Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* The method that proposes edits (SPECS §27.5): ends, and the one score that
* decides whether two of them belong together.
*
* A reference is a list of adjacencies — every base is next to the one after
* it — and a contact map tests every one of them, because contacts fall off
* with distance along the molecule: two stretches that truly meet share the
* densest contacts there are, two that do not share the background. So every
* place the reference could be wrong is a pair of **ends** — the sequence just
* left of a point, read leftwards, or just right of one, read rightwards — and
* the **junction score** says whether they meet: the evidence, over the window
* of their first cells, that the contacts there are an adjacency's rather than
* two strangers'. A junction the reference makes and the map refuses is a
* **breakpoint**; two ends it does not join and the map would is a **corner**.
* An edit trades junctions, and `suggest.ts` weighs the trades.
*
* Everything here reads the map **through the edit as it stands** — the cells
* of the picture each cell of the edited axis shows (`grid.ts`) — so the method
* always speaks of the reference as the reader has made it: a stretch already
* turned back is no longer a bow-tie, and the junctions a careless move made are
* refused like any other.
*
* Three kinds of number, each where it is needed: the cells nearest the
* diagonal as they are, where a junction's evidence is; the whole map on a
* coarse grid, where two far ends meet; and, measured from both once per file,
* what the map is expected to hold ({@link expectedOf}). Every one of them came
* from the file (`metacooler/picture.ts`'s gathering), never from the picture's
* bytes.
*/
import { endValue, triangleIndex, type GatherOptions, type PictureContacts, type PictureEnds } from '../metacooler/picture'
/**
* The most cells each end of a junction is read into (§27.5's `W`). A file's
* own window is set by its contact law ({@link Expected.window}): as far as
* contacts along the molecule stand well above the background, and no further,
* since past that a window weighs clustering — telomeres, centromeres — as if it
* were adjacency.
*/
export const WINDOW = 16
/** The fewest cells a window is read into. */
const LEAST_WINDOW = 4
/** Cells past the diagonal the pass keeps as they are: two windows, and room. */
export const BAND_WIDTH = 64
/** The most coarse cells a side the pass keeps of the whole map. */
export const COARSE_CELLS = 2048
/**
* Cells from each end of a sequence whose pairs with every other end the pass
* keeps as they are: three of the longest meeting window, since a window walks
* past the cells the balancer emptied at an end — a subtelomere's repeats, the
* edge of an rDNA array — to find its own.
*/
export const END_DEPTH = 160
/** What the picture's pass gathers for the method (§27.5). */
export const METHOD_GATHER: GatherOptions = { width: BAND_WIDTH, coarseCells: COARSE_CELLS, endDepth: END_DEPTH }
/** The longest window two ends' meeting is weighed over, in valid cells each. */
export const MEETING_REACH = 48
/** The fewest cells a meeting window is read into. */
const LEAST_MEETING = 8
/**
* The gaps a meeting is tried at, in cells: the sequence an assembly never
* closed between two ends — a repeat, an rDNA array, a stretch no read spanned —
* which moves every cell of the window that much further apart along the molecule.
*/
const GAPS = [0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048]
/** The share of each distance's highest values left out of its mean, so what is looked for does not lift what it is judged against. */
const TRIM = 0.01
/** The least coverage a raw map's cell is weighed at, as a share of the median cell's. */
const LEAST_COVERAGE = 0.1
/** What the map is expected to hold, measured from the map itself (§27.5). */
export interface Expected {
/**
* The contact law `P(d)`, `d` in cells from `0` (a cell with itself) to the
* grid's side: a trimmed mean per distance along every sequence, made
* non-increasing, and past the longest measured distance the power law of
* its last decade.
*/
law: Float64Array
/** The trans level: what two stretches of different molecules share, trimmed the same way. */
trans: number
/** Variance over mean near the diagonal: what one unit of the values is worth as evidence. */
dispersion: number
/**
* Each cell's coverage, as a factor its values are divided by: `1` on a
* balanced map, which is flat by construction; the marginal over its median
* on a raw one; `NaN` for a cell with nothing the balancer kept.
*/
bias: Float64Array
/**
* How much of a whole cell each cell pools, `0 … 1`: the bins of it the
* balancer kept over the most any cell keeps. A value is a mean over a
* cell's pairs of bins, and a sequence's last cell, a bin or two of a
* pooled one, holds its mean over a tenth of the pairs — a tenth of the
* evidence, whatever the mean.
*/
share: Float64Array
/**
* Cells each end of a junction is read into: half the distance at which the
* law falls to eight times the trans level, between four and {@link WINDOW} —
* so every cell of a window is one where an adjacency stands well out of the
* background.
*/
window: number
/**
* The score of two ends that truly meet — a window holding exactly the
* contact law, against its own level: the unit every gain is counted in, so
* one adjacency made is worth about one in any file, at any depth, and a clean
* misjoin taken away about two thirds of one.
