Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds

Let (S(t)) be a one-parameter family S = (S(t)) of positive integral operators on a locally compact space L. For a possibly non-uniform partition of [0,1] define a measure on the path space C([0,1],L) by using a) S(dt) for the transition between cosecutive partition times of distance dt, and b) a suitable continuous interpolation scheme (e.g. Brownian bridges or geodesics). If necessary normalize to get a probability measure. We prove a version of Chernoff's theorem of semigroup theory and tighness results which together yield convergence in law of such measures as the partition gets finer. In particular let L be a closed smooth submanifold of a Riemannian manifold M. We prove convergence of Brownian motion on M, conditioned to visit L at all partition times, to a process on L whose law has a Radon-Nikodym density with repect to Brownian motion on L which contains scalar, mean and sectional curvature terms. Various approximation schemes for Brownian motion are also given. These results substantially extend earlier work by the authors and by Andersson and Driver.Comment: 35 pages, revised version for publication, more detailed expositio

Sensory and demographic characteristics of deafblindness rehabilitation clients in Montreal, Canada

Purpose: Demographic changes are increasing the number of older adults with combined age-related vision and hearing loss, while medical advances increase the survival probability of children with congenital dual (or multiple) impairments due to pre-maturity or rare hereditary diseases. Rehabilitation services for these populations are highly in demand since traditional uni-sensory rehabilitation approaches using the other sense to compensate are not always utilizable. Very little is currently known about the client population characteristics with dual sensory impairment. The present study provides information about demographic and sensory variables of persons in the Montreal region that were receiving rehabilitation for dual impairment in December 2010. This information can inform researchers, clinicians, educators, as well as administrators about potential research and service delivery priorities. Method: A chart review of all client files across the three rehabilitation agencies that offer integrated dual sensory rehabilitation services in Montreal provided data on visual acuity, visual field, hearing detection thresholds, and demographic variables. Results: The 209 males and 355 females ranged in age from 4 months to 105 years (M = 71.9, S.D. = 24.6), indicating a prevalence estimate for dual sensory impairment at 15/100 000. Only 5.7% were under 18 years of age, while 69.1% were over the age of 65 years, with 43.1% over the age of 85 years. The diagnostic combination that accounted for 31% of the entire sample was age-related macular degeneration with presbycusis. Their visual and auditory measures indicated that older adults were likely to fall into moderate to severe levels of impairment on both measures. Individuals with Usher Syndrome comprised 20.9% (n = 118) of the sample. Conclusion: The age distribution in this sample of persons with dual sensory impairment indicates that service delivery planning will need to strongly consider the growing presence of older adults as the baby-boomers approach retirement age. The distribution of their visual and auditory limits indicates that the large majority of this client group has residual vision and hearing that can be maximized in the rehabilitation process in order to restore functional abilities and social participation. Future research in this area should identify the specific priorities in both rehabilitation and research in individuals affected with combined vision and hearing loss

Canadian research contributions to low vision rehabilitation: A quantitative systematic review

Purpose: Low vision rehabilitation research is a quickly growing area, due in part to the increase in the demand for services geared at older adults with age-related vision loss. Various professions collaborate to provide such rehabilitation services; however, it is currently unclear which profession takes the leading role in advancing the frontiers of low vision rehabilitation research. A recent review article proposed that in Canada, this role is held by physicians. The present study was conducted to replicate these findings under conditions of a systematic review. Method: A search of seven databases and a hand-search of four vision rehabilitation journals identified articles on low vision rehabilitation whose first author had an affiliation at a Canadian institution. Data on professional credentials, funding source, and study content was tabulated. Results: Of the 1,870 references, data from 215 eligible articles were extracted. The top four author credentials were optometrists (with or without PhD; 56 papers, 26.0%), followed by researchers with PhDs only (48 papers, 22.3%), researchers with master’s degrees (43 papers, 20.0%), and medical doctors (with or without PhD; 39 papers, 18.1%). Vision rehabilitation journals published 38 per cent of all papers, followed by ophthalmology (27%) and optometry journals (22%). Publications in the past 11 years amounted to over 50 per cent of the output over the 64-year publication history in this field in Canada, 70 per cent of which were based in universities. Conclusion: The results reflect the mosaic structure of low vision rehabilitation research in Canada, highlighting collaborations among researchers, clinicians, funding sources and rehabilitation agencies. Given its multidisciplinary nature, low vision rehabilitation research seems to be driven by collaboration among the professions

Towards more effective identification keys: A study of people identifying plant species characters

Abstract Accurate species identification is essential for ecological monitoring and biodiversity conservation. Interactive plant identification keys have been considerably improved in recent years, mainly by providing iconic symbols, illustrations, or images for the users, as these keys are also commonly used by people with relatively little plant knowledge. Only a few studies have investigated how well morphological characteristics can be recognized and correctly identified by people, which is ultimately the basis of an identification key's success. This study consists of a systematic evaluation of people's abilities in identifying plant‐specific morphological characters. We conducted an online survey where 484 participants were asked to identify 25 different plant character states on six images showing a plant from different perspectives. We found that survey participants correctly identified 79% of the plant characters, with botanical novices with little or no previous experience in plant identification performing slightly worse than experienced botanists. We also found that flower characters are more often correctly identified than leaf characteristics and that characters with more states resulted in higher identification errors. Additionally, the longer the time a participant needed for answering, the higher the probability of a wrong answer. Understanding what influences users' plant character identification abilities can improve the development of interactive identification keys, for example, by designing keys that adapt to novices as well as experts. Furthermore, our study can act as a blueprint for the empirical evaluation of identifications keys. Read the free Plain Language Summary for this article on the Journal blog

Robust nonparametric detection of objects in noisy images

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore important connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a finite sample performance of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049. Link to the abstract at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd

Delayed presentation of traumatic aortocaval fistula: A report of two cases and a review of the associated compensatory hemodynamic and structural changes

Chronic aortocaval fistula (ACF) is a rare complication of gunshot wounds to the abdomen. Herein we report two cases of traumatic ACF: one asymptomatic and the other presenting with congestive heart failure (CHF) 20 and 30 years, respectively, after their initial injury. The recent onset of CHF, the presence of a continuous abdominal bruit, and, in the second patient, a history of penetrating trauma suggested the diagnosis of ACF. The diagnosis was confirmed by computed tomography scanning in both patients. Surgical repair of the ACF in the symptomatic patient resulted in resolution of the CHF and reversed the dilatation of the aorta and inferior vena cava. The asymptomatic patient was lost to follow-up. CHF in a young male patient with a history of penetrating abdominal trauma should alert the surgeon to this rare complication

Disjoint minimal graphs

We prove that the number s(n) of disjoint minimal graphs supported on domains in R^n is bounded by e(n+1)^2. In the two-dimensional case we show that s(2) is at most three (the conjectured number is two).Comment: 14 page

The size of Wiman-Valiron disks

Wiman-Valiron theory and results of Macintyre about "flat regions" describe the asymptotic behavior of entire functions in certain disks around points of maximum modulus. We estimate the size of these disks for Macintyre's theory from above and below.Comment: 20 page