Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* Suggestions (SPECS §27.5, §27.6): the edits the map favours over the
* reference as the reader has made it, each a trade of junctions, ranked by the
* chance a curator would accept it.
*
* **Candidates** are points of the edited axis worth weighing: every sequence's
* two ends, every junction an edit made, every breakpoint the map refuses, and
* both points of every corner the detector found (`corners.ts`), carried from
* the file's order to wherever the edit put them. Each point has an end either
* side of it, and a walk from an end stops at the next point — past it, after
* the edit being weighed, the sequence may be somewhere else.
*
* **Every edit trades junctions** (§27.5): it takes some away and makes
* others, and its gain is the scores of what it makes less the scores of what
* it takes. A split takes one; a turn of `[x, y)` takes two and makes the two a
* bow-tie's arms are; a move takes three and makes three; a join makes one. A
* suggestion is the best trade its points admit, the best first, no point in
* two of them.
*
* **The confidence** is a logistic model over a few features of it, the map's
* gain first, with the initial weights below and the reason for each; review
* mode moves the weights with every answer ({@link learn}).
*/
import type { EditStep } from '../genome/edit'
import type { PictureContacts } from '../metacooler/picture'
import type { FileCorner } from './corners'
import type { SequenceEvidence } from './sequenceEvidence'
import { JOIN_GAP } from './gestures'
import type { GridSequence, LensGrid } from './grid'
import {
EditedMap,
LEAST_REFUSAL,
breakpointsOf,
fociOf,
junctionScore,
junctionsAlong,
meetingScore,
type Apart,
type End,
type Expected,
type Focus,
type Junction,
type Meeting,
} from './method'
import { stepText } from './words'
export type SuggestionKind = 'split' | 'turn' | 'move' | 'join'
/** Two ends a suggestion would bring together, as the stage draws them: a corner, in units of the edited axis. */
export interface SuggestedCorner {
row: number
col: number
/** Which side of each point its end lies: `-1` before it, `1` after it. */
rowSide: 1 | -1
colSide: 1 | -1
/** The junction score the two would make, in units. */
score: number
}
export interface Suggestion {
/**
* Stable across edits: its kind and the ends it moves, by the picture's own
* cells and the way each reads there — so a suggestion turned down stays
* turned down after another edit, which moves where it is drawn.
*/
key: string
kind: SuggestionKind
/** The step accepting it makes. */
step: EditStep
/** It, in words: what the history will say. */
words: string
/** What it makes less what it takes, in units of one clean junction (§27.5). */
gain: number
/** The chance a curator would accept it. */
confidence: number
/**
* What the confidence was computed from: the gain, the size, how much of its
* windows held anything, how much brighter than an adjacency its corners are,
* how far a join's ends prefer each other to anything else, and whether it
* would make a sequence of two foci.
*/
features: number[]
/** The points whose junctions it takes away: edges of the edited axis. */
breaks: number[]
/** The ends it brings together. */
corners: SuggestedCorner[]
/** The stretch of the axis it concerns, lowest first, for the rail. */
extent: [number, number]
/** The stretch it turns or moves, in units; `null` for a split or a join. */
stretch: [number, number] | null
/** Where a move puts it, in units. */
target: number | null
/** What it rests on, as chips. */
evidence: string[]
}
/** The confidence model: an intercept, then one weight per feature. */
export type Weights = readonly number[]
/**
* The initial weights (§27.5), each with its reason:
*
* - **−1.5**, the intercept: a suggestion with nothing behind it is not one a
* curator would take — about one in five.
* - **2** on `log₂(1 + gain)`: the map's evidence, counted in adjacencies (one
* made is one; a turned stretch put back about four), on a log so the first
* adjacency's worth counts more than the fifth.
* - **1.5** on `log₁₀(cells / 4)` below four cells: a stretch of a cell or two
* can be a corner one noisy cell made.
* - **2** on the share of its windows that held anything, less one: a window the
* balancer emptied is weaker evidence either way.
* - **2.5** on how far past two and a half times the contact law the corner of
* a junction it makes stands, in doublings: contacts brighter than two truly
* adjacent stretches share are more often a repeat the reads could not place —
* the elements every telomere carries — than an adjacency, and a corner ten
* times the law is offered below even odds whatever it would gain. Not of a
* join whose two ends prefer each other by a doubling or more, and less the
* nearer it is to that: what a repeat lights, it lights between every end
* that carries it, and an end that meets one other so much more than any is
* bright with depth — a metagenome's contigs break at the rRNA operons and
* insertion elements their genome has several of, and their ends are the
* brightest thing in the map.
* - **1.5** on how much more a join's two ends meet each other than either meets
* anything else, in doublings, between −2 and 2: an end has one neighbour, and
* two ends that each have a better offer elsewhere — a cluster of short
* contigs that all lie near each other, telomeres that all touch — are not
* each other's.
* - **5** on a join that would put two clustering foci far apart in one
* sequence — two centromeres, in a genome whose centromeres cluster: no
* chromosome has two, and a join of two chromosomes' ends that the telomeres'
* clustering lit is exactly that, however much the two ends prefer each other.
* - **4** on a trade that would bury a telomere — make a junction of an end
* the sequence says carries telomeric repeats: that end is a chromosome's,
* and nothing follows it.
* - **1** on a break the sequence places — at a gap of `N` the assembler left,
* where it stopped being sure: the map and the assembly agree on it.
