Mixed-state entanglement in the light of pure-state entanglement constrained by superselection rules

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted, e.g., constrained by local superselection rules, yields a structure that is analogous in many respects to that of mixed-state entanglement, including such exotic phenomena as bound entanglement and activation. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. Specifically, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Apparent motion photometry:evaluation and reliability of a novel method for the measurement of macular pigment

Background/aims Macular pigment is thought to protect the macula against exposure to light and oxidative stress, both of which may play a role in the development of age-related macular degeneration. The aim was to clinically evaluate a novel cathode-ray-tube-based method for measurement of macular pigment optical density (MPOD) known as apparent motion photometry (AMP). Methods The authors took repeat readings of MPOD centrally (0°) and at 3° eccentricity for 76 healthy subjects (mean (±SD) 26.5±13.2 years, range 18–74 years). Results The overall mean MPOD for the cohort was 0.50±0.24 at 0°, and 0.28±0.20 at 3° eccentricity; these values were significantly different (t=-8.905, p<0.001). The coefficients of repeatability were 0.60 and 0.48 for the 0 and 3° measurements respectively. Conclusions The data suggest that when the same operator is taking repeated 0° AMP MPOD readings over time, only changes of more than 0.60 units can be classed as clinically significant. In other words, AMP is not suitable for monitoring changes in MPOD over time, as increases of this magnitude would not be expected, even in response to dietary modification or nutritional supplementation.

Clinical evaluation of the MPS 9000 Macular Pigment Screener

Background/aims The MPS 9000 uses a psychophysical technique known as heterochromatic flicker photometry to measure macular pigment optical density (MPOD). Our aim was to determine the measurement variability (noise) of the MPS 9000. Methods Forty normally sighted participants who ranged in age from 18 to 50 years (25.4±8.2 years) were recruited from staff and students of Aston University (Birmingham, UK). Data were collected by two operators in two sessions separated by 1 week in order to assess test repeatability and reproducibility. Results The overall mean MPOD for the cohort was 0.35±0.14. There was no significant negative correlation between MPS 9000 MPOD readings and age (r=-0.192, p=0.236). Coefficients were 0.33 and 0.28 for repeatability, and 0.25 and 0.26 for reproducibility. There was no significant correlation between mean and difference MPOD values for any of the four pairs of results. Conclusions When MPOD is being monitored over time then any change less than 0.33 units should not be considered clinically significant as it is very likely to be due to measurement noise. The size of the coefficient appears to be positively correlated with MPOD.

Gaussian processes and SVM: Mean field results and leave-one-out

In this chapter, we elaborate on the well-known relationship between Gaussian processes (GP) and Support Vector Machines (SVM). Secondly, we present approximate solutions for two computational problems arising in GP and SVM. The first one is the calculation of the posterior mean for GP classifiers using a `naive' mean field approach. The second one is a leave-one-out estimator for the generalization error of SVM based on a linear response method. Simulation results on a benchmark dataset show similar performances for the GP mean field algorithm and the SVM algorithm. The approximate leave-one-out estimator is found to be in very good agreement with the exact leave-one-out error.

Advances in large margin classifiers

We apply methods of Statistical Mechanics to study the generalization performance of Support vector Machines in large data spaces.