*/
unit: number
/**
* Cells each end of a **meeting** is read into ({@link meetingScore}): a
* third of the distance at which the law falls to eight times the trans level,
* between eight and {@link MEETING_REACH} — longer than a junction's window,
* since whether two separate ends meet is asked of every contact that can
* still tell an adjacency from the background.
*/
reach: number
/** A meeting window holding exactly the law, gap nought, against the trans level: the unit meetings are counted in. */
meetUnit: number
}
/** The mean of the lowest `1 − TRIM` of some values, which it sorts. */
function trimmedMean(values: Float64Array): number {
if (values.length === 0) return Number.NaN
values.sort()
const keep = Math.max(1, Math.floor(values.length * (1 - TRIM)))
let sum = 0
for (let i = 0; i < keep; i++) sum += values[i]
return sum / keep
}
/** The median of some values, which it sorts; `NaN` for none. */
function median(values: Float64Array): number {
if (values.length === 0) return Number.NaN
values.sort()
const mid = values.length >> 1
return values.length % 2 === 1 ? values[mid] : (values[mid - 1] + values[mid]) / 2
}
/** A growable list of doubles, for the values of one distance. */
class Values {
private data = new Float64Array(64)
length = 0
push(value: number): void {
if (this.length === this.data.length) {
const next = new Float64Array(this.data.length * 2)
next.set(this.data)
this.data = next
}
this.data[this.length++] = value
}
view(): Float64Array {
return this.data.subarray(0, this.length)
}
}
/**
* The expected map of a file (§27.5): its contact law, its trans level, how
* noisy a value is, and each cell's coverage — once per file, from the contacts
* the picture's pass kept.
*
* @param balanced Whether the values are balanced; a raw map is flattened by
* its marginals, the one-step version of what balancing does.
*/
export function expectedOf(contacts: PictureContacts, balanced: boolean): Expected {
const { n, width, band, coarse, marginal, kept, sequenceOf } = contacts
// Coverage.
const bias = new Float64Array(n).fill(1)
if (!balanced) {
const positive = new Values()
for (let a = 0; a < n; a++) if (marginal[a] > 0) positive.push(marginal[a])
const middle = median(positive.view())
// A cell with under a tenth of the usual coverage is as good as masked: a
// contact or two there, over coverage that small, would be the loudest
// thing in any window it is in.
for (let a = 0; a < n; a++) bias[a] = marginal[a] >= LEAST_COVERAGE * middle && middle > 0 ? marginal[a] / middle : Number.NaN
}
for (let a = 0; a < n; a++) if (kept[a] === 0) bias[a] = Number.NaN
let fullest = 1
for (let a = 0; a < n; a++) if (kept[a] > fullest) fullest = kept[a]
const share = new Float64Array(n)
for (let a = 0; a < n; a++) share[a] = kept[a] / fullest
// The law near the diagonal, cell by cell, and how noisy it is.
const near = new Float64Array(width).fill(Number.NaN)
const ratios = new Values()
for (let d = 0; d < width; d++) {
if (!balanced) {
// A raw map's cells are counts at their own coverage: the law is the
// counts over the coverage that could have held them, and the noise is
// Pearson's — so a thinly covered cell, divided by its coverage, is not
// the loudest voice in the mean.
let counts = 0
let covered = 0
let cells = 0
for (let a = 0; a + d < n; a++) {
const pooled = share[a] * share[a + d]
const o = band[a * width + d] * pooled
const w = bias[a] * bias[a + d] * pooled
if (!(o >= 0) || !(w > 0)) continue
counts += o
covered += w
cells++
}
if (cells < 8 || !(covered > 0)) continue
const p = counts / covered
near[d] = p
if (d === 0 || !(p > 0)) continue
let pearson = 0
for (let a = 0; a + d < n; a++) {
const pooled = share[a] * share[a + d]
const o = band[a * width + d] * pooled
const w = bias[a] * bias[a + d] * pooled
if (!(o >= 0) || !(w > 0)) continue
pearson += (o - w * p) ** 2 / (w * p)
}
ratios.push(pearson / Math.max(1, cells - 1))
continue
}
const values = new Values()
for (let a = 0; a + d < n; a++) {
const v = band[a * width + d] / (bias[a] * bias[a + d])
if (v >= 0) values.push(v)
}
if (values.length < 8) continue
const view = values.view()
near[d] = trimmedMean(view)
if (d === 0) continue
// The same values the mean kept, for their spread: sorted by the mean.
const keep = Math.max(1, Math.floor(view.length * (1 - TRIM)))
let sum = 0
let squares = 0
for (let i = 0; i < keep; i++) {
sum += view[i]
squares += view[i] * view[i]
}
const mean = sum / keep
const variance = Math.max(0, squares / keep - mean * mean)
if (mean > 0) ratios.push(variance / mean)
}
// Far from it, from the coarse whole: a mean per coarse distance along one
// sequence, and the mean between sequences.
