Stochastic approximation of score functions for Gaussian processes

We discuss the statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number of the covariance matrix, the approach achieves $O(n)$ storage and nearly $O(n)$ computational effort per optimization step, where $n$ is the number of data sites. Here, we prove that if the condition number of the covariance matrix is bounded, then the approximate score equations are nearly optimal in a well-defined sense. Therefore, not only is the approximation efficient to compute, but it also has comparable statistical properties to the exact maximum likelihood estimates. We discuss a modification of the stochastic approximation in which design elements of the stochastic terms mimic patterns from a $2^n$ factorial design. We prove these designs are always at least as good as the unstructured design, and we demonstrate through simulation that they can produce a substantial improvement over random designs. Our findings are validated by numerical experiments on simulated data sets of up to 1 million observations. We apply the approach to fit a space-time model to over 80,000 observations of total column ozone contained in the latitude band $40^{\circ}$-$50^{\circ}$N during April 2012.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS627 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scaling Relations for Galaxies Prior to Reionization

The first galaxies in the Universe are the building blocks of all observed galaxies. We present scaling relations for galaxies forming at redshifts $z \ge 15$ when reionization is just beginning. We utilize the ``Rarepeak' cosmological radiation hydrodynamics simulation that captures the complete star formation history in over 3,300 galaxies, starting with massive Population III stars that form in dark matter halos as small as ~$10^6 M_\odot$. We make various correlations between the bulk halo quantities, such as virial, gas, and stellar masses and metallicities and their respective accretion rates, quantifying a variety of properties of the first galaxies up to halo masses of $10^9 M_\odot$. Galaxy formation is not solely relegated to atomic cooling halos with virial temperatures greater than $10^4$ K, where we find a dichotomy in galaxy properties between halos above and below this critical mass scale. Halos below the atomic cooling limit have a stellar mass -- halo mass relationship $\log M_\star \simeq 3.5 + 1.3\log(M_{\rm vir} / 10^7 M_\odot)$. We find a non-monotonic relationship between metallicity and halo mass for the smallest galaxies. Their initial star formation events enrich the interstellar medium and subsequent star formation to a median of $10^{-2} Z_\odot$ and $10^{-1.5} Z_\odot$, respectively, in halos of total mass $10^7 M_\odot$ that is then diluted by metal-poor inflows, well beyond Population III pre-enrichment levels of $10^{-3.5} Z_\odot$. The scaling relations presented here can be employed in models of reionization, galaxy formation and chemical evolution in order to consider these galaxies forming prior to reionization.Comment: 10 pages, 10 figures. Accepted to Ap

TGF-β-responsive CAR-T cells promote anti-tumor immune function.

A chimeric antigen receptor (CAR) that responds to transforming growth factor beta (TGF-β) enables the engineering of T cells that convert this immunosuppressive cytokine into a potent T-cell stimulant. However, clinical translation of TGF-β CAR-T cells for cancer therapy requires the ability to productively combine TGF-β responsiveness with tumor-targeting specificity. Furthermore, the potential concern that contaminating, TGF-β?producing regulatory T (Treg) cells may preferentially expand during TGF-β CAR-T cell manufacturing and suppress effector T (Teff) cells demands careful evaluation. Here, we demonstrate that TGF-β CAR-T cells significantly improve the anti-tumor efficacy of neighboring cytotoxic T cells. Furthermore, the introduction of TGF-β CARs into mixed T-cell populations does not result in the preferential expansion of Treg cells, nor do TGF-β CAR-Treg cells cause CAR-mediated suppression of Teff cells. These results support the utility of incorporating TGF-β CARs in the development of adoptive T-cell therapy for cancer

Income Distribution Dynamics With Endogenous Fertility

Developing countries with highly unequal income distributions, such as Brazil or South Africa, face an uphill battle in reducing inequality. Educated workers in these countries have a much lower birth rate than uneducated workers. Assuming children of educated workers are more likely to become educated, this fertility differential increaases the proportion of unskilled workers, reducing their wages, and thus their opportunity cost of having children, creating a vicious cycle. A model incorporating this effect generates multiple stedy-state levels of inequality, suggesting that in some circumstances, temporarily increasing access to educational opportunities could permanently reduce inequality. Empirical evidence suggests that the fertility differential between the educated and uneducated is greater in less equal countries, consistent with the model. An earlier version of this paper was published in the AEA Papers and Proceedings, May 1999 and is also available here

Fluctuation-dissipation ratios in the dynamics of self-assembly

We consider two seemingly very different self-assembly processes: formation of viral capsids, and crystallization of sticky discs. At low temperatures, assembly is ineffective, since there are many metastable disordered states, which are a source of kinetic frustration. We use fluctuation-dissipation ratios to extract information about the degree of this frustration. We show that our analysis is a useful indicator of the long term fate of the system, based on the early stages of assembly.Comment: 8 pages, 6 figure