Generator

log-odds on a drift model: what one substitution costs

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
log-odds on a drift model: what one substitution costsThe rule is the log-odds of one step of a random walk that stays put with probability 0.6 and otherwise moves, eight times more readily within a purine or pyrimidine pair than between them; a gap character costs 2. Read a row as the symbol expected and a column as the symbol seen; the entry is what the table charges for that pair, in bits. The diagonal is zero by construction so that a minimising fill can be used unchanged. Nothing here is copied from a published table: every entry is computed from the rule beside it, which is the difference between a matrix that can be checked and one that can only be quoted.acgtacgtseen ->0313303113033130a gap of k characters costs 2krows: expected · columns: seen · unit: bitslinear gaps

log-odds on a drift model: what one substitution costs

The rule is the log-odds of one step of a random walk that stays put with probability 0.6 and otherwise moves, eight times more readily within a purine or pyrimidine pair than between them; a gap character costs 2. Read a row as the symbol expected and a column as the symbol seen; the entry is what the table charges for that pair, in bits. The diagonal is zero by construction so that a minimising fill can be used unchanged. Nothing here is copied from a published table: every entry is computed from the rule beside it, which is the difference between a matrix that can be checked and one that can only be quoted.

Drawn at 700 × 326, wide on the page. Everything above is what cost-model returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

10 essays call cost-model. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.

Where it is called

Changing this generator changes every one of these figures.

acgtacgtseen ->0313303113033130a gap of k characters costs 2krows: expected · columns: seen · unit: bitslinear gaps When the algorithm is a table

A cost that is not one

0%25%50%75%100%11.522.533.545what a matching character is worthreported as the shared region, of the longer sequencea random pair scores zero hereunit cost, alphabet acgtthe region found: 13 characters at the left, 34 at the right When the algorithm is a table

The zero that moves the answer out of the corner

agcacacggatcagccagggagta09101112131415161718192021229110101212141416171819192122101021011121314151718191920221110113101212141516171920192112121012411131314151718202119131312111351214131416181921211414131312146131413151719202115141514131314714151316181921161614161514141571416141719191717171517161515168151615182018171818151816161617816171519one unit = one subproblem given a value495 cells across three tables, 980 transitions When the algorithm is a table

A cell that has to know where it is

cost per column of the alignmentab / ba1.00 over 2 · 0.67 over 3kitten / sitting0.43 over 7 · 0.43 over 7intention / execution0.56 over 9 · 0.50 over 10gattaca / gactata0.29 over 7 · 0.29 over 7abracadabra / abrocadabro0.18 over 11 · 0.18 over 11unit cost, in edits per columnupper bar: the optimum, divided · lower bar: the best rate When the algorithm is a table

A distance divided by a length is not a rate

pairs where the two disagreerestricted · unrestrictedab → bca3 against 2ac → cba3 against 2ba → acb3 against 2bc → cab3 against 2ca → abc3 against 2triples the restricted rule breaksab → bca costs 3, but by way of ba it costs 2ac → cba costs 3, but by way of ca it costs 2ba → acb costs 3, but by way of ab it costs 240 strings, 1,600 pairs, 64,000 triplesunrestricted: 0 triples broken When the algorithm is a table

The edit that reaches back two rows

stay 0.9, 400 pairsacgtacgt0525505225045240stay 0.5, 400 pairsacgtacgt0212202112022120cost of aligning the row letter with the column letterpseudocount 1 When the algorithm is a table

The matrix a corpus wrote

123456123456cost to open a gapcost to extend a gapintentionexecution571 settingsinte---ntion---execution3 settingsinte-ntion-execution1 setting-intentionexec-ution1 settingintention against execution, affine costseach colour is one optimal alignment When the algorithm is a table

The parameter plane has few answers

rounded to whole bitsunroundeda resample, 400 near pairs0.860.9340 pairs at stay 0.90.820.928 pairs at stay 0.90.710.88400 pairs at stay 0.70.680.86400 pairs at stay 0.50.620.790.5: no prediction200 test pairs, 16 directionsdashed: a coin flip When the algorithm is a table

The ties a rounded matrix makes

alignments on a tiedistinct costs · predictionwhole bits633 of 6 · 0.86half bits793 of 6 · 0.91quarter bits414 of 6 · 0.93a grain of 0.2235 of 6 · 0.89eighth bits156 of 6 · 0.93a grain of 0.05205 of 6 · 0.95unrounded156 of 6 · 0.93200 test pairs, 16 directionsbar: alignments within 0.01 of a tie When the algorithm is a table

The lattice that decides the ties

unit cost — triples broken0.02%unit cost — pivot bound failed0.02%log-odds on a keyboard walk — triples broken6.61%log-odds on a keyboard walk — pivot bound failed13.22%42,840 triples per model, enumerated0.02% shown where the true rate is zero What is taught wrongly

A distance that is not a distance

The library, page 1 of 5 — where cost-model sits