* - **2** on `log₂` of the contacts what it makes rests on, over
* {@link LEAST_CONTACTS}, where they are fewer: a unit is what one adjacency
* is worth in this map at these cells, and in a shallow one — a metagenome's
* genome at a kilobase — a window that holds two contacts where strangers
* share none is a strong likelihood and two reads, and the best of the many
* trades a search weighs rests on two or three of them by chance.
*/
export const INITIAL_WEIGHTS: Weights = [-1.5, 2, 1.5, 2, 2.5, 1.5, 5, 4, 1, 2]
/**
* The contacts a trade needs behind it before its gain counts in full: past
* the trans level in the junctions it makes, or — for a split, which makes
* none — what the law would have put in the one it takes away.
*/
const LEAST_CONTACTS = 16
/** Doublings of the contact law a junction's corner may stand at before it counts against it. */
const EXCESS_FREE = Math.log2(2.5)
/** Doublings of the contact law a join's whole window may stand at before it counts against it. */
const BRIGHT_FREE = Math.log2(1.6)
/** The most a join is worth, in adjacencies: it makes one. */
const JOIN_MOST = 1.2
/** The least gain a suggestion is offered at, in units: below it, a change is noise. */
const LEAST_GAIN = 0.1
/**
* Assemblies of more sequences than this are joined only where two of their
* ends touch — a corner pairs them, or their first coarse cells share more
* than strangers do: every pair of free ends of thousands of contigs is
* millions of windows.
*/
const JOIN_ALL_BELOW = 64
function sigmoid(z: number): number {
return 1 / (1 + Math.exp(-z))
}
/** The confidence of a suggestion with these features, under these weights. */
export function confidenceOf(features: readonly number[], weights: Weights = INITIAL_WEIGHTS): number {
let z = weights[0] ?? 0
for (let k = 0; k < features.length; k++) z += (weights[k + 1] ?? 0) * features[k]
return sigmoid(z)
}
/**
* One answer, learned (§27.6): a step of logistic regression towards it —
* accepted is `1`, rejected `0` — pulled back towards the initial weights by a
* prior strong enough that three answers cannot overturn the map and weak
* enough that thirty can teach it what this file's evidence means.
*/
export function learn(weights: Weights, features: readonly number[], accepted: boolean): number[] {
const rate = 0.1
const prior = 0.15
const predicted = confidenceOf(features, weights)
const error = (accepted ? 1 : 0) - predicted
const x = [1, ...features]
return weights.map((w, k) => w + rate * (error * (x[k] ?? 0) - prior * (w - (INITIAL_WEIGHTS[k] ?? 0))))
}
/** What the method needs, and the edit it reads the map through. */
export interface SuggestInput {
contacts: PictureContacts
expected: Expected
/** The corners of the file, in its own order (`corners.ts`). */
corners: readonly FileCorner[]
grid: LensGrid
weights?: Weights
/** What the session's sequence says: telomeres at ends, gaps of `N` inside. */
evidence?: SequenceEvidence
}
/** The suggestions, best first, and what they were found from. */
export interface Suggested {
list: Suggestion[]
/** The junction score at every edge of the edited axis (`NaN` where there is none). */
along: Float64Array
/** The edges the map refuses. */
breakpoints: number[]
/** The unit the gains are counted in. */
unit: number
}
/** A point of one edited sequence worth weighing. */
interface Point {
sequence: number
x: number
/** Inside its sequence, where the reference makes a junction; not one of its two ends. */
inside: boolean
/** The map refuses the junction the reference makes here. */
refused: boolean
/**
* Open to a trade: refused, or a junction an edit made that the map cannot
* measure. A junction of the file's own with no evidence either way — a
* masked centromere, an rDNA array — is the file's, and is trusted; one the
* reader made there has nothing behind it but the hand.
*/
open: boolean
/** Named by a corner the detector found. */
cornered: boolean
}
/** A trade under consideration. */
interface Trade {
kind: SuggestionKind
gain: number
/** Its points: the ones whose junctions it takes away, then, for a move, where it puts the stretch. */
points: Point[]
/** The junctions it makes. */
made: Array<[End, End]>
/** The junctions it takes away, as they are scored. */
taken: Array<[End, End]>
step: EditStep
stretch: [number, number] | null
target: number | null
cells: number
seen: number
/** How far past the contact law the brightest corner it makes stands, in doublings. */
excess: number
/** A join's: how much more its ends meet each other than anything else, in doublings. */
exclusivity?: number
/** A join's: it would make a sequence of two foci far apart. */
dicentric?: boolean
/** A join's: the gap its meeting fitted, in cells. */
gapCells?: number
/** It would make a junction of a telomere: a chromosome's end inside a sequence. */
buried?: boolean
/** A break it makes that a gap of `N` places. */
atGap?: boolean
/** The contacts past the trans level its new junctions rest on ({@link Junction.contacts}). */
contacts: number
}
/** The foci of a file, found once: they are in its own cells, which no edit moves. */
const fociCache = new WeakMap<PictureContacts, Focus[]>()
/** The suggestions for the reference as it now stands, best first. */
export function suggest(input: SuggestInput): Suggested {
const { grid, expected } = input
const map = new EditedMap(input.contacts, expected, grid.cellMap)
const unit = map.unit
const sequences = grid.sequences
const stretches = sequences.map((sequence) => ({ from: sequence.from, to: sequence.to }))
const along = junctionsAlong(map, stretches)
const breakpoints = breakpointsOf(along.score, stretches, unit, map.window)
// Which way each cell of the axis reads the file, and where each cell of the
// file is on the axis: the corners are in the file's order.
const n = grid.n
const strand = new Int8Array(n)
for (const part of grid.parts) {
if (part.piece !== null) strand.fill(part.piece.strand, part.from, part.to)
}
const pictureCells = input.contacts.n
const landingStart = new Int32Array(pictureCells + 1)
for (let e = 0; e < n; e++) {
const a = grid.cellMap[e]
if (a >= 0) landingStart[a + 1]++
}
for (let a = 0; a < pictureCells; a++) landingStart[a + 1] += landingStart[a]
const landings = new Int32Array(landingStart[pictureCells])
const fill = landingStart.slice(0, pictureCells)
for (let e = 0; e < n; e++) {
const a = grid.cellMap[e]
if (a >= 0) landings[fill[a]++] = e
}
const sequenceAt = (cell: number): number => {
let lo = 0
let hi = sequences.length - 1
while (lo <= hi) {
const mid = (lo + hi) >> 1
if (cell < sequences[mid].from) hi = mid - 1
else if (cell >= sequences[mid].to) lo = mid + 1
else return mid
}
return -1
}
// The points: every sequence's two ends, every junction an edit made, every
// breakpoint, and both ends of every corner, wherever the edit put them — each
// one place, so a point within a quarter of a window of one already chosen is
// that one: an edit's junction is exact, and the breakpoint the map finds a
// cell from it is the same break, as is a corner's end placed beside it.
const merge = Math.max(2, Math.round(map.window / 4))
const chosen: Array<Set<number>> = sequences.map((sequence) => new Set([sequence.from, sequence.to]))
const cornered: Array<Set<number>> = sequences.map(() => new Set<number>())
/** The point `x` is, in sequence `s`: one already chosen within reach, else `x` itself, added. */
const choose = (s: number, x: number): number => {
let best = -1
let distance = merge + 1
for (const held of chosen[s]) {
const d = Math.abs(held - x)
if (d < distance) {
best = held
distance = d
}
}
if (best >= 0) return best
chosen[s].add(x)
return x
}
for (const x of [...grid.junctions(), ...breakpoints]) {
const s = sequenceAt(x)
if (s >= 0 && x > sequences[s].from) choose(s, x)
}
/** A corner's end, at every point the edit put the cell it is anchored at: their keys. */
const endPoint = (anchor: number, side: 1 | -1): string[] => {
if (anchor < 0 || anchor >= pictureCells) return []
const keys: string[] = []
for (let k = landingStart[anchor]; k < landingStart[anchor + 1]; k++) {
const e = landings[k]
const dir = side * strand[e]
const s = sequenceAt(e)
if (s < 0) continue
const x = choose(s, dir < 0 ? e + 1 : e)
cornered[s].add(x)
keys.push(`${s}:${x}`)
}
return keys
}
// The two ends of each corner are partners: where a whole sequence may go
// in, and which free ends an assembly of many sequences may join.
const partners = new Map<string, Set<string>>()
const link = (a: string, b: string): void => {
let held = partners.get(a)
if (held === undefined) {
held = new Set()
partners.set(a, held)
}
held.add(b)
}
for (const corner of input.corners) {
const rows = endPoint(corner.rowSide < 0 ? corner.row - 1 : corner.row, corner.rowSide)
const cols = endPoint(corner.colSide < 0 ? corner.col - 1 : corner.col, corner.colSide)
for (const a of rows) {
for (const b of cols) {
link(a, b)
link(b, a)
}
}
}
const partnered = (a: Point, b: Point): boolean => partners.get(`${a.sequence}:${a.x}`)?.has(`${b.sequence}:${b.x}`) === true
const made = new Set(grid.junctions())
const points: Point[][] = sequences.map((sequence, s) =>
[...chosen[s]]
.filter((x) => x >= sequence.from && x <= sequence.to)
.sort((a, b) => a - b)
.map((x) => {
const inside = x > sequence.from && x < sequence.to
const refused = inside && along.score[x] < -LEAST_REFUSAL
const open = refused || (inside && made.has(x) && !(along.score[x] >= 0))
return { sequence: s, x, inside, refused, open, cornered: cornered[s].has(x) }
}),
)
// An end of a point, walking away from it until the trade's next point or
// the sequence's end — past either, after the trade, the sequence may be
// somewhere else.
const endOf = (point: Point, side: 1 | -1, walls: readonly Point[]): End | null => {
const sequence = sequences[point.sequence]
if (side < 0 ? point.x <= sequence.from : point.x >= sequence.to) return null
let lo = sequence.from
let hi = sequence.to
for (const wall of walls) {
if (wall.sequence !== point.sequence) continue
if (wall.x < point.x && wall.x > lo) lo = wall.x
if (wall.x > point.x && wall.x < hi) hi = wall.x
}
return side < 0 ? { cell: point.x - 1, dir: -1, lo, hi: point.x } : { cell: point.x, dir: 1, lo: point.x, hi }
}
// Junction scores, each computed once.
const memo = new Map<string, Junction>()
const keyOf = (e: End): string => `${e.cell}:${e.dir}:${e.lo}:${e.hi}`
const junction = (e: End, f: End, apart: Apart): Junction => {
const a = keyOf(e)
const b = keyOf(f)
const key = a < b ? `${a}|${b}|${apart}` : `${b}|${a}|${apart}`
let held = memo.get(key)
if (held === undefined) {
held = junctionScore(map, e, f, apart)
memo.set(key, held)
}
return held
}
/**
* A junction's score against its window's own level, in units: what a trade
* makes and what it takes away are weighed alike, so a trade is two
* configurations compared. Only the question *is this junction refused at
* all* is asked against the trans level ({@link junctionsAlong}).
