basal value. Aldosterone at T30 and T60 was significantly lower (p=0.003 for both) at 3600 m than at sea-level and the increment following synacthen was also significantly (p=0.003) less at 3600 m. Conclusions: At 3600 m there appears to be a divergent adrenal response to synthetic adrenocorticotrophic hormone with an intact cortisol response but a reduced aldosterone response, relative to sea-level. This may reflect a specific effect of hypoxia on aldosterone synthesis and may be beneficial to acclimatization

Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure

Entropy production and the arrow of time

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid for a wide family of initial conditions, such as canonical, constrained canonical, multi-canonical and grand canonical distributions, as well as both for classical and quantum systems.Comment: 15 pages, no figure

Newly-Discovered Globular Clusters in NGC 147 and NGC 185 from PAndAS

Using data from the Pan-Andromeda Archaeological Survey (PAndAS), we have discovered four new globular clusters (GCs) associated with the M31 dwarf elliptical (dE) satellites NGC 147 and NGC 185. Three of these are associated with NGC 147 and one with NGC 185. All lie beyond the main optical boundaries of the galaxies and are the most remote clusters yet known in these systems. Radial velocities derived from low resolution spectra are used to argue that the GCs are bound to the dwarfs and are not part of the M31 halo population. Combining PAndAS with UKIRT/WFCAM data, we present the first homogeneous optical and near-IR photometry for the entire GC systems of these dEs. Colour-colour plots and published colour-metallicity relations are employed to constrain GC ages and metallicities. It is demonstrated that the clusters are in general metal poor ([Fe/H] < -1.25 dex), while the ages are more difficult to constrain. The mean (V-I)$_0$ colours of the two GC systems are very similar to those of the GC systems of dEs in the Virgo and Fornax clusters, as well as the extended halo GC population in M31. The new clusters bring the GC specific frequency (S_N) to ~9 in NGC 147 and ~5 in NGC 185, consistent with values found for dEs of similar luminosity residing in a range of environments.Comment: 14 pages, 6 figures, 6 tables, accepted for publication in MNRA