Three dimensional Sklyanin algebras and Gröbner bases

We consider Sklyanin algebras $S$ with 3 generators, which are quadratic algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations $pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. this class of algebras has enjoyed much attention. In particular, using tools from algebraic geometry, Feigin, Odesskii \cite{odf}, and Artin, Tate and Van Den Bergh, showed that if at least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter regular. More specifically, $S$ is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates (PHS). It has became commonly accepted that it is impossible to achieve the same objective by purely algebraic and combinatorial means like the Groebner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi-Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van Den Bergh. Further, we study a wider class of Sklyanin algebras, namely
the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials on
3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements).

A study of HER2 gene amplification and protein expression in gastric cancer

Background Gastric cancer is a leading cause of cancer-related mortality, and current treatment outcomes for advanced disease remain poor. HER2 has been identified as a potential candidate for targeted therapy in gastric cancers displaying HER2 gene amplification and protein overexpression.

Permanent Genetic Resources added to Molecular Ecology Resources Database 1 May 2009-31 July 2009

This article documents the addition of 512 microsatellite marker loci and nine pairs of Single Nucleotide Polymorphism (SNP) sequencing primers to the Molecular Ecology Resources Database. Loci were developed for the following species: Alcippe morrisonia morrisonia, Bashania fangiana, Bashania fargesii, Chaetodon vagabundus, Colletes floralis, Coluber constrictor flaviventris, Coptotermes gestroi, Crotophaga major, Cyprinella lutrensis, Danaus plexippus, Fagus grandifolia, Falco tinnunculus, Fletcherimyia fletcheri, Hydrilla verticillata, Laterallus jamaicensis coturniculus, Leavenworthia alabamica, Marmosops incanus, Miichthys miiuy, Nasua nasua, Noturus exilis, Odontesthes bonariensis, Quadrula fragosa, Pinctada maxima, Pseudaletia separata, Pseudoperonospora cubensis, Podocarpus elatus, Portunus trituberculatus, Rhagoletis cerasi, Rhinella schneideri, Sarracenia alata, Skeletonema marinoi, Sminthurus viridis, Syngnathus abaster, Uroteuthis (Photololigo) chinensis, Verticillium dahliae, Wasmannia auropunctata, and Zygochlamys patagonica. These loci were cross-tested on the following species: Chaetodon baronessa, Falco columbarius, Falco eleonorae, Falco naumanni, Falco peregrinus, Falco subbuteo, Didelphis aurita, Gracilinanus microtarsus, Marmosops paulensis, Monodelphis Americana, Odontesthes hatcheri, Podocarpus grayi, Podocarpus lawrencei, Podocarpus smithii, Portunus pelagicus, Syngnathus acus, Syngnathus typhle,Uroteuthis (Photololigo) edulis, Uroteuthis (Photololigo) duvauceli and Verticillium albo-atrum. This article also documents the addition of nine sequencing primer pairs and sixteen allele specific primers or probes for Oncorhynchus mykiss and Oncorhynchus tshawytscha; these primers and assays were cross-tested in both species.

Steroid injection for inferior heel pain: a randomised controlled trial

BACKGROUND:

Plantar fasciitis is a common cause of heel pain. The aim of this study was twofold: to compare steroid injection with placebo injection and to compare ultrasound guided with unguided steroid injection in the management of this condition.

METHODS:

65 patients with inferior heel pain were recruited between November 2008 and June 2011. Heel pain was measured using a visual analogue scale (VAS) at baseline and follow-up 6 and 12 weeks after injection.

RESULTS:

22 patients were randomised to ultrasound guided steroid injection, 21 patients to palpation guided steroid injection and 22 to ultrasound guided placebo injection. There was a significant difference in VAS scores between the groups at 6 and 12 weeks (p=0.018 and p=0.004, respectively). There was a 19.7 (95% CI 2.5 to 37.0) difference in mean VAS scores at 6 weeks between the ultrasound guided steroid group and the placebo group and a 24.0 (95% CI 6.6 to 41.3) difference between the unguided steroid group and the placebo group at 6 weeks. At 12 weeks, the mean difference was 25.1 (95% CI 6.5 to 43.6) and 28.4 (95% CI 11.1 to 45.7) respectively between both steroid injection groups and the placebo group. There was no difference in VAS scores following steroid injection between the ultrasound guided and the unguided groups at either time point. Plantar fascia thickness was significantly reduced after injection in both active treatment groups (p=0.00).