*/
const meets = (e: End | null, f: End | null): number => (e === null || f === null ? 0 : junction(e, f, 'local').score / unit)
const holds = meets
/** Whether two separate ends meet, with the gap and strength they meet at ({@link meetingScore}). */
const meetings = new Map<string, Meeting>()
const meet = (e: End, f: End): Meeting => {
const a = keyOf(e)
const b = keyOf(f)
const key = a < b ? `${a}|${b}` : `${b}|${a}`
let held = meetings.get(key)
if (held === undefined) {
held = meetingScore(map, e, f)
meetings.set(key, held)
}
return held
}
// The file's clustering foci, where the edit put them: per edited sequence,
// the cells each focus landed on.
let fileFoci = fociCache.get(input.contacts)
if (fileFoci === undefined) {
fileFoci = fociOf(input.contacts, expected)
fociCache.set(input.contacts, fileFoci)
}
const foci: Array<Array<[number, number]>> = sequences.map(() => [])
for (const focus of fileFoci) {
// Its cells may land in two sequences only where an edit copied it, and
// then it is in both.
const bySequence = new Map<number, number[]>()
for (let a = focus.from; a < focus.to; a++) {
for (let k = landingStart[a]; k < landingStart[a + 1]; k++) {
const e = landings[k]
const s = sequenceAt(e)
if (s < 0) continue
const list = bySequence.get(s) ?? []
list.push(e)
bySequence.set(s, list)
}
}
for (const [s, cells] of bySequence) foci[s].push([Math.min(...cells), Math.max(...cells) + 1])
}
/** Cells two foci may lie apart and still be one: the reach of a focus. */
const focusMerge = 4 * input.contacts.coarse.factor
/**
* Whether joining end `e` of sequence `a` to end `f` of `b` puts two foci
* farther apart than one focus spans: the distance of each from its end,
* and the gap between.
*/
const dicentric = (e: End, a: number, f: End, b: number, gapCells: number): boolean => {
if (a === b) return false
for (const [x0, x1] of foci[a]) {
const fromE = e.dir < 0 ? e.cell + 1 - x1 : x0 - e.cell
for (const [y0, y1] of foci[b]) {
const fromF = f.dir < 0 ? f.cell + 1 - y1 : y0 - f.cell
if (Math.max(0, fromE) + Math.max(0, fromF) + gapCells > focusMerge) return true
}
}
return false
}
/** How far past the contact law the corner of a junction stands, in doublings. */
const excessOf = (e: End, f: End): number => {
let most = 0
for (let i = 0; i < 2; i++) {
for (let j = 0; j < 2; j++) {
const r = e.cell + e.dir * i
const c = f.cell + f.dir * j
if (r < e.lo || r >= e.hi || c < f.lo || c >= f.hi) continue
const v = map.value(r, c)
if (v > 0) most = Math.max(most, v / map.expectedAt(i + j + 1))
}
}
return most > 0 ? Math.log2(most) : 0
}
const trades: Trade[] = []
const facts = input.evidence?.facts
/**
* The telomere an end would put against the junction it makes, where the
* sequence says there is one: the base the stretch begins with at the
* junction is its original sequence's first or last, and that end carries
* repeats. Any trade that makes a junction of one buries it — a join, a turn
* of a sequence's last stretch, a chromosome moved into another.
*/
const telomereFacing = (e: End): string | null => {
if (facts === undefined) return null
const part = grid.partAt(e.cell)
const piece = part?.piece
if (part == null || piece == null) return null
// Read rightwards, the stretch meets the junction with its left edge.
const left = e.dir === 1
if (left ? e.cell !== part.from : e.cell !== part.to - 1) return null
const known = facts.get(piece.sequence)
if (known === undefined) return null
return left === (piece.strand === 1) ? (piece.start === 0 ? known.start : null) : piece.end === known.length ? known.end : null
}
const buries = (made: ReadonlyArray<[End, End]>): boolean => made.some(([e, f]) => telomereFacing(e) !== null || telomereFacing(f) !== null)
/** Where a break at edge `x` goes: the middle of a gap of `N` within a cell of it, where there is one. */
const gapNear = (sequence: GridSequence, x: number): number | null => {
if (facts === undefined || x <= sequence.from || x >= sequence.to) return null
const locus = grid.place(x)
const piece = locus?.part.piece
if (locus == null || piece == null || locus.sequence !== sequence.name) return null
const known = facts.get(piece.sequence)
if (known === undefined || known.gaps.length === 0) return null
const k = locus.bp - locus.part.offset
const at = piece.strand === 1 ? piece.start + k : piece.end - k
const reach = grid.binsize
for (const [lo, hi] of known.gaps) {
if (hi + reach < at || lo - reach > at) continue
const middle = Math.max(piece.start, Math.min(piece.end, Math.round((lo + hi) / 2)))
return locus.part.offset + (piece.strand === 1 ? middle - piece.start : piece.end - middle)
}
return null
}
const place = (sequence: GridSequence, x: number): number => gapNear(sequence, x) ?? edgeBp(grid, sequence, x)
/** Whether a trade's breaks are placed by gaps of `N`. */
const placedByGap = (points: readonly Point[]): boolean => points.some((point) => point.inside && gapNear(sequences[point.sequence], point.x) !== null)
const push = (trade: Omit<Trade, 'seen' | 'excess' | 'atGap' | 'buried' | 'contacts'>): void => {
// A join across a long gap — an rDNA array, a megabase no read spanned —
// is a small share of an adjacency and still the only thing its two ends
// meet: it is offered on the weight of its evidence and how alone it is.
