On an Asymptotic Series of Ramanujan

An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $\phi(X)$ for large $\lambda$ where $X$ is a Poisson random variable with mean $\lambda$ and $\phi$ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of $\phi(X)$ when the distribution of $X$ belongs to a suitable family indexed by a convolution parameter. Examples include the problem of inverse moments for distribution families such as the binomial or the negative binomial.Comment: To appear, Ramanujan

Epigenetic Silencing of Nucleolar rRNA Genes in Alzheimer's Disease

Background: Ribosomal deficits are documented in mild cognitive impairment (MCI), which often represents an early stage Alzheimer’s disease (AD), as well as in advanced AD. The nucleolar rRNA genes (rDNA), transcription of which is critical for ribosomal biogenesis, are regulated by epigenetic silencing including promoter CpG methylation. Methodology/Principal Findings: To assess whether CpG methylation of the rDNA promoter was dysregulated across the AD spectrum, we analyzed brain samples from 10 MCI-, 23 AD-, and, 24 age-matched control individuals using bisulfite mapping. The rDNA promoter became hypermethylated in cerebro-cortical samples from MCI and AD groups. In parietal cortex, the rDNA promoter was hypermethylated more in MCI than in advanced AD. The cytosine methylation of total genomic DNA was similar in AD, MCI, and control samples. Consistent with a notion that hypermethylation-mediated silencing of the nucleolar chromatin stabilizes rDNA loci, preventing their senescence-associated loss, genomic rDNA content was elevated in cerebrocortical samples from MCI and AD groups. Conclusions/Significance: In conclusion, rDNA hypermethylation could be a new epigenetic marker of AD. Moreover, silencing of nucleolar chromatin may occur during early stages of AD pathology and play a role in AD-related ribosoma

Differences in expression level of Helios and neuropilin-1 do not distinguish thymus-derived from extrathymically-induced CD4+Foxp3+ regulatory T cells

10.1371/journal.pone.0141161PLoS ONE1010e014116

Stochastic and deterministic models for agricultural production networks

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed

Electronic Spectra of the Tetraphenylcyclobutadienecyclopentadienylnickel(II) Cation and Radical

Properties of the tetraphenylcyclobutadienecyclopentadienylnickel­(II) cation <b>1</b> and its tetra-<i>o</i>-fluoro derivative <b>1a</b> have been measured and calculated. The B3LYP/TZP optimized geometry of the free cation <b>1</b> agrees with a single-crystal X-ray diffraction structure except that in the crystal one of the phenyl substituents is strongly twisted to permit a close-packing interaction of two of its hydrogens with a nearby BF₄^– anion. The low-energy parts of the solution electronic absorption and magnetic circular dichroism (MCD) spectra of <b>1</b> and <b>1a</b> have been interpreted by comparison with TD-DFT (B3LYP/TZP) results. Reduction or pulse radiolysis lead to a neutral 19-electron radical, whose visible absorption and MCD spectra have been recorded and interpreted as well. The reduction is facilitated by ∼0.1 V upon going from <b>1</b> to <b>1a</b>. Unsuccessful attempts to prepare several other aryl substituted derivatives of <b>1</b> by the classical synthetic route are described in the Supporting Information