A Caratheodory theorem for the bidisk via Hilbert space methods

If \ph is an analytic function bounded by 1 on the bidisk \D^2 and \tau\in\tb is a point at which \ph has an angular gradient \nabla\ph(\tau) then \nabla\ph(\la) \to \nabla\ph(\tau) as \la\to\tau nontangentially in \D^2. This is an analog for the bidisk of a classical theorem of Carath\'eodory for the disk. For \ph as above, if \tau\in\tb is such that the $\liminf$ of (1-|\ph(\la)|)/(1-\|\la\|) as \la\to\tau is finite then the directional derivative D_{-\de}\ph(\tau) exists for all appropriate directions \de\in\C^2. Moreover, one can associate with \ph and $\tau$ an analytic function $h$ in the Pick class such that the value of the directional derivative can be expressed in terms of $h$

Operator monotone functions and L\"owner functions of several variables

We prove generalizations of L\"owner's results on matrix monotone functions to several variables. We give a characterization of when a function of $d$ variables is locally monotone on $d$-tuples of commuting self-adjoint $n$-by-$n$ matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone

NLTE and LTE Lick indices for red giants from [M/H] 0.0 to -6.0 at SDSS and IDS spectral resolution

We investigate the dependence of the complete system of 22 Lick indices on overall metallicity scaled from solar abundances, [M/H], from the solar value, 0.0, down to the extremely-metal-poor (XMP) value of -6.0, for late-type giant stars (MK luminosity class III, log(g)=2.0) of MK spectral class late-K to late-F (3750 < Teff < 6500 K) of the type that are detected as "fossils" of early galaxy formation in the Galactic halo and in extra-galactic structures. Our investigation is based on synthetic index values, I, derived from atmospheric models and synthetic spectra computed with PHOENIX in LTE and Non-LTE (NLTE), where the synthetic spectra have been convolved to the spectral resolution, R, of both IDS and SDSS (and LAMOST) spectroscopy. We identify nine indices, that we designate "Lick-XMP", that remain both detectable and significantly [M/H]-dependent down to [M/H] values of at least ~-5.0, and down to [M/H] ~ -6.0 in five cases, while also remaining well-behaved . For these nine, we study the dependence of I on NLTE effects, and on spectral resolution. For our LTE I values for spectra of SDSS resolution, we present the fitted polynomial coefficients, C_n, from multi-variate linear regression for I with terms up to third order in the independent variable pairs (Teff, [M/H]), and (V-K, [M/H]), and compare them to the fitted C_n values of Worthey et al. (1994) at IDS spectral resolution.Comment: Accepted for publication in the Astrophysical Journal. Tables 6 and 7 available electronically from the autho

Regional data refine local abundance models: modeling plant species abundance distributions on the Central Plains

2010 Fall.Includes bibliographical references.Species distribution models are frequently used to predict species occurrences in novel conditions, yet few studies have examined the effects of extrapolating locally collected data to regional scale landscapes. Using boosted regression trees, I examined the issues of spatial scale and errors associated with extrapolating species distribution models developed using locally collected abundance data to regional extents for a native and alien plant species across a portion of the central plains in Colorado. Topographic, remotely sensed, land cover and soil taxonomic predictor variables were used to develop the models. Predicted means and ranges were compared among models and predictions were compared to observed values between local and regional extent models. All models had significant predictive ability (p < 0.001). My results suggested: (1) extrapolating local models to regional extents may restrict predictions; (2) modeling species abundance may prove more useful than models of species presence; (3) multiple sources of predictors may improve model results at different extents; and (4) regional data can help refine and improve local model predictions. Regional sampling designed in concert with large sampling frameworks such as the National Ecological Observatory Network, Inc (NEON) may improve our ability to monitor changes in local species abundanc

Evaluating Simplistic Methods to Understand Current Distributions and Forecast Distribution Changes Under Climate Change Scenarios: An Example With Coypu (Myocastor coypus)