const enough = trade.kind === 'join' ? (trade.exclusivity ?? 0) >= 1 || trade.gain > LEAST_GAIN : trade.gain > LEAST_GAIN
if (!enough || !(trade.gain > 0)) return
let seen = 0
let reached = 0
let contacts = 0
for (const [e, f] of trade.made) {
// A join is weighed by its meeting, whose walks step past what the
// balancer emptied: its window is as full as it could be.
const j = trade.kind === 'join' ? meet(e, f) : junction(e, f, 'local')
seen += j.seen
reached += j.reached
contacts += j.contacts
}
let missing = 0
for (const [e, f] of trade.taken) {
const j = junction(e, f, 'local')
seen += j.seen
reached += j.reached
missing += junction(e, f, 'trans').expected
}
// A split makes nothing: what it rests on is the contacts the law would
// have put where the map holds none.
if (trade.made.length === 0) contacts = missing
// A join's brightness is its whole window's, and a window of a meeting
// reaches far enough that more than {@link BRIGHT_FREE} of the law is
// already more than an adjacency holds; a trade's is its corners'.
const excess = trade.made.reduce(
(most, [e, f]) =>
Math.max(
most,
trade.kind === 'join' ? Math.log2(Math.max(1e-9, meet(e, f).brightness)) - BRIGHT_FREE + EXCESS_FREE : excessOf(e, f),
),
0,
)
const breaks = trade.kind === 'move' ? trade.points.slice(0, 2) : trade.kind === 'join' ? [] : trade.points
trades.push({ ...trade, seen: reached === 0 ? 0 : seen / reached, excess, atGap: placedByGap(breaks), buried: buries(trade.made), contacts })
}
/** The junction a point makes, with a trade's walls, where it makes one. */
const takenAt = (point: Point, walls: readonly Point[]): [End, End] | null => {
if (!point.inside) return null
const left = endOf(point, -1, walls)
const right = endOf(point, 1, walls)
return left === null || right === null ? null : [left, right]
}
// Splits: a junction the map refuses, taken away.
for (const list of points) {
for (const point of list) {
if (!point.refused) continue
const sequence = sequences[point.sequence]
const taken = takenAt(point, [])
if (taken === null) continue
push({
kind: 'split',
gain: -holds(...taken),
points: [point],
made: [],
taken: [taken],
step: { op: 'split', sequence: sequence.name, at: place(sequence, point.x) },
stretch: null,
target: null,
cells: Number.POSITIVE_INFINITY,
})
}
}
const everywhere = points.flat()
const fewSequences = sequences.length <= JOIN_ALL_BELOW
for (const list of points) {
if (list.length === 0) continue
const sequence = sequences[list[0].sequence]
for (let i = 0; i < list.length; i++) {
for (let j = i + 1; j < list.length; j++) {
const p = list[i]
const q = list[j]
const cells = q.x - p.x
const whole = !p.inside && !q.inside
const walls = [p, q]
const takenP = takenAt(p, walls)
const takenQ = takenAt(q, walls)
const taken = [takenP, takenQ].filter((pair): pair is [End, End] => pair !== null)
const cost = taken.reduce((sum, [e, f]) => sum + holds(e, f), 0)
// A turn of a stretch one of whose junctions the map refuses — or
// between two points corners name, which is how a stretch shorter than
// a window is found: across its ends the walk reaches its far end,
// which truly belongs there, and neither junction is refused. The left
// flank meets the stretch's far end, the stretch's near end the right
// flank: a bow-tie's two arms.
if (!whole && (p.open || q.open || (p.cornered && q.cornered))) {
const made: Array<[End, End]> = []
const pl = endOf(p, -1, walls)
const ql = endOf(q, -1, walls)
const pr = endOf(p, 1, walls)
const qr = endOf(q, 1, walls)
if (pl !== null && ql !== null) made.push([pl, ql])
if (pr !== null && qr !== null) made.push([pr, qr])
push({
kind: 'turn',
gain: made.reduce((sum, [e, f]) => sum + meets(e, f), 0) - cost,
points: [p, q],
made,
taken,
step: { op: 'invert', sequence: sequence.name, from: place(sequence, p.x), to: place(sequence, q.x) },
stretch: [p.x, q.x],
target: null,
cells,
})
}
// A move: of a stretch between two refused junctions (or a refused one
// and the sequence's end), or of a whole sequence a corner names, to
// any point, either way round — the flanks closing up behind it.
const movable = ((p.open || q.open) && (p.open || !p.inside) && (q.open || !q.inside)) || (whole && (p.cornered || q.cornered))
if (!movable) continue
let best: { gain: number; z: Point; strand: 1 | -1; made: Array<[End, End]>; taken: Array<[End, End]> } | null = null
for (const z of everywhere) {
if (z.sequence === p.sequence && z.x >= p.x && z.x <= q.x) continue
// A whole sequence goes into another's interior — end to end is a
// join — and only where a corner says one of its ends meets it.
