The paper describes and studies an iterative algorithm for finding small values of a set of linear forms over vectors of integers. The algorithm uses a linear recurrence relation to generate a vector sequence, the basic idea being to choose the integral coefficients in the recurrence relation in such a way that the linear forms take small values, subject to the requirement that the integers sho...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We investigate how free probability allows us to approximate the density of states in tight-binding models of disor...

The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries, occurs when the lattice configuration loses stability, that is, when an eigenvalue of the Hessian of the lattice energy functional becomes negative. When the atomistic energy is approximated by a hybrid energy that couples atomistic and continuum models, the accuracy of the approximation can only be g...

We have studied collinear and noncollinear magnetic structures of a Mn monolayer on Cu~111! by use of the generalized gradient approximation to the density-functional theory using the full-potential linearized augmented plane-wave method. We found that the inclusion of the gradient correction did not significantly modify earlier results obtained in the local-density approximation. Irrespective ...

We discuss some recent results on the statistics of the Coulomb Blockade in disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime rs > ∼ 1, with finite dimensionless conductance g. We present significantly different results for the cases of a Coulomb and a nearest-neighbour bare interaction. We show th...

The rank function rank(·) is neither continuous nor convex which brings much difficulty to the solution of rank minimization problems. In this paper, we provide a unified framework to construct the approximation functions of rank(·), and study their favorable properties. Particularly, with two families of approximation functions, we propose a convex relaxation method for the rank minimization p...

Abstract. We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation is derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical “ghost” forces that occur in the atomistic to continuum ...

1. Models of coupled oscillators 2. Two main classes (a) Models with on-site potentials; e.g. Frenkel-Kontorova or discrete NLS (b) Models with only nearest neighbor coupling; e.g. FPU type models 3. Focus on: (a) localized oscillations (b) traveling waves 4. Numerical experiments of Kruskal and Zabusky and the discovery of solitons. 5. The formal approximation of the FPU model by the KdV equat...

We have developed a high level library, the Nearest Neighbor Tool (NNT), to facilitate the coding of finite difference approximation weather prediction models on parallel computers. NNT provides portability and ease of programming and at the same time optimizes performance by allowing the overlap of computation and communication to tolerate the latency of remote data moves. In this paper we des...

The success of reinforcement learning in practical problems depends on the ability to combine function approximation with temporal di erence methods such as value iteration. Experiments in this area have produced mixed results; there have been both notable successes and notable disappointments. Theory has been scarce, mostly due to the difculty of reasoning about function approximators that gen...