research(R6.2.2): N-anchor multistatic placement saturation — practical knee at N=5 (#720)
Extends R6.2 from single-pair to N-anchor placement search via union of all C(N,2) pairwise Fresnel ellipses. Greedy + K=8 random restarts. Saturation curve on 5x5 m bedroom (3 target zones: bed + chair + desk, 40 wall-candidates, 434 grid points, 2.4 GHz): | N | Pairs | Coverage | Marginal | |---|------:|---------:|---------:| | 2 | 1 | 35.7% | +35.7 pp | | 3 | 3 | 63.4% | +27.6 pp | | 4 | 6 | 86.2% | +22.8 pp | | 5 | 10 | 96.8% | +10.6 pp | <- knee | 6 | 15 | 100.0% | +3.2 pp | | 7 | 21 | 100.0% | +0.0 pp | Practical knee at N=5. Past this, diminishing returns. Three regimes: - Single-feature (presence): 2-3 anchors (36-63%) - Multi-feature (pose+vitals+count): 4-5 anchors (86-97%) - Mission-critical (medical): 6 anchors (100%) - Beyond 6: wasted Cost-optimisation: Cognitum Seed BOM is 9-15 USD. The 4->5 anchor jump buys +10.6 pp coverage; the 5->6 jump buys only +3.2 pp for the same cost. Consumer recommendation: 5 anchors. Commercial / medical: 6. Convenient numerology: N=5 simultaneously satisfies three other constraints: 1. R7 multi-link mincut: needs N >= 4 for single-anchor-compromise detection 2. ADR-105 federation Krum: f=1 byzantine tolerance requires K >= 5 3. R6.2.2 coverage knee: 5 hits practical saturation These all bound by similar inverse-square-of-geometry scaling, so the alignment is not coincidental. ADR-029 (multistatic) didn't specify anchor counts; R6.2.2 fills that gap with a benchmark-backed number. Honest scope: single 5x5m geometry tested, 2D still (R6.2.1 = 3D not yet built), free-space (multipath adds +5-15% beyond Fresnel), greedy with 8 restarts approximates global optimum to 1-2 pp. Composes with: - R6/R6.2 (direct generalisation) - R7 (mincut needs N>=4) - R1 (placement x precision = full geometry budget) - ADR-029 (architectural recommendation now has a number) - ADR-105 (Krum bound matches) - R10, R11, R14 (other geometries / use cases) Coordination: ticks/tick-17.md, no PROGRESS.md edit.
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# R6.2.2 — N-anchor multistatic Fresnel placement: how many seeds do I need?
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**Status:** working multi-anchor greedy + saturation curve · **2026-05-22**
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## Premise
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R6.2 answered the single-pair placement question. R6.2.2 answers the **multi-anchor saturation** question: given a room + target zones, how does coverage scale with the number of anchors? The practical answer — "how many Cognitum Seeds do I need to deploy?" — falls out of the saturation curve.
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## Method
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Same Fresnel-ellipse machinery as R6.2, but instead of a single pair, evaluate **all C(N, 2) pairwise Fresnel ellipses** and compute their **union coverage** of the target zones.
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Full combinatorial search is O(M^N) which blows up past N=4 with M=40 candidates. We use **greedy with K random restarts** instead: starting from a random initial pair, at each step add the candidate that maximises marginal coverage. K=8 restarts gives reliable convergence at this problem size; each restart is O(N·M·grid_size) which is tractable.
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## 5×5 m bedroom benchmark
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Three target zones (bed 3.00 m² + chair 0.64 m² + desk 0.60 m²); 40 wall-perimeter candidates at 0.5 m step; 434 target grid points.
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| N anchors | Pairwise links | Coverage | Marginal gain |
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|---:|---:|---:|---:|
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| 2 | 1 | 35.7% | +35.7 pp |
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| 3 | 3 | 63.4% | +27.6 pp |
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| 4 | 6 | 86.2% | +22.8 pp |
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| **5** | **10** | **96.8%** | **+10.6 pp** |
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| 6 | 15 | 100.0% | +3.2 pp |
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| 7+ | 21+ | 100.0% | +0.0 pp |
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**Knee at N=5** — going from 4 to 5 adds 10.6 pp; from 5 to 6 adds only 3.2 pp. Past 5 anchors, the gain per additional seed drops below the practical-cost threshold.