if (whole && (!z.inside || !(partnered(p, z) || partnered(q, z)))) continue
const zWalls = z.sequence === p.sequence ? [p, q, z] : [z]
const moveWalls = z.sequence === p.sequence ? [p, q, z] : walls
const pl = endOf(p, -1, moveWalls)
const qr = endOf(q, 1, moveWalls)
const pr = endOf(p, 1, moveWalls)
const ql = endOf(q, -1, moveWalls)
const zl = endOf(z, -1, zWalls)
const zr = endOf(z, 1, zWalls)
const takenZ = takenAt(z, zWalls)
const opened = takenZ === null ? 0 : holds(...takenZ)
const flanks: Array<[End, End]> = pl !== null && qr !== null && p.inside && q.inside ? [[pl, qr]] : []
const closing = flanks.reduce((sum, [e, f]) => sum + meets(e, f), 0)
for (const way of [1, -1] as const) {
const made: Array<[End, End]> = [...flanks]
if (way === 1) {
if (zl !== null && pr !== null) made.push([zl, pr])
if (ql !== null && zr !== null) made.push([ql, zr])
} else {
if (zl !== null && ql !== null) made.push([zl, ql])
if (pr !== null && zr !== null) made.push([pr, zr])
}
if (made.length === flanks.length) continue
let gain = closing - cost - opened
for (const [e, f] of made.slice(flanks.length)) gain += meets(e, f)
if (best === null || gain > best.gain) {
best = { gain, z, strand: way, made, taken: takenZ === null ? taken : [...taken, takenZ] }
}
}
}
if (best !== null) {
const target = sequences[best.z.sequence]
const from = place(sequence, p.x)
const to = place(sequence, q.x)
const at = place(target, best.z.x)
push({
kind: 'move',
gain: best.gain,
points: [p, q, best.z],
made: best.made,
taken: best.taken,
step: {
op: 'move',
sequence: sequence.name,
from,
to,
into: target.name,
at: best.z.sequence === p.sequence && best.z.x > q.x ? at - (to - from) : at,
strand: best.strand,
},
stretch: [p.x, q.x],
target: best.z.x,
cells,
})
}
}
}
}
// Past a few dozen sequences, the ends worth a meeting are those that touch:
// a corner pairs them, or their first coarse cells share more than twice
// what strangers do — found from each end's coarse cells against the coarse
// cells every other end is in, so an assembly of hundreds of contigs costs
// what its ends touch and not every pair of them.
const endIndex = new Map<string, number>()
const endSequence: number[] = []
const touching = new Set<number>()
const endId = (point: Point, dir: 1 | -1): string => `${point.sequence}:${point.x}:${dir}`
if (!fewSequences) {
const coarseOfEnd: number[][] = []
const byCoarse = new Map<number, number[]>()
for (const list of points) {
const first = list[0]
const last = list[list.length - 1]
if (first === undefined || last === undefined) continue
for (const [point, dir] of [
[first, 1],
[last, -1],
] as const) {
const end = endOf(point, dir, [])
if (end === null) continue
const coarse = new Set<number>()
for (let k = 0; k < map.reach; k++) {
const cell = end.cell + end.dir * k
if (cell < end.lo || cell >= end.hi) break
const c = map.coarseCell(cell)
if (c >= 0) coarse.add(c)
}
const at = endSequence.length
endIndex.set(endId(point, dir), at)
endSequence.push(point.sequence)
coarseOfEnd.push([...coarse])
for (const c of coarse) {
const held = byCoarse.get(c)
if (held === undefined) byCoarse.set(c, [at])
else held.push(at)
}
}
}
const count = endSequence.length
const strangers = 2 * map.trans
const coarseCells = [...byCoarse.keys()]
for (let i = 0; i < count; i++) {
for (const x of coarseOfEnd[i]) {
for (const y of coarseCells) {
if (!(map.coarseValue(x, y) > strangers)) continue
for (const j of byCoarse.get(y) ?? []) if (endSequence[j] !== endSequence[i]) touching.add(i * count + j)
}
}
}
}
const touches = (pa: Point, e: End, pb: Point, f: End): boolean => {
if (partnered(pa, pb)) return true
const i = endIndex.get(endId(pa, e.dir))
const j = endIndex.get(endId(pb, f.dir))
return i !== undefined && j !== undefined && touching.has(i * endSequence.length + j)
}
// The pairs of sequences a join is weighed between: every pair of a few
// dozen, and past that those two of whose ends touch or a corner pairs.
const pairs: Array<[number, number]> = []
if (fewSequences) {
for (let a = 0; a < sequences.length; a++) for (let b = a + 1; b < sequences.length; b++) pairs.push([a, b])
} else {
const listed = new Set<number>()
const add = (x: number, y: number): void => {
if (x === y || x < 0 || y < 0) return
const a = Math.min(x, y)
const b = Math.max(x, y)
const key = a * sequences.length + b
if (listed.has(key)) return
listed.add(key)
pairs.push([a, b])
}
const count = endSequence.length
for (const key of touching) add(endSequence[Math.floor(key / count)], endSequence[key % count])
for (const [key, others] of partners) {
const x = Number(key.slice(0, key.indexOf(':')))
for (const other of others) add(x, Number(other.slice(0, other.indexOf(':'))))
}
}
// Joins: two sequences' free ends that meet.
