Dualizability of automatic algebras

We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra is dualizable if its letters act as an abelian group of permutations on its states. To illustrate the potential difficulty of the general problem, we exhibit an infinite ascending chain $\mathbf A_1 \le \mathbf A_2 \le \mathbf A_3 \le ...b$ of finite automatic algebras that are alternately dualizable and non-dualizable

Methods to improve recruitment to randomised controlled trials : Cochrane systematic review and meta-analysis

Peer reviewedPublisher PD

Hemangiopericytomas of the spine: case report and review of the literature

We describe a rare case of a primary intracranial meningeal hemangiopericytoma (HPC) with late metastasis to the cervical spine. A 36-year-old woman had a left occipital lesion that was histopathologically identified as HPC. Fourteen years after resection, the tumor recurred and was treated with radiotherapy. Three years later, CT imaging showed a large mass in the liver consistent with metastatic HPC, and MRI of the cervical spine showed an extensive lesion of the C3 vertebral body. The patient underwent C3 corpectomy with en-bloc tumor removal and follow-up radiation with no local recurrence or other spinal metastasis for the following 4 years. Regardless of the subtype of spinal HPC, complete surgical removal and radiotherapy appear to be treatment of choice

Drought Impact Is Alleviated in Sugar Beets (Beta vulgaris L.) by Foliar Application of Fullerenol Nanoparticles

Over the past few years, significant efforts have been made to decrease the effects of drought stress on plant productivity and quality. We propose that fullerenol nanoparticles (FNPs, molecular formula C-60(OH)(24)) may help alleviate drought stress by serving as an additional intercellular water supply. Specifically, FNPs are able to penetrate plant leaf and root tissues, where they bind water in various cell compartments. This hydroscopic activity suggests that FNPs could be beneficial in plants. The aim of the present study was to analyse the influence of FNPs on sugar beet plants exposed to drought stress. Our results indicate that intracellular water metabolism can be modified by foliar application of FNPs in drought exposed plants. Drought stress induced a significant increase in the compatible osmolyte proline in both the leaves and roots of control plants, but not in FNP treated plants. These results indicate that FNPs could act as intracellular binders of water, creating an additional water reserve, and enabling adaptation to drought stress. Moreover, analysis of plant antioxidant enzyme activities (CAT, APx and GPx), MDA and GSH content indicate that fullerenol foliar application could have some beneficial effect on alleviating oxidative effects of drought stress, depending on the concentration of nanoparticles applied. Although further studies are necessary to elucidate the biochemical impact of FNPs on plants; the present results could directly impact agricultural practice, where available water supplies are often a limiting factor in plant bioproductivity