const f = coarse.factor
const nc = coarse.n
const coarseSequence = new Int32Array(nc).fill(-1)
const coarseBias = new Float64Array(nc)
const coarseCount = new Float64Array(nc)
for (let a = 0; a < n; a++) {
const c = coarse.of[a]
coarseSequence[c] = sequenceOf[a]
if (bias[a] > 0) {
coarseBias[c] += bias[a]
coarseCount[c]++
}
}
for (let c = 0; c < nc; c++) coarseBias[c] = coarseCount[c] > 0 ? coarseBias[c] / coarseCount[c] : Number.NaN
const byDistance: Values[] = []
const trans = new Values()
// A raw map's, as the law near the diagonal is: counts over the coverage
// that could have held them, so the level strangers share is what they do
// share, and not what the thinly covered cells, divided up, say they do.
const rawSums = new Float64Array(nc)
const rawCover = new Float64Array(nc)
const rawCells = new Int32Array(nc)
let transSum = 0
let transCover = 0
for (let a = 0; a < nc; a++) {
let at = triangleIndex(a, a, nc)
for (let b = a; b < nc; b++, at++) {
const w = coarseBias[a] * coarseBias[b]
const v = coarse.values[at] / w
if (!(v >= 0)) continue
if (coarseSequence[a] === coarseSequence[b]) {
const d = b - a
if (d === 0) continue
;(byDistance[d] ??= new Values()).push(v)
rawSums[d] += coarse.values[at]
rawCover[d] += w
rawCells[d]++
} else {
trans.push(v)
transSum += coarse.values[at]
transCover += w
}
}
}
const far = new Float64Array(byDistance.length).fill(Number.NaN)
for (let d = 1; d < byDistance.length; d++) {
const values = byDistance[d]
if (values === undefined || values.length < 4) continue
far[d] = balanced ? trimmedMean(values.view()) : rawCover[d] > 0 ? rawSums[d] / rawCover[d] : Number.NaN
}
// The law in cells: as measured near the diagonal; interpolated in log–log
// between the coarse distances past it; non-increasing; and past the longest
// distance measured, the power law of its last decade.
const law = new Float64Array(n + 1).fill(Number.NaN)
const coarseAt = (d: number): number => {
const x = d / f
const lo = Math.floor(x)
const hi = lo + 1
const a = far[lo]
const b = far[hi]
if (lo >= 1 && a > 0 && b > 0) return Math.exp(Math.log(a) + (Math.log(b) - Math.log(a)) * (x - lo))
if (lo >= 1 && a > 0) return a
if (b > 0 && lo < 1) return b
return Number.NaN
}
let longest = 0
for (let d = 0; d <= n; d++) {
const v = d < width && near[d] > 0 ? near[d] : d >= 1 ? coarseAt(d) : Number.NaN
if (v > 0) {
law[d] = v
longest = d
}
}
// Holes (a distance nothing measured) take the value before them.
for (let d = 1; d <= longest; d++) if (!(law[d] > 0)) law[d] = law[d - 1]
for (let d = 1; d <= longest; d++) if (law[d] > law[d - 1]) law[d] = law[d - 1]
const slope = tailSlope(law, longest)
for (let d = longest + 1; d <= n; d++) law[d] = law[longest] * Math.pow(d / Math.max(1, longest), slope)
if (!(law[0] > 0)) law[0] = law[1] > 0 ? law[1] : 1
let transLevel = balanced ? trimmedMean(trans.view()) : transCover > 0 ? transSum / transCover : Number.NaN
// A file of one molecule has no trans: two ends apart are then as far apart
// as it has anything, half of that.
if (!(transLevel > 0)) transLevel = 0.5 * law[Math.max(1, longest)]
transLevel = Math.max(transLevel, law[1] * 1e-9)
const dispersion = Math.max(median(ratios.view()) || 1, 1e-12)
let reach = 1
while (reach < 2 * WINDOW && reach < n && law[reach] >= 8 * transLevel) reach++
const window = Math.max(LEAST_WINDOW, Math.min(WINDOW, Math.ceil(reach / 2)))
let mean = 0
for (let i = 0; i < window; i++) for (let j = 0; j < window; j++) mean += law[Math.min(n, i + j + 1)]
mean /= window * window
const level = Math.max(transLevel, mean)
let unit = 0
for (let i = 0; i < window; i++) {
for (let j = 0; j < window; j++) {
const p = law[Math.min(n, i + j + 1)]
unit += p * Math.log(p / level) - (p - level)
}
}
unit = Math.max(unit / dispersion, 1e-9)
let far8 = 1
while (far8 < 3 * MEETING_REACH && far8 < n && law[far8] >= 8 * transLevel) far8++
const meetReach = Math.max(LEAST_MEETING, Math.min(MEETING_REACH, Math.ceil(far8 / 3)))
let meetUnit = 0
for (let i = 0; i < meetReach; i++) {
for (let j = 0; j < meetReach; j++) {
const p = law[Math.min(n, i + j + 1)]
meetUnit += p * Math.log((p + transLevel) / transLevel) - p
}
}
meetUnit = Math.max(meetUnit / dispersion, 1e-9)
return { law, trans: transLevel, dispersion, bias, share, window, unit, reach: meetReach, meetUnit }
}
/** The slope of the law's last decade in log–log, between −3 and −0.3. */
function tailSlope(law: Float64Array, longest: number): number {
const from = Math.max(1, Math.floor(longest / 10))
let n = 0
let sx = 0
let sy = 0
let sxx = 0
let sxy = 0
for (let d = from; d <= longest; d++) {
if (!(law[d] > 0)) continue
const x = Math.log(d)
const y = Math.log(law[d])
n++
sx += x
sy += y
sxx += x * x
sxy += x * y
}
const denominator = n * sxx - sx * sx
const slope = n >= 2 && denominator !== 0 ? (n * sxy - sx * sy) / denominator : -1
return Math.max(-3, Math.min(-0.3, slope))
}
// ---------------------------------------------------------------------------
// The map through the edit
// ---------------------------------------------------------------------------
/**
* The map as the edit draws it: the value of any two cells of the edited axis,
* read from the cells of the picture they show, divided by their coverage.