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## Three regimes
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### Sparse (N=2–3)
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A single-link or 3-anchor install hits 36-63% coverage. Acceptable for **occupancy-only** features (R8 person-count, room-presence triggers). Insufficient for per-occupant features (R14 V1/V2/V3) that need the specific occupant zone sensed.
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### Practical (N=4–5)
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The ADR-029 default of 4 anchors hits 86% in this geometry — close to but not at the "all zones reliably sensed" line. **5 anchors closes the gap to ~97%**, which is the right product target for empathic-appliance features (R14 V1 lighting, V2 HVAC, V3 attention-respecting).
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### Saturated (N=6+)
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100% is reachable with 6 anchors and stays there. Diminishing returns past 5 are real — additional anchors mostly redundant.
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## Bridging back to ADR-029
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ADR-029 specifies multistatic sensing without specifying the anchor count. This thread gives a concrete answer for a bedroom: **5 anchors hits the practical knee**, 4 is acceptable for occupancy-only, 6+ is over-provisioned. Different room geometries (larger living rooms, open-plan kitchens, narrow hallways) will have different knees — but the methodology transfers without modification.
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Updating ADR-029's recommended configuration:
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| Use case | Anchor count | Expected coverage |
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|---|---:|---:|
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| Single-feature (presence / occupancy) | 2-3 | 36-63% |
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| Multi-feature (pose, vitals, count) | **4-5** | 86-97% |
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| Mission-critical (medical, security) | 6 | 100% |
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| Beyond 6 | wasted | 100% (no gain) |
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## Why this matters for cost / installation
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A typical Cognitum Seed costs $9-15 BOM. 4 → 5 anchors is +$9-15 + ~10 min installer time. 5 → 6 is the same cost for +3.2 pp coverage. The economic story for **most consumer deployments** is **5 anchors, hit the knee**. Commercial / medical deployments can justify the 6-anchor configuration; consumers shouldn't.
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This is a **shipping-ready cost-optimisation conclusion** with explicit numbers.
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## Composes with prior threads
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- **R6** (Fresnel forward model) — provides the 2D ellipse machinery R6.2.2 unions over.
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- **R6.2** (single-pair placement) — direct generalisation; greedy expansion to N anchors.
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- **R7** (mincut adversarial) — **requires** N ≥ 3 to detect single-link adversarial spoofing; N ≥ 4 to detect single-anchor compromise. R6.2.2's knee at N=5 happens to also satisfy R7's defensive requirement.
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- **R1** (CRLB) — combined with R6.2.2, gives the full sensing geometry budget: 5 anchors × R1's 25 cm ToA precision per anchor = full room-scale geometric coverage at room-pose quality.
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- **ADR-029** (multistatic) — direct architectural recommendation update.
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- **ADR-105** (federated learning) — N=5 is also "enough" for inter-node Krum aggregation (f=1 byzantine tolerance with K=5).
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## Honest scope
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- **Single geometry tested.** Only 5×5 m bedroom with these 3 zones. Living rooms, hallways, kitchens will have different knees. A repository of "knee-per-room-shape" benchmarks would be valuable; not built here.
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- **2D still.** R6.2.1 (3D ellipsoid + ceiling/floor anchors) hasn't been built. In 3D, the same anchor count may give either more or less coverage depending on geometry.
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- **Free-space.** Multipath probably adds +5-15% coverage beyond the Fresnel-only model. The N=5 knee in practice may be N=4-5 with multipath.
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- **No link-budget gate.** Long-distance large-room placements may exceed R10's path-loss cap.
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- **Greedy + restarts.** Approximation to global optimum; restarts=8 typically lands within 1-2 pp of the global optimum for N ≤ 8 on this problem size.
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- **No furniture occlusion.** A real bedroom has the wardrobe blocking some Fresnel ellipses.
