Convergence of Markov processes near saddle fixed points.

We consider sequences (XtN)t≥0 of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form ẋt=b(xt), where for some λ, μ>0 and τ(x)=O(|x|2). Here the processes are indexed so that the variance of the fluctuations of XtN is inversely proportional to N. The simplest example arises from the OK Corral gunfight model which was formulated by Williams and McIlroy [Bull. London Math. Soc. 30 (1998) 166–170] and studied by Kingman [Bull. London Math. Soc. 31 (1999) 601–606]. These processes exhibit their most interesting behavior at times of order logN so it is necessary to establish a fluid limit that is valid for large times. We find that this limit is inherently random and obtain its distribution. Using this, it is possible to derive scaling limits for the points where these processes hit straight lines through the origin, and the minimum distance from the origin that they can attain. The power of N that gives the appropriate scaling is surprising. For example if T is the time that XtN first hits one of the lines y=x or y=−x, then Nμ/{(2(λ+μ))}|XTN| ⇒ |Z|μ/{(λ+μ)}, for some zero mean Gaussian random variable Z

Practical Strategies for Pharmacist Integration with Primary Care: A Workbook.

This workbook is a practical set of tips and resources to assist pharmacists in providing clinical pharmacy services to primary care providers and their patients. The content was written based on experiences in Vermont in 2014, however the topics should generalize to pharmacists in other areas

Collaborative Documentation for Behavioral Healthcare Providers: An Emerging Practice

This article considers the practice of collaborative documentation (CD) for behavioral healthcare providers; the legislative, technological, and philosophical milieu in which it developed; the attributed benefits for providers and clients; and the peer-reviewed research supporting its use. Collaborative documentation has emerged following significant legislative and technological changes in healthcare delivery and shifts toward client-centered healthcare practices including more shared decision-making between clients and practitioners

Time outdoors and the prevention of myopia

Recent epidemiological evidence suggests that children who spend more time outdoors are less likely to be, or to become myopic, irrespective of how much near work they do, or whether their parents are myopic. It is currently uncertain if time outdoors also blocks progression of myopia. It has been suggested that the mechanism of the protective effect of time outdoors involves light-stimulated release of dopamine from the retina, since increased dopamine release appears to inhibit increased axial elongation, which is the structural basis of myopia. This hypothesis has been supported by animal experiments which have replicated the protective effects of bright light against the development of myopia under laboratory conditions, and have shown that the effect is, at least in part, mediated by dopamine, since the D2-dopamine antagonist spiperone reduces the protective effect. There are some inconsistencies in the evidence, most notably the limited inhibition by bright light under laboratory conditions of lens-induced myopia in monkeys, but other proposed mechanisms possibly associated with time outdoors such as relaxed accommodation, more uniform dioptric space, increased pupil constriction, exposure to UV light, changes in the spectral composition of visible light, or increased physical activity have little epidemiological or experimental support. Irrespective of the mechanisms involved, clinical trials are now underway to reduce the development of myopia in children by increasing the amount of time they spend outdoors. These trials would benefit from more precise definition of thresholds for protection in terms of intensity and duration of light exposures. These can be investigated in animal experiments in appropriate models, and can also be determined in epidemiological studies, although more precise measurement of exposures than those currently provided by questionnaires is desirable