* `NaN` where either is in a gap or holds nothing the balancer kept — which is
* no evidence, never evidence of a break (§27.5).
*/
export class EditedMap {
readonly law: Float64Array
readonly trans: number
readonly dispersion: number
readonly window: number
readonly unit: number
readonly reach: number
readonly meetUnit: number
/** The law, and its log, for the distances a window spans: `near[d]` is `P(d)`, clamped to the grid. */
readonly near: Float64Array
readonly logNear: Float64Array
private readonly band: Float32Array
private readonly width: number
private readonly sequenceOf: Int32Array
private readonly coarseOf: Int32Array
private readonly coarseValues: Float32Array
private readonly coarseN: number
private readonly bias: Float64Array
private readonly share: Float64Array
/** The cells between sequence ends, as they are; `null` where the pass kept none. */
private readonly ends: PictureEnds | null
constructor(
contacts: PictureContacts,
expected: Expected,
/** The picture's cell each edited cell shows; `-1` in a gap. */
readonly cellMap: Int32Array,
) {
this.law = expected.law
this.trans = expected.trans
this.dispersion = expected.dispersion
this.window = expected.window
this.unit = expected.unit
this.reach = expected.reach
this.meetUnit = expected.meetUnit
this.band = contacts.band
this.width = contacts.width
this.sequenceOf = contacts.sequenceOf
this.coarseOf = contacts.coarse.of
this.coarseValues = contacts.coarse.values
this.coarseN = contacts.coarse.n
this.bias = expected.bias
this.share = expected.share
this.ends = contacts.ends ?? null
this.near = new Float64Array(2 * this.window + 2)
this.logNear = new Float64Array(this.near.length)
for (let d = 0; d < this.near.length; d++) {
this.near[d] = this.law[Math.min(this.law.length - 1, d)]
this.logNear[d] = Math.log(this.near[d])
}
}
/** Cells on the edited axis. */
get n(): number {
return this.cellMap.length
}
/** The value at edited cells `(i, j)`. */
value(i: number, j: number): number {
const a = this.cellMap[i]
const b = this.cellMap[j]
if (a < 0 || b < 0) return Number.NaN
return this.original(a, b)
}
/** The value at cells `(a, b)` of the picture, in the file's own order. */
original(a: number, b: number): number {
const lo = a < b ? a : b
const hi = a < b ? b : a
const d = hi - lo
let v: number
if (d < this.width && this.sequenceOf[lo] === this.sequenceOf[hi]) {
v = this.band[lo * this.width + d]
} else {
const ends = this.ends
const zoned = ends !== null && ends.zone[lo] >= 0 && ends.zone[hi] >= 0
const held = zoned ? endValue(ends, lo, hi) : undefined
// Listed, it is the value; not listed, it held nothing — unless the
// budget ran out before its row, and then the coarse grid says.
if (held !== undefined) v = held
else if (zoned && ends.complete) v = 0
else v = this.coarseValues[triangleIndex(this.coarseOf[lo], this.coarseOf[hi], this.coarseN)]
}
return v / (this.bias[a] * this.bias[b])
}
/**
* What the value at edited cells `(i, j)` is worth as evidence, a whole
* cell's of a balanced map being one: the coverage it was divided by — on a
* raw map, a cell a tenth covered holds a tenth of the counts, and its value,
* ten times them, is not ten times the evidence — and the pairs of bins its
* mean is over ({@link Expected.share}).