Invasive species provide a unique opportunity to evaluate factors controlling biogeographic distributions; we can consider introduction success as an experiment testing suitability of environmental conditions. Predicting potential distributions of spreading species is not easy, and forecasting potential distributions with changing climate is even more difficult. Using the globally invasive coypu (Myocastor coypus [Molina, 1782]), we evaluate and compare the utility of a simplistic ecophysiological based model and a correlative model to predict current and future distribution. The ecophysiological model was based on winter temperature relationships with nutria survival. We developed correlative statistical models using the Software for Assisted Habitat Modeling and biologically relevant climate data with a global extent. We applied the ecophysiological based model to several global circulation model (GCM) predictions for mid-century. We used global coypu introduction data to evaluate these models and to explore a hypothesized physiological limitation, finding general agreement with known coypu distribution locally and globally and support for an upper thermal tolerance threshold. Global circulation model based model results showed variability in coypu predicted distribution among GCMs, but had general agreement of increasing suitable area in the USA. Our methods highlighted the dynamic nature of the edges of the coypu distribution due to climate non-equilibrium, and uncertainty associated with forecasting future distributions. Areas deemed suitable habitat, especially those on the edge of the current known range, could be used for early detection of the spread of coypu populations for management purposes. Combining approaches can be beneficial to predicting potential distributions of invasive species now and in the future and in exploring hypotheses of factors controlling distributions

PCNA Ubiquitination Is Important, But Not Essential for Translesion DNA Synthesis in Mammalian Cells

Translesion DNA synthesis (TLS) is a DNA damage tolerance mechanism in which specialized low-fidelity DNA polymerases bypass replication-blocking lesions, and it is usually associated with mutagenesis. In Saccharomyces cerevisiae a key event in TLS is the monoubiquitination of PCNA, which enables recruitment of the specialized polymerases to the damaged site through their ubiquitin-binding domain. In mammals, however, there is a debate on the requirement for ubiquitinated PCNA (PCNA-Ub) in TLS. We show that UV-induced Rpa foci, indicative of single-stranded DNA (ssDNA) regions caused by UV, accumulate faster and disappear more slowly in Pcna(K164R/K164R) cells, which are resistant to PCNA ubiquitination, compared to Pcna(+/+) cells, consistent with a TLS defect. Direct analysis of TLS in these cells, using gapped plasmids with site-specific lesions, showed that TLS is strongly reduced across UV lesions and the cisplatin-induced intrastrand GG crosslink. A similar effect was obtained in cells lacking Rad18, the E3 ubiquitin ligase which monoubiquitinates PCNA. Consistently, cells lacking Usp1, the enzyme that de-ubiquitinates PCNA exhibited increased TLS across a UV lesion and the cisplatin adduct. In contrast, cells lacking the Rad5-homologs Shprh and Hltf, which polyubiquitinate PCNA, exhibited normal TLS. Knocking down the expression of the TLS genes Rev3L, PolH, or Rev1 in Pcna(K164R/K164R) mouse embryo fibroblasts caused each an increased sensitivity to UV radiation, indicating the existence of TLS pathways that are independent of PCNA-Ub. Taken together these results indicate that PCNA-Ub is required for maximal TLS. However, TLS polymerases can be recruited to damaged DNA also in the absence of PCNA-Ub, and perform TLS, albeit at a significantly lower efficiency and altered mutagenic specificity

Flux Crystal Growth of the RE2Ru3Ge5 (RE = La, Ce, Nd, Gd, Tb) Series and Their Magnetic and Metamagnetic Transitions

Previously synthesized only as powders, single crystals of the RE2Ru3Ge5 (RE = La, Ce, Nd, Gd, Tb) series of compounds have now been obtained from molten In. These materials crystallize with the U2Co3Si5-type structure in orthorhombic space group Ibam with lattice parameters a ≈ 10.00–9.77 Å (La–Tb), b ≈ 12.51–12.35 Å, and c ≈ 5.92–5.72 Å. The structure is a three-dimensional framework consisting of RuGe5 and RuGe6 units, as well as Ge–Ge zigzag chains. This structure type and those of the other five (Sc2Fe3Si5, Lu2Co3Si5, Y2Rh3Sn5, Yb2Ir3Ge5, and Yb2Pt3Sn5) to compose the RE2T3X5 phase space are discussed in depth. For the three compounds with RE = Nd, Gd, Tb, multiple magnetic transitions and metamagnetic behavior are observed. Electronic band structure calculations performed on La2Ru3Ge5 indicate that these materials have a negative band gap and are semimetallic in nature