A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Birth-death processes with disaster and instantaneous resurrection

A new structure with the special property that instantaneous resurrection and mass disaster are imposed on an ordinary birth-death process is considered. Under the condition that the underlying birth-death process is exit or bilateral, we are able to give easily checked existence criteria for such Markov processes. A very simple uniqueness criterion is also established. All honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. Surprisingly, it can be proved that all the honest processes are not only recurrent but also ergodic without imposing any extra conditions. Equilibrium distributions are then established. Symmetry and reversibility of such processes are also investigated. Several examples are provided to illustrate our results.

Entanglement between a qubit and the environment in the spin-boson model

The quantitative description of the quantum entanglement between a qubit and its environment is considered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin is calculated as a function of α, the strength of the ohmic coupling to the environment, and ɛ, the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For ɛ=0, the entanglement increases monotonically with α, until it becomes maximal for α→1-. For fixed ɛ>0, the entanglement is a maximum as a function of α for a value, α=αM

Cyclopropyl fatty acids implicate a radical but not a cation as an intermediate in P450(BM3)-catalysed hydroxylations

Novel cyclopropyl containing fatty acids are good substrates for P450(BM3) catalysed hydroxylation and analysis of their oxidation products indicates the presence of a radical intermediate (maximum rebound rate 2.6x10(10) s(-1)) and the absence of any cationic intermediate.

Equine laminitis: glucose deprivation and MMP activation induce dermo-epidermal separation in vitro

Reasons for performing study: Acute laminitis is characterised by hoof lamellar dermal-epidermal separation at the basement membrane (BM) zone. Hoof lamellar explants cultured in vitro can also be made to separate at the basement membrane zone and investigating how this occurs may give insight into the poorly understood pathophysiology of laminitis. Objectives: To investigate why glucose deprivation and metalloproteinase (MMP) activation in cultured lamellar explants leads to dermo-epidermal separation. Methods: Explants, cultured without glucose or with the MMP activator p-amino-phenol-mercuric acetate (APMA), were subjected to tension and processed for transmission electron microscopy (TEM). Results: Without glucose, or with APMA, explants under tension separated at the dermo-epidermal junction. This in vitro separation occurred via 2 different ultrastructural processes. Lack of glucose reduced hemidesmosomes (HDs) numbers until they disappeared and the basal cell cytoskeleton collapsed. Anchoring filaments (AFs), connecting the basal cell plasmalemma to the BM, were unaffected although they failed under tension. APMA activation of constituent lamellar MMPs did not affect HDs but caused AFs to disappear, also leading to dermo-epidermal separation under tension. Conclusions: Natural laminitis may occur in situations where glucose uptake by lamellar basal cells is compromised (e.g. equine Cushing's disease, obesity, hyperlipaemia, ischaemia and septicaemia) or when lamellar MMPs are activated (alimentary carbohydrate overload). Potential relevance: Therapies designed to facilitate peripheral glucose uptake and inhibit lamellar MMP activation may prevent or ameliorate laminitis.

Cyclopropyl containing fatty acids as mechanistic probes for cytochromes P450

The mechanism of aliphatic hydroxylation by cytochromes P450 has been the subject of intense debate with several proposed mechanistic alternatives. Various cyclopropyl containing compounds (radical clocks), which can produce both unrearranged and ring opened products upon oxidation, have been key tools in these investigations. In this study, we introduce several cyclopropyl containing fatty acids 1a-4a with which to probe the mechanism of P450s capable of fatty acid hydroxylation. The probes are shown to be capable of distinguishing radical from cationic intermediates due to the rapid equilibration of isomeric cyclopropyl cations. Ring opening of a radical intermediate in an oxidative transformation is expected to yield a single rearranged alcohol, whereas a cation isomerizes prior to ring opening, leading to two isomeric homoallylic alcohols. Oxidation of these probes by P450(BM3) and P450(Biol) gives results consistent with a radical but not a cationic intermediate in fatty acid hydroxylation by these enzymes. Quantitation of the unrearranged and ring opened products gives remarkably homogeneous rates for oxygen rebound of (2-3) x 10(10) s(-1). The effects of introduction of a cyclopropane ring into a fatty acid upon the regiochemistry of hydroxylation are discussed.

Criteria for quantum coherent transfer of excitations between chromophores in a polar solvent

We show that the quantum decoherence of Forster resonant energy transfer between two optically active molecules can be described by a spin-boson model. This allows us to give quantitative criteria that are necessary for coherent quantum oscillations of excitations between the chromophores. Experimental tests of our results should be possible with flourescent resonant energy transfer (FRET) spectroscopy. Although we focus on the case of protein-pigment complexes our results are also relevant to quantum dots and organic molecules in a dielectric medium. (c) 2006 Elsevier B.V. All rights reserved.

Assessing flow in physical activity: The Flow State Scale-2 and Dispositional Flow Scale-2

The Flow State Scale-2 (FSS-2) and Dispositional Flow Scale-2 (DFS-2) are presented as two self-report instruments designed to assess flow experiences in physical activity. Item modifications were made to the original versions of these scales in order to improve the measurement of some of the flow dimensions. Confirmatory factor analyses of an item identification and a cross-validation sample demonstrated a good fit of the new scales. There was support for both a 9-first-order factor model and a higher order model with a global flow factor. The item identification sample yielded mean item loadings on the first-order factor of .78 for the FSS-2 and .77 for the DFS-2. Reliability estimates ranged from .80 to .90 for the FSS-2, and .81 to .90 for the DFS-2. In the cross-validation sample, mean item loadings on the first-order factor were .80 for the FSS-2, and .73 for the DFS-2. Reliability estimates ranged between .80 to .92 for the FSS-2 and .78 to .86 for the DFS-2. The scales are presented as ways of assessing flow experienced within a particular event (FSS-2) or the frequency of flow experiences in chosen physical activity in general (DFS-2).

O-2 uptake during solid-state fermentation in a rotating drum bioreactor

The maximum O-2 uptake by Rhizopus oligosporus grown in a 200 litre rotating drum bioreactor at 0.5 rpm ranged from 6.7 to 7.6 mmol per min per kg initial dry substrate (IDS), for runs done with 4 baffles each 17 cm wide, and 12 baffles each 5 cm wide. Without baffles, the maximum O-2 uptake rate at 5 rpm was 6.9 mmol/(min.kg IDS), compared to 5.1 mmol/(min.kg IDS) obtained at 0.5 rpm. Therefore O-2 supply is adequate in rotating drum bioreactors as long as slumping flow regimes of the substrate bed are avoided.

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.