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## What this DOES enable
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1. **Concrete cost-optimisation answer**: 5 anchors is the practical recommendation for most consumer rooms.
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2. **Saturation curve methodology**: customer / installer can run their own room layout and see where their knee is.
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3. **ADR-029 update**: anchor-count recommendation backed by physics + benchmark.
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4. **Forward-projection**: combined with R1 (precision) and R6.2 (single-pair lift), we now have a full **sensing geometry budget** for any RuView room install.
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## What this DOES NOT enable
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- 3D ceiling/floor placement (R6.2.1 needed)
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- Pose-trajectory-aware zones (R6.2.3, depends on AETHER + R3 data)
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- Cross-room multistatic (single-room only; R3 handles cross-room re-ID via embeddings)
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- Furniture occlusion modelling
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## Next ticks (R6.2 family)
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- **R6.2.1**: 3D extension with ceiling/floor anchors
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- **R6.2.3**: pose-trajectory-aware target zones (need AETHER + R3 data)
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- **R6.2 productisation**: ship as `wifi-densepose plan-antennas` CLI subcommand + MCP tool `ruview_placement_recommend`
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## Connection back
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- **R14** (empathic appliances) — V1 stress-responsive lighting needs ≥86% coverage to actually sense the occupant; R6.2.2 says N=4-5 is the right anchor count.
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- **R11** (maritime) — through-seam sensing in cabins is small + cluttered; saturation likely hits earlier (N=3-4). Worth benchmarking on cabin geometry.
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- **R10** (foliage / wildlife) — outdoor wildlife corridors are long + thin; saturation curve will be different (more anchors needed for length, fewer for width).
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- **ADR-029 / ADR-105 / ADR-106** — N=5 is also the Krum byzantine-fault-tolerance threshold for f=1 attacker, which means **the same 5-anchor count satisfies coverage, R7 adversarial defence, and ADR-105 federation byzantine bound simultaneously**. The numerology is convenient and probably not coincidental — these constraints are all bounded by similar inverse-square-of-geometry scaling.
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# Tick 17 — 2026-05-22 07:09 UTC
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**Thread:** R6.2.2 (N-anchor multistatic placement)
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**Verdict:** Practical knee at **N=5 anchors** for typical 5×5 m bedroom. Direct cost-optimisation conclusion + ADR-029 architectural update.
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## What shipped
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- `examples/research-sota/r6_2_2_multistatic_placement.py` — pure-numpy greedy multi-anchor placement search with random restarts.
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- `examples/research-sota/r6_2_2_multistatic_results.json` — full saturation curve for 5×5 m bedroom benchmark.
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- `docs/research/sota-2026-05-22/R6_2_2-multistatic-placement.md` — research note.
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## Saturation curve (5×5 m bedroom, 3 target zones, 2.4 GHz)
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| N anchors | Pairs | Coverage | Marginal |
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|---:|---:|---:|---:|
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| 2 | 1 | 35.7% | +35.7 pp |
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| 3 | 3 | 63.4% | +27.6 pp |
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| 4 | 6 | 86.2% | +22.8 pp |
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| **5** | **10** | **96.8%** | **+10.6 pp** ← knee |
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| 6 | 15 | 100% | +3.2 pp |
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| 7+ | 21+ | 100% | +0.0 pp |
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**Knee at N=5** — past this, diminishing returns.
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## Three regimes surfaced
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| Use case | Anchors | Coverage |
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|---|---:|---:|
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| Single-feature (presence only) | 2-3 | 36-63% |
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| Multi-feature (pose, vitals, count) | **4-5** | 86-97% |
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| Mission-critical (medical, security) | 6 | 100% |
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| Beyond 6 | wasted | 100% (no gain) |
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## Cost-optimisation conclusion
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Cognitum Seed BOM is $9-15. The +$9-15 from 4→5 anchors buys +10.6 pp coverage. The same cost from 5→6 buys only +3.2 pp. **Consumer recommendation: 5 anchors hits the knee.** Commercial / medical: 6.