CONCLUSIONS:

In this study, steroid injection showed a clear benefit over placebo at 6 weeks and this difference was maintained at 12 weeks.Trial Registration No ISRCTN79628180 (www.controlled-trials.com).

Clinical and therapeutic relevance of PIM1 kinase in gastric cancer

Gastric cancer is a leading cause of cancer-related mortality, and chemotherapeutic options are currently limited. PIM1 kinase, an oncogene that promotes tumorigenesis in several cancer types, might represent a novel therapeutic target in gastric cancer.

Dual-colour HER2/chromosome 17 chromogenic in situ hybridisation assay enables accurate assessment of HER2 genomic status in gastric cancer and has potential utility in HER2 testing of biopsy samples

Determination of HER2 protein expression by immunohistochemistry (IHC) and genomic status by fluorescent in situ hybridisation (FISH) are important in identifying a subset of high HER2-expressing gastric cancers that might respond to trastuzumab. Although FISH is considered the standard for determination of HER2 genomic status, brightfield ISH is being increasingly recognised as a viable alternative. Also, the impact of HER2 protein expression/genomic heterogeneity on the accuracy of HER2 testing has not been well studied in the context of gastric biopsy samples.

Factors influencing success of clinical genome sequencing across a broad spectrum of disorders

To assess factors influencing the success of whole-genome sequencing for mainstream clinical diagnosis, we sequenced 217 individuals from 156 independent cases or families across a broad spectrum of disorders in whom previous screening had identified no pathogenic variants. We quantified the number of candidate variants identified using different strategies for variant calling, filtering, annotation and prioritization. We found that jointly calling variants across samples, filtering against both local and external databases, deploying multiple annotation tools and using familial transmission above biological plausibility contributed to accuracy. Overall, we identified disease-causing variants in 21% of cases, with the proportion increasing to 34% (23/68) for mendelian disorders and 57% (8/14) in family trios. We also discovered 32 potentially clinically actionable variants in 18 genes unrelated to the referral disorder, although only 4 were ultimately considered reportable. Our results demonstrate the value of genome sequencing for routine clinical diagnosis but also highlight many outstanding challenges.

Solar coronal magnetic fields derived using seismology techniques applied to omnipresent sunspot waves

Sunspots on the surface of the Sun are the observational signatures of intense manifestations of tightly packed magnetic field lines, with near-vertical field strengths exceeding 6,000 G in extreme cases1. It is well accepted that both the plasma density and the magnitude of the magnetic field strength decrease rapidly away from the solar surface, making high-cadence coronal measurements through traditional Zeeman and Hanle effects difficult as the observational signatures are fraught with low-amplitude signals that can become swamped with instrumental noise2, 3. Magneto-hydrodynamic (MHD) techniques have previously been applied to coronal structures, with single and spatially isolated magnetic field strengths estimated as 9–55 G (refs 4,5,6,7). A drawback with previous MHD approaches is that they rely on particular wave modes alongside the detectability of harmonic overtones. Here we show, for the first time, how omnipresent magneto-acoustic waves, originating from within the underlying sunspot and propagating radially outwards, allow the spatial variation of the local coronal magnetic field to be mapped with high precision. We find coronal magnetic field strengths of 32 ± 5 G above the sunspot, which decrease rapidly to values of approximately 1 G over a lateral distance of 7,000 km, consistent with previous isolated and unresolved estimations. Our results demonstrate a new, powerful technique that harnesses the omnipresent nature of sunspot oscillations to provide magnetic field mapping capabilities close to a magnetic source in the solar corona.