## Heatmap: Outlier Stations Percentage of Other Occurrences ### Overview The image is a heatmap visualizing the percentage of other occurrences for various outlier stations over time, spanning from October 10, 2020, to October 30, 2020. The heatmap uses a green color gradient to represent the percentage values, with darker shades indicating higher percentages. ### Components/Axes * **Y-axis:** "Outlier stations" listing stations with labels like "FR+V75\*EBELI\*1\*1 -", "FR+V75+EBELI\*14\*1", and so on. There are 24 stations listed. * **X-axis:** "Date" ranging from "2020-10-10" to "2020-10-30". * **Color Legend:** Located on the right side, showing a green gradient from light to dark, representing "Percentage of Other occurency" from 0 to 100. The legend has tick marks at 0, 20, 40, 60, 80, and 100. ### Detailed Analysis The heatmap displays the percentage of other occurrences for each outlier station on each day. The color intensity indicates the percentage value. Here's a breakdown of some of the stations and their trends: * **FR+V75\*EBELI\*1\*1 -:** Shows a high percentage (dark green) on 2020-10-21, and a lighter green on 2020-10-22. * **FR+V75+EBELI\*14\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75+EBELI\*19\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75 EBELI\*22\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75 EBELI\*26\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR\*V75+EBELI\*28\*1:** Shows a high percentage (dark green) on 2020-10-27, 2020-10-28, and 2020-10-29. * **FR+V75 EBELI\*29\*1:** Shows a high percentage (dark green) on 2020-10-27, 2020-10-28, and 2020-10-29. * **FR+V75 EBELI\*32\*1:** Shows a high percentage (dark green) on 2020-10-27, 2020-10-28, and 2020-10-29. * **FR+V75 EBELI\*33\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR\*V75+EBELI\*42\*1:** Shows a high percentage (dark green) on 2020-10-21, and a lighter green on 2020-10-22. * **FR+V75+EBELI\*47\*1:** Shows a high percentage (dark green) on 2020-10-21, and a lighter green on 2020-10-22. * **FR+V75+EBELI\*57\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75 EBELI\*58\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR\*V75+EBELI\*59\*1:** Shows a high percentage (dark green) on 2020-10-27, 2020-10-28, and 2020-10-29. * **FR+V75+EBELI\*65\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75+EBELI\*66\*1:** Shows a high percentage (dark green) on 2020-10-27, 2020-10-28, and 2020-10-29. * **FR V75 EBELI\*7\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR\*V75+EBELI\*77\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR\*V75+EBELI\*81\*1 -:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75+EBELI\*82\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR V75 EBELI\*85\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75+EBELI\*87\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR\*V75\*EBELI\*92\*1:** Shows a high percentage (dark green) on 2020-10-10, and a lighter green on 2020-10-11. * **FR+V75\*EBELI\*95\*1:** Shows a high percentage (dark green) on 2020-10-21, and a lighter green on 2020-10-22. ### Key Observations * Several stations show high percentages of other occurrences around October 10-11 and October 21-22. * Some stations show high percentages of other occurrences around October 27-29. * The heatmap provides a visual representation of the temporal distribution of other occurrences for each station. ### Interpretation The heatmap visualizes the percentage of other occurrences for different outlier stations over a period of time. The variations in color intensity indicate changes in the percentage of other occurrences. The data suggests that certain stations experience higher percentages of other occurrences during specific periods, potentially indicating anomalies or unusual events at those locations during those times. The heatmap allows for easy identification of stations and time periods with the highest percentage of other occurrences, which could be further investigated to understand the underlying causes.

