How has our knowledge of dinosaur diversity through geologic time changed through research history?

Assessments of dinosaur macroevolution at any given time can be biased by the historical publication record. Recent studies have analysed patterns in dinosaur diversity that are based on secular variations in the numbers of published taxa. Many of these have employed a range of approaches that account for changes in the shape of the taxonomic abundance curve, which are largely dependent on databases compiled from the primary published literature. However, how these ‘corrected’ diversity patterns are influenced by the history of publication remains largely unknown. Here, we investigate the influence of publication history between 1991 and 2015 on our understanding of dinosaur evolution using raw diversity estimates and shareholder quorum subsampling for the three major subgroups: Ornithischia, Sauropodomorpha, and Theropoda. We find that, while sampling generally improves through time, there remain periods and regions in dinosaur evolutionary history where diversity estimates are highly volatile (e.g. the latest Jurassic of Europe, the mid-Cretaceous of North America, and the Late Cretaceous of South America). Our results show that historical changes in database compilation can often substantially influence our interpretations of dinosaur diversity. ‘Global’ estimates of diversity based on the fossil record are often also based on incomplete, and distinct regional signals, each subject to their own sampling history. Changes in the record of taxon abundance distribution, either through discovery of new taxa or addition of existing taxa to improve sampling evenness, are important in improving the reliability of our interpretations of dinosaur diversity. Furthermore, the number of occurrences and newly identified dinosaurs is still rapidly increasing through time, suggesting that it is entirely possible for much of what we know about dinosaurs at the present to change within the next 20 years

Parabolic oblique derivative problem in generalized Morrey spaces

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space

Singularities of Nonlinear Elliptic Systems

Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities as well as Hausdorff contents/dimensions, this paper estimates the singular sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a class of quadratic functionals inducing harmonic maps.Comment: 18 pages Communications in Partial Differential Equation

On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in Arch. Rational Mech. Ana

A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

A Novel fry1 Allele Reveals the Existence of a Mutant Phenotype Unrelated to 5′->3′ Exoribonuclease (XRN) Activities in Arabidopsis thaliana Roots

BACKGROUND Mutations in the FRY1/SAL1 Arabidopsis locus are highly pleiotropic, affecting drought tolerance, leaf shape and root growth. FRY1 encodes a nucleotide phosphatase that in vitro has inositol polyphosphate 1-phosphatase and 3',(2'),5'-bisphosphate nucleotide phosphatase activities. It is not clear which activity mediates each of the diverse biological functions of FRY1 in planta. PRINCIPAL FINDINGS A fry1 mutant was identified in a genetic screen for Arabidopsis mutants deregulated in the expression of Pi High affinity Transporter 1;4 (PHT1;4). Histological analysis revealed that, in roots, FRY1 expression was restricted to the stele and meristems. The fry1 mutant displayed an altered root architecture phenotype and an increased drought tolerance. All of the phenotypes analyzed were complemented with the AHL gene encoding a protein that converts 3'-polyadenosine 5'-phosphate (PAP) into AMP and Pi. PAP is known to inhibit exoribonucleases (XRN) in vitro. Accordingly, an xrn triple mutant with mutations in all three XRNs shared the fry1 drought tolerance and root architecture phenotypes. Interestingly these two traits were also complemented by grafting, revealing that drought tolerance was primarily conferred by the rosette and that the root architecture can be complemented by long-distance regulation derived from leaves. By contrast, PHT1 expression was not altered in xrn mutants or in grafting experiments. Thus, PHT1 up-regulation probably resulted from a local depletion of Pi in the fry1 stele. This hypothesis is supported by the identification of other genes modulated by Pi deficiency in the stele, which are found induced in a fry1 background. CONCLUSIONS/SIGNIFICANCE Our results indicate that the 3',(2'),5'-bisphosphate nucleotide phosphatase activity of FRY1 is involved in long-distance as well as local regulatory activities in roots. The local up-regulation of PHT1 genes transcription in roots likely results from local depletion of Pi and is independent of the XRNs.This work was supported by an ANR-GENOPLANT grant (RIBOROOT-ANR06 GPLA 011) and the CEA agency. Array hybridizations have been partly supported by RNG (Réseau National des Génopoles, Evry, France). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. No additional external funding received for this study

Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to $x$.Comment: 24 pages, to be submitte

A novel role for the root cap in phosphate uptake and homeostasis

The root cap has a fundamental role in sensing environmental cues as well as regulating root growth via altered meristem activity. Despite this well-established role in the control of developmental processes in roots, the root cap's function in nutrition remains obscure. Here, we uncover its role in phosphate nutrition by targeted cellular inactivation or phosphate transport complementation in Arabidopsis, using a transactivation strategy with an innovative high-resolution real-time P-33 imaging technique. Remarkably, the diminutive size of the root cap cells at the root-to-soil exchange surface accounts for a significant amount of the total seedling phosphate uptake (approximately 20%). This level of Pi absorption is sufficient for shoot biomass production (up to a 180% gain in soil), as well as repression of Pi starvation-induced genes. These results extend our understanding of this important tissue from its previously described roles in environmental perception to novel functions in mineral nutrition and homeostasis control

A limit model for thermoelectric equations

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.Comment: 20 page

UV-Optical Pixel Maps of Face-On Spiral Galaxies -- Clues for Dynamics and Star Formation Histories

UV and optical images of the face-on spiral galaxies NGC 6753 and NGC 6782 reveal regions of strong on-going star formation that are associated with structures traced by the old stellar populations. We make NUV--(NUV-I) pixel color-magnitude diagrams (pCMDs) that reveal plumes of pixels with strongly varying NUV surface brightness and nearly constant I surface brightness. The plumes correspond to sharply bounded radial ranges, with (NUV-I) at a given NUV surface brightness being bluer at larger radii. The plumes are parallel to the reddening vector and simple model mixtures of young and old populations, thus neither reddening nor the fraction of the young population can produce the observed separation between the plumes. The images, radial surface-brightness, and color plots indicate that the separate plumes are caused by sharp declines in the surface densities of the old populations at radii corresponding to disk resonances. The maximum surface brightness of the NUV light remains nearly constant with radius, while the maximum I surface brightness declines sharply with radius. An MUV image of NGC 6782 shows emission from the nuclear ring. The distribution of points in an (MUV-NUV) vs. (NUV-I) pixel color-color diagram is broadly consistent with the simple mixture model, but shows a residual trend that the bluest pixels in (MUV-NUV) are the reddest pixels in (NUV-I). This may be due to a combination of red continuum from late-type supergiants and [SIII] emission lines associated with HII regions in active star-forming regions. We have shown that pixel mapping is a powerful tool for studying the distribution and strength of on-going star formation in galaxies. Deep, multi-color imaging can extend this to studies of extinction, and the ages and metallicities of composite stellar populations in nearby galaxies.Comment: LaTeX with AASTeX style file, 29 pages with 12 figures (some color, some multi-part). Accepted for publication in The Astrophysical Journa