In the Post Correspondence Problem (PCP) an instance (h, g) consists of two morphisms h and g, and the problem is to determine whether or not there exists a word w such that h(w) = g(w). Here we prove that the PCP is decidable for instances with unique blocks and that the infinite PCP is decidable for instance with unique continuation in the construction of the solution. These results establish...

Correctly propagating waves from overhanging reflectors is crucial for imaging in complex geology. This type of reflections are difficult or impossible to use in imaging using one-way downward continuation, because they violate an intrinsic assumption of this imaging method, i.e. vertical upward propagation of reflection data. Riemannian wavefield extrapolation is one of the techniques develope...

We develop the theoretical foundations, numerical algorithms and computer programs to retrieve the 3D geometry of a density interface from gridded gravity data. The solution depends on constraining assumptions on permissible density values. An integral equation is solved by a new method of local corrections to find the density interface. The method is efficient and does not require trial-and-er...

The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal nonasymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may be local or global, with the only requirement being that the deviations of the...

Continuation model predictive control (MPC), introduced by T. Ohtsuka in 2004, uses Krylov-Newton approaches to solve MPC optimization and is suitable for nonlinear and minimum time problems. We suggest particle continuation MPC in the case, where the system dynamics or constraints can discretely change on-line. We propose an algorithm for on-line controller implementation of continuation MPC f...

In this paper, the four-precision-point geometric design problem of serial-link robot manipulators with three revolute joints is solved using a polynomial continuation method. At each precision point, the end-effector spatial locations are defined. The dimensions of the geometric parameters of the 3R manipulator are computed so that the manipulator’s end-effector will be able to reach these fou...

We consider the problem of calculating the electronic absorption spectrum of a chromophore with intramolecular degrees of freedom coupled to a condensed phase environment. We approach this calculation in the framework of the imaginary-time path integral Monte Carlo techniques, and focus on the problem of the analytic continuation of the imaginary-time data to the real-time axis. Two alternative...

We develop a primal dual active set with continuation algorithm for solving the l-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates...

A wavelet transform algorithm combined with a conjugate gradient method is used for the inversion of Poisson’s integral (downward continuation), used in airborne gravimetry applications. The wavelet approximation is dependent on orthogonal wavelet base functions. The integrals are approximated in finite multiresolution analysis subspaces. Mallat’s algorithm is used in the multiresolution analys...

Most known continuation methods for P 0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and a properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose in this paper a new homotopy formulation for the complementarity problem based on which a new h...