Set Of Cut Points Research Articles

The TWEAK: application in a prenatal setting.

The TWEAK is a screening instrument used to identify women who are risk drinkers. Potential limitations of previous studies of the TWEAK in the prenatal setting include indirect administration of the instrument to minority, indigent pregnant women. The purpose of this study is to assess the efficacy of the TWEAK when it is given directly to a sample of pregnant women of different socioeconomic backgrounds. The original TWEAK, with two different tolerance questions, was administered to a sample of 135 pregnant women enrolled in a study of alcohol use during pregnancy at the obstetrics practices of the Brigham and Women's Hospital in Boston, Massachusetts. The TWEAK, using the first tolerance question (number of drinks before feeling the first effects of alcohol) with the cut point set at more than two drinks, had the best predictive ability for lifetime alcohol diagnoses and risk drinking. The sensitivity of the TWEAK can be increased if the cut point for the first tolerance question is set at two drinks, with some loss of specificity and predictive ability. Medical record assessment was the least sensitive but most specific method of identifying alcohol use by pregnant women. The TWEAK has promise as a screening instrument for identifying risk drinking during pregnancy. Future work should include testing in other clinical populations.

Alternative short tests for inspection and maintenance of in-use cars with respect to their emissions performance

This paper presents the first results of a project aimed at evaluation of a number of short tests that can be alternatively used for Inspection and Maintenance of in-use cars emissions performance. For this purpose, a large number of in-use cars from four European countries was tested according to a test protocol that included a wide selection of short tests (idle and fast idle tests, a steady-state loaded test and short transient loaded tests), in addition to the legislated New European Driving Cycle and a number of real-world cycles. The test results were statistically analysed in a number of different combinations, with the objective to define a set of reasonable cutpoints, taking into account various criteria such as errors of commission, errors of omission, excess emitter identification rate and excess emission identification rate.

The case identification of dementia in the community: A comparison of methods

AbstractFew studies have compared methods of case identification in dementia in detail. In this epidemiological study of cognitive function and dementia, scales and clinical diagnoses were compared in 365 women aged between 70 and 79. The women were interviewed using CAMDEX (Cambridge Examination for Mental Disorders of the Elderly), which includes established and new scales of cognitive function and behaviour. In addition, the information/orientation subscale of the Clifton Assessment Procedure for the Elderly was recorded. The proportions of the population identified by various recommended cutpoints for these scales were calculated. Sensitivities and specificities for these were compared, using CAMDEX clinical diagnosis as the standard. Large differences were found in these according to both the cutpoint set and the level of dementia examined. Each subject was rated by her own general practitioner and a random 10% of the sample was seen using the Geriatric Mental State Examination in addition to CAMDEX. The different diagnoses were compared and considerable variation found.

An optimal variable cell histogram

A simple procedure for specifying a histogram with variable cell sizes is proposed. The procedure chooses a set of cutpoints that maximizes a criterion function based on the sample spacings:Under some conditions, this estimated set of cutpoints is shown to converge in probability to the theoretical set of cutpoints for the histogram estimate that minimizes the Hellingerdistance to the underlying density. An algorithm for finding the set of cutpoints that numerically maximizes the criterion function is presented along with an example. Performance for finite sample sizes is evaluated by simulations.

The Orderability and Suborderability of Metrizable Spaces

A space is defined to be suborderable if it is embeddable in a (totally) orderable space. It is shown that a metrizable space X is suborderable iff (1) each component of X is orderable, (2) the set of cut points of each component of X is open, and (3) each closed subset of X which is a union of components has a base of clopen neighborhoods. Note that condition (1) and hence this result is topological since there are many good topological characterizations of connected orderable spaces. In a space X let Q denote the union of all nondegenerate components each of whose noncut points has no compact neighborhood. It is also shown that a metrizable space X is orderable iff (1) X is suborderable, (2) $X - Q$ is not a proper compact open subset of X, and (3) if W is a neighborhood of $p \in X$ and K is the component in X containing p such that $(W - K) - Q$ has compact closure and $\{ p\}$ is the intersection of the closures of $(W - K) - Q$ and $(W - K) \cap Q$, then K is a singleton. Corollaries are given; every condition in each of these corollaries is concisely stated and sufficient for a space to be orderable when it is metrizable and suborderable. Both of these results are extended to a class properly containing the metrizable spaces.