*/
weight(i: number, j: number): number {
const a = this.cellMap[i]
const b = this.cellMap[j]
if (a < 0 || b < 0) return 0
const w = this.bias[a] * this.bias[b] * this.share[a] * this.share[b]
return w > 0 ? w : 0
}
/** The coarse cell an edited cell is in, or `-1` in a gap. */
coarseCell(i: number): number {
const a = this.cellMap[i]
return a < 0 ? -1 : this.coarseOf[a]
}
/** The coarse grid's value between two coarse cells: a mean over their cells, not divided by coverage. */
coarseValue(x: number, y: number): number {
return this.coarseValues[x <= y ? triangleIndex(x, y, this.coarseN) : triangleIndex(y, x, this.coarseN)]
}
/** Whether an edited cell holds anything the balancer kept: a cell of no gap, with coverage. */
holds(i: number): boolean {
const a = this.cellMap[i]
return a >= 0 && this.bias[a] > 0
}
/** What a cell pair `d` cells apart along one molecule is expected to hold. */
expectedAt(d: number): number {
return this.law[Math.min(this.law.length - 1, Math.max(0, d))]
}
}
// ---------------------------------------------------------------------------
// Ends and junctions
// ---------------------------------------------------------------------------
/**
* An end (§27.5): a cell of the edited axis and the way its sequence runs away
* from the point — `-1`, the sequence just left of it read leftwards; `+1`, just
* right of it read rightwards — and the cells a walk from it may use, half-open,
* which are the stretch it bounds: a walk never crosses another point the
* method is weighing, since past it the sequence may be somewhere else.
*/
export interface End {
cell: number
dir: 1 | -1
lo: number
hi: number
}
/** A junction's score, and how much of its window held anything. */
export interface Junction {
/**
* The evidence that the two ends meet rather than lie apart: positive, the
* map would rather they met; negative, it would rather they did not (§27.5).
*/
score: number
/** Cells of the window that held a value, of those its two walks reached. */
seen: number
reached: number
/**
* The contacts the window holds past what strangers share, over the
* dispersion — so on any map about the reads it rests on: what a claim a
* shallow map makes from two or three of them is worth, whatever the
* likelihood of so many where the trans level expects none.
*/
contacts: number
/**
* The contacts the law would put in the window, over the dispersion: what
* a refusal of it rests on — an empty window where the law expects two
* contacts is no absence at all.
*/
expected: number
}
/**
* What two ends lying apart would hold, the other side of a junction score:
*
* - `trans`: the trans level — the question a junction the reference makes
* is asked, *does the map refuse it*, and it refuses only contacts down at
* what two strangers share;
* - `local`: the window's own mean, where that is above the trans level — the
* question two ends the reference does not join are asked, *do they meet*,
* and they meet only where the contacts fall away from the corner as an
* adjacency's do. Telomeres and centromeres clustering light a window evenly;
* against its own level that is no evidence of meeting at all.
*/
export type Apart = 'trans' | 'local'
/** A window's values, by row, reused from one junction to the next. */
const scratch = new Float64Array(WINDOW * WINDOW)
const weights = new Float64Array(WINDOW * WINDOW)
/**
* The junction score of two ends (§27.5): over the window of their first
* cells each, the log-likelihood of their meeting — each cell expected at the
* contact law's value for the distance it would then span, `i + j + 1` cells —
* against their lying apart ({@link Apart}), a quasi-Poisson log-likelihood
* divided by the file's dispersion. A cell with no value is left out of both.
*/
export function junctionScore(map: EditedMap, e: End, f: End, apart: Apart = 'trans'): Junction {
const law = map.near
const logLaw = map.logNear
const trans = map.trans
const w = map.window
let seen = 0
let reached = 0
let total = 0
let covered = 0
for (let i = 0; i < w; i++) {
const r = e.cell + e.dir * i
const inside = r >= e.lo && r < e.hi
for (let j = 0; j < w; j++) {
const c = f.cell + f.dir * j
let v = Number.NaN
let weight = 0
if (inside && c >= f.lo && c < f.hi) {
reached++
v = map.value(r, c)
weight = map.weight(r, c)
if (v >= 0 && weight > 0) {
seen++
total += weight * v
covered += weight
} else {
v = Number.NaN
}
}
scratch[i * w + j] = v
weights[i * w + j] = weight
}
}
const level = apart === 'local' && covered > 0 ? Math.max(trans, total / covered) : trans
let score = 0
let lawful = 0
const logLevel = Math.log(level)
for (let i = 0; i < w; i++) {
for (let j = 0; j < w; j++) {
const v = scratch[i * w + j]
if (Number.isNaN(v)) continue
const d = i + j + 1
score += weights[i * w + j] * (v * (logLaw[d] - logLevel) - (law[d] - level))
lawful += weights[i * w + j] * law[d]
}
}
const dispersion = map.dispersion
return { score: score / dispersion, seen, reached, contacts: Math.max(0, total - covered * trans) / dispersion, expected: lawful / dispersion }
}
/** Two ends' meeting (§27.5): the evidence they meet, and the gap and strength it was found at. */
export interface Meeting {
/** The log-likelihood of their meeting over their lying apart at the trans level, over the dispersion. */
score: number
/** The gap the meeting fits best, in cells: what the assembly left out between them. */
gap: number
/** How much of the law the window holds at that gap, above the trans level, `0 … 1`. */
amplitude: number
/**
* The window over the law at gap nought, uncapped: above one, brighter than
* any adjacency — the whole window, so one hot cell at a thinly covered end is
* not a bright corner, and a repeat both ends carry is.
