Gr\"{o}bner-Shirshov bases for metabelian Lie algebras

In this paper, we establish the Gr\"{o}bner-Shirshov bases theory for metabelian Lie algebras. As applications, we find the Gr\"{o}bner-Shirshov bases for partial commutative metabelian Lie algebras related to circuits, trees and some cubes.Comment: 20 page

Gr\"obner-Shirshov bases for Lie algebras over a commutative algebra

In this paper we establish a Gr\"{o}bner-Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embeddable in associative algebras over the same ring) and non-special Lie algebras (following a suggestion of P.M. Cohn (1963) \cite{Conh}). In particular, Cohn's Lie algebras over the characteristic $p$ are non-special when $p=2,\ 3,\ 5$. We present an algorithm that one can check for any $p$, whether Cohn's Lie algebras is non-special. Also we prove that any finitely or countably generated Lie algebra is embeddable in a two-generated Lie algebra

Transplantation of Human Undifferentiated Embryonic Stem Cells into A Myocardial Infarction Rat Model

Human embryonic stem (hES) cells hold great therapeutic potential for cell transplantation. To date, it remains uncertain whether undifferentiated hES cells can differentiate into cardiac lineage in vivo during myocardial infarction. Here we provide the first report that undifferentiated hES cells can survive in rat hearts during myocardial infarction without the formation of teratoma using undifferentiated green fluorescent protein (GFP)-transgenic hES cells. Using a laser-capture microscope to dissect the GFP-positive cell area from the hES-injected hearts, we documented the expression of human cardiac-specific genes, including GATA-4, Nkx-2.5, and cardiac troponin I. Taken together, our results demonstrate that undifferentiated hES cells can be driven to the cardiac lineage under the local injured environment in the heart, which may provide a potential method for regenerating de novo myocardium to treat myocardial infarction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63274/1/scd.2006.110206.pd

Composition-Diamond Lemma for Tensor Product of Free Algebras

In this paper, we establish Composition-Diamond lemma for tensor product $k< X> \otimes k$ of two free algebras over a field. As an application, we construct a Groebner-Shirshov basis in $k \otimes k$ by lifting a Groebner-Shirshov basis in $k[X] \otimes k$, where $k[X]$ is a commutative algebra.Comment: 19 page

The Effect of Treadmill Training Pre-Exercise on Glutamate Receptor Expression in Rats after Cerebral Ischemia

Physical exercise has been demonstrated to be neuroprotective in both clinical and laboratory settings. However, the exact mechanism underlying this effect is unclear. Our study aimed to investigate whether pre-ischemic treadmill training could serve as a form of ischemic preconditioning in a rat model undergoing middle cerebral artery occlusion (MCAO). Thirty-six rats were divided into three groups: a sham control group, a non-exercise with operation group and an exercise with operation group. After treadmill training, ischemia was induced by occluding the MCA for 2 h, followed by reperfusion. Half of the rats in each group were sacrificed for mRNA detection of mGluR5 and NR2B 80 min after occlusion. The remaining animals were evaluated for neurological deficits by behavioral scoring and then decapitated to assess the infarct volume. The mRNA expression of mGluR5 and NR2B was detected by real-time PCR. The results suggest that pre-ischemic treadmill training may induce brain ischemic tolerance by reducing the mRNA levels of mGluR5 and NR2B, and thus, the results indicate that physical exercise might be an effective method to establish ischemic preconditioning

Whole-genome sequencing of <em>Oryza brachyantha</em> reveals mechanisms underlying <em>Oryza</em> genome evolution

The wild species of the genus Oryza contain a largely untapped reservoir of agronomically important genes for rice improvement. Here we report the 261-Mb de novo assembled genome sequence of Oryza brachyantha. Low activity of long-terminal repeat retrotransposons and massive internal deletions of ancient long-terminal repeat elements lead to the compact genome of Oryza brachyantha. We model 32,038 protein-coding genes in the Oryza brachyantha genome, of which only 70% are located in collinear positions in comparison with the rice genome. Analysing breakpoints of non-collinear genes suggests that double-strand break repair through non-homologous end joining has an important role in gene movement and erosion of collinearity in the Oryza genomes. Transition of euchromatin to heterochromatin in the rice genome is accompanied by segmental and tandem duplications, further expanded by transposable element insertions. The high-quality reference genome sequence of Oryza brachyantha provides an important resource for functional and evolutionary studies in the genus Oryza

Two Antarctic penguin genomes reveal insights into their evolutionary history and molecular changes related to the Antarctic environment. GigaScience

Abstract Background: Penguins are flightless aquatic birds widely distributed in the Southern Hemisphere. The distinctive morphological and physiological features of penguins allow them to live an aquatic life, and some of them have successfully adapted to the hostile environments in Antarctica. To study the phylogenetic and population history of penguins and the molecular basis of their adaptations to Antarctica, we sequenced the genomes of the two Antarctic dwelling penguin species, the Adélie penguin [Pygoscelis adeliae] and emperor penguin [Aptenodytes forsteri]. Results: Phylogenetic dating suggests that early penguins arose~60 million years ago, coinciding with a period of global warming. Analysis of effective population sizes reveals that the two penguin species experienced population expansions from~1 million years ago to~100 thousand years ago, but responded differently to the climatic cooling of the last glacial period. Comparative genomic analyses with other available avian genomes identified molecular changes in genes related to epidermal structure, phototransduction, lipid metabolism, and forelimb morphology. Conclusions: Our sequencing and initial analyses of the first two penguin genomes provide insights into the timing of penguin origin, fluctuations in effective population sizes of the two penguin species over the past 10 million years, and the potential associations between these biological patterns and global climate change. The molecular changes compared with other avian genomes reflect both shared and diverse adaptations of the two penguin species to the Antarctic environment

Composition-diamond lemma for modules

summary:We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and "double-free" left modules (that is, free modules over a free algebra). We first give Chibrikov's Composition-Diamond lemma for modules and then we show that Kang-Lee's Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra $sl_2$, the Verma module over a Kac-Moody algebra, the Verma module over the Lie algebra of coefficients of a free conformal algebra, and a universal enveloping module for a Sabinin algebra. As applications, we also obtain linear bases for the above modules