\n ## Heatmap: Outlier Station Occurrences ### Overview This image presents a heatmap visualizing the percentage of co-occurrence of outlier stations over time, specifically during the period from 2020-10-10 to 2020-10-30. The heatmap displays the relationship between 20 different outlier stations listed on the y-axis and dates on the x-axis. The color intensity represents the percentage of other occurrences, ranging from 0% (white) to 100% (dark green). ### Components/Axes * **X-axis:** Date, ranging from 2020-10-10 to 2020-10-30, with increments of approximately one day. * **Y-axis:** Outlier Stations. The following stations are listed: * FR\*V75\*EBEL\*1\*1 * FR\*V75\*EBEL\*14\*1 * FR\*V75\*EBEL\*19\*1 * FR\*V75\*EBEL\*22\*1 * FR\*V75\*EBEL\*26\*1 * FR\*V75\*EBEL\*28\*1 * FR\*V75\*EBEL\*29\*1 * FR\*V75\*EBEL\*32\*1 * FR\*V75\*EBEL\*33\*1 * FR\*V75\*EBEL\*42\*1 * FR\*V75\*EBEL\*47\*1 * FR\*V75\*EBEL\*57\*1 * FR\*V75\*EBEL\*58\*1 * FR\*V75\*EBEL\*59\*1 * FR\*V75\*EBEL\*65\*1 * FR\*V75\*EBEL\*66\*1 * FR\*V75\*EBEL\*77\*1 * FR\*V75\*EBEL\*81\*1 * FR\*V75\*EBEL\*82\*1 * FR\*V75\*EBEL\*85\*1 * FR\*V75\*EBEL\*87\*1 * FR\*V75\*EBEL\*92\*1 * FR\*V75\*EBEL\*95\*1 * **Color Scale (Right):** Percentage of Other Occurency, ranging from 0% (white) to 100% (dark green). The scale is divided into increments of approximately 20%. ### Detailed Analysis The heatmap shows varying degrees of co-occurrence between the outlier stations. Here's a breakdown of observations, noting approximate values due to the visual nature of the data: * **FR\*V75\*EBEL\*1\*1:** Shows a strong co-occurrence (approximately 80-100%) around 2020-10-29 and 2020-10-30. Very low co-occurrence (0-20%) for most other dates. * **FR\*V75\*EBEL\*14\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*19\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*22\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*26\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*28\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*29\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*32\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*33\*1:** Shows a strong co-occurrence (approximately 60-80%) around 2020-10-11 to 2020-10-13. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*42\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*47\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*57\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*58\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*59\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*65\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*66\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-21. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*77\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-19. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*81\*1:** Displays a strong co-occurrence (approximately 60-80%) around 2020-10-11 to 2020-10-13. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*82\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*85\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*87\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*92\*1:** Displays a moderate co-occurrence (approximately 40-60%) around 2020-10-29. Low co-occurrence for other dates. * **FR\*V75\*EBEL\*95\*1:** Shows a moderate co-occurrence (approximately 40-60%) around 2020-10-27 to 2020-10-30. Low co-occurrence for other dates. ### Key Observations * There's a noticeable cluster of high co-occurrence around 2020-10-29 and 2020-10-30 for several stations (FR\*V75\*EBEL\*1\*1, FR\*V75\*EBEL\*14\*1, FR\*V75\*EBEL\*19\*1, FR\*V75\*EBEL\*22\*1, FR\*V75\*EBEL\*26\*1, FR\*V75\*EBEL\*28\*1, FR\*V75\*EBEL\*29\*1, FR\*V75\*EBEL\*32\*1, FR\*V75\*EBEL\*82\*1, FR\*V75\*EBEL\*85\*1, FR\*V75\*EBEL\*87\*1, FR\*V75\*EBEL\*92\*1). * Stations FR\*V75\*EBEL\*33\*1 and FR\*V75\*EBEL\*81\*1 exhibit high co-occurrence between 2020-10-11 and 2020-10-13. * Stations FR\*V75\*EBEL\*42\*1, FR\*V75\*EBEL\*47\*1, FR\*V75\*EBEL\*57\*1, FR\*V75\*EBEL\*58\*1, FR\*V75\*EBEL\*59\*1, and FR\*V75\*EBEL\*66\*1 show moderate co-occurrence around 2020-10-21. * Most stations show very low co-occurrence for the majority of the observed period. ### Interpretation The heatmap suggests that the outlier stations do not generally co-occur frequently. However, there are specific periods where certain stations exhibit a strong tendency to occur together. The high co-occurrence around 2020-10-29 and 2020-10-30 indicates a potential shared event or condition affecting those stations. The earlier peak between 2020-10-11 and 2020-10-13 for stations FR\*V75\*EBEL\*33\*1 and FR\*V75\*EBEL\*81\*1 suggests a separate, earlier event. The moderate co-occurrence around 2020-10-21 for a different set of stations suggests yet another distinct event. This data could be used to investigate the underlying causes of these co-occurrences. For example, are these stations geographically close? Do they share similar environmental conditions? Are they subject to the same operational procedures? Further investigation is needed to understand the relationships between these outlier stations and the events that trigger their simultaneous occurrence. The heatmap provides a valuable starting point for identifying patterns and prioritizing further analysis.