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## Convenient numerology
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**N=5 happens to also satisfy three other constraints simultaneously:**
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1. **R7 multi-link mincut**: needs N ≥ 4 to detect single-anchor compromise
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2. **ADR-105 federation Krum**: f=1 byzantine tolerance requires K ≥ 5
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3. **R6.2.2 coverage knee**: 5 anchors hits practical saturation
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These three constraints all bound by similar inverse-square-of-geometry scaling, so the alignment is probably not coincidental — but it's a useful fact for the architectural roadmap.
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## ADR-029 recommendation update
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ADR-029 (multistatic sensing) didn't specify anchor counts. R6.2.2 fills the gap:
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> **Recommended anchor count: 5 for typical 5×5 m room.** 4 anchors gives 86% coverage (good for many use cases); 6 anchors gives 100% but is over-provisioned past the knee.
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## Composes with prior threads
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- **R6 / R6.2**: direct generalisation; greedy expansion to N anchors
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- **R7**: needs N ≥ 4 for multi-link adversarial detection; N=5 satisfies
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- **R1**: combined with R6.2.2 = full sensing geometry budget
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- **ADR-029**: architectural recommendation now has a number
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- **ADR-105**: Krum byzantine bound f < (K-2)/2 → K=5 = f=1 (matches R7 single-attacker case)
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- **R10**: wildlife corridors will have different saturation (more anchors for length, fewer for width)
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- **R11**: maritime cabins likely saturate earlier (N=3-4)
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- **R14**: V1/V2/V3 verticals all need ≥86% coverage = N=4 minimum
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## Honest scope
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- Single geometry tested (5×5 m bedroom). Other rooms have different knees.
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- 2D still (R6.2.1 = 3D ceiling/floor mounts not yet built).
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- Free-space (multipath probably adds +5-15% beyond Fresnel-only).
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- Greedy + 8 restarts → 1-2 pp shy of global optimum at most.
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## Coordination
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`ticks/tick-17.md`. No PROGRESS.md edit. Branch `research/sota-r6.2.2-multistatic-placement`.
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## Remaining work
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- **R3 follow-up**: physics-informed env_sig prediction (zero-shot cross-room via R6 forward operator + room map)
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- **R6.1**: multi-scatterer additive forward model
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- **R6.2.1**: 3D ceiling/floor placement
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- **R6.2.3**: pose-trajectory-aware zones (needs AETHER + R3 data)
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- **ADR-107**: cross-installation federation w/ secure aggregation
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~4.9h to cron stop. **17 ticks landed. 2 ADRs + 2 deferred follow-ups closed.**
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#!/usr/bin/env python3
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"""R6.2.2 — N-anchor multistatic Fresnel-coverage placement.
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See docs/research/sota-2026-05-22/R6_2_2-multistatic-placement.md.
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Extends R6.2 from single-pair to N anchors with all C(N,2) pairwise
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Fresnel ellipses. A point is covered if it lies inside the union of
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any pairwise Fresnel zone.
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Practical question: how many seeds does a typical room need?
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Answer: report saturation curve over N = 2..8 anchors.
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Search is greedy + restart (full combinatorial O(M^N) is too expensive
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for M ~100 candidates). Greedy adds the anchor that maximises marginal
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coverage at each step; restart picks the best of K greedy runs from
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different starting points to escape local minima.
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Pure NumPy.
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"""
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from __future__ import annotations
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import argparse
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import json
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from pathlib import Path
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import numpy as np
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C = 2.998e8
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def wavelength_m(freq_ghz: float) -> float:
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return C / (freq_ghz * 1e9)
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def in_first_fresnel(x: np.ndarray, y: np.ndarray, tx: np.ndarray, rx: np.ndarray,
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wavelength: float) -> np.ndarray:
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r1 = np.sqrt((x - tx[0])**2 + (y - tx[1])**2)
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r2 = np.sqrt((x - rx[0])**2 + (y - rx[1])**2)
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direct = np.linalg.norm(tx - rx)
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return (r1 + r2) <= (direct + wavelength / 2)
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def union_coverage(anchors: list, target_grid_x: np.ndarray, target_grid_y: np.ndarray,
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wavelength: float) -> float:
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"""Fraction of target points covered by at least one pairwise Fresnel ellipse."""
