A block α\alpha-circulant based preconditioned MINRES method for wave equations

In this work, we propose an absolute value block $\alpha$-circulant preconditioner for the minimal residual (MINRES) method to solve an all-at-once system arising from the discretization of wave equations. Since the original block $\alpha$-circulant preconditioner shown successful by many recently is non-Hermitian in general, it cannot be directly used as a preconditioner for MINRES. Motivated by the absolute value block circulant preconditioner proposed in [E. McDonald, J. Pestana, and A. Wathen. SIAM J. Sci. Comput., 40(2):A1012-A1033, 2018], we propose an absolute value version of the block $\alpha$-circulant preconditioner. Our proposed preconditioner is the first Hermitian positive definite variant of the block $\alpha$-circulant preconditioner, which fills the gap between block $\alpha$-circulant preconditioning and the field of preconditioned MINRES solver. The matrix-vector multiplication of the preconditioner can be fast implemented via fast Fourier transforms. Theoretically, we show that for properly chosen $\alpha$ the MINRES solver with the proposed preconditioner has a linear convergence rate independent of the matrix size. To the best of our knowledge, this is the first attempt to generalize the original absolute value block circulant preconditioner in the aspects of both theory and performance. Numerical experiments are given to support the effectiveness of our preconditioner, showing that the expected optimal convergence can be achieved

The Particulate Methane Monooxygenase from Methylococcus capsulatus (Bath) Is a Novel Copper-containing Three-subunit Enzyme: isolation and charactization

The particulate methane monooxygenase (pMMO) is known to be very difficult to study mainly due to its unusual activity instability in vitro. By cultivating Methylococcus capsulatus (Bath) under methane stress conditions and high copper levels in the growth medium, membranes highly enriched in the pMMO with exceptionally stable activity can be isolated from these cells. Purified and active pMMO can be subsequently obtained from these membrane preparations using protocols in which an excess of reductants and anaerobic conditions were maintained during membrane solubilization by dodecyl beta-D-maltoside and purification by chromatography. The pMMO was found to be the major constituent in these membranes, constituting 60-80% of total membrane proteins. The dominant species of the pMMO was found to consist of three subunits, alpha, beta, and gamma, with an apparent molecular mass of 45, 26, and 23 kDa, respectively. A second species of the pMMO, a proteolytically processed version of the enzyme, was found to be composed of three subunits, alpha', beta, and gamma, with an apparent molecular mass of 35, 26, and 23 kDa, respectively. The alpha and alpha' subunits from these two forms of the pMMO contain identical N-terminal sequences. The gamma subunit, however, exhibits variation in its N-terminal sequence. The pMMO is a copper-containing protein only and shows a requirement for Cu(I) ions. Approximately 12-15 Cu ions per 94-kDa monomeric unit were observed. The pMMO is sensitive to dioxygen tension. On the basis of dioxygen sensitivity, three kinetically distinct forms of the enzyme can be distinguished. A slow but air-stable form, which is converted into a "pulsed" state upon direct exposure to atmospheric oxygen pressure, is considered as type I pMMO. This form was the subject of our pMMO isolation effort. Other forms (types II and III) are deactivated to various extents upon exposure to atmospheric dioxygen pressure. Under inactivating conditions, these unstable forms release protons to the buffer (~10 H+/94-kDa monomeric unit) and eventually become completely inactive

A preconditioned MINRES method for optimal control of wave equations and its asymptotic spectral distribution theory

In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear coefficient matrices from the optimal control problem. Namely, we first show that the all-at-once system stemming from the wave control problem is associated to a structured coefficient matrix-sequence possessing an eigenvalue distribution. Then, based on such a spectral distribution of which the symbol is explicitly identified, we develop an ideal preconditioner and two parallel-in-time preconditioners for the saddle point system composed of two block Toeplitz matrices. For the ideal preconditioner, we show that the eigenvalues of the preconditioned matrix-sequence all belong to the set $\left(-\frac{3}{2},-\frac{1}{2}\right)\bigcup \left(\frac{1}{2},\frac{3}{2}\right)$ well separated from zero, leading to mesh-independent convergence when the minimal residual method is employed. The proposed {parallel-in-time} preconditioners can be implemented efficiently using fast Fourier transforms or discrete sine transforms, and their effectiveness is theoretically shown in the sense that the eigenvalues of the preconditioned matrix-sequences are clustered around $\pm 1$, which leads to rapid convergence. When these parallel-in-time preconditioners are not fast diagonalizable, we further propose modified versions which can be efficiently inverted. Several numerical examples are reported to verify our derived localization and spectral distribution result and to support the effectiveness of our proposed preconditioners and the related advantages with respect to the relevant literature

