Dedekind sums arising from newform Eisenstein series

For primitive non-trivial Dirichlet characters $\chi_1$ and $\chi_2$, we study the weight zero newform Eisenstein series $E_{\chi_1,\chi_2}(z,s)$ at $s=1$. The holomorphic part of this function has a transformation rule that we express in finite terms as a generalized Dedekind sum. This gives rise to the explicit construction (in finite terms) of elements of $H^1(\Gamma_0(N), \mathbb{C})$. We also give a short proof of the reciprocity formula for this Dedekind sum.Comment: 9 page

Bioactive Phenolics of the Genus Artemisia (Asteraceae): HPLC-DAD-ESI-TQ-MS/MS Profile of the Siberian Species and Their Inhibitory Potential Against α-Amylase and α-Glucosidase

Artemisia genus of Asteraceae family is a source of medicinal plants known worldwide and used as ethnopharmacological remedies for the treatment of diabetes in Northern Asia (Siberia). The aim of this study was to determine the phenolic profile of 12 Siberian Artemisia species (A. anethifolia, A. commutata, A. desertorum, A. integrifolia, A. latifolia, A. leucophylla, A. macrocephala, A. messerschmidtiana, A. palustris, A. sericea, A. tanacetifolia, A. umbrosa) and to test the efficacy of plant extracts and pure compounds for antidiabetic potential. Finally, by HPLC-DAD-ESI-TQ-MS/MS technique, 112 individual phenolic compounds were detected in Artemisia extracts in a wide range of concentrations. Some species accumulated rare plant phenolics, such as coumarin-hemiterpene ethers (lacarol derivatives) from A. latifolia and A. tanacetifolia; melilotoside from A. tanacetifolia; dihydrochalcones (davidigenin analogs) from A. palustris; chrysoeriol glucosides from A. anethifolia, A. sericea, and A. umbrosa; eriodictyol glycosides from A. messerschmidtiana; and some uncommon flavones and flavonols. The predominant phenolic group from Artemisia species herb was caffeoylquinic acid (CQAs), and in all species, the major CQAs were 5-O-CQA (20.28–127.99 μg/g) and 3,5-di-O-CQA (7.35–243.61 μg/g). In a series of in vitro bioassays, all studied Artemisia extracts showed inhibitory activity against principal enzymes of carbohydrate metabolism, such as α-amylase (IC50 = 150.24–384.14 μg/mL) and α-glucosidase (IC50 = 214.42–754.12 μg/mL). Although many phenolic compounds can be inhibitors, experimental evidence suggests that the CQAs were key to the biological response of Artemisia extracts. Mono-, di- and tri-substituted CQAs were assayed and showed inhibition of α-amylase and α-glucosidase, with IC50 values of 40.57–172.47 μM and 61.08–1240.35 μM, respectively, and they were more effective than acarbose, a well-known enzyme inhibitor. The results obtained in this study reveal that Siberian Artemisia species and CQAs possess a pronounced inhibitory activity against α-amylase and α-glucosidase and could become a complement to synthetic antidiabetic drugs for controlling blood glucose level

Altered gene expression in the Werner and Bloom syndromes is associated with sequences having G-quadruplex forming potential

The human Werner and Bloom syndromes (WS and BS) are caused by deficiencies in the WRN and BLM RecQ helicases, respectively. WRN, BLM and their Saccharomyces cerevisiae homologue Sgs1, are particularly active in vitro in unwinding G-quadruplex DNA (G4-DNA), a family of non-canonical nucleic acid structures formed by certain G-rich sequences. Recently, mRNA levels from loci containing potential G-quadruplex-forming sequences (PQS) were found to be preferentially altered in sgs1Δ mutants, suggesting that G4-DNA targeting by Sgs1 directly affects gene expression. Here, we extend these findings to human cells. Using microarrays to measure mRNAs obtained from human fibroblasts deficient for various RecQ family helicases, we observe significant associations between loci that are upregulated in WS or BS cells and loci that have PQS. No such PQS associations were observed for control expression datasets, however. Furthermore, upregulated genes in WS and BS showed no or dramatically reduced associations with sequences similar to PQS but that have considerably reduced potential to form intramolecular G4-DNA. These findings indicate that, like Sgs1, WRN and BLM can regulate transcription globally by targeting G4-DNA

Shannon Entropy Loss in Mixed-Radix Conversions

This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size 2J to a set of arbitrary size n. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed n value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, n, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size J of the source domain 2J. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino