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Table 4 Constraints

From: Topology independent protein structural alignment

Interval clique inequalities:

(2)

y χ 5 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiwda1iabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37EB@

Line sweep at a t = 1

y χ 1 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabigdaXiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E3@

Line sweep at a t = 5

y χ 4 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabisda0iabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E9@

Line sweep at a t = 9

y χ 3 , λ a + y χ 4 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiodaZiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgUcaRiabdMha5naaBaaaleaacqWFhpWydaWgaaadbaGaeGinaqJaeiilaWIae83UdW2aaSbaaeaacqWGHbqyaeqaaaqabaaaleqaaOGaeyizImQaeGymaedaaa@4155@

Line sweep at a t = 10

y χ 3 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiodaZiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E7@

Line sweep at a t = 12

y χ 3 , λ a + y χ 2 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiodaZiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgUcaRiabdMha5naaBaaaleaacqWFhpWydaWgaaadbaGaeGOmaiJaeiilaWIae83UdW2aaSbaaeaacqWGHbqyaeqaaaqabaaaleqaaOGaeyizImQaeGymaedaaa@4151@

Line sweep at a t = 14

y χ 2 , λ a ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabikdaYiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E5@

Line sweep at a t = 16

Interval clique inequalities:

(3)

y χ 1 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabigdaXiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E5@

Line sweep at b t = 1

y χ 4 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabisda0iabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37EB@

Line sweep at b t = 6

y χ 4 , λ b + y χ 3 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabisda0iabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgUcaRiabdMha5naaBaaaleaacqWFhpWydaWgaaadbaGaeG4mamJaeiilaWIae83UdW2aaSbaaeaacqWGIbGyaeqaaaqabaaaleqaaOGaeyizImQaeGymaedaaa@4159@

Line sweep at b t = 7

y χ 3 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiodaZiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E9@

Line sweep at b t = 9

y χ 2 , λ b + y χ 3 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabikdaYiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgUcaRiabdMha5naaBaaaleaacqWFhpWydaWgaaadbaGaeG4mamJaeiilaWIae83UdW2aaSbaaeaacqWGIbGyaeqaaaqabaaaleqaaOGaeyizImQaeGymaedaaa@4155@

Line sweep at b t = 12

y χ 2 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabikdaYiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37E7@

Line sweep at b t = 13

y χ 5 , λ b ≤ 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiwda1iabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgsMiJkabigdaXaaa@37ED@

Line sweep at b t = 14

Consistency inequalities:

(4,5)

y χ 1 , λ a − x χ 1 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabigdaXiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGymaedabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D68@

y χ 1 , λ b − x χ 1 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabigdaXiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGymaedabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D6A@

y χ 2 , λ a − x χ 2 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabikdaYiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGOmaidabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D6C@

y χ 2 , λ b − x χ 2 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabikdaYiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGOmaidabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D6E@

y χ 3 , λ a − x χ 3 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiodaZiabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeG4mamdabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D70@

y χ 3 , λ b − x χ 3 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiodaZiabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeG4mamdabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D72@

y χ 4 , λ a − x χ 4 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabisda0iabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGinaqdabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D74@

y χ 4 , λ b − x χ 4 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabisda0iabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGinaqdabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D76@

y χ 5 , λ a − x χ 5 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiwda1iabcYcaSiab=T7aSnaaBaaabaGaemyyaegabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGynaudabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D78@

y χ 5 , λ b − x χ 5 ≥ 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEdaWgaaWcbaacciGae83Xdm2aaSbaaWqaaiabiwda1iabcYcaSiab=T7aSnaaBaaabaGaemOyaigabeaaaeqaaaWcbeaakiabgkHiTiabdIha4naaBaaaleaacqWFhpWydaWgaaadbaGaeGynaudabeaaaSqabaGccqGHLjYScqaIWaamaaa@3D7A@

  1. The constraints of the conflict graph for the set of fragments in Figure 6c.