Inhomogeneous universes in observational coordinates

Isotropic inhomogeneous dust universes are analysed via observational coordinates based on the past light cones of the observer's galactic worldline. The field equations are reduced to a single first--order {\sc ode} in observational variables on the past light cone, completing the observational integration scheme. This leads naturally to an explicit exact solution which is locally nearly homogeneous (i.e. {\sc frw}), but at larger redshift develops inhomogeneity. New observational characterisations of homogeneity ({\sc frw} universes) are also given.Comment: 17 pages LaTeX, no figures; to appear in Classical and Quantum Gravit

The Neural Covariance SDE: Shaped Infinite Depth-and-Width Networks at Initialization

The logit outputs of a feedforward neural network at initialization are conditionally Gaussian, given a random covariance matrix defined by the penultimate layer. In this work, we study the distribution of this random matrix. Recent work has shown that shaping the activation function as network depth grows large is necessary for this covariance matrix to be non-degenerate. However, the current infinite-width-style understanding of this shaping method is unsatisfactory for large depth: infinite-width analyses ignore the microscopic fluctuations from layer to layer, but these fluctuations accumulate over many layers. To overcome this shortcoming, we study the random covariance matrix in the shaped infinite-depth-and-width limit. We identify the precise scaling of the activation function necessary to arrive at a non-trivial limit, and show that the random covariance matrix is governed by a stochastic differential equation (SDE) that we call the Neural Covariance SDE. Using simulations, we show that the SDE closely matches the distribution of the random covariance matrix of finite networks. Additionally, we recover an if-and-only-if condition for exploding and vanishing norms of large shaped networks based on the activation function.Comment: 48 pages, 10 figures. To appear, Advances in Neural Information Processing Systems (2022

A portable audio/video recorder for longitudinal study of child development

Collection and analysis of ultra-dense, longitudinal observational data of child behavior in natural, ecologically valid, non-laboratory settings holds significant promise for advancing the understanding of child development and developmental disorders such as autism. To this end, we created the Speechome Recorder - a portable version of the embedded audio/video recording technology originally developed for the Human Speechome Project - to facilitate swift, cost-effective deployment in home environments. Recording child behavior daily in these settings will enable detailed study of developmental trajectories in children from infancy through early childhood, as well as typical and atypical dynamics of communication and social interaction as they evolve over time. Its portability makes possible potentially large-scale comparative study of developmental milestones in both neurotypical and developmentally delayed children. In brief, the Speechome Recorder was designed to reduce cost, complexity, invasiveness and privacy issues associated with naturalistic, longitudinal recordings of child development.National Institutes of Health (U.S.) (Grant R01 2DC007428)Nancy Lurie Marks Family Foundatio

Brexit Report - Impact on Business Models of Scottish Companies

The Brexit Business Model Report is a preliminary assessment of research, interviews and survey results regarding the impact of Brexit on the business models of Scottish companies as they prepare for post-Brexit scenarios. The survey was used to compile data to support research questions gathered during the research and interview process for this graduate class project. Questions were designed to assess how Brexit is impacting the ability of Scottish companies in the areas of business model, contingency planning, supply chain, staffing, innovation, global reach, risk assessment, and opportunities. The questions reflected areas of the business model that may have present and future implications. The answers help measure the Brexit impact on Scottish firms’ business models and the potential for international growth. The upper management of Scottish companies from the “Insider Top 500” list, “FactSet list, and various trade organizations were selected to receive the survey. The focus of this study was on the potential impact of Brexit on Scottish companies’ business models. The survey findings show the importance of understanding the elements of a business model in the Brexit context (see Additional File, Executive Summary below for Business Model Brexit Implications on Scottish Companies based on Key Findings table)

Lung Cancer Metastasis Presenting as a Solitary Skull Mass

Lung cancer has been well documented to spread to bone and the axial skeleton after metastasis to adjacent organs. Bony metastasis is not, however, the typical presenting manifestation. The differential diagnosis for a tissue mass on the skull should warrant a workup for metastatic disease. Bony metastasis plays an important role in treatment and disease management. We report an exceptionally rare case of stage IV lung adenocarcinoma that presented with a solitary skull metastasis and a significant soft-tissue component. The lesion was treated by excision via craniotomy and subsequent medical management of the adenocarcinoma. This case illustrates a very rare presentation of lung adenocarcinoma and also represents what the authors believe to be the first report of a solitary skull mass originating from a lung primary. We also present a review of the literature surrounding bony metastasis to the skull and implications for patient care

Performance of wheat varieties, Oklahoma - 1983

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