Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

The Expected Perimeter in Eden and Related Growth Processes

Following Richardson and using results of Kesten on First-passage percolation, we obtain an upper bound on the expected perimeter in an Eden Growth Process. Using results of the author from a problem in Statistical Mechanics, we show that the average perimeter of the lattice animals resulting from a very natural family of "growth histories" does not obey a similar bound.Comment: 11 page

Yield Reserve Program Costs in the Virginia Coastal Plain

A proposed Yield Reserve Program designed to compensate farmers for any reduced yields resulting from nitrogen (N) application rates reduced to below recommended rates is evaluated. Assuming that farmers currently follow Extension recommendations for applying N, Yield Reserve Program participation reduces expected net revenue by $10 to$13/ha. The Yield Reserve Program reduces expected net revenue by $17 to$20/ha for farmers who apply N to maximize expected net revenue. Farmers’ costs of participation increase with lower probabilities of inadequate rainfall and higher corn prices and decline with higher N prices. The Yield Reserve Program can significantly reduce N applications to cropland, which may reduce N content of surface waters, but the costs to taxpayers and farmers will depend on how the program is implemented.compliance cost, nitrogen fertilizer, nonpoint source pollution, policy, yield response function, Agricultural and Food Policy, Crop Production/Industries,

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.Comment: 11 pages (Revtex) + 5 figures (postscript

An Over-Massive Black Hole in a Typical Star-Forming Galaxy, 2 Billion Years After the Big Bang

Supermassive black holes (SMBHs) and their host galaxies are generally thought to coevolve, so that the SMBH achieves up to about 0.2 to 0.5% of the host galaxy mass in the present day. The radiation emitted from the growing SMBH is expected to affect star formation throughout the host galaxy. The relevance of this scenario at early cosmic epochs is not yet established. We present spectroscopic observations of a galaxy at redshift z = 3.328, which hosts an actively accreting, extremely massive BH, in its final stages of growth. The SMBH mass is roughly one-tenth the mass of the entire host galaxy, suggesting that it has grown much more efficiently than the host, contrary to models of synchronized coevolution. The host galaxy is forming stars at an intense rate, despite the presence of a SMBH-driven gas outflow.Comment: Author's version, including the main paper and the Supplementary Materials (16+21 pages, 3+3 figures

Properties of Galaxy Groups in the SDSS: II.- AGN Feedback and Star Formation Truncation

Successfully reproducing the galaxy luminosity function and the bimodality in the galaxy distribution requires a mechanism that can truncate star formation in massive haloes. Current models of galaxy formation consider two such truncation mechanisms: strangulation, which acts on satellite galaxies, and AGN feedback, which predominantly affects central galaxies. The efficiencies of these processes set the blue fraction of galaxies as function of galaxy luminosity and halo mass. In this paper we use a galaxy group catalogue extracted from the Sloan Digital Sky Survey (SDSS) to determine these fractions. To demonstrate the potential power of this data as a benchmark for galaxy formation models, we compare the results to the semi-analytical model for galaxy formation of Croton et al. (2006). Although this model accurately fits the global statistics of the galaxy population, as well as the shape of the conditional luminosity function, there are significant discrepancies when the blue fraction of galaxies as a function of mass and luminosity is compared between the observations and the model. In particular, the model predicts (i) too many faint satellite galaxies in massive haloes, (ii) a blue fraction of satellites that is much too low, and (iii) a blue fraction of centrals that is too high and with an inverted luminosity dependence. In the same order, we argue that these discrepancies owe to (i) the neglect of tidal stripping in the semi-analytical model, (ii) the oversimplified treatment of strangulation, and (iii) improper modeling of dust extinction and/or AGN feedback. The data presented here will prove useful to test and calibrate future models of galaxy formation and in particular to discriminate between various models for AGN feedback and other star formation truncation mechanisms.Comment: 16 pages, 5 figures, submitted to MNRA

External Operators and Anomalous Dimensions in Soft-Collinear Effective Theory

It has recently been argued that soft-collinear effective theory for processes involving both soft and collinear partons contains a new soft-collinear mode, which can communicate between the soft and collinear sectors of the theory. The formalism incorporating the corresponding fields into the effective Lagrangian is extended to include external current and four-quark operators relevant to weak interactions. An explicit calculation of the anomalous dimensions of these operators reveals that soft-collinear modes are needed for correctly describing the ultraviolet behavior of the effective theory.Comment: 15 pages, 2 figure

Maturation of biomimetic hydroxyapatite in physiological fluids: a physicochemical and proteomic study

Biomimetic calcium-deficient hydroxyapatite (CDHA) as a bioactive material exhibits exceptional intrinsic osteoinductive and osteogenic properties because of its nanostructure and composition, which promote a favorable microenvironment. Its high reactivity has been hypothesized to play a relevant role in the in vivo performance, mediated by the interaction with the biological fluids, which is amplified by its high specific surface area. Paradoxically, this high reactivity is also behind the in vitro cytotoxicity of this material, especially pro-nounced in static conditions. The present work explores the structural and physicochemical changes that CDHA undergoes in contact with physiological fluids and to investigate its interaction with proteins. Calcium-deficient hydroxyapatite discs with different micro/nanostructures, coarse (C) and fine (F), were exposed to cell-free complete culture medium over extended periods of time: 1, 7, 14, 21, 28, and 50 days. Precipitate formation was not observed in any of the materials in contact with the physiological fluid, which would indicate that the ionic exchanges were linked to incorporation into the crystal structure of CDHA or in the hydrated layer. In fact, CDHA experienced a maturation process, with a progressive increase in crystallinity and the Ca/P ratio, accompanied by an uptake of Mg and a B-type carbonation process, with a gradual propagation into the core of the samples. However, the reactivity of biomimetic hydroxyapatite was highly dependent on the specific surface area and was amplified in nanosized needle-like crystal structures (F), whereas in coarse specimens the ionic exchanges were restricted to the surface, with low penetration in the material bulk. In addition to showing a higher protein adsorption on F substrates, the proteomics study revealed the existence of protein selectivity to-ward F or C microstructures, as well as the capability of CDHA, and more remarkably of F-CDHA, to concentrate specific proteins from the culture medium. Finally, a substantial improvement in the material's ability to support cell proliferation was observed after the CDHA maturation process