Limit theory for point processes in manifolds

Let $Y_i,i\geq1$, be i.i.d. random variables having values in an $m$-dimensional manifold $\mathcal {M}\subset \mathbb{R}^d$ and consider sums $\sum_{i=1}^n\xi(n^{1/m}Y_i,\{n^{1/m}Y_j\}_{j=1}^n)$, where $\xi$ is a real valued function defined on pairs $(y,\mathcal {Y})$, with $y\in \mathbb{R}^d$ and $\mathcal {Y}\subset \mathbb{R}^d$ locally finite. Subject to $\xi$ satisfying a weak spatial dependence and continuity condition, we show that such sums satisfy weak laws of large numbers, variance asymptotics and central limit theorems. We show that the limit behavior is controlled by the value of $\xi$ on homogeneous Poisson point processes on $m$-dimensional hyperplanes tangent to $\mathcal {M}$. We apply the general results to establish the limit theory of dimension and volume content estimators, R\'{e}nyi and Shannon entropy estimators and clique counts in the Vietoris-Rips complex on $\{Y_i\}_{i=1}^n$.Comment: Published in at http://dx.doi.org/10.1214/12-AAP897 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Caudal pneumaticity and pneumatic hiatuses in the sauropod dinosaurs Giraffatitan and Apatosaurus

Skeletal pneumaticity is found in the presacral vertebrae of most sauropod dinosaurs, but pneumaticity is much less common in the vertebrae of the tail. We describe previously unrecognized pneumatic fossae in the mid-caudal vertebrae of specimens of Giraffatitan and Apatosaurus. In both taxa, the most distal pneumatic vertebrae are separated from other pneumatic vertebrae by sequences of three to seven apneumatic vertebrae. Caudal pneumaticity is not prominent in most individuals of either of these taxa, and its unpredictable development means that it may be more widespread than previously recognised within Sauropoda and elsewhere in Saurischia. The erratic patterns of caudal pneumatization in Giraffatitan and Apatosaurus, including the pneumatic hiatuses, show that pneumatic diverticula were more broadly distributed in the bodies of the living animals than are their traces in the skeleton. Together with recently published evidence of cryptic diverticula--those that leave few or no skeletal traces--in basal sauropodomorphs and in pterosaurs, this is further evidence that pneumatic diverticula were widespread in ornithodirans, both across phylogeny and throughout anatomy

Organisational culture and effectiveness: a multi-perspective analysis on Indian knowledge-intensive firm

Purpose - The purpose of this paper is to critically evaluate the theorised relationship between organisational culture and effectiveness. Design/methodology/approach - The empirical data were collected through a five month ethnographic study in an Indian knowledge-intensive firm. It adopts the three perspectives framework of culture that encompasses integration, differentiation and fragmentation perspectives and a comprehensive examination of effectiveness. Findings: Integrated, differentiated and fragmented perspectives of culture capture multiple organizational values and they affect effectiveness in varied ways. Appropriate cultures, although not sufficient conditions, are crucial for effectiveness, especially in knowledge- intensive firms. High levels of differentiation and fragmentation prevent the formation of strong cultures. This challenges organisational integration. Practical implications: There is a heightened need for the application of sophisticated HRM systems in rhe software sector. Some context specific measures of effectiveness are documented. Originality/value: Through an insightful evaluation of culture effectiveness theorisation till date, the article amplifies current theorisation and illustrates the potential and limitations of organisational cultures in achieving effectiveness. Paper type - Research pape