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

Correlation test to assess low-level processing of high-density oligonucleotide microarray data

BACKGROUND: There are currently a number of competing techniques for low-level processing of oligonucleotide array data. The choice of technique has a profound effect on subsequent statistical analyses, but there is no method to assess whether a particular technique is appropriate for a specific data set, without reference to external data. RESULTS: We analyzed coregulation between genes in order to detect insufficient normalization between arrays, where coregulation is measured in terms of statistical correlation. In a large collection of genes, a random pair of genes should have on average zero correlation, hence allowing a correlation test. For all data sets that we evaluated, and the three most commonly used low-level processing procedures including MAS5, RMA and MBEI, the housekeeping-gene normalization failed the test. For a real clinical data set, RMA and MBEI showed significant correlation for absent genes. We also found that a second round of normalization on the probe set level improved normalization significantly throughout. CONCLUSION: Previous evaluation of low-level processing in the literature has been limited to artificial spike-in and mixture data sets. In the absence of a known gold-standard, the correlation criterion allows us to assess the appropriateness of low-level processing of a specific data set and the success of normalization for subsets of genes

scLM: Automatic Detection of Consensus Gene Clusters Across Multiple Single-cell Datasets

In gene expression profiling studies, including single-cell RNA sequencing (scRNA-seq) analyses, the identification and characterization of co-expressed genes provides critical information on cell identity and function. Gene co-expression clustering in scRNA-seq data presents certain challenges. We show that commonly used methods for single-cell data are not capable of identifying co-expressed genes accurately, and produce results that substantially limit biological expectations of co-expressed genes. Herein, we present single-cell Latent-variable Model (scLM), a gene co-clustering algorithm tailored to single-cell data that performs well at detecting gene clusters with significant biologic context. Importantly, scLM can simultaneously cluster multiple single-cell datasets, i.e., consensus clustering, enabling users to leverage single-cell data from multiple sources for novel comparative analysis. scLM takes raw count data as input and preserves biological variation without being influenced by batch effects from multiple datasets. Results from both simulation data and experimental data demonstrate that scLM outperforms the existing methods with considerably improved accuracy. To illustrate the biological insights of scLM, we apply it to our in-house and public experimental scRNA-seq datasets. scLM identifies novel functional gene modules and refines cell states, which facilitates mechanism discovery and understanding of complex biosystems such as cancers. A user-friendly R package with all the key features of the scLM method is available at https://github.com/QSong-github/scLM

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

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 tomographic weak lensing: Quantifying accurate redshift distributions

The Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) comprises deep multi-colour (u*g'r'i'z') photometry spanning 154 square degrees, with accurate photometric redshifts and shape measurements. We demonstrate that the redshift probability distribution function summed over galaxies provides an accurate representation of the galaxy redshift distribution accounting for random and catastrophic errors for galaxies with best fitting photometric redshifts z_p < 1.3. We present cosmological constraints using tomographic weak gravitational lensing by large-scale structure. We use two broad redshift bins 0.5 < z_p <= 0.85 and 0.85 < z_p <= 1.3 free of intrinsic alignment contamination, and measure the shear correlation function on angular scales in the range ~1-40 arcmin. We show that the problematic redshift scaling of the shear signal, found in previous CFHTLS data analyses, does not afflict the CFHTLenS data. For a flat Lambda-CDM model and a fixed matter density Omega_m=0.27, we find the normalisation of the matter power spectrum sigma_8=0.771 \pm 0.041. When combined with cosmic microwave background data (WMAP7), baryon acoustic oscillation data (BOSS), and a prior on the Hubble constant from the HST distance ladder, we find that CFHTLenS improves the precision of the fully marginalised parameter estimates by an average factor of 1.5-2. Combining our results with the above cosmological probes, we find Omega_m=0.2762 \pm 0.0074 and sigma_8=0.802 \pm 0.013.Comment: 17 pages, 12 figures, submitted to MNRA

CDKN1C (p57KIP2) Is a Direct Target of EZH2 and Suppressed by Multiple Epigenetic Mechanisms in Breast Cancer Cells

CDKN1C (encoding tumor suppressor p57KIP2) is a cyclin-dependent kinase (CDK) inhibitor whose family members are often transcriptionally downregulated in human cancer via promoter DNA methylation. In this study, we show that CDKN1C is repressed in breast cancer cells mainly through histone modifications. In particular, we show that CDKN1C is targeted by histone methyltransferase EZH2-mediated histone H3 lysine 27 trimethylation (H3K27me3), and can be strongly activated by inhibition of EZH2 in synergy with histone deacetylase inhibitor. Consistent with the overexpression of EZH2 in a variety of human cancers including breast cancer, CDKN1C in these cancers is downregulated, and breast tumors expressing low levels of CDKN1C are associated with a poor prognosis. We further show that assessing both EZH2 and CDKN1C expression levels as a measurement of EZH2 pathway activity provides a more predictive power of disease outcome than that achieved with EZH2 or CDKN1C alone. Taken together, our study reveals a novel epigenetic mechanism governing CDKN1C repression in breast cancer. Importantly, as a newly identified EZH2 target with prognostic value, it has implications in patient stratification for cancer therapeutic targeting EZH2-mediated gene repression