Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution

We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a single-dimensional heat equation solver that uses fast O(N) convolution. This fundamental solver has arbitrary order of accuracy in space, and is based on the use of the Green's function to invert a modified Helmholtz equation. Higher orders of accuracy in time are then constructed through a novel technique known as successive convolution (or resolvent expansions). These resolvent expansions facilitate our proofs of stability and convergence, and permit us to construct schemes that have provable stiff decay. The multi-dimensional solver is built by repeated application of dimensionally split independent fundamental solvers. Finally, we solve nonlinear parabolic problems by using the integrating factor method, where we apply the basic scheme to invert linear terms (that look like a heat equation), and make use of Hermite-Birkhoff interpolants to integrate the remaining nonlinear terms. Our solver is applied to several linear and nonlinear equations including heat, Allen-Cahn, and the Fitzhugh-Nagumo system of equations in one and two dimensions

Method of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion for Phase-Field Models

In this work, we develop an $\mathcal{O}(N)$ implicit real space method in 1D and 2D for the Cahn--Hilliard (CH) and vector Cahn--Hilliard (VCH) equations, based on the method of lines transpose (MOL$^{T}$) formulation. This formulation results in a semidiscrete time stepping algorithm, which we prove is gradient stable in the $H^{-1}$ norm. The spatial discretization follows from dimensional splitting and an $\mathcal{O}(N)$ matrix-free solver, which applies fast convolution to the modified Helmholtz equation. We propose a novel factorization technique, in which fourth-order spatial derivatives are incorporated into the solver. The splitting error is included in the nonlinear fixed point iteration, resulting in a high-order, logically Cartesian (line-by-line) update. Our method is fast but not restricted to periodic boundaries like the fast Fourier transform (FFT). The basic solver is implemented using the backward Euler formulation, and we extend this to both backward difference formula (BDF) stencils, singly diagonal implicit Runge--Kutta (SDIRK), and spectral deferred correction (SDC) frameworks to achieve high orders of temporal accuracy. We demonstrate with numerical results that the CH and VCH equations maintain gradient stability in one and two spatial dimensions. We also explore time-adaptivity, so that meta-stable states and ripening events can be simulated both quickly and efficiently

Method of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion for Phase-Field Models

In this work, we develop an $\mathcal{O}(N)$ implicit real space method in 1D and 2D for the Cahn--Hilliard (CH) and vector Cahn--Hilliard (VCH) equations, based on the method of lines transpose (MOL$^{T}$) formulation. This formulation results in a semidiscrete time stepping algorithm, which we prove is gradient stable in the $H^{-1}$ norm. The spatial discretization follows from dimensional splitting and an $\mathcal{O}(N)$ matrix-free solver, which applies fast convolution to the modified Helmholtz equation. We propose a novel factorization technique, in which fourth-order spatial derivatives are incorporated into the solver. The splitting error is included in the nonlinear fixed point iteration, resulting in a high-order, logically Cartesian (line-by-line) update. Our method is fast but not restricted to periodic boundaries like the fast Fourier transform (FFT). The basic solver is implemented using the backward Euler formulation, and we extend this to both backward difference formula (BDF) stencils, singly diagonal implicit Runge--Kutta (SDIRK), and spectral deferred correction (SDC) frameworks to achieve high orders of temporal accuracy. We demonstrate with numerical results that the CH and VCH equations maintain gradient stability in one and two spatial dimensions. We also explore time-adaptivity, so that meta-stable states and ripening events can be simulated both quickly and efficiently

Issues, Challenges, and Needs of High School ESL and Content-Area Teachers in the Richmond Metropolitan Area

n recent years, public schools in Central Virginia have experienced a fast growing ESL population. School districts throughout the state have reported increases in their ESL population that range from 300% to 700% in the past ten years. Unlike states with big cities that traditionally have a high immigrant population, the Virginia schools where the number of English language learners (ELLs) has increased recently, are less likely prepared to meet the needs of this particular group of students (Echevarria, Vogt & Short, 2004). With the passage of the federal No Child Left Behind (NCLB) Act (2002), academic success is increasingly being measured by standardized exams in a variety of content areas, such as math, science and social studies (Darling-Hammond, 2004). Responding to the NCLB act, Virginia state policy expects all ELLs to demonstrate not only language proficiency but also academic proficiency in content area after their first year in the U.S. school system. This one-year exemption policy does not agree with the research findings that it takes 5-7 years, or even longer, for ESL students to achieve average grade-level performance (Collier, 1987; Cummins, 1981, 1989, 1996s)

Method of Lines Transpose: High Order L-Stable {O}(N) Schemes for Parabolic Equations Using Successive Convolution

We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a one-dimensional heat equation solver that uses fast $\mathcal O(N)$ convolution. This fundamental solver has arbitrary order of accuracy in space and is based on the use of the Green\u27s function to invert a modified Helmholtz equation. Higher orders of accuracy in time are then constructed through a novel technique known as successive convolution (or resolvent expansions). These resolvent expansions facilitate our proofs of stability and convergence, and permit us to construct schemes that have provable stiff decay. The multidimensional solver is built by repeated application of dimensionally split independent fundamental solvers. Finally, we solve nonlinear parabolic problems by using the integrating factor method, where we apply the basic scheme to invert linear terms (that look like a heat equation), and make use of Hermite--Birkhoff interpolants to integrate the remaining nonlinear terms. Our solver is applied to several linear and nonlinear equations including heat, Allen--Cahn, and the FitzHugh--Nagumo system of equations in one and two dimensions

