Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States

We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. An encoded parent Hamiltonian for the double semion string net ground state is explicitly constructed as a concrete example.Comment: 26 pages, 4 figures, v2 published versio

A Profile of Top Performers on the Uniform CPA Exam

The Elijah Watt Sells Award, one of the most prestigious professional awards in the US, honors top performers on the Uniform CPA Examination. This article provides statistics by state and by gender of past award winners, from the first CPA exam in 1923 through the most recent available exam results for 2012. In addition, it presents a profile of the top performers based on the results of a survey administered by the authors to recent Sells Award winners. Specifically, the survey examined the recipient\u27s educational level, the amount and type of preparation, and the impact of the award on the winner\u27s career. It is hoped that future candidates and state boards of accountancy will find this information useful and that this discussion will further promote the award\u27s prestige. This discussion focused on winners of the Elijah Watt Sells Award for outstanding performance on the CPA exam, providing data by state and by gender for the period from 1924 through 2012

Critical Pebbling Numbers of Graphs

We define three new pebbling parameters of a connected graph $G$, the $r$-, $g$-, and $u$-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $n$ and the diameter $d$ of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the $r$-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the $r$-critical pebbling number is $2^d$.Comment: 26 page