On Lower Bounds for ss-multiplicities

A recent continuous family of multiplicity functions on local rings was introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz multiplicities. The obvious goal is to use this as a tool for deforming results from one to the other. The values in this family which do not match these classic variants however are not known yet to be well-behaved. This article explores lower bounds for these intermediate multiplicities as well as gives evidence for analogies of the Watanabe-Yoshida minimality conjectures for unmixed singular rings.Comment: 10 page

The s-multiplicity function of 2x2-determinantal rings

This article generalizes joint work of the first author and I. Swanson to the $s$-multiplicity recently introduced by the second author. For $k$ a field and $X = [ x_{i,j}]$ a $m \times n$-matrix of variables, we utilize Gr\"obner bases to give a closed form the length $\lambda( k[X] / (I_2(X) + \mathfrak{m}^{ \lceil sq \rceil} + \mathfrak{m}^{[q]} ))$ where $s \in \mathbf{Z}[p^{-1}]$, $q$ is a sufficiently large power of $p$, and $\mathfrak{m}$ is the homogeneous maximal ideal of $k[X]$. This shows this length is always eventually a {\it polynomial} function of $q$ for all $s$.Comment: 9 pages, Errors fixe

RAS Mutations and Oncogenesis: Not all RAS Mutations are Created Equally

Mutation in RAS proteins is one of the most common genetic alterations observed in human and experimentally induced rodent cancers. In vivo, oncogenic mutations have been shown to occur at exons 12, 13, and 61, resulting in any 1 of 19 possible point mutations in a given tumor for a specific RAS isoform. While some studies have suggested a possible role of different mutant alleles in determining tumor severity and phenotype, no general consensus has emerged on the oncogenicity of different mutant alleles in tumor formation and progression. Part of this may be due to a lack of a single, signature pathway that shows significant alterations between different mutations. Rather, it is likely that subtle differences in the activation, or lack thereof, of downstream effectors by different RAS mutant alleles may determine the eventual outcome in terms of tumor phenotype. This paper reviews our current understanding of the potential role of different RAS mutations on tumorigenesis, highlights studies in model cell culture and in vivo systems, and discusses the potential of expression array and computational network modeling to dissect out differences in activated RAS genes in conferring a transforming phenotype

CFHTLenS: Weak lensing constraints on the ellipticity of galaxy-scale matter haloes and the galaxy-halo misalignment

We present weak lensing constraints on the ellipticity of galaxy-scale matter haloes and the galaxy-halo misalignment. Using data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), we measure the weighted-average ratio of the aligned projected ellipticity components of galaxy matter haloes and their embedded galaxies, $f_\mathrm{h}$, split by galaxy type. We then compare our observations to measurements taken from the Millennium Simulation, assuming different models of galaxy-halo misalignment. Using the Millennium Simulation we verify that the statistical estimator used removes contamination from cosmic shear. We also detect an additional signal in the simulation, which we interpret as the impact of intrinsic shape-shear alignments between the lenses and their large-scale structure environment. These alignments are likely to have caused some of the previous observational constraints on $f_\mathrm{h}$ to be biased high. From CFHTLenS we find $f_\mathrm{h}=-0.04 \pm 0.25$ for early-type galaxies, which is consistent with current models for the galaxy-halo misalignment predicting $f_\mathrm{h}\simeq 0.20$. For late-type galaxies we measure $f_\mathrm{h}=0.69_{-0.36}^{+0.37}$ from CFHTLenS. This can be compared to the simulated results which yield $f_\mathrm{h}\simeq 0.02$ for misaligned late-type models.Comment: 21 pages, 3 tables, 9 figures. This replacement matches the version accepted for publication in MNRA

CFHTLenS: Co-evolution of galaxies and their dark matter haloes

Galaxy-galaxy weak lensing is a direct probe of the mean matter distribution around galaxies. The depth and sky coverage of the CFHT Legacy Survey yield statistically significant galaxy halo mass measurements over a much wider range of stellar masses ($10^{8.75}$ to $10^{11.3} M_{\odot}$) and redshifts ($0.2 < z < 0.8$) than previous weak lensing studies. At redshift $z \sim 0.5$, the stellar-to-halo mass ratio (SHMR) reaches a maximum of $4.0\pm0.2$ percent as a function of halo mass at $\sim 10^{12.25} M_{\odot}$. We find, for the first time from weak lensing alone, evidence for significant evolution in the SHMR: the peak ratio falls as a function of cosmic time from $4.5 \pm 0.3$ percent at $z \sim 0.7$ to $3.4 \pm 0.2$ percent at $z \sim 0.3$, and shifts to lower stellar mass haloes. These evolutionary trends are dominated by red galaxies, and are consistent with a model in which the stellar mass above which star formation is quenched "downsizes" with cosmic time. In contrast, the SHMR of blue, star-forming galaxies is well-fit by a power law that does not evolve with time. This suggests that blue galaxies form stars at a rate that is balanced with their dark matter accretion in such a way that they evolve along the SHMR locus. The redshift dependence of the SHMR can be used to constrain the evolution of the galaxy population over cosmic time.Comment: 18 pages, MNRAS, in pres

Yin Yang 1 contains G-quadruplex structures in its promoter and 5′-UTR and its expression is modulated by G4 resolvase 1

Yin Yang 1 (YY1) is a multifunctional protein with regulatory potential in tumorigenesis. Ample studies demonstrated the activities of YY1 in regulating gene expression and mediating differential protein modifications. However, the mechanisms underlying YY1 gene expression are relatively understudied. G-quadruplexes (G4s) are four-stranded structures or motifs formed by guanine-rich DNA or RNA domains. The presence of G4 structures in a gene promoter or the 5′-UTR of its mRNA can markedly affect its expression. In this report, we provide strong evidence showing the presence of G4 structures in the promoter and the 5′-UTR of YY1. In reporter assays, mutations in these G4 structure forming sequences increased the expression of Gaussia luciferase (Gluc) downstream of either YY1 promoter or 5′-UTR. We also discovered that G4 Resolvase 1 (G4R1) enhanced the Gluc expression mediated by the YY1 promoter, but not the YY1 5′-UTR. Consistently, G4R1 binds the G4 motif of the YY1 promoter in vitro and ectopically expressed G4R1 increased endogenous YY1 levels. In addition, the analysis of a gene array data consisting of the breast cancer samples of 258 patients also indicates a significant, positive correlation between G4R1 and YY1 expressio

GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.Comment: 32 pages + 15 pages of technical appendices; 28 figures; submitted to MNRAS; latest version has minor updates in presentation of 4 figures, no changes in content or conclusion

CFHTLenS: co-evolution of galaxies and their dark matter haloes

Galaxy-galaxy weak lensing is a direct probe of the mean matter distribution around galaxies. The depth and sky coverage of the Canada-France-Hawaii Telescope Legacy Survey yield statistically significant galaxy halo mass measurements over a much wider range of stellar masses (108.75 to 1011.3 M⊙) and redshifts (0.2<z<0.8) than previous weak lensing studies. At redshift z∼0.5, the stellar-to-halo mass ratio (SHMR) reaches a maximum of 4.0±0.2 per cent as a function of halo mass at ∼1012.25 M⊙. We find, for the first time from weak lensing alone, evidence for significant evolution in the SHMR: the peak ratio falls as a function of cosmic time from 4.5±0.3 per cent at z∼0.7 to 3.4±0.2 per cent at z∼0.3, and shifts to lower stellar mass haloes. These evolutionary trends are dominated by red galaxies, and are consistent with a model in which the stellar mass above which star formation is quenched ‘downsizes' with cosmic time. In contrast, the SHMR of blue, star-forming galaxies is well fitted by a power law that does not evolve with time. This suggests that blue galaxies form stars at a rate that is balanced with their dark matter accretion in such a way that they evolve along the SHMR locus. The redshift dependence of the SHMR can be used to constrain the evolution of the galaxy population over cosmic tim