Some Aspects of Measurement Error in Linear Regression of Astronomical Data

I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression relationship. The method is based on deriving a likelihood function for the measured data, and I focus on the case when the intrinsic distribution of the independent variables can be approximated using a mixture of Gaussians. I generalize the method to incorporate multiple independent variables, non-detections, and selection effects (e.g., Malmquist bias). A Gibbs sampler is described for simulating random draws from the probability distribution of the parameters, given the observed data. I use simulation to compare the method with other common estimators. The simulations illustrate that the Gaussian mixture model outperforms other common estimators and can effectively give constraints on the regression parameters, even when the measurement errors dominate the observed scatter, source detection fraction is low, or the intrinsic distribution of the independent variables is not a mixture of Gaussians. I conclude by using this method to fit the X-ray spectral slope as a function of Eddington ratio using a sample of 39 z < 0.8 radio-quiet quasars. I confirm the correlation seen by other authors between the radio-quiet quasar X-ray spectral slope and the Eddington ratio, where the X-ray spectral slope softens as the Eddington ratio increases.Comment: 39 pages, 11 figures, 1 table, accepted by ApJ. IDL routines (linmix_err.pro) for performing the Markov Chain Monte Carlo are available at the IDL astronomy user's library, http://idlastro.gsfc.nasa.gov/homepage.htm

Additive manufacturing for solid oxide cell electrode fabrication

© The Electrochemical Society.Additive manufacturing can potentially offer a highly-defined electrode microstructure, as well as fast and reproducible electrode fabrication. Selective laser sintering is an additive manufacturing technique in which three-dimensional structures are created by bonding subsequent layers of powder using a laser. Although selective laser sintering can be applied to a wide range of materials, including metals and ceramics, the scientific and technical aspects of the manufacturing parameters and their impact on microstructural evolution during the process are not well understood. In the present study, a novel approach for electrode fabrication using selective laser sintering was evaluated by conducting a proof of concept study. A Ni-patterned fuel electrode was laser sintered on an yttria-stabilized zirconia substrate. The optimization process of laser parameters (laser sintering rate and laser power) and the electrochemical results of a full cell with a laser sintered electrode are presented. The challenges and prospects of using selective laser sintering for solid oxide cell fabrication are discussed

Virial Masses of Black Holes from Single Epoch Spectra of AGN

We describe the general problem of estimating black hole masses of AGN by calculating the conditional probability distribution of M_BH given some set of observables. Special attention is given to the case where one uses the AGN continuum luminosity and emission line widths to estimate M_BH, and we outline how to set up the conditional probability distribution of M_BH given the observed luminosity, line width, and redshift. We show how to combine the broad line estimates of M_BH with information from an intrinsic correlation between M_BH and L, and from the intrinsic distribution of M_BH, in a manner that improves the estimates of M_BH. Simulation was used to assess how the distribution of M_BH inferred from the broad line mass estimates differs from the intrinsic distribution, and we find that this can lead to an inferred distribution that is too broad. We use these results and a sample of 25 sources that have recent reverberation mapping estimates of AGN black hole masses to investigate the effectiveness of using the C IV emission line to estimate M_BH and to indirectly probe the C IV region size--luminosity (R--L) relationship. We estimated M_BH from both C IV and H-Beta for a sample of 100 sources, including new spectra of 29 quasars. We find that the two emission lines give consistent estimates if one assumes R \propto L^{1/2}_{UV} for both lines.Comment: 38 pages, 6 figures, accepted by Ap

Beyond glucose and Warburg: finding the sweet spot in cancer metabolism models

Advances in cancer biology have highlighted metabolic reprogramming as an essential aspect of tumorigenesis and progression. However, recent efforts to study tumor metabolism in vivo have identified some disconnects between in vitro and in vivo biology. This is due, at least in part, to the simplified nature of cell culture models and highlights a growing need to utilize more physiologically relevant approaches to more accurately assess tumor metabolism. In this review, we outline the evolution of our understanding of cancer metabolism and discuss some discrepancies between in vitro and in vivo conditions. We describe how the development of physiological media, in combination with advanced culturing methods, can bridge the gap between in vitro and in vivo metabolism

Bogomol'nyi Limit For Magnetic Vortices In Rotating Superconductor

This work is the sequel of a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. In the present paper, we carry out our analysis with a generalized Ginzburg-Landau description of the superconductor, which provides a prescription for the radial profile of the normal density within the vortex. Within this framework, it is shown that the Bogomol'nyi limit condition marking the boundary between type I and type II behavior is unaffected by the rotation of the background.Comment: 7 pages, uses RevTeX, submitted to Phys.Rev.

The Trouble With Fathers: The Impact of Time and Gendered-Thinking on Working Relationships Between Fathers and Social Workers in Child Protection Practice in England

The lives of families entering the child protection arena may be shaped by a range of troubles, including material deprivation, physical and mental health problems, and substance misuse or domestic abuse. Despite the interest in whole family approaches, the issue of how professionals fail to work effectively with fathers is long-standing and resistant to change. This article illustrates challenges in building working relationships with men, including the challenge of avoiding binary thinking in the assessment of fathers as “risk” or “resource.” Drawing on our qualitative longitudinal study of men’s experiences of child protection in England, we highlight how both organizational (clashing time perspectives) and cultural (gendered-thinking) factors can trouble the potential relationship between social workers and fathers. We argue for a more gender sensitive approach to social work practice, which can respond more fully and effectively to the experiences of fathers and mothers

Renormalisation of gravitational self interaction for wiggly strings

It is shown that for any elastic string model with energy density $U$ and tension $T$, the divergent contribution from gravitational self interaction can be allowed for by an action renormalisation proportional to $(U-T)^2$. This formula is applied to the important special case of a bare model of the transonic type (characterised by a constant value of the product $UT$) that represents the macroscopically averaged effect of shortwavelength wiggles on an underlying microscopic model of the Nambu-Goto type (characterised by $U=T$).Comment: 11 pages, Latex; original 8 page version extended to include estimates of relevant orders of magnitude. To be published in Physical Review,

Transonic Elastic Model for Wiggly Goto-Nambu String

The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a firm mathematical basis.Comment: 8 pages, plain TeX, no figure

Scale-invariant temporal history (SITH): optimal slicing of the past in an uncertain world

In both the human brain and any general artificial intelligence (AI), a representation of the past is necessary to predict the future. However, perfect storage of all experiences is not possible. One possibility, utilized in many applications, is to retain information about the past in a buffer. A limitation of this approach is that although events in the buffer are represented with perfect accuracy, the resources necessary to represent information at a particular time scale go up rapidly. Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH). This representation covers an exponentially large period of time in the past at the cost of sacrificing temporal accuracy for events further in the past. The form of this decay is scale-invariant and can be shown to be optimal in that it is able to respond to worlds with a wide range of time scales. We demonstrate the utility of this representation in learning to play a simple video game. In this environment, SITH exhibits better learning performance than a fixed-size buffer history representation. Whereas the buffer performs well as long as the temporal dependencies can be represented within the buffer, SITH performs well over a much larger range of time scales for the same amount of resources. Finally, we discuss how the application of SITH, along with other human-inspired models of cognition, could improve reinforcement and machine learning algorithms in general.First author draf