It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show tthat Monotone 1-in-3...

In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete- and continuous-time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability...

Quantum computing was so far mainly concerned with discrete problems. Recently, Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, what advantages quantum computing can bring over classical deterministic or randomized methods for this...

The stochastic method used to simulate the stationary transport in semiconductor devices is revised in terms of the numerical Monte Carlo theory. A mathematically based approach has been used to derive the basic simulation algorithms, previously devised from physical considerations. The approach...

We propose a nonparametric approach to multiple calibration of numerical general equilibrium models, where counterfactual equilibria are solutions to the Walrasian inequalities. We present efficient approximation schemes for deciding the solvability of Walrasian inequalities.

We consider the convergency of the basic Monte Carlo (MC) algorithms for solving the Boltzmann transport equation (BTE). It is a linear kinetic equation describing a broad class of particle transport phenomena such as electron and neutron transport, radiative transfer, medium energy electron and...

We present applications of a new Monte Carlo algorithm for the calculation of excited state energies of multi-dimensional quantum systems. The method relies on computation of imaginary time correlation functions of appropriately chosen projection operators, followed by a numerical inverse...