Finding Transition Pathways on Manifolds

We consider noise-induced transition paths in randomly perturbed dynami- cal systems on a smooth manifold. The classical Freidlin-Wentzell large devia- tion theory in Euclidean spaces is generalized and new forms of action functionals are derived in the spaces of functions and the space of curves to accommodate the intrinsic constraints associated with the manifold. Numerical meth- ods are proposed to compute the minimum action paths for the systems with constraints. The examples of conformational transition paths for a single and double rod molecules arising in polymer science are numerically investigated

Commercial Revitalization in Low-Income Urban Communities: General Tax Incentives vs. Direct Incentives to Developers

This paper proposes a commercial development model, based on Fujita's (1988) monopolistic competition model of spatial agglomeration, to examine stores' decisions to enter urban communities. The model focuses on commercial developers and large stores, and identifies a potential holdup problem in the commercial development market arising because developers incur costs before negotiating with anchor tenants over pro fit sharing; the holdup problem is more likely to occur in low-income communities where the profitability of commercial projects is small. The model predicts that direct incentives to developers are preferred to general tax incentives for addressing this market failure.urban redevelopment programs; economic agglomeration; holdup problem