A crossover for the bad configurations of random walk in random scenery

In this paper, we consider a random walk and a random color scenery on Z. The increments of the walk and the colors of the scenery are assumed to be i.i.d. and to be independent of each other. We are interested in the random process of colors seen by the walk in the course of time. Bad configurations for this random process are the discontinuity points of the conditional probability distribution for the color seen at time zero given the colors seen at all later times. We focus on the case where the random walk has increments 0, +1 or -1 with probability epsilon, (1-epsilon)p and (1-epsilon)(1-p), respectively, with p in [1/2,1] and epsilon in [0,1), and where the scenery assigns the color black or white to the sites of Z with probability 1/2 each. We show that, remarkably, the set of bad configurations exhibits a crossover: for epsilon=0 and p in (1/2,4/5) all configurations are bad, while for (p,epsilon) in an open neighborhood of (1,0) all configurations are good. In addition, we show that for epsilon=0 and p=1/2 both bad and good configurations exist. We conjecture that for all epsilon in [0,1) the crossover value is unique and equals 4/5. Finally, we suggest an approach to handle the seemingly more difficult case where epsilon>0 and p in [1/2,4/5), which will be pursued in future work.Comment: Published in at http://dx.doi.org/10.1214/11-AOP664 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Heat content and inradius for regions with a Brownian boundary

In this paper we consider $\beta[0; s]$, Brownian motion of time length $s > 0$, in $m$-dimensional Euclidean space $\mathbb R^m$ and on the $m$-dimensional torus $\mathbb T^m$. We compute the expectation of (i) the heat content at time $t$ of $\mathbb R^m\setminus \beta[0; s]$ for fixed $s$ and $m = 2,3$ in the limit $t \downarrow 0$, when $\beta[0; s]$ is kept at temperature 1 for all $t > 0$ and $\mathbb R^m\setminus \beta[0; s]$ has initial temperature 0, and (ii) the inradius of $\mathbb R^m\setminus \beta[0; s]$ for $m = 2,3,\cdots$ in the limit $s \rightarrow \infty$.Comment: 13 page

Patient and Health System Experience With Implementation of an Enterprise-Wide Telehealth Scheduled Video Visit Program: Mixed-Methods Study.

BACKGROUND: Real-time video visits are increasingly used to provide care in a number of settings because they increase access and convenience of care, yet there are few reports of health system experiences. OBJECTIVE: The objective of this study is to report health system and patient experiences with implementation of a telehealth scheduled video visit program across a health system. METHODS: This is a mixed methods study including (1) a retrospective descriptive report of implementation of a telehealth scheduled visit program at one large urban academic-affiliated health system and (2) a survey of patients who participated in scheduled telehealth visits. Health system and patient-reported survey measures were aligned with the National Quality Forum telehealth measure reporting domains of access, experience, and effectiveness of care. RESULTS: This study describes implementation of a scheduled synchronous video visit program over an 18-month period. A total of 3018 scheduled video visits were completed across multiple clinical departments. Patient experiences were captured in surveys of 764 patients who participated in telehealth visits. Among survey respondents, 91.6% (728/795) reported satisfaction with the scheduled visits and 82.7% (628/759) reported perceived quality similar to an in-person visit. A total of 86.0% (652/758) responded that use of the scheduled video visit made it easier to get care. Nearly half (46.7%, 346/740) of patients estimated saving 1 to 3 hours and 40.8% (302/740) reported saving more than 3 hours of time. The net promoter score, a measure of patient satisfaction, was very high at 52. CONCLUSIONS: A large urban multihospital health system implemented an enterprise-wide scheduled telehealth video visit program across a range of clinical specialties with a positive patient experience. Patients found use of scheduled video visits made it easier to get care and the majority perceived time saved, suggesting that use of telehealth for scheduled visits can improve potential access to care across a range of clinical scenarios with favorable patient experiences

Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Synthesis of polyethers of hexafluorobenzene and hexafluoropentanediol

Two new polyethers, poly /hexafluoropentamethylene tetrafluoro-p-phenylene ether/ and a completely hydroxyl-terminated polyether, is prepared by reactions of hexafluorobenzene with hexafluoropentanediol. The polyethers can be prepared as low molecular weight oils, as intermediate molecular weight waxes, or as high molecular weight elastomers

Quality Assurance in Telehealth: Adherence to Evidence-Based Indicators.

Background: Value enhancing telehealth (TH) lacks a robust body of formal clinically focused quality assessment studies. Innovations such as telehealth must always demonstrate that it preserves or hopefully advances quality. Introduction: We sought to determine whether adherence to the evidence-based Choosing Wisely (CW) recommendations (antibiotic stewardship) for acute sinusitis differs for encounters through direct-to-consumer (DTC) telemedicine verses in-person care in an emergency department (ED) or an urgent care (UC) center. Materials and Methods: Study design was a retrospective review. Patients with a symptom complex consistent with acute sinusitis treated through DTC were matched with ED and UC patients, based upon time of visit. Charts were reviewed to determine patient characteristics, chief complaint, final diagnosis, presence or absence of criteria within the CW guidelines, and whether or not antibiotics were prescribed. The main outcome was adherence to the CW campaign recommendations. Results: A total of 570 visits were studied: 190 DTC, 190 ED, and 190 UC visits. The predominant chief complaints were upper respiratory infection (36%), sore throat (25%), and sinusitis (18%). Overall, there was a 67% (95% CI 62.3-71.7) adherence rate with the CW guidelines for sinusitis: DTC visits (71%), ED visits (68%), and UC visits (61%). There was a nonsignificant difference (p = 0.29) in adherence to CW guidelines based upon type of visit (DTC, UC, and ED). Discussion: The challenge is to demonstrate whether or not DTC TH compromises quality. Conclusion: In this study, DTC visits were associated with at least as good an adherence to the CW campaign recommendations as emergency medicine (EM) and UC in-person visits. © Daniel Halpren-Ruder et al

Purification of quantum trajectories

We prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of `dark' subspaces, where the time evolution is unitary.Comment: 10 page

It’s Complicated: Reflections on Teaching Negotiation for Women

What does it mean to be a woman negotiator? In the two decades that I have been teaching negotiation, I have encountered a wide range of human behavior in the negotiation setting. Individuals run the gamut in terms of their strategies, tactics, worldviews, charisma, perspicacity, flexibility, and other factors that affect negotiation behavior and negotiation outcomes. But one area that negotiation students are always curious about—be they top executives, law students, government employees, lawyers, or doctors—is the role of gender in negotiation. The maddening but intriguing answer to this question is the same as the answer to many other questions about negotiation: it’s complicated. The most important quality of negotiation is its dynamic and fluid nature, each encounter completely unique to its own participants and its own contexts, yet always with the possibility of analysis along a set of identifiable dimensions

Mrs. J.E. Hollander to Mr. Meredith (2 October 1962)

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