Quaterionic Construction of the W(F_4) Polytopes with Their Dual Polytopes and Branching under the Subgroups B(B_4) and W(B_3)*W(A_1)

4-dimensional $F_{4}$ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary \textbf{$W(F_{4})$} orbit under the Coxeter groups $W(B_{4}$ and $W(B_{3}) \times W(A_{1})$ have been presented. The role of group theoretical technique and the use of quaternions have been emphasizedComment: 26 pages, 10 figure

The effect of diclofenac sodium on neural tube development in the early stage of chick embryos

Background: Neural tube defects are congenital malformations of the central nervous system. Genetic predisposition and some environmental factors play an important role in the development of neural tube defects. This study aimed to investigate the effects of diclofenac sodium on the neural tube development in a chick embryo model that corresponds to the first month of vertebral deve- lopment in mammals.  Materials and methods: Seventy-five fertile, specific pathogen-free eggs were incubated for 28 h and were divided into five groups of 15 eggs each. Diclofenac sodium was administered via the sub-blastodermic route at this stage. Incubation was continued till the end of the 48th h. All eggs were then opened and embryos were dissected from embryonic membranes and evaluated morphologically and histopathologically.  Results: It was determined that the use of increasing doses of diclofenac sodium led to defects of midline closure in early chicken embryos. There were statistically significant differences in neural tube positions (open or close) among the groups. In addition; crown–rump length, somite number were significantly decreased in high dose experimental groups compared with control group.  Conclusions: This study showed that development of neurons is affected in chi- cken embryos after administration of diclofenac sodium. The exact teratogenic mechanism of diclofenac sodium is not clear; therefore it should be investigated.

Autonomous Bidding Coordinated Acceptance in one-to-many negotiations

This work presents the Autonomous Bidding Coordinated Acceptance framework (ABCA): An agent-Team design that allows general bilateral agents to engage in oneto-many negotiations in a setting where (possibly overlapping) deals with multiple opponents are desirable. We propose also a coordinated acceptance strategy that uses the estimated outcomes of its bilateral negotiations while deciding to accept a deal

Saliency for animated meshes with material properties

We propose a technique to calculate the saliency of animated meshes with material properties. The saliency computation considers multiple features of 3D meshes including their geometry, material and motion. Each feature contributes to the final saliency map which is view independent; and therefore, can be used for view dependent and view independent applications. To verify our saliency calculations, we performed an experiment in which we use an eye tracker to compare the saliencies of the regions that the viewers look with the other regions of the models. The results confirm that our saliency computation gives promising results. We also present several applications in which the saliency information is used. © 2010 ACM

Family Unification in Five and Six Dimensions

In family unification models, all three families of quarks and leptons are grouped together into an irreducible representation of a simple gauge group, thus unifying the Standard Model gauge symmetries and a gauged family symmetry. Large orthogonal groups, and the exceptional groups $E_7$ and $E_8$ have been much studied for family unification. The main theoretical difficulty of family unification is the existence of mirror families at the weak scale. It is shown here that family unification without mirror families can be realized in simple five-dimensional and six-dimensional orbifold models similar to those recently proposed for SU(5) and SO(10) grand unification. It is noted that a family unification group that survived to near the weak scale and whose coupling extrapolated to high scales unified with those of the Standard model would be evidence accessible in principle at low energy of the existence of small (Planckian or GUT-scale) extra dimensions.Comment: 13 pages, 2 figures, minor corrections, references adde

Spatiotemporal graph indicators for air traffic complexity analysis

There has been extensive research in formalising air traffic complexity, but existing works focus mainly on a metric to tie down the peak air traffic controllers workload rather than a dynamic approach to complexity that could guide both strategical, pre-tactical and tactical actions for a smooth flow of aircraft. In this paper, aircraft interdependencies are formalized using graph theory and four complexity indicators are described, which combine spatiotemporal topological information with the severity of the interdependencies. These indicators can be used to predict the dynamic evolution of complexity, by not giving one single score, but measuring complexity in a time window. Results show that these indicators can capture complex spatiotemporal areas in a sector and give a detailed and nuanced view of sector complexity

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