WEBVTT

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Distribution of distress. Two 100 m sections; 30 m total affected length in each.

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MATHEMATICS · define the relationship and the meaning of each symbol before calculating.

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lj: non-overlapping affected patch length (m); L: assessed length (m). Extent is a proportion. Degree and spatial arrangement are separate inputs.

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INPUT · patch lengths in the distributed section · read the axis units and the numerical values.

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Two 100 m sections; 30 m total affected length in each.

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30/100 = 30% in each section. Six patches × 5 m = the same length, a different pattern.

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OUTPUT · extent, same denominator · read the axis units and the numerical values.

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Both sections have 30% extent. The sum preserves length but discards where the patches occur.

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CALCULATION · substitute the defined inputs; keep units through each intermediate step.

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Continuous pattern: 30 / 100 × 100 = 30 percent

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Distributed pattern: (5 + 5 + 5 + 5 + 5 + 5) / 100 × 100 = 30 percent

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Overlapping records: [0,20] and [10,30]: union length = 30, not 40 metres

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Longer denominator: 30 / 120 × 100 = 25 percent

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SENSITIVITY · change one declared input · read the axis units and the numerical values.

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100 m section: 30 % coverage. Thirty unique affected metres divided by 100 m.

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120 m section: 25 % coverage. Same affected length; denominator increases to 120 m.

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200 m section: 15 % coverage. Same affected length; denominator doubles.

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Check: Test disjoint, overlapping and fully nested intervals. The merged affected length must lie between zero and the assessed length. Retain degree, distress identity and the original interval coordinates alongside the percentage.

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ONE ROW · Would you send a crew to one continuous defect or sixty tiny interruptions? The total length alone cannot answer.

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PARAMETER MAP · 6000 evaluated cells. The colour limits stay fixed across every row.

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Each row distributes an ideal 30 m affected length into n equal patches over 100 m. The map samples their starts at one-metre intervals. Thin patches can fall between samples:

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count the coloured cells and you will see aliasing rather than a change in the underlying continuous coverage. That is a useful warning about reporting support.

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INTERPRETATION · These are discrete states. Read the map cell by cell; a smooth surface would invent intermediate categories.

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Equal extent does not imply equal degree, pattern or cause.