Toward a Quantization of Null Dust Collapse

Spherically symmetric, null dust clouds, like their time-like counterparts, may collapse classically into black holes or naked singularities depending on their initial conditions. We consider the Hamiltonian dynamics of the collapse of an arbitrary distribution of null dust, expressed in terms of the physical radius, $R$, the null coordinates, $V$ for a collapsing cloud or $U$ for an expanding cloud, the mass function, $m$, of the null matter, and their conjugate momenta. This description is obtained from the ADM description by a Kucha\v{r}-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions.Comment: 10 pages, 2 figures (eps), RevTeX4. The last two sections have been revised and corrected. To appear in Phys. Rev.

The guanine nucleotide exchange factor Arhgef7/beta Pix promotes axon formation upstream of TC10

The characteristic six layers of the mammalian neocortex develop sequentially as neurons are generated by neural progenitors and subsequently migrate past older neurons to their final position in the cortical plate. One of the earliest steps of neuronal differentiation is the formation of an axon. Small GTPases play essential roles during this process by regulating cytoskeletal dynamics and intracellular trafficking. While the function of GTPases has been studied extensively in cultured neurons and in vivo much less is known about their upstream regulators. Here we show that Arhgef7 (also called \u3b2Pix or Cool1) is essential for axon formation during cortical development. The loss of Arhgef7 results in an extensive loss of axons in cultured neurons and in the developing cortex. Arhgef7 is a guanine-nucleotide exchange factor (GEF) for Cdc42, a GTPase that has a central role in directing the formation of axons during brain development. However, active Cdc42 was not able to rescue the knockdown of Arhgef7. We show that Arhgef7 interacts with the GTPase TC10 that is closely related to Cdc42. Expression of active TC10 can restore the ability to extend axons in Arhgef7-deficient neurons. Our results identify an essential role of Arhgef7 during neuronal development that promotes axon formation upstream of TC10

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Looking forward through the past: identification of 50 priority research questions in palaeoecology

1. Priority question exercises are becoming an increasingly common tool to frame future agendas in conservation and ecological science. They are an effective way to identify research foci that advance the field and that also have high policy and conservation relevance. 2. To date, there has been no coherent synthesis of key questions and priority research areas for palaeoecology, which combines biological, geochemical and molecular techniques in order to reconstruct past ecological and environmental systems on time-scales from decades to millions of years. 3. We adapted a well-established methodology to identify 50 priority research questions in palaeoecology. Using a set of criteria designed to identify realistic and achievable research goals, we selected questions from a pool submitted by the international palaeoecology research community and relevant policy practitioners. 4. The integration of online participation, both before and during the workshop, increased international engagement in question selection. 5. The questions selected are structured around six themes: human–environment interactions in the Anthropocene; biodiversity, conservation and novel ecosystems; biodiversity over long time-scales; ecosystem processes and biogeochemical cycling; comparing, combining and synthesizing information from multiple records; and new developments in palaeoecology. 6. Future opportunities in palaeoecology are related to improved incorporation of uncertainty into reconstructions, an enhanced understanding of ecological and evolutionary dynamics and processes and the continued application of long-term data for better-informed landscape management

The guanine nucleotide exchange factor Arhgef7/βPix promotes axon formation upstream of TC10

The characteristic six layers of the mammalian neocortex develop sequentially as neurons are generated by neural progenitors and subsequently migrate past older neurons to their final position in the cortical plate. One of the earliest steps of neuronal differentiation is the formation of an axon. Small GTPases play essential roles during this process by regulating cytoskeletal dynamics and intracellular trafficking. While the function of GTPases has been studied extensively in cultured neurons and in vivo much less is known about their upstream regulators. Here we show that Arhgef7 (also called βPix or Cool1) is essential for axon formation during cortical development. The loss of Arhgef7 results in an extensive loss of axons in cultured neurons and in the developing cortex. Arhgef7 is a guanine-nucleotide exchange factor (GEF) for Cdc42, a GTPase that has a central role in directing the formation of axons during brain development. However, active Cdc42 was not able to rescue the knockdown of Arhgef7. We show that Arhgef7 interacts with the GTPase TC10 that is closely related to Cdc42. Expression of active TC10 can restore the ability to extend axons in Arhgef7-deficient neurons. Our results identify an essential role of Arhgef7 during neuronal development that promotes axon formation upstream of TC10

Efficiency of profile likelihood in semi-parametric models

Semi-parametric model, Profile likelihood, Two-phase outcome-dependent sampling, Efficiency, M-estimator, Maximum likelihood estimator, Efficient score, Efficient information bound,

Semiparametric mixtures in case-controlstudies

AbstractWe consider likelihood based inference in a class of logistic models for case- control studies with a partially observed covariate. The likelihood is a combination of a nonparametric mixture, a parametric likelihood, and an empirical likelihood. We prove the asymptotic normality of the maximum likelihood estimator for the regression slope, the asymptotic chi-squared distribution of the likelihood ratio statistic, and the consistency of the observed information, in both the prospective and the retrospective model