A rubric based approach towards Automated Essay Grading : focusing on high level content issues and ideas

Assessment of a student’s work is by no means an easy task. Even if the student response is in the form of multiple choice answers, manually marking those answer sheets is a task that most teachers regard as rather tedious. The development of an automated method to grade these essays was thus an inevitable step.This thesis proposes a novel approach towards Automated Essay Grading through the use of various concepts found within the field of Narratology. Through a review of the literature, several methods in which essays are graded were identified together with some of the problems. Mainly, the issues and challenges that plague AEG systems were that those following the statistical approach needed a way to deal with more implicit features of free text, while other systems which did manage that were highly dependent on the type of student response, the systems having pre-knowledge pertaining to the subject domain in addition to requiring more computational power. It was also found that while narrative essays are one of the main methods in which a student might be able to showcase his/her mastery over the English language, no system thus far has attempted to incorporate narrative concepts into analysing these type of free text responses.It was decided that the proposed solution would be centred on the detection of Events, which was in turn used to determine the score an essay receives under the criteria of Audience, Ideas, Character and Setting and Cohesion, as defined by the NAPLAN rubric. From the results gathered from experiments conducted on the four criteria mentioned above, it was concluded that the concept of detecting Events as they were within a narrative type story when applied to essay grading, does have a relation towards the score the essay receives. All experiments achieved an average F-measure score of 0.65 and above while exact agreement rates were no lower than 70%. Chi-squared and paired T-test values all indicated that there was insufficient evidence to show that there was any significant difference between the scores generated by the computer and those of the human markers

Experimental Infection of a North American Raptor, American Kestrel (Falco sparverius), with Highly Pathogenic Avian Influenza Virus (H5N1)

Several species of wild raptors have been found in Eurasia infected with highly pathogenic avian influenza virus (HPAIV) subtype H5N1. Should HPAIV (H5N1) reach North America in migratory birds, species of raptors are at risk not only from environmental exposure, but also from consuming infected birds and carcasses. In this study we used American kestrels as a representative species of a North American raptor to examine the effects of HPAIV (H5N1) infection in terms of dose response, viral shedding, pathology, and survival. Our data showed that kestrels are highly susceptible to HPAIV (H5N1). All birds typically died or were euthanized due to severe neurologic disease within 4–5 days of inoculation and shed significant amounts of virus both orally and cloacally, regardless of dose administered. The most consistent microscopic lesions were necrosis in the brain and pancreas. This is the first experimental study of HPAIV infection in a North American raptor and highlights the potential risks to birds of prey if HPAIV (H5N1) is introduced into North America

Population genomic analyses of protected incense trees Aquilaria sinensis reveal the existence of genetically distinct subpopulations

The incense tree Aquilaria sinensis (Thymelaeaceae) can produce agarwood with commercial values and is now under threat from illegal exploitation in Hong Kong, impairing the local population and biodiversity. Together with other species of Aquilaria, it is listed in the CITES Appendix II, which strictly regulates its international trade. To understand the population structure of A. sinensis and to make relevant conservation measures, we have sequenced 346 individuals collected in Hong Kong and southern mainland China. Population genomic analyses including principal component analysis, neighbor-joining tree construction, ADMIXTURE, and hierarchical pairwise-FST analyses suggested that genetically distinct populations are contained in certain areas. Genomic scan analyses further detected single-nucleotide polymorphism (SNP) outliers related to plant defense, including the CYP71BE gene cluster. In addition to the population analyses, we have developed a modified hexadecyltrimethyl-ammonium bromide (CTAB) DNA extraction protocol for obtaining DNA from agarwood samples in this study, and resequencing of DNA extracted from two agarwood samples using this method allows us to successfully map to the sample corresponding localities in the phylogenetic tree. To sum up, this study suggested that there is a genetically distinct subpopulation of incense tree in Hong Kong that would require special conservation measures and established a foundation for future conservation measures