Quaternionic Root Systems and Subgroups of the Aut(F4)Aut(F_{4})

Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms of the integer elements of the division algebras of real numbers, complex numbers, quaternions and octonions. Starting with the roots and weights of SU(2) expressed as the real numbers one can construct the root systems of the Lie algebras of SO(4),SP(2)= SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the division algebras. The roots themselves display the group structures besides the octonionic roots of E_{8} which form a closed octonion algebra. The automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the largest crystallographic group in 4-dimensional Euclidean space, is realized as the direct product of two binary octahedral group of quaternions preserving the quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192 with different conjugacy classes occur as maximal subgroups in the finite subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be useful in their constructions. The triality of SO(8) manifesting itself as the cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and F_{4} respectively

Non-crystallographic reduction of generalized Calogero-Moser models

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero–Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic types, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models, how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group

Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

Screening of medicinal plant extracts as novel DNA gyrase inhibitors

Bioactivities of a number of medicinal plants; Alkanna tinctoria (L.) Tausch, Alnus glutinosa (L.) Gaertn., Calamintha nepeta Willk. and C. nepeta, Centaurea iberica Trevir. ex Spreng., Citrus paradisi Macfad., C. paradisi, Citrus sinensis (L.) Osbeck, Colutea cilicica Boiss. & Balansa, Cotinus coggygria Scop., Cuscuta arvensis Beyr. ex Engelm., Equisetum palustre L., Lapsana communis L., Laurus nobilis L., Olea europea L., Plantago major L., Rhus coriaria L, Salvia verticillata L., Sambucus ebulus L., Sedum acre L, Thymus capitatus (L.) Hoffmanns. & Link, T. capitatus, Thymbra spicata L., T. spicata (n: 20), which are used for the prevention and treatment of diverse diseases, were investigated. The antimicrobial activities of extracts were evaluated using broth microdilution assay. The cytotoxicities of extracts were investigated on HeLa cell line by MTT assay. Statistical analysis was performed using GraphPad Prism (5.0). The effects of the extracts, which have the highest antimicrobial activity, on the Escherichia coli and Staphylococcus aureus DNA gyrase gene expression were determined by using quantitative reverse transcription polymerase chain reaction (qRT-PCR). The MICs (µg/ml) of extracts were determined as 32-64, 2-128, 8-128,1-128, 4-128 against Gram-positive, Gram-negative bacteria, yeasts, dermatophytes, and Mycobacterium spp., respectively. No cytotoxicity has been observed in plant extracts tested. DNA gyrase activity was determined for T. capitatus-SFE (128 µg/mL) and L. nobilis-Hx (128 µg/mL) extracts according to the inhibition of DNA gyrase gene expression. Overall, T. capitatus-SFE and L. nobilis-Hx are good candidates for further antimicrobial studies.

Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory

We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions and we determine all four-dimensional gauge theories resulting from the generalized dimensional reduction a la Forgacs-Manton over coset spaces, followed by a subsequent application of the Wilson flux spontaneous symmetry breaking mechanism. Our investigation is constrained only by the requirements that (i) the dimensional reduction leads to the potentially phenomenologically interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and (ii) the Wilson flux mechanism makes use only of the freely acting discrete symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty, ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C

Increased accuracy in climate impact studies by incorporating forest management practices within a process-based regional ecosystem modelling framework

Process-based simulation models of terrestrial ecosystem dynamics are increasingly being applied as practical tools in forest management. Regional applications of such models are, however, very limited to date. This study presents and tests the performance of a process-based regional ecosystem modelling framework, LPJ-GUESS, which incorporates forest management practices. The model is driven by historical climate data and applied on a grid across Sweden to simulate the influence of recent historical management practices on the forest structure and its productivity. The study focuses on species-level interactions and investigates how stem wood volume increment has changed during the historical time period. The performance of the model is evaluated by comparing the simulated forest composition and growth with the observed forest inventory data from Swedish forest regions. The model estimates tend to be somewhat low in the southern and high in the northern part of the country, but generally comparable with observations in all regions of Sweden. Our results emphasize the potential that models like LPJ-GUESS offers to support forestry practice, especially with regard to the choice of species and management regime in a changing environment

Linkage disequilibrium mapping of a breast cancer susceptibility locus near RAI/PPPIRI3L/iASPP

Background: Previous results have suggested an association of the region of 19q13.3 with several forms of cancer. In the present study, we investigated 27 public markers within a previously identified 69 kb stretch of chromosome 19q for association with breast cancer by using linkage disequilibrium mapping. The study groups included 434 postmenopausal breast cancer cases and an identical number of individually matched controls. Methods and Results: Studying one marker at a time, we found a region spanning the gene RAI ( alias PPP1R13L or iASPP) and the 5' portion of XPD to be associated with this cancer. The region corresponds to a haplotype block, in which there seems to be very limited recombination in the Danish population. Studying combinations of markers, we found that two to four neighboring markers gave the most consistent and strongest result. The haplotypes with strongest association with cancers were located in the gene RAI and just 3' to the gene. Coinciding peaks were seen in the region of RAI in groups of women of different age. In a follow-up to these results we sequenced 10 cases and 10 controls in a 44 kb region spanning the peaks of association. This revealed 106 polymorphisms, many of which were not in the public databases. We tested an additional 44 of these for association with disease and found a new tandem repeat marker, called RAI-3' d1, located downstream of the transcribed region of RAI, which was more strongly associated with breast cancer than any other marker we have tested (RR = 2.44 (1.41 - 4.23, p = 0.0008, all cases; RR = 6.29 (1.49 - 26.6), p = 0.01, cases up to 55 years of age). Conclusion: We expect the marker RAI-3' d1 to be (part of) the cause for the association of the chromosome 19q13.3 region's association with cancer