*/
brightness: number
/** The window's mean over the trans level. */
level: number
/** The contacts past the trans level it rests on, as a junction's ({@link Junction.contacts}). */
contacts: number
/**
* The score its own window would have holding exactly the law, gap nought:
* what a clean adjacency of these two ends would score, so `score / ideal`
* says how much of one this meeting is, however short the ends.
*/
ideal: number
seen: number
reached: number
}
/** One end's walk into its stretch: the cells it read, and how far from the end each is. */
interface Walk {
cells: Int32Array
distance: Int32Array
length: number
}
/**
* The cells a meeting reads from an end: its first `reach` that hold
* anything, walking past those that do not — a subtelomere's repeats, an
* array's edge — as far as three times `reach`, each kept with its true
* distance from the end; never more than half the stretch, so that a short
* sequence's two ends read different cells, which is what tells which way
* round it goes.
*/
function walk(map: EditedMap, end: End, reach: number): Walk {
const span = end.hi - end.lo
const most = Math.max(1, Math.min(reach, Math.floor(span / 2)))
const cells = new Int32Array(most)
const distance = new Int32Array(most)
let length = 0
for (let k = 0; k < 3 * most && length < most; k++) {
const cell = end.cell + end.dir * k
if (cell < end.lo || cell >= end.hi) break
if (!map.holds(cell)) continue
cells[length] = cell
distance[length] = k
length++
}
return { cells, distance, length }
}
/** Whether the coarse cells two walks lie in hold more than twice the trans level between them: worth the fine window. */
function coarselyMeets(map: EditedMap, we: Walk, wf: Walk): boolean {
const xs = new Set<number>()
const ys = new Set<number>()
for (let i = 0; i < we.length; i++) xs.add(map.coarseCell(we.cells[i]))
for (let j = 0; j < wf.length; j++) ys.add(map.coarseCell(wf.cells[j]))
let total = 0
let count = 0
for (const x of xs) {
if (x < 0) continue
for (const y of ys) {
if (y < 0) continue
const v = map.coarseValue(x, y)
if (!(v >= 0)) continue
total += v
count++
}
}
return count === 0 || total > 2 * count * map.trans
}
/**
* Whether two separate ends meet (§27.5): over their walks' windows, the
* log-likelihood that the contacts are an adjacency's — each cell expected at
* `A · P(d + g) + T`, `d` the cells it spans across the junction, `g` a gap the
* assembly left out, `A` how much of the law survived what flanks the gap —
* over their lying apart at the trans level `T`, a quasi-Poisson likelihood
* over the file's dispersion. `A` is fitted, not assumed: an assembly breaks in
* repeats, and the reads that would have mapped beside a break often did not,
* so a true adjacency is regularly a fraction of the law — and what then tells
* it from two strangers is that its contacts fall away from the corner as the
* law does, and which of its ends they fall away from. `g` is the best of a
* ladder of gaps; the score is the best of those.
*/
export function meetingScore(map: EditedMap, e: End, f: End): Meeting {
const reach = map.reach
const we = walk(map, e, reach)
const wf = walk(map, f, reach)
const reached = we.length * wf.length
const empty: Meeting = { score: 0, gap: 0, amplitude: 0, brightness: 0, level: 0, ideal: 0, seen: 0, reached, contacts: 0 }
if (reached === 0) return empty
// First the coarse grid: most pairs of an assembly's ends share no more than
// strangers do, and a few coarse cells say so without the window's.
if (!coarselyMeets(map, we, wf)) return empty
const values = new Float64Array(reached)
const weights = new Float64Array(reached)
const span = new Int32Array(reached)
let seen = 0
// Sums weighed by each cell's coverage (see `EditedMap.weight`): counts, and
// the coverage that could have held them.
let total = 0
let covered = 0
for (let i = 0; i < we.length; i++) {
for (let j = 0; j < wf.length; j++) {
const v = map.value(we.cells[i], wf.cells[j])
const w = map.weight(we.cells[i], wf.cells[j])
if (!(v >= 0) || !(w > 0)) continue
values[seen] = v
weights[seen] = w
span[seen] = we.distance[i] + wf.distance[j] + 1
total += w * v
covered += w
seen++
}
}
if (seen === 0) return empty
const trans = map.trans
// Two ends whose window holds no more than two strangers share meet in no
// way worth a fit: most pairs of an assembly's ends are these.
if (total < 1.5 * covered * trans) return { ...empty, level: total / covered / trans, seen }
let ideal = 0
let lawTotal = 0
for (let k = 0; k < seen; k++) {
const p = map.expectedAt(span[k])
ideal += weights[k] * (p * Math.log((p + trans) / trans) - p)
lawTotal += weights[k] * p
}
let best = { score: Number.NEGATIVE_INFINITY, gap: 0, amplitude: 0 }
for (const gap of GAPS) {
let expected = 0
for (let k = 0; k < seen; k++) expected += weights[k] * map.expectedAt(span[k] + gap)
if (!(expected > 0)) continue
const amplitude = Math.min(1, Math.max(1e-6, (total - covered * trans) / expected))
let score = 0
for (let k = 0; k < seen; k++) {
const mean = amplitude * map.expectedAt(span[k] + gap) + trans
score += weights[k] * (values[k] * Math.log(mean / trans) - (mean - trans))
}
if (score > best.score) best = { score, gap, amplitude }
// Past the gap where the law has flattened below the window's own level,
// a longer one explains nothing more.
