We show that the zig-zag chain Z3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {φij} under which the zig-zag chain Z3 n is an extremal value of the induced topological index T defined by T (G) = ∑ 1≤i≤j≤n−1 mijφij where G is a graph with n vertices and mij is the number of edges of...

When can t terminal pairs in an m× n grid be connected by t vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch’s 1975 proof without the “cover all vertices” constraint, and Kotsuma and Takenaga’s 2010 proof when the paths are restricted to have the fewest possible cor...

Relatively little is known about adoption, use, and disadoption of new internet-based services. Using data from an Internet grocer in a market where it was the monopoly provider of this service, we examine customer adoption, use, and disadoption of online grocery shopping. We find that adoption was significant. In zip codes where the service was offered, 1-3 percent of households signed-up for ...

Patient-level health data from the State of Washington can be purchased for $50. This publicly available dataset has virtually all hospitalizations occurring in the State in a given year, including patient demographics, diagnoses, procedures, attending physician, hospital, a summary of charges, and how the bill was paid. It does not contain patient names or addresses (only ZIPs). Newspaper stor...

This paper extends the work of Glaeser et al. (1992) by looking at effects of agglomeration economies on employment growth in Dutch city-industries and in very small (postal) zip code-industries in the Dutch province of South-Holland. At both levels of geographic detail, findings are broadly consistent with results from the earlier study in that employment growth is enhanced by industrial diver...

Wilson (1987) and others argue that poor neighborhoods lack important organizational resources the middle class takes for granted, such as childcare centers, grocery stores and pharmacies. However, this approach does not distinguish poor neighborhoods from segregated neighborhoods, ignores immigration and neglects city differences. Using Department of Commerce and 2000 Census data for zip codes...

We construct a zig-zag process targeting posterior distributions arising in genetics from the Kingman coalescent and several popular models of mutation. show that can lead to efficiency gains up orders magnitude over classical Metropolis-Hastings, argue it is also well suited parallel computation for models. Our construction based on embedding discrete variables into continuous space; technique...

It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity restored via an amended inner-product metric $\Theta$. In Hermitian cases evaluation spectrum (i.e., bound-state energies) usually achieved diagonalization Hamiltonian. (or, more precisely, in $\Theta-$quasi-Hermitian) mechanics w...

Construction 7.1 (Margulis [Mar]) Fix a positive integerM and let [M ] = {1, 2, . . . ,M}. Define the bipartite graph G = (V,E) as follows. Let V = [M ]2∪ [M ]2, where vertices in the first partite set are denoted (x, y)1 and vertices in the second partite set are denoted (x, y)2. From each vertex (x, y)1, put in edges to (x, y)2, (x, x+ y)2, (x, x+ y+1)2, (x+ y, y)2, and (x+ y+ 1, y)2, where a...