Twisted KK-theory

Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary $K$-theory. (We omit, however, its relations to classical cohomology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group $H^3_G(X;\Z)$. We also consider some basic examples of twisted $K$-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman.Comment: 49 pages;some minor corrections have been made to the earlier versio

A mathematical system for human implantable wound model studies

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between the time response of the variables of our system and those reported by the literature for normal healing. Once a suitable choice of parameters has been made, we then compare simulation results with data obtained from clinical investigations. While more data is desired, we have a promising first step towards describing the primary events of wound repair within the confines of an implantable system

Antitrust in Innovative Industries

We study the effects of antitrust policy in industries with continual innovation. A more protective antitrust policy may have conflicting effects on innovation incentives, raising the profits of new entrants, but lowering those of continuing incumbents. We show that the direction of the net effect can be determined by analyzing shifts in innovation benefit and supply holding the innovation rate fixed. We apply this framework to analyze several specific antitrust policies. We show that in some cases, holding the innovation rate fixed, as suggested by our comparative statics results, the tension does not arise and a more protective policy necessarily raises the rate of innovation.

Intermediate coherent-incoherent charge transport: DNA as a case study

We study an intermediate quantum coherent-incoherent charge transport mechanism in metal-molecule-metal junctions using B\"uttiker's probe technique. This tool allows us to include incoherent effects in a controlled manner, and thus to study situations in which partial decoherence affects charge transfer dynamics. Motivated by recent experiments on intermediate coherent-incoherent charge conduction in DNA molecules [L. Xiang {\it et al.}, Nature Chem. 7, 221-226 (2015)], we focus on two representative structures: alternating (GC)$_n$ and stacked G$_n$C$_n$ sequences; the latter structure is argued to support charge delocalization within G segments, and thus an intermediate coherent-incoherent conduction. We begin our analysis with a highly simplified 1-dimensional tight-binding model, while introducing environmental effects through B\"uttiker's probes. This minimal model allows us to gain fundamental understanding of transport mechanisms and derive analytic results for molecular resistance in different limits. We then use a more detailed ladder-model Hamiltonian to represent double-stranded DNA structures---with environmental effects captured by B\"uttiker's probes. We find that hopping conduction dominates in alternating sequences, while in stacked sequences charge delocalization (visualized directly through the electronic density matrix) supports significant resonant-ballistic charge dynamics reflected by an even-odd effect and a weak distance dependence for resistance. Our analysis illustrates that lessons learned from minimal models are helpful for interpreting charge dynamics in DNA.Comment: 16 pages, 14 figure

The Long-Term Effects of Cross-Listing Investor Recognition, and Ownership Structure on Valuation

The authors show that the widening of a foreign firm's U.S. investor base and the improved information environment associated with cross-listing on a U.S. exchange each have a separately identifiable effect on a firm's valuation. The increase in valuation associated with cross-listing is transitory, not permanent. Valuations of Canadian firms peak in the year of cross-listing and fall monotonically thereafter, regardless of the level of U.S. investor holdings or the ownership structure of the firm. Cross-listed firms with a 20 per cent or more blockholder attract a similar number of U.S. institutional investors as widely held firms, on average, but experience a lower increase in valuation at high levels of investor recognition. While U.S. investors are less willing to invest in firms with dual-class shares, these firms benefit more from cross-listing even when they fail to widen their U.S. investor base, suggesting that the reduction in information asymmetry between controlling and minority investors has a separate impact on valuation for firms where agency problems are greatest.Financial markets; International topics