if (map.expectedAt(gap) < trans) break
}
return {
score: best.score / map.dispersion,
gap: best.gap,
amplitude: best.amplitude,
brightness: lawTotal > 0 ? Math.max(0, total - covered * trans) / lawTotal : 0,
level: total / covered / trans,
ideal: ideal / map.dispersion,
seen,
reached,
contacts: Math.max(0, total - covered * trans) / map.dispersion,
}
}
/** A stretch of the edited axis, half-open: an edited sequence's cells. */
export interface AxisStretch {
from: number
to: number
}
/**
* The junction score at every edge of every sequence — the reference's own
* junctions, each weighed (§27.5's cut score is its negative). `out[x]` is the
* edge between cells `x − 1` and `x`; `NaN` at a sequence's two ends, which join
* nothing, and where the window held too little to say.
*/
export function junctionsAlong(map: EditedMap, sequences: readonly AxisStretch[]): { score: Float64Array; seen: Float64Array } {
const score = new Float64Array(map.n + 1).fill(Number.NaN)
const seen = new Float64Array(map.n + 1)
for (const sequence of sequences) {
for (let x = sequence.from + 1; x < sequence.to; x++) {
const junction = junctionScore(
map,
{ cell: x - 1, dir: -1, lo: sequence.from, hi: x },
{ cell: x, dir: 1, lo: x, hi: sequence.to },
)
seen[x] = junction.reached === 0 ? 0 : junction.seen / junction.reached
if (junction.seen >= Math.max(4, junction.reached / 4)) score[x] = junction.score
}
}
return { score, seen }
}
/**
* The least evidence a refusal is, in natural log-likelihood whatever the
* unit: twenty to one. A map too shallow at its cells to hold an adjacency's
* worth of contacts in a window — a metagenome's genome at a kilobase — has
* windows whose every emptiness is chance, and a unit so small that a fifth of
* one is no evidence at all.
*/
export const LEAST_REFUSAL = 3
/**
* The breakpoints along the axis (§27.5): edges where the map refuses the
* junction the reference makes — a score under `−floor` units, and under
* {@link LEAST_REFUSAL} — and refuses it more than anywhere within half a
* window, so a break is one point and not the run of edges around it.
*/
export function breakpointsOf(
score: Float64Array,
sequences: readonly AxisStretch[],
unit: number,
window: number,
floor = 0.2,
): number[] {
const out: number[] = []
const reach = Math.max(1, window >> 1)
const least = Math.max(floor * unit, LEAST_REFUSAL)
for (const sequence of sequences) {
for (let x = sequence.from + 1; x < sequence.to; x++) {
const here = score[x]
if (!(here < -least)) continue
let lowest = true
for (let y = Math.max(sequence.from + 1, x - reach); y <= Math.min(sequence.to - 1, x + reach); y++) {
const there = score[y]
if (y !== x && there < here) {
lowest = false
break
}
// The first of a run of equals is the one.
if (y < x && there === here) {
lowest = false
break
}
}
if (lowest) out.push(x)
}
}
return out
}
// ---------------------------------------------------------------------------
// Clustering foci
// ---------------------------------------------------------------------------
/** A place of one sequence of the file that the others' own such places cluster with: a centromere, most often. */
export interface Focus {
/** The sequence of the file it is on. */
sequence: number
/** Its cells of the picture, half-open. */
from: number
to: number
/** Of the other sequences asked, the share whose brightest contact with this one is here. */
agreement: number
}
/** The fewest coarse cells a sequence must have to be asked where its focus is. */
const FOCUS_LEAST_CELLS = 4
/** Coarse cells either side of a vote that count as the same place. */
const FOCUS_REACH = 1
/**
* The share of the clustering sequences that must name one place for it to be
* a focus. Asked only of sequences that cluster themselves, a place a stray
* peak made is named by one or two of them, never by nearly half; the smallest
* chromosomes, whose telomeres lie near their centromeres, are named by about
* half — yeast I and III, at 1 kb.
*/
const FOCUS_AGREEMENT = 0.45
/**
* Where each sequence's contacts with every other sequence peak, where they
* agree (§27.5): in a genome whose centromeres cluster — yeasts, many fungi,
* plants in a Rabl configuration — each chromosome's brightest contact with any
* other chromosome is its centromere with the other's, so each sequence is asked,
* of every other one, where in it the brightest coarse cell of their block lies,
* and a place half of them name is its focus. A genome whose centromeres do not
* cluster answers every question somewhere else, and has none; nor does a
* sequence too short to have a place of its own. What it is for: a join that
* would put two foci far apart in one sequence makes a chromosome with two
* centromeres, which no curator takes.
