RESUMO
Diffuse optical tomography (DOT) is an imaging modality that uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are chosen. We propose a numerical scheme of DOT, which works even when good initial guesses of optical parameters are not available. We use simulated annealing (SA), which is a method of the Markov-chain Monte Carlo. To implement SA for DOT, a spin Hamiltonian is introduced in the cost function, and the Metropolis algorithm or single-component Metropolis-Hastings algorithm is used. By numerical experiments, it is shown that an initial random spin configuration is brought to a converged configuration by SA, and targets in the medium are reconstructed. The proposed numerical method solves the inverse problem for DOT by finding the ground state of a spin Hamiltonian with SA.
RESUMO
It is conjectured that the four classes of elementary cellular automata classified by Wolfram are related to phase transitions; however, the structure of the phase diagram is yet to be clarified. Hence, we propose two parameters that are calculated using the s-step transition function of elementary cellular automata. We calculate these two quantities based on a second-order approximation of the transition function. The phase diagram of these two parameters can separate the rules into four Wolfram classes. Based on this phase diagram, it is clear that the rules of class 4 are located on the phase boundary between the regions of classes 2 and 3.
