Public goods in networks

This paper considers incentives to provide goods that are non-excludable along social or geographic links. We find, first, that networks can lead to specialization in public good provision. In every social network there is an equilibrium where some individuals contribute and others free ride. In many networks, this extreme is the only outcome. Second, specialization can benefit society as a whole. This outcome arises when contributors are linked, collectively, to many agents. Finally, a new link increases access to public goods, but reduces individual incentives to contribute. Hence, overall welfare can be higher when there are holes in a network. © 2006 Elsevier Inc. All rights reserved.

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals.

Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.