A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems

Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent. In this article, we study a two-dimensional semilinear singularly perturbed convection-diffusion problems. Our approach requires linearization of the continuous semilinear problem using the quasilinearization technique. We then discretize the resulting linear problems in the framework of non-standard finite difference methods. A rigorous convergence analysis is conducted showing that the proposed method is first-order parameter-uniform convergent. Finally, two test examples are used to validate the theoretical findings

Intragenic DNA methylation: implications of this epigenetic mechanism for cancer research

Epigenetics is the study of all mechanisms that regulate gene transcription and genome stability that are maintained throughout the cell division, but do not include the DNA sequence itself. The best-studied epigenetic mechanism to date is DNA methylation, where methyl groups are added to the cytosine base within cytosine–guanine dinucleotides (CpG sites). CpGs are frequently clustered in high density (CpG islands (CGIs)) at the promoter of over half of all genes. Current knowledge of transcriptional regulation by DNA methylation centres on its role at the promoter where unmethylated CGIs are present at most actively transcribed genes, whereas hypermethylation of the promoter results in gene repression. Over the last 5 years, research has gradually incorporated a broader understanding that methylation patterns across the gene (so-called intragenic or gene body methylation) may have a role in transcriptional regulation and efficiency. Numerous genome-wide DNA methylation profiling studies now support this notion, although whether DNA methylation patterns are a cause or consequence of other regulatory mechanisms is not yet clear. This review will examine the evidence for the function of intragenic methylation in gene transcription, and discuss the significance of this in carcinogenesis and for the future use of therapies targeted against DNA methylation

Contrasting patterns of local richness of seedlings, saplings and trees may have implications for regeneration in rainforest remnants

Remnants of lowland rainforest remain following deforestation, but the longer-term effects of fragmentation remain poorly understood, partly due to the long generation times of trees. We study rainforest trees in three size classes: seedlings (5 cm), that broadly reflect pre- and post-fragmentation communities, and we examine the impacts of fragmentation on forest regeneration in Sabah, Malaysian Borneo. We found that seedling richness (measured as the number of genera per plot) in fragments was about 30 percent lower than in plots in undisturbed forest, and about 20 percent lower than in an extensive tract of selectively logged forest, providing evidence of recruitment declines in fragments. Seedling richness was lowest in small, isolated, and disturbed fragments, potentially signalling an extinction debt given that these fragmentation impacts were not observed in trees. Unlike seedlings, saplings showed no declines in richness in fragments, suggesting that density dependent mortality (where rare individuals have a higher survival rate) and/or year-to-year variation in which species are recruiting could potentially compensate for the reductions in seedling richness we observed. Longer-term studies are required to determine whether sporadic or failed recruitment in small fragments will eventually translate into reduced richness of mature trees, or whether the processes that currently retain high sapling richness will continue in fragments

Global diversification of a tropical plant growth form: environmental correlates and historical contingencies in climbing palms

Tropical rain forests (TRF) are the most diverse terrestrial biome on Earth, but the diversification dynamics of their constituent growth forms remain largely unexplored. Climbing plants contribute significantly to species diversity and ecosystem processes in TRF. We investigate the broad-scale patterns and drivers of species richness as well as the diversification history of climbing and non-climbing palms (Arecaceae). We quantify to what extent macroecological diversity patterns are related to contemporary climate, forest canopy height and paleoclimatic changes. We test whether diversification rates are higher for climbing than non-climbing palms and estimate the origin of the climbing habit. Climbers account for 22% of global palm species diversity mostly concentrated in Southeast Asia. Global variation in climbing palm species richness can be partly explained by past and present-day climate and rain forest canopy height, but regional differences in residual species richness after accounting for current and past differences in environment suggest a strong role of historical contingencies in climbing palm diversification. Climbing palms show a higher net diversification rate than non-climbers. Diversification analysis of palms detected a diversification rate increase along the branches leading to the most species-rich clade of climbers. Ancestral character reconstructions revealed that the climbing habit originated between early Eocene and Miocene. These results imply that changes from non-climbing to climbing habit may have played an important role in palm diversification, resulting in the origin of one fifth of all palm species. We suggest that, in addition to current climate and paleoclimatic changes after the late Neogene, present-day diversity of climbing palms can be explained by morpho-anatomical innovations, the biogeographic history of Southeast Asia, and/or ecological opportunities due to the diversification of high-stature dipterocarps in Asian TRFs

Plant DNA barcodes and assessment of phylogenetic community structure of a tropical mixed dipterocarp forest in Brunei Darussalam (Borneo)

