32,122 research outputs found

    Splitting of liftings in products of probability spaces

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    We prove that if (X,\mathfrakA,P) is an arbitrary probability space with countably generated \sigma-algebra \mathfrakA, (Y,\mathfrakB,Q) is an arbitrary complete probability space with a lifting \rho and \hat R is a complete probability measure on \mathfrakA \hat \otimes_R \mathfrakB determined by a regular conditional probability {S_y:y\in Y} on \mathfrakA with respect to \mathfrakB, then there exist a lifting \pi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R) and liftings \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\pi(E)]^y=\sigma_y\bigl([\pi(E)]^y\bigr). Assuming the absolute continuity of R with respect to P\otimes Q, we prove the existence of a regular conditional probability {T_y:y\in Y} and liftings \varpi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R), \rho' on (Y,\mathfrakB,\hat Q) and \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\varpi(E)]^y=\sigma_y\bigl([\varpi(E)]^y\bigr) and \varpi(A\times B)=\bigcup_{y\in\rho'(B)}\sigma_y(A)\times{y}\qquadif A\times B\in\mathfrakA\times\mathfrakB. Both results are generalizations of Musia\l, Strauss and Macheras [Fund. Math. 166 (2000) 281-303] to the case of measures which are not necessarily products of marginal measures. We prove also that liftings obtained in this paper always convert \hat R-measurable stochastic processes into their \hat R-measurable modifications.Comment: Published at http://dx.doi.org/10.1214/009117904000000018 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Juvenile rank acquisition is associated with fitness independent of adult rank

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    Social rank is a significant determinant of fitness in a variety of species. The importance of social rank suggests that the process by which juveniles come to establish their position in the social hierarchy is a critical component of development. Here, we use the highly predictable process of rank acquisition in spotted hyenas to study the consequences of variation in rank acquisition in early life. In spotted hyenas, rank is ‘inherited’ through a learning process called ‘maternal rank inheritance.’ This pattern is very consistent: approximately 80% of juveniles acquire the exact rank expected under the rules of maternal rank inheritance. The predictable nature of rank acquisition in these societies allows the process of rank acquisition to be studied independently from the ultimate rank that each juvenile attains. In this study, we use Elo-deviance scores, a novel application of the Elo-rating method, to calculate each juvenile’s deviation from the expected pattern of maternal rank inheritance during development. Despite variability in rank acquisition among juveniles, most of these juveniles come to attain the exact rank expected of them according to the rules of maternal rank inheritance. Nevertheless, we find that transient variation in rank acquisition in early life is associated with long-term fitness consequences for these individuals: juveniles ‘underperforming’ their expected ranks show reduced survival and lower lifetime reproductive success than better-performing peers, and this relationship is independent of both maternal rank and rank achieved in adulthood. We also find that multiple sources of early life adversity have cumulative, but not compounding, effects on fitness. Future work is needed to determine if variation in rank acquisition directly affects fitness, or if some other variable, such as maternal investment or juvenile condition, causes variation in both of these outcomes. (Includes Supplemental Materials and Reviewers\u27 Comments.

    Long-term survival for a cohort of adults with cerebral palsy

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    The aim of this study was to investigate long-term survival and examine causes of death in adult patients with cerebral palsy (CP). A 1940–1950 birth cohort based on paediatric case referral allows for long-term survival follow-up. Survival is analyzed by birth characteristics and severity of disability from age 20 years (and age 2y for a subset of the data). Survival outcome compared with that expected in the general population based on English life tables. The main cohort consisted of 341 individuals, with 193 males and 148 females. Conditional on surviving to age 20 years, almost 85% of the cohort survived to age 50 years (a comparable estimate for the general population is 96%). Very few deaths were attributed to CP for those people dying over 20 years of age. Females survived better than males. However, females faced a greater increase in risk relative to the general population than did males. We conclude that survival outlook is good though lower than in the general population. The relative risk of death compared with the UK population decreases with age, although it shows some indication of rising again after age 50 years. Many more deaths were caused by diseases of the respiratory system among those dying in their 20s and 30s than would be expected in the general population. Many fewer deaths than expected in this age group are caused by injuries and accidents. For those people who die in their 40s and 50s, an increase in deaths due to diseases of the circulatory system and neoplasms is observed. More deaths than expected in this age group are due to diseases of the nervous system

    Convergence properties of simple genetic algorithms

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    The essential parameters determining the behaviour of genetic algorithms were investigated. Computer runs were made while systematically varying the parameter values. Results based on the progress curves obtained from these runs are presented along with results based on the variability of the population as the run progresses

    Don't stop the song and dance: an evaluation of Write Dance practices in schools and early years settings

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    This evaluation explored the significance of physical movement and dance (known as Write Dance) to teach handwriting. The results highlight teacher observation in young children's mark-making, handwriting and the children's willingness to write and draw. Very young children demonstrated that they have greater enthusiasm and motivation to write and draw when teachers and practitioners plan dynamic, physical (dance) activities. Principally the message is; teachers and practitioners need to understand the importance of teaching gross-motor movements for handwriting. Furthermore, music and dance motivates children to engage with handwriting

    The large-scale morphology of IRAS galaxies

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    At present, visual inspection is the only method for comparing the large-scale morphologies in the distribution of galaxies to those in model universes generated by N-body simulations. To remedy the situation, we have developed a set of three structure functions (S1, S2, S3) that quantify the degree of large-scale prolateness, oblateness, and sphericity/uniformity of a 3-D particle distribution and have applied them to a volume-limited (less than = 4000 km/s) sample of 699 IRAS galaxies with f sub 60 greater than 1.2 Jy. To determine the structure functions, we randomly select 500 galaxies as origins of spherical windows of radius R sub w, locate the centroid of the galaxies in the window (assuming all galaxies have equal mass) and then, compute the principal moments of inertia (I sub 1, I sub 2, I sub 3) about the centroid. Each S sub i is a function of (I sub 2)/(I sub 1) and (I sub 3)/I sub 1). S1, S2, and S3 tend to unity for highly prolate, oblate, and uniform distributions, respectively and tend to zero otherwise. The resulting 500 values of S sub i at each scale R sub w are used to construct a histogram
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