*/
export function fociOf(contacts: PictureContacts, expected: Expected): Focus[] {
const { coarse, sequenceOf, n } = contacts
const nc = coarse.n
// Each coarse cell's sequence, first cell and coverage. A coarse cell most
// of whose cells the balancer emptied is not asked: its mean is the few
// cells left, and a subtelomere's few are its repeats, which shine in trans.
const coarseSequence = new Int32Array(nc).fill(-1)
const coarseFirst = new Int32Array(nc + 1).fill(n)
const coverage = new Float64Array(nc)
const counted = new Float64Array(nc)
const cellsIn = new Float64Array(nc)
for (let a = n - 1; a >= 0; a--) {
const c = coarse.of[a]
coarseSequence[c] = sequenceOf[a]
coarseFirst[c] = a
cellsIn[c]++
if (expected.bias[a] > 0) {
coverage[c] += expected.bias[a]
counted[c]++
}
}
for (let c = 0; c < nc; c++) coverage[c] = counted[c] >= 0.6 * cellsIn[c] ? coverage[c] / counted[c] : Number.NaN
// The sequences' coarse ranges.
const ranges: Array<[number, number]> = []
for (let c = 0; c < nc; c++) {
const s = coarseSequence[c]
if (s < 0) continue
const range = ranges[s]
if (range === undefined) ranges[s] = [c, c + 1]
else range[1] = c + 1
}
const asked: number[] = []
ranges.forEach((range, s) => {
if (range !== undefined && range[1] - range[0] >= FOCUS_LEAST_CELLS) asked.push(s)
})
if (asked.length < 3) return []
const value = (x: number, y: number): number => {
const v = coarse.values[x <= y ? triangleIndex(x, y, nc) : triangleIndex(y, x, nc)] / (coverage[x] * coverage[y])
return v >= 0 ? v : Number.NaN
}
// Each pair's brightest place, once: `peaks[i][j]` is where in the `i`th
// sequence asked its block with the `j`th peaks, or `-1`.
const peaks: Int32Array[] = asked.map(() => new Int32Array(asked.length).fill(-1))
for (let i = 0; i < asked.length; i++) {
const [a0, a1] = ranges[asked[i]]
for (let j = i + 1; j < asked.length; j++) {
const [b0, b1] = ranges[asked[j]]
let best = 0
let bx = -1
let by = -1
for (let x = a0; x < a1; x++) {
for (let y = b0; y < b1; y++) {
// A cell and its eight neighbours, so one noisy cell is not a peak.
let sum = 0
let count = 0
for (let dx = -1; dx <= 1; dx++) {
for (let dy = -1; dy <= 1; dy++) {
const xx = x + dx
const yy = y + dy
if (xx < a0 || xx >= a1 || yy < b0 || yy >= b1) continue
const v = value(xx, yy)
if (Number.isNaN(v)) continue
sum += v
count++
}
}
const mean = count > 0 ? sum / count : 0
if (mean > best) {
best = mean
bx = x
by = y
}
}
}
// A peak no brighter than a few times two strangers is no place at all.
if (bx < 0 || best < 4 * expected.trans) continue
peaks[i][j] = bx
peaks[j][i] = by
}
}
/** The place most of `partners` name in the `i`th sequence, and the share that do. */
const modeOf = (i: number, partners: readonly number[]): { mode: number; agreement: number } => {
const list: number[] = []
for (const j of partners) if (j !== i && peaks[i][j] >= 0) list.push(peaks[i][j])
const asking = partners.filter((j) => j !== i).length
if (list.length < 3 || asking === 0) return { mode: -1, agreement: 0 }
let mode = -1
let most = 0
for (const candidate of list) {
let near = 0
for (const other of list) if (Math.abs(other - candidate) <= FOCUS_REACH) near++
if (near > most) {
most = near
mode = candidate
}
}
return { mode, agreement: most / asking }
}
// Twice: first every sequence asked of all the others, and those a third of
// them agree on kept as the clustering ones; then every sequence asked again
// of those alone — a stretch with no centromere of its own, a plasmid, a
// fragment of a chromosome's arm, answers the first question anywhere, and
// would dilute every other sequence's agreement.
const everyone = asked.map((_, i) => i)
const clustering = everyone.filter((i) => modeOf(i, everyone).agreement >= 1 / 3)
if (clustering.length < 3) return []
const out: Focus[] = []
asked.forEach((s, i) => {
const { mode, agreement } = modeOf(i, clustering)
if (mode < 0 || agreement < FOCUS_AGREEMENT) return
const lo = Math.max(ranges[s][0], mode - FOCUS_REACH)
const hi = Math.min(ranges[s][1], mode + FOCUS_REACH + 1)
out.push({ sequence: s, from: coarseFirst[lo], to: coarseFirst[hi], agreement })
})
return out
}
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