Series of nilpotent orbits

We organize the nilpotent orbits in the exceptional complex Lie algebras into series using the triality model and show that within each series the dimension of the orbit is a linear function of the natural parameter a=1,2,4,8, respectively for f_4,e_6,e_7,e_8. We also obtain explicit representatives in a uniform manner. We observe similar regularities for the centralizers of nilpotent elements in a series and graded components in the associated grading of the ambient Lie algebra. More strikingly, for a greater than one, the degrees of the unipotent characters of the corresponding Chevalley groups, associated to these series through the Springer correspondance are given by polynomials which have uniform expressions in terms of a.Comment: 20 pages, revised version with more formulas for unipotent character

Wildflower Strip Establishment for the Delivery of Ecosystem Services in Sweet Cherry Orchards

The practice of introducing wildflower habitats in cropped areas is an approach that can be used to enhance ecosystem services. The value of such an approach will be affected by the establishment success of the sown species. To investigate this, 12 strips of wildflower habitat were established in alleyways between rows of cherry trees at three sites in the West Midlands (UK). The establishment of plants in sown strips was compared to six untreated alleyways that received conventional management. Eight forb species and one grass species was sown in strips measuring 1 m × 95 m. The establishment success of the sown species and their contribution to the vegetation of the alleyway was determined using percentage cover assessments in replicate quadrats. Dactylis glomerata, Leucanthemum vulgare, Prunella vulgaris and Lotus corniculatus established most consistently and with greater cover values in the sown strips. However, the sown strips were also associated with a greater abundance of unsown species, some of which are classed as weeds

Gene expression profiling of human dermal fibroblasts exposed to bleomycin sulphate does not differentiate between radiation sensitive and control patients

Background: Gene expression profiling of the transcriptional response of human dermal fibroblasts to in vitro radiation has shown promise as a predictive test of radiosensitivity. This study tested if treatment with the radiomimetic drug bleomycin sulphate could be used to differentiate radiation sensitive patients and controls in patients who had previously received radiotherapy for early breast cancer.Findings: Eight patients who developed marked late radiation change assessed by photographic breast appearance and 8 matched patients without any change were selected from women entered in a prospective randomised trial of breast radiotherapy fractionation. Gene expression profiling of primary skin fibroblasts exposed in vitro to bleomycin sulphate and mock treated fibroblast controls was performed. 973 genes were up-regulated and 923 down-reguated in bleomycin sulphate treated compared to mock treated control fibroblasts. Gene ontology analysis revealed enriched groups were cellular localisation, apoptosis, cell cycle and DNA damage response for the deregulated genes. No transcriptional differences were identified between fibroblasts from radiation sensitive cases and control patients; subgroup analysis using cases exhibiting severe radiation sensitivity or with high risk alleles present in TGF beta 1 also showed no difference.Conclusions: The transcriptional response of human dermal fibroblasts to bleomycin sulphate has been characterised. No differences between clinically radiation sensitive and control patients were detected using this approach

Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n=9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5,...,9 for the quadratic Casimir operator, in each case providing a formula (see eq. (11) to (15)) for the dimensions of the representations in the family as a function of D=dim g. This generalises previous results for powers j and Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the dimension formulas are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos correcte

Clinical academic career pathway for nursing and allied health professionals: clinical academic role descriptors

The clinical academic pathway outlined highlights the range of typical practice and research-focused activities that a practitioner on a clinical academic career pathway might normally engage in at different levels and points along this career path. The activities are intended as a guide for practitioners interested in learning more about the practice and research components of a clinical academic career, as well as those already employed in clinical academic roles. They may also be useful for health care organisations and Higher Education Institutions as a tool for developing clinical academic roles

Primality-testing Mersenne numbers

Report of a systematic review of Mersenne numbers 2^p-1 for p < 62982

Ferromagnetic Ordering of Energy Levels for Uq(sl2)U_q(\mathfrak{sl}_2) Symmetric Spin Chains

We consider the class of quantum spin chains with arbitrary $U_q(\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\textrm{SU}_q(2)$ for the quantum deformation of $\textrm{SU}(2)$, for $q>0$. We derive sufficient conditions for the Hamiltonian to satisfy the property we call {\em Ferromagnetic Ordering of Energy Levels}. This is the property that the ground state energy restricted to a fixed total spin subspace is a decreasing function of the total spin. Using the Perron-Frobenius theorem, we show sufficient conditions are positivity of all interactions in the dual canonical basis of Lusztig. We characterize the cone of positive interactions, showing that it is a simplicial cone consisting of all non-positive linear combinations of "cascade operators," a special new basis of $U_q(\mathfrak{sl}_2)$ intertwiners we define. We also state applications to interacting particle processes.Comment: 23 page

Predicting Potential Distribution of Orchis Galilaea in Lebanon Using GIS

Orchis galilaea is the only Lebanese orchid that is restricted geographically to Lebanon, Palestine and Jordan. It is a terrestrial orchid that attracts its pollinator by sexual deception while offering no reward. The full distribution of this orchid in Lebanon has not been determined. This study is part of ongoing research into the population dynamics of the orchid to form a management plan for its conservation. A Geographic Information System (GIS) was used to identify the habitat characteristics of O. galilaea and map its distribution in Lebanon by combining known locations with digital layers of environmental variables, including topography, land cover, soil type, geology and precipitation. Classes within each environmental parameter were defined and weighted according to their frequency of occurrence at extant sites. A predictive GIS model was developed by overlaying the five layers of the habitat characteristics. The predicted distribution map of O. galilaea was then validated by confirming presence of the orchid in the predicted locations and absence in the unsuitable areas through exploration field trips. Eighty five locations were surveyed and seven previously unknown populations of O. galilaea were discovered. These new O. galilaea locations were all correctly predicted by the model as potential habitat. The accuracy of the model was confirmed as it was significantly more likely to find the orchid in predicted suitable habitat compared with unsuitable habitat. Combining ecological habitat characteristics using GIS proved to be a useful tool to successfully predict the potential distribution of O. galilaea in Lebanon and will assist in planning its conservation measures