Entry, Pricing and Product Design in an Initially Monopolized Market

We analyze entry, pricing and product design in a model with differentiated products. Under plausible conditions, entry into an initially monopolized market leads to higher prices for some, possibly all, consumers. Entry can induce a misallocation of goods to consumers, segment the market in a way that transfers surplus to producers and undermine aggressive pricing by the incumbent. Post entry, firms have strong incentives to modify product designs so as to raise price by strengthening market segmentation. Firms may also forego socially beneficial product improvements in the post-entry equilibrium, because they intensify price competition too much. Multi-product monopoly can lead to better design incentives than the non-cooperative pricing that prevails under competition.

Anchored Critical Percolation Clusters and 2-D Electrostatics

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find that they are given by simple functions of the potentials of 2-D electrostatic dipoles, and that a kind of superposition {\it cum} factorization applies. Our results broaden this connection, already known from previous studies, and we present evidence that it is more generally valid. An exact result similar to the Kirkwood superposition approximation emerges.Comment: 4 pages, 1 (color) figure. More numerics, minor corrections, references adde

The density of critical percolation clusters touching the boundaries of strips and squares

We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our theoretical results follow from conformal field theory, and are compared with high-precision numerical simulation. For example, we show that the density of clusters touching both boundaries of an infinite strip of unit width (i.e. crossing clusters) is proportional to $(\sin \pi y)^{-5/48}\{[\cos(\pi y/2)]^{1/3} +[\sin (\pi y/2)]^{1/3}-1\}$. We also determine numerically contours for the density of clusters crossing squares and long rectangles with open boundaries on the sides, and compare with theory for the density along an edge.Comment: 11 pages, 6 figures. Minor revision

Predicting the effectiveness of hepatitis C virus neutralizing antibodies by bioinformatic analysis of conserved epitope residues using public sequence data

Hepatitis C virus (HCV) is a global health issue. Although direct-acting antivirals are available to target HCV, there is currently no vaccine. The diversity of the virus is a major obstacle to HCV vaccine development. One approach toward a vaccine is to utilize a strategy to elicit broadly neutralizing antibodies (bNAbs) that target highly-conserved epitopes. The conserved epitopes of bNAbs have been mapped almost exclusively to the E2 glycoprotein. In this study, we have used HCV-GLUE, a bioinformatics resource for HCV sequence data, to investigate the major epitopes targeted by well-characterized bNAbs. Here, we analyze the level of conservation of each epitope by genotype and subtype and consider the most promising bNAbs identified to date for further study as potential vaccine leads. For the most conserved epitopes, we also identify the most prevalent sequence variants in the circulating HCV population. We examine the distribution of E2 sequence data from across the globe and highlight regions with no coverage. Genotype 1 is the most prevalent genotype worldwide, but in many regions, it is not the dominant genotype. We find that the sequence conservation data is very encouraging; several bNAbs have a high level of conservation across all genotypes suggesting that it may be unnecessary to tailor vaccines according to the geographical distribution of genotypes

Entanglement under restricted operations: Analogy to mixed-state entanglement

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.Comment: 10 pages, 2 figures; published versio