A Quality and Cost Approach for Comparison of Small-World Networks

We propose an approach based on analysis of cost-quality tradeoffs for comparison of efficiency of various algorithms for small-world network construction. A number of both known in the literature and original algorithms for complex small-world networks construction are shortly reviewed and compared. The networks constructed on the basis of these algorithms have basic structure of 1D regular lattice with additional shortcuts providing the small-world properties. It is shown that networks proposed in this work have the best cost-quality ratio in the considered class.Comment: 27 pages, 16 figures, 1 tabl

Space-Time Noncommutativity, Discreteness of Time and Unitarity

Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences, they still violate unitarity while in a usual field theory such a violation occurs when the theory is nonrenormalizable. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time. Violation of causality, among others, occurs also as the nonvanishing of the commutation relations between observables at space-like distances with a typical scale of noncommutativity. While this feature allows for a possible violation of the spin-statistics theorem, such a violation does not rescue the situation but makes the scale of causality violation as the inverse of the mass appearing in the considered model, i.e., even more severe. We also stress the role of smearing over the noncommutative coordinates entering the field operator symbols.Comment: 10 pages, plain LaTe

Manifestations of Space-Time Multidimensionality in Scattering of Scalar Particles

We analyze a possibility of experimental detection of the contribution of the Kaluza-Klein tower of heavy particles to scattering cross-section in a six-dimensional scalar model with two dimensions being compactified to the torus with the radii $R$. It is shown that there is a noticeable effect even for the energies of colliding particles below $R^{-1}$ which may be observed in future collider experiments if $R^{-1}$ is of the order of $1 TeV$.Comment: 12 pages, LATEX, UB-ECM-PF 93/1