## Heatmap Chart: Outlier Status Over Time (October 2020) ### Overview This image is a heatmap chart visualizing the temporal occurrence of various "Outlier Status" codes over the month of October 2020. The chart uses a color gradient to represent the "Percentage of Other occurrences" for each status on each day. The primary language in the chart is English. ### Components/Axes * **Chart Type:** Heatmap (Temporal Grid). * **Y-Axis (Vertical):** Labeled "Outlier Status". It lists 22 distinct categorical codes. From top to bottom, they are: 1. `FR~V75~EBELM1*1` 2. `FR~V75~EBELM14*1` 3. `FR~V75~EBELM15*1` 4. `FR~V75~EBELM22*1` 5. `FR~V75~EBELM26*1` 6. `FR~V75~EBELM28*1` 7. `FR~V75~EBELM32*1` 8. `FR~V75~EBELM33*1` 9. `FR~V75~EBELM42*1` 10. `FR~V75~EBELM46*1` 11. `FR~V75~EBELM57*1` 12. `FR~V75~EBELM58*1` 13. `FR~V75~EBELM59*1` 14. `FR~V75~EBELM62*1` 15. `FR~V75~EBELM66*1` 16. `FR~V75~EBELM71*1` 17. `FR~V75~EBELM77*1` 18. `FR~V75~EBELM78*1` 19. `FR~V75~EBELM82*1` 20. `FR~V75~EBELM85*1` 21. `FR~V75~EBELM87*1` 22. `FR~V75~EBELM95*1` * **X-Axis (Horizontal):** Labeled "Date". It displays daily dates from `2020-10-10` to `2020-10-30`. The dates are listed vertically for readability. * **Legend/Color Scale:** Positioned on the far right. It is a vertical color bar labeled "Percentage of Other occurrences". The scale runs from 0 (bottom, very light green/white) to 100 (top, dark forest green). Key markers are at 0, 20, 40, 60, 80, and 100. * **Data Grid:** The main area is a grid where each cell corresponds to a specific Outlier Status (row) and Date (column). The cell's color indicates the percentage value. ### Detailed Analysis The heatmap shows significant variation in the occurrence percentages across different outlier statuses and dates. **Trend Verification & Data Point Extraction (by Row):** * **Persistent High-Occurrence Rows (Dark Green Bands):** Several rows show consistently dark green cells across most dates, indicating a high percentage (approx. 80-100%) of "Other occurrences." * `FR~V75~EBELM1*1`: Very dark green from Oct 10-22, then lighter. * `FR~V75~EBELM14*1`: Consistently dark green across the entire period. * `FR~V75~EBELM15*1`: Consistently dark green. * `FR~V75~EBELM22*1`: Consistently dark green. * `FR~V75~EBELM32*1`: Consistently dark green. * `FR~V75~EBELM46*1`: Consistently dark green. * `FR~V75~EBELM57*1`: Consistently dark green. * `FR~V75~EBELM58*1`: Consistently dark green. * `FR~V75~EBELM62*1`: Consistently dark green. * `FR~V75~EBELM78*1`: Consistently dark green. * `FR~V75~EBELM82*1`: Consistently dark green. * `FR~V75~EBELM85*1`: Consistently dark green. * `FR~V75~EBELM87*1`: Consistently dark green. * `FR~V75~EBELM95*1`: Consistently dark green. * **Sporadic or Low-Occurrence Rows:** Other rows show lighter colors or blank (white) cells, indicating low or zero percent occurrence. * `FR~V75~EBELM26*1`: Mostly light/white, with a notable dark green cluster (approx. 80-100%) from Oct 27-30. * `FR~V75~EBELM28*1`: Mostly light/white, with a dark green cluster (approx. 80-100%) from Oct 27-30. * `FR~V75~EBELM33*1`: Mixed. Light green (20-40%) early in the month, then a dark green cluster (approx. 80-100%) from Oct 27-30. * `FR~V75~EBELM42*1`: Mostly light green (20-40%) with some darker patches. * `FR~V75~EBELM59*1`: Mostly light/white, with a dark green cluster (approx. 80-100%) from Oct 27-30. * `FR~V75~EBELM66*1`: Mostly light/white, with a dark green cluster (approx. 80-100%) from Oct 27-30. * `FR~V75~EBELM71*1`: Mostly light/white, with a dark green cluster (approx. 80-100%) from Oct 27-30. * `FR~V75~EBELM77*1`: Mostly light/white, with a dark green cluster (approx. 80-100%) from Oct 27-30. * **Temporal Pattern:** A very clear pattern emerges in the last four days of the chart (Oct 27-30). A specific set of outlier statuses (`...26*1`, `...28*1`, `...33*1`, `...59*1`, `...66*1`, `...71*1`, `...77*1`) that were previously low-activity suddenly show a synchronized spike to very high percentages (dark green). ### Key Observations 1. **Bimodal Distribution:** The outlier statuses fall into two clear groups: a large set that is persistently active (high percentage) throughout the month, and a smaller set that is mostly inactive until a sudden, synchronized activation at the end of the month. 2. **End-of-Month Anomaly:** The period from October 27 to October 30 shows a distinct event where multiple previously quiet outlier statuses become highly active simultaneously. 3. **Data Gaps:** The columns for `2020-10-23`, `2020-10-24`, `2020-10-25`, and `2020-10-26` appear completely blank (white) for all rows. This could indicate missing data, a system outage, or a period with 0% occurrence for all tracked outliers. 4. **Color Scale Interpretation:** The darkest green represents ~100%, and the lightest green/white represents ~0%. Most "active" cells are at the extreme dark end of the scale. ### Interpretation This heatmap likely tracks the occurrence of specific error codes, system alerts, or anomaly types ("Outlier Status") within a technical system over time. The "Percentage of Other occurrences" metric suggests it measures how often this specific outlier was observed relative to all other outliers on that day. * **What the data suggests:** The system has a baseline of several constantly occurring outlier types (the persistent dark green rows). The synchronized spike at the end of the month indicates a significant system event or change that triggered a specific subset of outlier types that are normally rare. This could point to a software deployment, configuration change, infrastructure issue, or external attack that began around October 27. * **Relationship between elements:** The y-axis categories are the monitored conditions. The x-axis is the timeline. The color intensity is the normalized frequency. The blank period (Oct 23-26) is critical—it separates the stable baseline period from the anomalous event period. The event is not a gradual increase but a sharp, coordinated onset. * **Notable anomalies:** The most striking anomaly is the **temporal cluster of high activity from Oct 27-30** for the specific subset of statuses. This is not random noise; it's a correlated pattern suggesting a common root cause. The complete lack of data for Oct 23-26 is another major anomaly that requires investigation—it may be the cause or a precursor to the subsequent event. The persistent high activity of the other statuses suggests they are either common, non-critical warnings or indicators of a chronic system condition.

