Quantum walks as a probe of structural anomalies in graphs

We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external vertices, are connected by edges. In the basic star graph, these are the only edges. If we now connect a subset of the external vertices to form a complete subgraph, a quantum walk can be used to find these vertices with a quantum speedup. Thus, under some circumstances, a quantum walk can be used to locate where the connectivity of a network changes. We also look at the case of two stars connected at one of their external vertices. A quantum walk can find the vertex shared by both graphs, again with a quantum speedup. This provides an example of using a quantum walk in order to find where two networks are connected. Finally, we use a quantum walk on a complete bipartite graph to find an extra edge that destroys the bipartite nature of the graph.Comment: 10 pages, 2 figure

Observing Nucleon Decay in Lead Perchlorate

Lead perchlorate, part of the OMNIS supernova neutrino detector, contains two nuclei, 208Pb and 35Cl, that might be used to study nucleon decay. Both would produce signatures that will make them especially useful for studying less-well-studied neutron decay modes, e.g., those in which only neutrinos are emitted.Comment: 6 pages, 2 figure

Parity Violation in Proton-Proton Scattering at 221 MeV

The parity-violating longitudinal analyzing power, Az, has been measured in pp elastic scattering at an incident proton energy of 221 MeV. The result obtained is Az =(0.84 +/- 0.29 (stat.) +/- 0.17 (syst.)) x 10^{-7}. This experiment is unique in that it selects a single parity violating transition amplitude, 3P2-1D2, and consequently directly constrains the weak meson-nucleon coupling constant h^pp_rho When this result is taken together with the existing pp parity violation data, the weak meson-nucleon coupling constants h^pp_rho and h^pp_omega can, for the first time, both be determined.Comment: 8 pages RevTeX4, 3 PostScript figures. Conclusion revised. New information about weak coupling constants adde

Parity Violation in Proton-Proton Scattering at 221 MeV

TRIUMF experiment 497 has measured the parity violating longitudinal analyzing power, A_z, in pp elastic scattering at 221.3 MeV incident proton energy. This paper includes details of the corrections, some of magnitude comparable to A_z itself, required to arrive at the final result. The largest correction was for the effects of first moments of transverse polarization. The addition of the result, A_z=(0.84 \pm 0.29 (stat.) \pm 0.17 (syst.)) \times 10^{-7}, to the pp parity violation experimental data base greatly improves the experimental constraints on the weak meson-nucleon coupling constants h^{pp}_\rho and h^{pp}_\omega, and has implications for the interpretation of electron parity violation experiments.Comment: 17 pages RevTeX, 14 PostScript figures. Revised version with additions suggested by Phys. Rev.

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting