Cubic structures, equivariant Euler characteristics and lattices of modular forms

We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective flat schemes over Z with a tame action of a finite abelian group. This formula supports a conjecture concerning the extent to which such equivariant Euler characteristics may be determined from the restriction of the sheaf to an infinitesimal neighborhood of the fixed point locus. Our results are applied to study the module structure of modular forms having Fourier coefficients in a ring of algebraic integers, as well as the action of diamond Hecke operators on the Mordell-Weil groups and Tate-Shafarevich groups of Jacobians of modular curves.Comment: 40pp, Final version, to appear in the Annals of Mathematic

Dispersion of biased swimming microorganisms in a fluid flowing through a tube

Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments, and compared with an approximation a la Taylor. As in the Taylor-Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming microorganisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.Comment: 20 pages, 4 figures. Published version available at http://rspa.royalsocietypublishing.org/content/early/2010/02/09/rspa.2009.0606.short?rss=

Time Variable Faraday Rotation Measures of 3C-273 and 3C-279

Multifrequency polarimetry with the VLBA confirms the previously reported time-varying Faraday rotation measure (RM) in the quasar 3C-279. Variability in the RM and electric vector position angle (EVPA) of the jet component (C4) is seen making it an unreliable absolute EVPA calibrator. 3C-273 is also shown to vary its RM structure on 1.5 year time-scales. Variation in the RM properties of quasars may result from a Faraday screen which changes on time-scales of a few years, or from the motion of jet components which sample spatial variations in the screen. A new component emerging from the core of 3C-279 appears to be starting to sample such a spatial variation. Future monitoring of this component and its RM properties is suggested as a diagnostic of the narrow line region in 3C-279. We also present a new method of EVPA calibration using the VLA Monitoring Program.Comment: Accepted to ApJ Letters. 12 pages, 5 figure

Fossil Imprints of the First Generation Supernova Ejecta in Extremely Metal-Deficient Stars

Using results of nucleosynthesis calculations for theoretical core-collapse supernova models with various progenitor's masses, it is shown that abundance patterns of C, Mg, Si, Ca, and H seen in extremely metal-deficient stars with [Fe/H] < -2.5 follow those seen in the individual first generation supernova remnants (SNRs). This suggests that most of the stars with [Fe/H] < -2.5 were made from individual supernova (SN) events. To obtain the ratio of heavy elements to hydrogen, a formula is derived to estimate the mass of hydrogen swept up by a SNR when it occurs in the interstellar matter with the primordial abundances. We use [Mg/H] to indicate the metallicities instead of [Fe/H]. The metallicities [Mg/H] predicted from these SNRs range from ~-4 to ~-1.5 and the mass of Mg in a SN is well correlated with its progenitor's mass. Thus the observed [Mg/H] in an extremely metal deficient star has a correspondence to the progenitor's mass. A larger [Mg/H] corresponds to a larger progenitor's mass. Therefore, so called `age-metallicity relation' does not hold for stars with [Fe/H] < -2.5. In contrast, the [Mg/Fe] ratios in the theoretical SNRs have a different trend from those in extremely metal-deficient stars. It is also shown that the observed trend of [Mg/Fe] can predict the Fe yield of each SN given the correspondence of [Mg/H] to the progenitor's mass. The Fe yields thus obtained are consistent with those derived from SN light curve analyses. This indicates that there is still a problem in modelling a core-collapse supernova at its beginning of explosion or mass cut.Comment: 6 pages, 4 figures, 1 table; Accepted for publication in the Astrophysical Journal Letter

The Ontological Basis of Strong Artificial Life

This article concerns the claim that it is possible to create living organisms, not merely models that represent organisms, simply by programming computers ("virtual" strong alife). I ask what sort of things these computer-generated organisms are supposed to be (where are they, and what are they made of?). I consider four possible answers to this question: (a) The organisms are abstract complexes of pure information; (b) they are material objects made of bits of computer hardware; (c) they are physical processes going on inside the computer; and (d) they are denizens of an entire artificial world, different from our own, that the programmer creates. I argue that (a) could not be right, that (c) collapses into (b), and that (d) would make strong alife either absurd or uninteresting. Thus, "virtual" strong alife amounts to the claim that, by programming a computer, one can literally bring bits of its hardware to life