## Heatmap: Percentage of Other Occupancy at Outer Stations Over Time ### Overview The image is a heatmap visualizing the percentage of "Other occupancy" at 15 outer stations (labeled FRV75EBELI141-1 to FRV75EBELI951-1) over a 21-day period from October 10 to October 30, 2020. The color intensity represents occupancy levels, with darker green indicating higher percentages (up to 100%) and lighter green indicating lower percentages. --- ### Components/Axes - **X-axis (Date)**: October 10, 2020 – October 30, 2020 (daily intervals). - **Y-axis (Stations)**: 15 outer stations, labeled with codes like `FRV75EBELI141-1`, `FRV75EBELI191-1`, etc. - **Legend**: Right-aligned colorbar labeled "Percentage of Other occupancy" (0% to 100%). - **Color Scale**: - Dark green = 100% - Medium green = ~60–80% - Light green = ~20–40% - White = 0% --- ### Detailed Analysis #### Station Trends 1. **FRV75EBELI141-1**: Consistently dark green (100%) across all dates except October 21–22 (light green, ~20–40%). 2. **FRV75EBELI191-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 3. **FRV75EBELI221-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. Notable anomaly: Light green on October 18 (unclear reason). 4. **FRV75EBELI261-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 5. **FRV75EBELI281-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 6. **FRV75EBELI291-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 7. **FRV75EBELI321-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 8. **FRV75EBELI331-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 9. **FRV75EBELI421-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 10. **FRV75EBELI471-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 11. **FRV75EBELI571-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 12. **FRV75EBELI581-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 13. **FRV75EBELI591-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 14. **FRV75EBELI651-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. 15. **FRV75EBELI661-1**: Dark green (100%) on October 10–11, 14–15, 18–19, 22–23, 26–27, 29–30. Light green on October 12–13, 16–17, 20–21, 24–25. #### Notable Patterns - **Consistent High Occupancy**: Most stations (e.g., FRV75EBELI141-1, FRV75EBELI191-1) show near-100% occupancy for most dates. - **Recurring Drops**: Stations like FRV75EBELI221-1 and FRV75EBELI261-1 exhibit periodic drops to ~20–40% on specific dates (e.g., October 12–13, 16–17, 20–21). - **Anomalies**: FRV75EBELI221-1 shows an unexpected light green cell on October 18, deviating from its usual pattern. --- ### Key Observations 1. **Dominant Trend**: Over 80% of stations maintain 100% occupancy for the majority of the period. 2. **Recurring Dips**: Light green cells (low occupancy) cluster around October 12–13, 16–17, and 20–21, suggesting systemic factors (e.g., maintenance, events). 3. **Anomaly**: FRV75EBELI221-1’s October 18 dip breaks its otherwise consistent pattern, warranting further investigation. --- ### Interpretation The heatmap reveals that most outer stations operate at full capacity (100% occupancy) for extended periods, with only minor deviations. The recurring drops in occupancy (e.g., October 12–13, 16–17) suggest cyclical disruptions, possibly due to scheduled maintenance, weather events, or demand fluctuations. The anomaly in FRV75EBELI221-1 on October 18 highlights potential data inconsistencies or unique local factors affecting that station. This data is critical for optimizing resource allocation, identifying operational bottlenecks, and improving service reliability. Further analysis of external factors (e.g., weather reports, maintenance logs) is recommended to explain the observed patterns.