Mico Mrkaic

Predictive power of motor unit potential parameters in anal sphincter electromyography

The diagnostic utility of motor unit potential (MUP) parameters is usually based exclusively on their diagnostic sensitivity, disregarding specificity. In the present study, advanced statistical methods were used to determine MUP parameters with the highest predictive power for the separation of neuropathic and normal external anal sphincter (EAS) muscles. Using multi‐MUP analysis, 3,720 MUPs from 138 muscles of 52 patients with cauda equina lesion and 2,526 from 112 muscles of 64 controls were obtained. Only two principal components (PCs), which put weight on the MUP area and amplitude, were needed to explain all the data variability. On logistic and probit regression analyses, MUP area, duration, and number of turns gave results identical to all MUP parameters. Our results suggest that only these three MUP parameters are needed, and that they are as effective as PCs, in MUP analysis of chronic neuropathic EAS muscles. Reduced number of MUP parameters is expected to simplify MUP analysis and increase its specificity.

Size of motor unit potential sample

In quantitative electromyography (EMG), a sample size of 20 motor unit potentials (MUPs) is standard. The effect of increase in the number of MUPs above 20 is not known, although advanced MUP analysis techniques make such samples practical. In the present study, using multi‐MUP analysis, pools of 3,720 neuropathic and 2,526 control MUPs were obtained from external anal sphincter muscles. From each pool, 10,000 random samples of 5, 10, 15, 20, 30, 40, 50, and 100 MUPs were obtained by a computer. For each sample size, 95% normative limits for mean values, SDs, and “outliers,” and sensitivities were calculated for eight MUP parameters. As the magnitude of MUP samples increased, normative limits narrowed and sensitivities increased (at 5: 20–30%; at 20: 30–55%; at 100: 80–100%) for all statistics of all MUP parameters. Our results demonstrated a substantial increase in sensitivity by increasing the MUP sample to more than 20. This option deserves consideration in an attempt to improve the usefulness of quantitative EMG. Muscle Nerve 27: 196–201, 2003

Policy iteration accelerated with Krylov methods

Abstract Policy iteration is accelerated by substituting direct solution methods for solving systems of linear equations with faster iterative ones. The iterative methods used are nonstationary, or Krylov methods, that are very efficient at solving large sparse systems. Performance of accelerated policy iteration is evaluated by solving a standard stochastic growth model. Accelerated policy iteration is up to 100 times faster and as accurate as standard policy iteration and value iteration for problems of ‘moderate’ size (up to 1000 states). Further improvements are achieved by a multigrid algorithm, based on the accelerated policy iteration. This algorithm is particularly efficient at solving large problems (exceeding 100,000 states) where it can be several million times faster than standard policy iteration.

Chapter 58 – Preconditioning in Economic Stochastic Growth Models

Publisher Summary This chapter describes the preconditioning in economic stochastic growth models. Preconditioning significantly improves the performance of Krylov subspace methods (KSM) used in policy iteration for solving stochastic growth models. The performance improvement is especially large in models where the discount factor approaches 1. The potential of KSM in solving economic models should be further investigated along the following lines. The role of KSM in solving stochastic growth models with larger values of the risk aversion coefficient and models with more persistent productivity shocks should be evaluated. The effect of drop-off tolerance strategies with ILU on the performance of KSM should be explored, especially for BiCSTAB. The impact of the starting policy iterate on the performance should be evaluated. It is suggested that the performance of KSM with preconditioning should be evaluated on parallel computers. High performance algorithms in such applications should include finely tuned policy improvement search over smaller action sets, multigrid policy interpolation, and potentially multigrid interpolation of preconditioners.

Preconditioning in Economic Stochastic Growth Models

Publisher Summary This chapter describes the preconditioning in economic stochastic growth models. Preconditioning significantly improves the performance of Krylov subspace methods (KSM) used in policy iteration for solving stochastic growth models. The performance improvement is especially large in models where the discount factor approaches 1. The potential of KSM in solving economic models should be further investigated along the following lines. The role of KSM in solving stochastic growth models with larger values of the risk aversion coefficient and models with more persistent productivity shocks should be evaluated. The effect of drop-off tolerance strategies with ILU on the performance of KSM should be explored, especially for BiCSTAB. The impact of the starting policy iterate on the performance should be evaluated. It is suggested that the performance of KSM with preconditioning should be evaluated on parallel computers. High performance algorithms in such applications should include finely tuned policy improvement search over smaller action sets, multigrid policy interpolation, and potentially multigrid interpolation of preconditioners.