On an easy transition from operator dynamics to generating functionals by Clifford algebras

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture relying on geometry does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to corresponding generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerable short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a non-linear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]

Mixed Symmetry Solutions of Generalized Three-Particle Bargmann-Wigner Equations in the Strong-Coupling Limit

Starting from a nonlinear isospinor-spinor field equation, generalized three-particle Bargmann-Wigner equations are derived. In the strong-coupling limit, a special class of spin 1/2 bound-states are calculated. These solutions which are antisymmetric with respect to all indices, have mixed symmetries in isospin-superspin space and in spin orbit space. As a consequence of this mixed symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these solution manifolds are interpreted as the three generations of leptons and quarks. This interpretation will be justified in a forthcoming paper.Comment: 17 page

Statistical analysis of network data and evolution on GPUs: High-performance statistical computing

Network analysis typically involves as set of repetitive tasks that are particularly amenable to poor-man's parallelization. This is therefore an ideal application are for GPU architectures, which help to alleviate the tedium inherent to statistically sound analysis of network data. Here we will illustrate the use of GPUs in a range of applications, which include percolation processes on networks, the evolution of protein-protein interaction networks, and the fusion of different types of biomedical and disease data in the context of molecular interaction networks. We will pay particular attention to the numerical performance of different routines that are frequently invoked in network analysis problems. We conclude with a review over recent developments in the generation of random numbers that address the specific requirements posed by GPUs and high-performance computing needs

Surface circulation in the Great Lakes as observed by LANDSAT-1 August 1972 - December 1973: Southern Lake Michigan

The surface current circulation patterns of southern Lake Michigan were charted for all cardinal and subcardinal wind directions, employing LANDSAT-1 observations of the distribution of natural tracing material borne in the surface waters. These colorants consist chiefly of river discharges composed of suspended sediments, pollutants, and algae; extensive chemical precipitations proved valuable for areas farther from shore. Comparison of the satellite-derived surface current charts with previous theoretical and empirical studies shows good agreement