Variation of Hilbert Coefficients

For a Noetherian local ring (\RR, \m), the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an \m-primary ideal $I$ are known to code for properties of \RR, of the blowup of \spec(\RR) along $V(I)$, and even of their normalizations. We give estimations for these coefficients when $I$ is enlarged (in the case of $e_1$ 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 γ (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 2–6 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 estrogen–estrogen 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