DNA barcoding is a fast and reliable tool to assess and monitor biodiversity and, via community phylogenetics, to investigate ecological and evolutionary processes that may be responsible for the community structure of forests. In this study, DNA barcodes for the two widely used plastid coding regions rbcL and matK are used to contribute to identification of morphologically undetermined individuals, as well as to investigate phylogenetic structure of tree communities in 70 subplots (10 × 10m) of a 25-ha forest-dynamics plot in Brunei (Borneo, Southeast Asia). The combined matrix (rbcL + matK) comprised 555 haplotypes (from ≥154 genera, 68 families and 25 orders sensu APG, Angiosperm Phylogeny Group, 2016), making a substantial contribution to tree barcode sequences from Southeast Asia. Barcode sequences were used to reconstruct phylogenetic relationships using maximum likelihood, both with and without constraining the topology of taxonomic orders to match that proposed by the Angiosperm Phylogeny Group. A third phylogenetic tree was reconstructed using the program Phylomatic to investigate the influence of phylogenetic resolution on results. Detection of non-random patterns of community assembly was determined by net relatedness index (NRI) and nearest taxon index (NTI). In most cases, community assembly was either random or phylogenetically clustered, which likely indicates the importance to community structure of habitat filtering based on phylogenetically correlated traits in determining community structure. Different phylogenetic trees gave similar overall results, but the Phylomatic tree produced greater variation across plots for NRI and NTI values, presumably due to noise introduced by using an unresolved phylogenetic tree. Our results suggest that using a DNA barcode tree has benefits over the traditionally used Phylomatic approach by increasing precision and accuracy and allowing the incorporation of taxonomically unidentified individuals into analyses

Forest Fruit Production Is Higher on Sumatra Than on Borneo

BACKGROUND: Various studies have shown that the population densities of a number of forest vertebrates, such as orangutans, are higher on Sumatra than Borneo, and that several species exhibit smaller body sizes on Borneo than Sumatra and mainland Southeast Asia. It has been suggested that differences in forest fruit productivity between the islands can explain these patterns. Here we present a large-scale comparison of forest fruit production between the islands to test this hypothesis. METHODOLOGY/PRINCIPAL FINDINGS: Data on fruit production were collated from Sumatran and Bornean sites. At six sites we assessed fruit production in three forest types: riverine, peat swamp and dryland forests. We compared fruit production using time-series models during different periods of overall fruit production and in different tree size classes. We examined overall island differences and differences specifically for fruiting period and tree size class. The results of these analyses indicate that overall the Sumatran forests are more productive than those on Borneo. This difference remains when each of the three forest types (dryland, riverine, and peat) are examined separately. The difference also holds over most tree sizes and fruiting periods. CONCLUSIONS/SIGNIFICANCE: Our results provide strong support for the hypothesis that forest fruit productivity is higher on Sumatra than Borneo. This difference is most likely the result of the overall younger and more volcanic soils on Sumatra than Borneo. These results contribute to our understanding of the determinants of faunal density and the evolution of body size on both islands

The S phase checkpoint promotes the Smc5/6 complex dependent SUMOylation of Pol2, the catalytic subunit of DNA polymerase ε

Replication fork stalling and accumulation of single-stranded DNA trigger the S phase checkpoint, a signalling cascade that, in budding yeast, leads to the activation of the Rad53 kinase. Rad53 is essential in maintaining cell viability, but its targets of regulation are still partially unknown. Here we show that Rad53 drives the hyper-SUMOylation of Pol2, the catalytic subunit of DNA polymerase ε, principally following replication forks stalling induced by nucleotide depletion. Pol2 is the main target of SUMOylation within the replisome and its modification requires the SUMO-ligase Mms21, a subunit of the Smc5/6 complex. Moreover, the Smc5/6 complex co-purifies with Pol ε, independently of other replisome components. Finally, we map Pol2 SUMOylation to a single site within the N-terminal catalytic domain and identify a SUMO-interacting motif at the C-terminus of Pol2. These data suggest that the S phase checkpoint regulate Pol ε during replication stress through Pol2 SUMOylation and SUMO-binding abilit

On Semi-Classical Orthogonal Polynomials Associated with a Modified Sextic Freud-Type Weight

Polynomials that are orthogonal with respect to a perturbation of the Freud weight function by some parameter, known to be modified Freudian orthogonal polynomials, are considered. In this contribution, we investigate certain properties of semi-classical modified Freud-type polynomials in which their corresponding semi-classical weight function is a more general deformation of the classical scaled sextic Freud weight |x|αexp(−cx6),c>0,α>−1. Certain characterizing properties of these polynomials such as moments, recurrence coefficients, holonomic equations that they satisfy, and certain non-linear differential-recurrence equations satisfied by the recurrence coefficients, using compatibility conditions for ladder operators for these orthogonal polynomials, are investigated. Differential-difference equations were also obtained via Shohat’s quasi-orthogonality approach and also second-order linear ODEs (with rational coefficients) satisfied by these polynomials. Modified Freudian polynomials can also be obtained via Chihara’s symmetrization process from the generalized Airy-type polynomials. The obtained linear differential equation plays an essential role in the electrostatic interpretation for the distribution of zeros of the corresponding Freudian polynomials