Quasi-stationary distributions

This paper contains a survey of results related to quasi-stationary distributions, which arise in the setting of stochastic dynamical systems that eventually evanesce, and which may be useful in describing the long-term behaviour of such systems before evanescence. We are concerned mainly with continuous-time Markov chains over a finite or countably infinite state space, since these processes most often arise in applications, but will make reference to results for other processes where appropriate. Next to giving an historical account of the subject, we review the most important results on the existence and identification of quasi-stationary distributions for general Markov chains, and give special attention to birth-death processes and related models. Results on the question of whether a quasi-stationary distribution, given its existence, is indeed a good descriptor of the long-term behaviour of a system before evanescence, are reviewed as well. The paper is concluded with a summary of recent developments in numerical and approximation methods

Limiting the spread of disease through altered migration patterns

We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations by the migration of infected individuals. We show how susceptible individuals can act collectively to limit the spread of disease during the initial phase of an epidemic, by specifying the distribution that minimises the growth rate of the epidemic when the infectives are migrating so as to maximise the growth rate. We also give an explicit strategy that minimises the basic reproduction number, which is also shown be optimal in terms of the probability of extinction and total size of the epidemic

Local approximation of a metapopulation's equilibrium

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset $\Omega$ of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at $z$ being occupied is shown to be close to $q_1(z)$, the equilibrium occupation probability in Levins's model, at any point $z \in \Omega$ not too close to the boundary, if the local colonization pressure and extinction rates appropriate to $z$ are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously

Connecting deterministic and stochastic metapopulation models

In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-015-0865-

Dynamics of a structured slug population model in the absence of seasonal variation

We develop a novel, nonlinear structured population model for the slug Deroceras reticulatum, a highly significant agricultural pest of great economic impact, in both organic and non-organic settings. In the absence of seasonal variations, we numerically explore the effect of life history traits that are dependent on an individual's size and measures of population biomass. We conduct a systematic exploration of parameter space and highlight the main mechanisms and implications of model design. A major conclusion of this work is that strong size dependent predation significantly adjusts the competitive balance, leading to non-monotonic steady state solutions and slowly decaying transients consisting of distinct generational cycles. Furthermore, we demonstrate how a simple ratio of adult to juvenile biomass can act as a useful diagnostic to distinguish between predated and non-predated environments, and may be useful in agricultural settings

Cortical AAV-CNTF gene therapy combined with intraspinal mesenchymal precursor cell transplantation promotes functional and morphological outcomes after spinal cord injury in adult rats

Ciliary neurotrophic factor (CNTF) promotes survival and enhances long-distance regeneration of injured axons in parts of the adult CNS. Here we tested whether CNTF gene therapy targeting corticospinal neurons (CSN) in motor-related regions of the cerebral cortex promotes plasticity and regrowth of axons projecting into the female adult F344 rat spinal cord after moderate thoracic (T10) contusion injury (SCI). Cortical neurons were transduced with a bicistronic adeno-associated viral vector (AAV1) expressing a secretory form of CNTF coupled to mCHERRY (AAV-CNTFmCherry) or with control AAV only (AAV-GFP) two weeks prior to SCI. In some animals, viable or nonviable F344 rat mesenchymal precursor cells (rMPCs) were injected into the lesion site two weeks after SCI to modulate the inhibitory environment. Treatment with AAV-CNTFmCherry, as well as with AAV-CNTFmCherry combined with rMPCs, yielded functional improvements over AAV-GFP alone, as assessed by open-field and Ladderwalk analyses. Cyst size was significantly reduced in the AAV-CNTFmCherry plus viable rMPC treatment group. Cortical injections of biotinylated dextran amine (BDA) revealed more BDA-stained axons rostral and alongside cysts in the AAV-CNTFmCherry versus AAV-GFP groups. After AAV-CNTFmCherry treatments, many sprouting mCherry-immunopositive axons were seen rostral to the SCI, and axons were also occasionally found caudal to the injury site. These data suggest that CNTF has the potential to enhance corticospinal repair by transducing parent CNS populations

On the computational power of probabilistic and quantum branching program

In this paper, we show that one-qubit polynomial time computations are as powerful as NC1 circuits. More generally, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show that any NC1 language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless NC 1 = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC1. For read-once quantum branching programs (QBPs), we give a symmetric Boolean function which is computable by a read-once QBP with O (log n) width, but not by a deterministic read-once BP with o (n) width, or by a classical randomized read-once BP with o (n) width which is "stable" in the sense that its transitions depend on the value of the queried variable but do not vary from step to step. Finally, we present a general lower bound on the width of read-once QBPs, showing that our O (log n) upper bound for this symmetric function is almost tight. © 2005 Elsevier Inc. All rights reserved

A role for cell sex in stem cell-mediated skeletal muscle regeneration: Female cells have higher muscle regeneration efficiency

We have shown that muscle-derived stem cells (MDSCs) transplanted into dystrophic (mdx) mice efficiently regenerate skeletal muscle. However, MDSC populations exhibit heterogeneity in marker profiles and variability in regeneration abilities. We show here that cell sex is a variable that considerably influences MDSCs' regeneration abilities. We found that the female MDSCs (F-MDSCs) regenerated skeletal muscle more efficiently. Despite using additional isolation techniques and cell cloning, we could not obtain a male subfraction with a regeneration capacity similar to that of their female counterparts. Rather than being directly hormonal or caused by host immune response, this difference in MDSCs' regeneration potential may arise from innate sex-related differences in the cells' stress responses. In comparison with F-MDSCs, male MDSCs have increased differentiation after exposure to oxidative stress induced by hydrogen peroxide, which may lead to in vivo donor cell depletion, and a proliferative advantage for F-MDSCs that eventually increases muscle regeneration. These findings should persuade researchers to report cell sex, which is a largely unexplored variable, and consider the implications of relying on cells of one sex. © The Rockefeller University Press

Using outbreak science to strengthen the use of models during epidemics.

Infectious disease modeling has played a prominent role in recent outbreaks, yet integrating these analyses into public health decision-making has been challenging. We recommend establishing ‘outbreak science’ as an inter-disciplinary field to improve applied epidemic modeling