A Novel Convex Relaxation for Non-Binary Discrete Tomography

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations

On the Design and Pareto-Optimality of Participating Mortgages

This paper develops a micro-economic model and proceeds with numerical simulation to demonstrate that participating mortgages can improve social welfare when the real estate ownership is shared among the different taxable entities. The optimal distribution of real estate ownership and lending will tend to be concentrated in taxable and nontaxable hands, respectively, with lending conducted via participating mortgages. This paper also demonstrates the violation of the well-known, risk-neutral valuation argument of the Black and Scholes (1973) model because of the lack of a riskless hedge due to the uniqueness of real estate. Copyright American Real Estate and Urban Economics Association.