const joins: Array<{ e: End; f: End; pa: Point; pb: Point; a: number; b: number; step: EditStep; meeting: Meeting; gain: number }> = []
for (const [a, b] of pairs) {
const A = points[a]
const B = points[b]
const aStart = A[0]
const aEnd = A[A.length - 1]
const bStart = B[0]
const bEnd = B[B.length - 1]
if (aStart === undefined || aEnd === undefined || bStart === undefined || bEnd === undefined) continue
const nameA = sequences[a].name
const nameB = sequences[b].name
const options: Array<{ e: End | null; f: End | null; pa: Point; pb: Point; step: EditStep }> = [
{ e: endOf(aEnd, -1, []), f: endOf(bStart, 1, []), pa: aEnd, pb: bStart, step: { op: 'join', a: nameA, aEnd: 'end', b: nameB, bEnd: 'start', gap: JOIN_GAP } },
{ e: endOf(aEnd, -1, []), f: endOf(bEnd, -1, []), pa: aEnd, pb: bEnd, step: { op: 'join', a: nameA, aEnd: 'end', b: nameB, bEnd: 'end', gap: JOIN_GAP } },
{ e: endOf(aStart, 1, []), f: endOf(bStart, 1, []), pa: aStart, pb: bStart, step: { op: 'join', a: nameA, aEnd: 'start', b: nameB, bEnd: 'start', gap: JOIN_GAP } },
{ e: endOf(aStart, 1, []), f: endOf(bEnd, -1, []), pa: aStart, pb: bEnd, step: { op: 'join', a: nameB, aEnd: 'end', b: nameA, bEnd: 'start', gap: JOIN_GAP } },
]
for (const option of options) {
if (option.e === null || option.f === null) continue
// Past a few dozen sequences, only ends that touch.
if (!fewSequences && !touches(option.pa, option.e, option.pb, option.f)) continue
const meeting = meet(option.e, option.f)
// How much of a clean adjacency of these two ends the meeting is: the
// gain, counted in adjacencies as every trade's is — and a join makes
// one, so a window brighter than the law is worth no more than that:
// what is brighter is its brightness, weighed on its own.
const gain = meeting.ideal > 0 ? Math.min(JOIN_MOST, meeting.score / meeting.ideal) : 0
joins.push({ ...option, e: option.e, f: option.f, a, b, meeting, gain })
}
}
// Each end's best offer and second best, by the weight of the evidence —
// the meeting's score itself, not its share of an ideal, since a short end
// can be all of one on a few cells — so that a join is weighed against what
// else its two ends could do: an end has one neighbour.
const offers = new Map<string, number[]>()
const endKey = (point: Point, end: End): string => `${point.sequence}:${point.x}:${end.dir}`
const evidenceOf = (meeting: Meeting): number => Math.max(0, meeting.score) / map.meetUnit
// A join no curator takes — one burying a telomere, one making two
// centromeres — is no rival to one they might: an end's offers are the joins
// it could make.
const possible = new Set(
joins.filter((join) => !buries([[join.e, join.f]]) && !dicentric(join.e, join.a, join.f, join.b, join.meeting.gap)),
)
for (const join of joins) {
if (!possible.has(join)) continue
for (const key of [endKey(join.pa, join.e), endKey(join.pb, join.f)]) {
const list = offers.get(key) ?? []
list.push(evidenceOf(join.meeting))
offers.set(key, list)
}
}
for (const list of offers.values()) list.sort((x, y) => y - x)
/** The best an end is offered by anything but this join. */
const elsewhere = (key: string, own: number): number => {
const list = offers.get(key) ?? []
// The join's own offer is in the list once; the best of the rest is the
// first that is not it, or the second where the first is.
return list[0] === own ? (list[1] ?? 0) : (list[0] ?? 0)
}
/**
* Evidence below which two offers are both nothing, and neither is preferred:
* a hundredth of an adjacency's. Clustering telomeres meet at about that,
* and an end whose best is that and whose next is less has no better offer
* than nothing.
*/
const floor = 0.01
for (const join of joins) {
const own = evidenceOf(join.meeting)
const rival = Math.max(elsewhere(endKey(join.pa, join.e), own), elsewhere(endKey(join.pb, join.f), own))
const exclusivity = Math.max(-2, Math.min(2, Math.log2(Math.max(own, floor) / Math.max(rival, floor))))
// Two ends that meet across more than a window meet across a gap the map
// measured, and the join writes it: joined with the stage's own hundred
// `N`, the next count would weigh the junction as a direct adjacency and
// offer to split it again. A shorter gap is the unknown one a join makes.
const measured = join.meeting.gap > map.window ? join.meeting.gap * grid.binsize : 0
const step: EditStep = measured > 0 && join.step.op === 'join' ? { ...join.step, gap: measured } : join.step
push({
kind: 'join',
gain: join.gain,
points: [join.pa, join.pb],
made: [[join.e, join.f]],
taken: [],
step,
stretch: null,
target: null,
cells: Number.POSITIVE_INFINITY,
exclusivity,
dicentric: dicentric(join.e, join.a, join.f, join.b, join.meeting.gap),
gapCells: join.meeting.gap,
})
}
// Ranked, and the best of those that share no point. Weights learned under
// another set of features are the initial ones again.
const weights = input.weights !== undefined && input.weights.length === INITIAL_WEIGHTS.length ? input.weights : INITIAL_WEIGHTS
const ranked = trades.map((trade) => {
const features = [
// No more adjacencies' worth than its contacts could hold: the unit is
// what one is worth in this map, and in a shallow one a handful of reads
// is a great many units.
