A quantitative three-dimensional image analysis tool for maximal acquisition of spatial heterogeneity data

Three-dimensional (3D) imaging techniques provide spatial insight into environmental and cellular interactions and are implemented in various fields, including tissue engineering, but have been restricted by limited quantification tools that misrepresent or underutilize the cellular phenomena captured. This study develops image postprocessing algorithms pairing complex Euclidean metrics with Monte Carlo simulations to quantitatively assess cell and microenvironment spatial distributions while utilizing, for the first time, the entire 3D image captured. Although current methods only analyze a central fraction of presented confocal microscopy images, the proposed algorithms can utilize 210% more cells to calculate 3D spatial distributions that can span a 23-fold longer distance. These algorithms seek to leverage the high sample cost of 3D tissue imaging techniques by extracting maximal quantitative data throughout the captured image

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

Tectonic motion site survey of the National Radio Astronomy Observatory, Green Bank, West Virginia

A geological and geophysical site survey was made of the area around the National Radio Astronomy Observatory (NRAO) to determine whether there are at present local tectonic movements that could introduce significant errors to Very Long Baseline Interferometry (VLBI) geodetic measurements. The site survey consisted of a literature search, photogeologic mapping with Landsat and Skylab photographs, a field reconnaissance, and installation of a seismometer at the NRAO. It is concluded that local tectonic movement will not contribute significantly to VLBI errors. It is recommended that similar site surveys be made of all locations used for VLBI or laser ranging

Reproducibility of the computational fluid dynamic analysis of a cerebral aneurysm monitored over a decade

Computational fluid dynamics (CFD) simulations are increasingly utilised to evaluate intracranial aneurysm (IA) haemodynamics to aid in the prediction of morphological changes and rupture risk. However, these models vary and differences in published results warrant the investigation of IA-CFD reproducibility. This study aims to explore sources of intra-team variability and determine its impact on the aneurysm morphology and CFD parameters. A team of four operators were given six sets of magnetic resonance angiography data spanning a decade from one patient with a middle cerebral aneurysm. All operators were given the same protocol and software for model reconstruction and numerical analysis. The morphology and haemodynamics of the operator models were then compared. The segmentation, smoothing factor, inlet and outflow branch lengths were found to cause intra-team variability. There was 80% reproducibility in the time-averaged wall shear stress distribution among operators with the major difference attributed to the level of smoothing. Based on these findings, it was concluded that the clinical applicability of CFD simulations may be feasible if a standardised segmentation protocol is developed. Moreover, when analysing the aneurysm shape change over a decade, it was noted that the co-existence of positive and negative values of the wall shear stress divergence (WSSD) contributed to the growth of a daughter sac

Assessing the capacity of local ecosystems to meet industrial demand for ecosystem services

Despite the importance of ecosystems, engineering activities continue to ignore or greatly undervalue their role. Consequently, engineered systems often overshoot nature's capacity to support them, causing ecological degradation. Such systems tend to be inherently unsustainable, and they often fail to benefit from nature's ability to provide essential goods and services. This work explores the idea of including ecosystems in chemical processes, and assesses whether such a techno-ecological synergistic system can operate within ecological constraints. The demand for ecosystem services is quantified by emissions and resources used, while the supply is provided by ecosystems on the manufacturing site. Application to a biodiesel manufacturing site demonstrates that ecosystems can be economically and environmentally superior to conventional technologies for making progress toward zero emissions and net positive impact manufacturing. These results highlight the need for shifting the paradigm of engineering from that of dominating nature to embracing nature and respecting its limits

Non-orientable surface-plus-one-relation groups

Recently Dicks-Linnell determined the $L^2$-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the $L^2$-Betti numbers of the non-orientable surface-plus-one-relation groups.Comment: Version 1. 37 pages. 0 figures. Dedicated to the memory of Karl Gruenber