The Genome Sequence of 'Mycobacterium massiliense' Strain CIP 108297 Suggests the Independent Taxonomic Status of the Mycobacterium abscessus Complex at the Subspecies Level

Members of the Mycabacterium abscessus complex are rapidly growing mycobacteria that are emerging as human pathogens. The M. abscassus complex was previously composed of three species, namely M. abscessus sensu strict, 'M. massiliense', and M. bolletii', In 2011, 'M. massiliense' and 'M. bolletre' were united and reclassified as a single subspecies within M. abscessus: M. abscessus subsp. bolletii. However, the placement of 'M. massiliense' Within the boundary of M. abscessus subsp. balletii remains highly controversial with regard to clinical aspects. In this study, we revisited the taxonomic status of members of the M. abscessus complex based on comparative analysis of he whole-genome sequences of 53 strains, The genome sequence of the previous type strain of 'Mycobacterium massiliense' (CIP 108297) was determined using next-generation sequencing. The genome tree based on average nucleotide identity (AN I) values supported the differentiation of M. bolletii' and M. massiliense' at the subspecies level. The genome tree also clearly illustrated that 'M. bolletil' and 'M. massiliense' form a distinct phylogenetic clade within the radiation of the M. abscessus complex. The genomic distances observed in this study suggest that the current M. abscessus subsp. bolletii taxon should be divided into two subspecies, M. abscessus subsp. massiliense subsp. nov. and M. abscessus subsp. bolletii, to correspondingly accommodate the previously known 'M. assiliense' and 'M. bolletii' strains.

Duplex-specific nuclease efficiently removes rRNA for prokaryotic RNA-seq

Next-generation sequencing has great potential for application in bacterial transcriptomics. However, unlike eukaryotes, bacteria have no clear mechanism to select mRNAs over rRNAs; therefore, rRNA removal is a critical step in sequencing-based transcriptomics. Duplex-specific nuclease (DSN) is an enzyme that, at high temperatures, degrades duplex DNA in preference to single-stranded DNA. DSN treatment has been successfully used to normalize the relative transcript abundance in mRNA-enriched cDNA libraries from eukaryotic organisms. In this study, we demonstrate the utility of this method to remove rRNA from prokaryotic total RNA. We evaluated the efficacy of DSN to remove rRNA by comparing it with the conventional subtractive hybridization (Hyb) method. Illumina deep sequencing was performed to obtain transcriptomes from Escherichia coli grown under four growth conditions. The results clearly showed that our DSN treatment was more efficient at removing rRNA than the Hyb method was, while preserving the original relative abundance of mRNA species in bacterial cells. Therefore, we propose that, for bacterial mRNA-seq experiments, DSN treatment should be preferred to Hyb-based methods.

Interleukin-2 induces the in vitro maturation of human pluripotent stem cell-derived intestinal organoids.

Human pluripotent stem cell (hPSC)-derived intestinal organoids (hIOs) form 3D structures organized into crypt and villus domains, making them an excellent in vitro model system for studying human intestinal development and disease. However, hPSC-derived hIOs still require in vivo maturation to fully recapitulate adult intestine, with the mechanism of maturation remaining elusive. Here, we show that the co-culture with human T lymphocytes induce the in vitro maturation of hIOs, and identify STAT3-activating interleukin-2 (IL-2) as the major factor inducing maturation. hIOs exposed to IL-2 closely mimic the adult intestinal epithelium and have comparable expression levels of mature intestinal markers, as well as increased intestine-specific functional activities. Even after in vivo engraftment, in vitro-matured hIOs retain their maturation status. The results of our study demonstrate that STAT3 signaling can induce the maturation of hIOs in vitro, thereby circumventing the need for animal models and in vivo maturation

Ameliorating effects of Mango (Mangifera indica L.) fruit on plasma ethanol level in a mouse model assessed with 1H-NMR based metabolic profiling

The ameliorating effects of Mango (Mangifera indica L.) flesh and peel samples on plasma ethanol level were investigated using a mouse model. Mango fruit samples remarkably decreased mouse plasma ethanol levels and increased the activities of alcohol dehydrogenase and acetaldehyde dehydrogenase. The 1H-NMR-based metabolomic technique was employed to investigate the differences in metabolic profiles of mango fruits, and mouse plasma samples fed with mango fruit samples. The partial least squares-discriminate analysis of 1H-NMR spectral data of mouse plasma demonstrated that there were clear separations among plasma samples from mice fed with buffer, mango flesh and peel. A loading plot demonstrated that metabolites from mango fruit, such as fructose and aspartate, might stimulate alcohol degradation enzymes. This study suggests that mango flesh and peel could be used as resources for functional foods intended to decrease plasma ethanol level after ethanol uptake