102 research outputs found
Variation of Hilbert Coefficients
For a Noetherian local ring (\RR, \m), the first two Hilbert coefficients,
and , of the -adic filtration of an \m-primary ideal are
known to code for properties of \RR, of the blowup of \spec(\RR) along
, and even of their normalizations. We give estimations for these
coefficients when is enlarged (in the case of in the same integral
closure class) for general Noetherian local rings
Equivalence, reduction and minimization of finite fuzzy-automata
AbstractA new algebraic approach to the problem of equivalence, reduction and minimization of some kinds of fuzzy-automata is given. A system of necessary and sufficient conditions for equivalence of weakly initial fuzzy-automata is formulated. Some algorithms considering the equivalence for two fuzzy-automata are constructed
Shapes of free resolutions over a local ring
We classify the possible shapes of minimal free resolutions over a regular
local ring. This illustrates the existence of free resolutions whose Betti
numbers behave in surprisingly pathological ways. We also give an asymptotic
characterization of the possible shapes of minimal free resolutions over
hypersurface rings. Our key new technique uses asymptotic arguments to study
formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially
and exposition has been streamline
Betti numbers for numerical semigroup rings
We survey results related to the magnitude of the Betti numbers of numerical
semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra
and Applications (V. Ene, E. Miller Eds.
The fate of oxidative strand breaks in mitochondrial DNA
Mitochondrial DNA (mtDNA) is particularly vulnerable to somatic mutagenesis. Potential mechanisms include DNA polymerase Ξ³ (POLG) errors and the effects of mutagens, such as reactive oxygen species. Here, we studied the effects of transient hydrogen peroxide (H(2)O(2) pulse) on mtDNA integrity in cultured HEK 293 cells, applying Southern blotting, ultra-deep short-read and long-read sequencing. In wild-type cells, 30 min after the H(2)O(2) pulse, linear mtDNA fragments appear, representing double-strand breaks (DSB) with ends characterized by short GC stretches. Intact supercoiled mtDNA species reappear within 2β6 h after treatment and are almost completely recovered after 24 h. BrdU incorporation is lower in H(2)O(2)-treated cells compared to non-treated cells, suggesting that fast recovery is not associated with mtDNA replication, but is driven by rapid repair of single-strand breaks (SSBs) and degradation of DSB-generated linear fragments. Genetic inactivation of mtDNA degradation in exonuclease deficient POLG p.D274A mutant cells results in the persistence of linear mtDNA fragments with no impact on the repair of SSBs. In conclusion, our data highlight the interplay between the rapid processes of SSB repair and DSB degradation and the much slower mtDNA re-synthesis after oxidative damage, which has important implications for mtDNA quality control and the potential generation of somatic mtDNA deletions
Estrogen directly activates AID transcription and function
The immunological targets of estrogen at the molecular, humoral, and cellular level have been well documented, as has estrogen's role in establishing a gender bias in autoimmunity and cancer. During a healthy immune response, activation-induced deaminase (AID) deaminates cytosines at immunoglobulin (Ig) loci, initiating somatic hypermutation (SHM) and class switch recombination (CSR). Protein levels of nuclear AID are tightly controlled, as unregulated expression can lead to alterations in the immune response. Furthermore, hyperactivation of AID outside the immune system leads to oncogenesis. Here, we demonstrate that the estrogenβestrogen receptor complex binds to the AID promoter, enhancing AID messenger RNA expression, leading to a direct increase in AID protein production and alterations in SHM and CSR at the Ig locus. Enhanced translocations of the c-myc oncogene showed that the genotoxicity of estrogen via AID production was not limited to the Ig locus. Outside of the immune system (e.g., breast and ovaries), estrogen induced AID expression by >20-fold. The estrogen response was also partially conserved within the DNA deaminase family (APOBEC3B, -3F, and -3G), and could be inhibited by tamoxifen, an estrogen antagonist. We therefore suggest that estrogen-induced autoimmunity and oncogenesis may be derived through AID-dependent DNA instability
Inferring novel disease indications for known drugs by semantically linking drug action and disease mechanism relationships
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