Theory

Figure: A 3D graph of SInc[] matrix made regular by checking Average and rotated around the Stability increase axis (vertical). The graph is based on 272 repetition cases (all data points included) for items with difficulty=0.05. The Average checkbox helps you extract best data using data-rich neighboring entries and theoretical SInc[] predictions where no data is available. This is particularly useful for scarce data in new collections (as the one used in the picture)

Figure: Exemplary graph enabling a more meaningful analysis of the forgetting index. Changes to forgetting index in Analysis use the daily measured forgetting index (previously: less informative cumulative measured forgetting index value was taken for the entire period since the last use of Tools : Statistics : Reset parameters : Forgetting index record). Note that the priority queue may distort the actual retention in your collection as measured values are primarily taken from top-priority material. Thus measured forgetting index should be understood as "forgetting index measured at repetitions", not as "overall measured forgetting index".

Figure: R-Metric graph demonstrates superiority of Algorithm SM-17 over the old Algorithm SM-15 for the presented collection used in the testing period of 12 months before the release of SuperMemo 17. It was plotted using 10,699 data points (i.e. repetition cases with data from both algorithms), and smoothed up to show the trends. One spot beneath the line of 0 at the vertical axis (R-metric<0) corresponds with a moment in time when the previous version of the algorithm appeared superior (in this case, due to a small sample of repetitions). Some positive and negative trends correspond with changes in the algorithm as data were collected in the new algorithm's testing period. A gradual increase in the metric in the months Feb-May 2016, might be a statistical aberration, or it might be the result of new interval values and a bigger R-metric for intervals departing from the optimum used in earlier SuperMemos. The latter might indicate that the benefits of Algorithm SM-17 might gradually increase over time.

Figure: Repetition history dialog box displaying the history of repetitions for the current element. In this example, no data before the 5th repetition is a result of the fact that the repetition history was collected in SuperMemo only as of 1996, while the presented collection is much older (with 4 repetitions executed before or in 1996). Also, the hour data is missing in older repetitions due to the fact that the repetition hour is registered in repetition history only as of SuperMemo 2006 (hours are used in correlating retention with sleep data available from SleepChart).

Figure: The horizontal axis corresponds with the repetition number and the vertical axis represents intervals (logarithmic scale). Despite a popular belief, the semi-log scale does not produce a linear graph here. Clearly the increase in the length of intervals slows down with successive repetitions. Moreover, the graph corresponding with zero lapses (red curve), results from the superposition of items with lower and faster increase in intervals (determined by difficulty). The bell-shaped curve is determined by all contributing items (below repetition number 10) and then only by difficult items or items with low forgetting index for which the increase in the length of intervals is significantly slower (above repetition 10). To see the above graph in your own collection, use Tools : Repetitions graph on the browser menu

Figure: Sleep and learning timeline. Sleep blocks are marked in blue. Learning blocks in red. Total learning time on individual days is displayed on the right. The currently selected sleep block turns yellow. Its length is displayed at the bottom. A sleep block whose color bleeds from blue into pink denotes interrupted sleep (e.g. with an alarm clock). A sleep block with the color changing from black to blue marks a delayed sleep episode (e.g. caused by watching a late tennis match).

Figure: Sleep and repetitions timeline displaying repetitions blocks of the current collection (in red) and sleep blocks (in blue) with recomputed circadian approximations on the current data. Blue and red continuous lines are predictions of optimum sleep time using the SleepChart model (based on sleep statistics). Yellow continuous line shows the prediction of the maximum of circadian sleepiness (circadian middle-of-the-night peak) using a phase response curve model. Note that, theoretically, the yellow line should roughly fall into the middle between blue and red lines. However, when a disruption of the sleep pattern is severe, those lines might diverge testifying to the fact that it is very hard to build models that fully match the chaotic behavior of the sleep control system subjected to a major perturbation. Aqua dots point to the predicted daytime dip in alertness (i.e. the time when a nap might be most productive).

Figure: Tools : Sleep Chart : Alertness (H) graph makes it possible for you to visually inspect how recall (and grades) decrease during the waking day. It also shows the impact of circadian factors with grades slightly lower immediately after waking and slightly higher after the mid-day dip in the 9th hour. The blue dots are recall data illustrating decline in performance during a waking day from 87.5% at waking to 81.5% at midday nadir (size of the circles corresponds with the number of repetitions collected, where minimum 50 repetitions are needed to paint a circle in this particular graph). The yellow line is the estimated homeostatic alertness derived from the sleep log data. The aqua line represents the circadian alertness estimate derived from the same sleep log data. Recall is a resultant of the impact of both sleep-drive processes: homeostatic (yellow) and circadian (aqua). 0.1 (hours) (at the bottom) is the minimum sleep block length taken into consideration. 101,230 repetitions cases were taken to plot the graph. The Deviation parameter displayed at the top tells you how well the chosen approximation curve fits the data (in the picture: negatively exponential recall curve). The lesser the deviation, the better the fit. The deviation is computed as a square root of the average of squared differences (as used in the method of least squares). Depressed Use R will use grade-R correlations for an average student to estimate recall (R derived from the DSR model is not used here, as on the Alertness (C) tab, due to the slowness of the computation). Those correlated R figures may differ from actual recall