The orderability and suborderability of metrizable spaces

A space is defined to be suborderable if it is embeddable in a (totally) orderable space. It is shown that a metrizable space X is suborderable iff (1) each component of X is orderable, (2) the set of cut points of each component of X is open, and (3) each closed subset of X which is a union of components has a base of clopen neighborhoods. Note that condition (1) and hence this result is topological since there are many good topological characterizations of connected orderable spaces. In a space X let Q denote the union of all nondegenerate components each of whose noncut points has no compact neighborhood. It is also shown that a metrizable space X is orderable iff (1) X is suborderable, (2) X − Q X - Q is not a proper compact open subset of X, and (3) if W is a neighborhood of p ∈ X p \in X and K is the component in X containing p such that ( W − K ) − Q (W - K) - Q has compact closure and { p } \{ p\} is the intersection of the closures of ( W − K ) − Q (W - K) - Q and ( W − K ) ∩ Q (W - K) \cap Q , then K is a singleton. Corollaries are given; every condition in each of these corollaries is concisely stated and sufficient for a space to be orderable when it is metrizable and suborderable. Both of these results are extended to a class properly containing the metrizable spaces.

Semi-local-connectedness and cut points in metric continua

In the first section of this paper, the notion of a space being rational at a point is generalized to what is here called quasi-rational at a point. It is shown that a compact metric continuum which is quasi-rational at each point of a dense subset of an open set is both connected im kleinen and semi-locally-connected on a dense subset of that open set. In the second section a G, set is constructed such that every point in the GQ at which the space is not semi-locally-connected is a cut point. A condition is given for this G, set to be dense. This condition, in addition to requiring that the space be not semi-locally-connected at any point of a dense G5 set gives a sufficient condition for the space to contain a G, set of cut points. The condition generalizes that given by Grace. 1. Throughout this paper M will be taken to be a compact metric continuum. Many of the lemmas, however, can be proven with less hypotheses. Lemma 2, for example, requires only that the sets P, (defined below) be subcontinua of M. Compact Hausdorff is sufficient for this to happen [4]. Let x, y, and z be points of M (not necessarily distinct). The point x cuts between y and z in M when every subcontinuum of M which contains both y and z must also contain x. The point x is a cut point of M when x cuts between two points distinct from x. M is said to be aposyndetic (semi-locally-connected) at x wvith respect to y if and only if there is a subcontinuum of M with x (y) in its interior that does not contain y (x). M is aposyndetic (semi-locally-connected) at x when it is aposyndetic (semi-locally-connected) at x with respect to every other point. Finally, M is connected im kleinen at x when each neighborhood of x contains a closed neighborhood of x which is also connected. One should note that when M is connected im kleinen at a point, it is also aposyndetic at that point. For x E M, P, denotes {y E M I M is not aposyndetic at y with respect to x}, and for T c M, PT denotes n {H I T c HO and H is a Received by the editors May 20, 1970. AMS 1969 subject classifications. Primary 5455.

On the category of the set of cut points of continua of a certain type

On the category of the set of cut points of continua of a certain type

The Dimension of the Planar Brownian Frontier is 4/3

In a series of recent preprints, we have proven that with probability one the Hausdorff dimension on the outer boundary of planar Brownian motion is 4/3, confirming a conjecture by Mandelbrot. It is also shown that the Hausdorff dimension of the set of cut points is a.s. 3/4. The present paper is an expository outline of the arguments involved in the proof of these and related results.