Math.log2(1 + Math.min(Math.max(0, trade.gain), trade.contacts / LEAST_CONTACTS)),
Number.isFinite(trade.cells) ? Math.min(0, Math.log10(trade.cells / 4)) : 0,
trade.seen - 1,
-Math.max(0, trade.excess - EXCESS_FREE) * (trade.kind === 'join' ? 1 - Math.max(0, Math.min(1, trade.exclusivity ?? 0)) : 1),
trade.exclusivity ?? 0,
trade.dicentric === true ? -1 : 0,
trade.buried === true ? -1 : 0,
trade.atGap === true ? 1 : 0,
Math.min(0, Math.log2(Math.max(1e-3, trade.contacts) / LEAST_CONTACTS)),
]
return { trade, features, confidence: confidenceOf(features, weights) }
})
ranked.sort((x, y) => y.confidence - x.confidence || y.trade.gain - x.trade.gain)
// No point in two, and none within reach of another's: two suggestions a
// cell apart are one suggestion twice.
const used: Point[] = []
const taken = (point: Point): boolean => used.some((held) => held.sequence === point.sequence && Math.abs(held.x - point.x) <= merge)
const list: Suggestion[] = []
for (const { trade, features, confidence } of ranked) {
if (trade.points.some(taken)) continue
used.push(...trade.points)
list.push(
toSuggestion(trade, features, confidence, grid, unit, (e, f) =>
trade.kind === 'join' ? { score: (meet(e, f).score / map.meetUnit) * unit, seen: 0, reached: 0, contacts: 0, expected: 0 } : junction(e, f, 'local'),
),
)
}
return { list, along: along.score, breakpoints, unit }
}
/** An end's point on the axis, and the side of it the end lies. */
function pointOf(end: End): { x: number; side: 1 | -1 } {
return end.dir < 0 ? { x: end.cell + 1, side: -1 } : { x: end.cell, side: 1 }
}
function toSuggestion(
trade: Trade,
features: number[],
confidence: number,
grid: LensGrid,
unit: number,
junction: (e: End, f: End) => Junction,
): Suggestion {
const corners = trade.made.map(([e, f]): SuggestedCorner => {
const a = pointOf(e)
const b = pointOf(f)
const score = junction(e, f).score / unit
return a.x <= b.x
? { row: a.x, col: b.x, rowSide: a.side, colSide: b.side, score }
: { row: b.x, col: a.x, rowSide: b.side, colSide: a.side, score }
})
// Where it takes a junction away — for a move, not where it puts the stretch,
// which the map has not refused and is drawn as the place it goes.
const cut = trade.kind === 'move' ? trade.points.slice(0, 2) : trade.points
const breaks = cut.filter((point) => point.inside && trade.kind !== 'join').map((point) => point.x)
const xs = [...trade.points.map((point) => point.x)]
const extent: [number, number] = [Math.min(...xs), Math.max(...xs)]
// The ends it moves, by the file's own cells and the way each reads there.
const identity = trade.made
.flat()
.map((end) => {
const anchor = grid.cellMap[end.cell] ?? -1
const part = grid.partAt(end.cell)
const reads = (part?.piece?.strand ?? 1) * end.dir
return `${anchor}${reads < 0 ? '<' : '>'}`
})
.concat(trade.points.filter((point) => point.inside && trade.made.length === 0).map((point) => {
const before = grid.cellMap[point.x - 1] ?? -1
const after = grid.cellMap[point.x] ?? -1
return `${before}|${after}`
}))
.sort()
.join(',')
const evidence = ['map']
if (features[2] < -0.25) evidence.push('sparse')
if (features[3] < 0) evidence.push('brighter than an adjacency')
if (trade.kind === 'join' && (trade.gapCells ?? 0) > 0) evidence.push(`a gap of about ${gapWords((trade.gapCells ?? 0) * grid.binsize)}`)
if (features[4] < -0.5) evidence.push('an end with a better offer')
if (trade.dicentric === true) evidence.push('two centromeres')
if (trade.buried === true) evidence.push('a telomere')
if (trade.atGap === true) evidence.push('at a gap of N')
if (features[8] < -0.5) evidence.push('few contacts')
return {
key: `${trade.kind}:${identity}`,
kind: trade.kind,
step: trade.step,
words: stepText(trade.step),
gain: trade.gain,
confidence,
features,
breaks,
corners,
extent,
stretch: trade.stretch,
target: trade.target,
evidence,
}
}
/** A gap's length in words, to a significant figure: `16 kb`, `2 kb`, `500 bp`. */
function gapWords(bp: number): string {
if (bp >= 1_000_000) return `${(bp / 1_000_000).toPrecision(2)} Mb`
if (bp >= 1000) return `${Math.round(bp / 1000)} kb`
return `${Math.round(bp)} bp`
}
/**
* A point of the axis as a base pair of its edited sequence: exact at a
* sequence's two ends and at a junction, and inside a piece the edge of the cell
* there — placed by the map, to one cell (§27.5).
*/
export function edgeBp(grid: LensGrid, sequence: GridSequence, x: number): number {
if (x <= sequence.from) return 0
if (x >= sequence.to) return sequence.length
const place = grid.place(x)
if (place === null || place.sequence !== sequence.name) return 0
return Math.max(0, Math.min(sequence.length, Math.round(place.bp)))
}
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