One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

Effect of changing data collection parameters on statistical motor unit number estimates

The effect of number of samples and selection of data for analysis on the calculation of surface motor unit potential (SMUP) size in the statistical method of motor unit number estimates (MUNE) was determined in 10 normal subjects and 10 with amyotrophic lateral sclerosis (ALS). We recorded 500 sequential compound muscle action potentials (CMAPs) at three different stable stimulus intensities (10–50% of maximal CMAP). Estimated mean SMUP sizes were calculated using Poisson statistical assumptions from the variance of 500 sequential CMAP obtained at each stimulus intensity. The results with the 500 data points were compared with smaller subsets from the same data set. The results using a range of 50–80% of the 500 data points were compared with the full 500. The effect of restricting analysis to data between 5–20% of the CMAP and to standard deviation limits was also assessed. No differences in mean SMUP size were found with stimulus intensity or use of different ranges of data. Consistency was improved with a greater sample number. Data within 5% of CMAP size gave both increased consistency and reduced mean SMUP size in many subjects, but excluded valid responses present at that stimulus intensity. These changes were more prominent in ALS patients in whom the presence of isolated SMUP responses was a striking difference from normal subjects. Noise, spurious data, and large SMUP limited the Poisson assumptions. When these factors are considered, consistent statistical MUNE can be calculated from a continuous sequence of data points. A 2 to 2.5 SD or 10% window are reasonable methods of limiting data for analysis. Muscle Nerve 27: 320–331, 2003

Unraveling the barriers to reconceptualization of the problem in chronic pain: The actual and perceived ability of patients and health professionals to understand the neurophysiology

To identify why reconceptualization of the problem is difficult in chronic pain, this study aimed to evaluate whether (1) health professionals and patients can understand currently accurate information about the neurophysiology of pain and (2) health professionals accurately estimate the ability of patients to understand the neurophysiology of pain. Knowledge tests were completed by 276 patients with chronic pain and 288 professionals either before (untrained) or after (trained) education about the neurophysiology of pain. Professionals estimated typical patient performance on the test. Untrained participants performed poorly (mean +/- standard deviation, 55% +/- 19% and 29% +/- 12% for professionals and patients, respectively), compared to their trained counterparts (78% +/- 21% and 61% +/- 19%, respectively). The estimated patient score (46% +/- 18%) was less than the actual patient score (P < .005). The results suggest that professionals and patients can understand the neurophysiology of pain but professionals underestimate patients' ability to understand. The implications are that (1) a poor knowledge of currently accurate information about pain and (2) the underestimation of patients' ability to understand currently accurate information about pain represent barriers to reconceptualization of the problem in chronic pain within the clinical and lay arenas. (C) 2003 by the American Pain Society.