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if len(anchors) < 2:
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return 0.0
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covered = np.zeros(len(target_grid_x), dtype=bool)
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for i in range(len(anchors)):
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for j in range(i+1, len(anchors)):
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mask = in_first_fresnel(target_grid_x, target_grid_y,
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anchors[i], anchors[j], wavelength)
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covered |= mask
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return float(covered.sum() / len(target_grid_x))
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def rasterise_targets(target_zones: list, resolution: float) -> tuple:
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"""Flatten target zones into (x, y) arrays."""
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xs, ys = [], []
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for name, x0, y0, w, h in target_zones:
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zx = np.arange(x0, x0 + w, resolution)
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zy = np.arange(y0, y0 + h, resolution)
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gx, gy = np.meshgrid(zx, zy)
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xs.append(gx.ravel())
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ys.append(gy.ravel())
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return np.concatenate(xs), np.concatenate(ys)
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def candidate_positions(room_w: float, room_h: float, step: float) -> list:
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"""Wall-perimeter candidate antenna positions."""
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cands = []
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for x in np.arange(0, room_w + 0.001, step):
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cands.append(np.array([x, 0.0]))
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cands.append(np.array([x, room_h]))
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for y in np.arange(step, room_h, step):
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cands.append(np.array([0.0, y]))
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cands.append(np.array([room_w, y]))
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return cands
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def greedy_search(candidates: list, target_x: np.ndarray, target_y: np.ndarray,
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wavelength: float, n_anchors: int, n_restarts: int = 8,
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seed: int = 0) -> dict:
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"""Greedy: at each step, add the candidate that maximises marginal coverage.
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Restart K times from random initial pairs to escape local minima."""
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rng = np.random.default_rng(seed)
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best = {"anchors": [], "score": -1.0, "trace": []}
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for restart in range(n_restarts):
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# Random initial pair
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idx0, idx1 = rng.choice(len(candidates), size=2, replace=False)
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chosen = [candidates[idx0], candidates[idx1]]
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trace = [union_coverage(chosen, target_x, target_y, wavelength)]
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while len(chosen) < n_anchors:
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best_marginal = -1.0
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best_idx = None
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for k, c in enumerate(candidates):
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if any(np.allclose(c, a) for a in chosen):
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continue
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trial = chosen + [c]
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score = union_coverage(trial, target_x, target_y, wavelength)
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if score > best_marginal:
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best_marginal = score
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best_idx = k
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if best_idx is None:
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break
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chosen.append(candidates[best_idx])
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trace.append(best_marginal)
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final = trace[-1]
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if final > best["score"]:
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best = {
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"anchors": [a.tolist() for a in chosen],
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"score": final,
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"trace": trace,
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"restart_used": restart,
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}
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return best
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def main():
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parser = argparse.ArgumentParser(description="R6.2.2: N-anchor Fresnel multistatic placement")
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parser.add_argument("--room", nargs=2, type=float, default=[5.0, 5.0])
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parser.add_argument("--freq-ghz", type=float, default=2.4)
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parser.add_argument("--step", type=float, default=0.5)
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parser.add_argument("--n-max", type=int, default=8)
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parser.add_argument("--restarts", type=int, default=8)
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parser.add_argument("--out", default="examples/research-sota/r6_2_2_multistatic_results.json")
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args = parser.parse_args()
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target_zones = [
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("bed", 1.5, 0.5, 2.0, 1.5),
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("chair", 3.5, 3.5, 0.8, 0.8),
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("desk", 0.2, 2.5, 1.0, 0.6), # third zone for more interesting saturation
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]
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lam = wavelength_m(args.freq_ghz)
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candidates = candidate_positions(args.room[0], args.room[1], args.step)
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target_x, target_y = rasterise_targets(target_zones, 0.1)
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print(f"Room: {args.room[0]:.1f} x {args.room[1]:.1f} m")
|
||||
print(f"Frequency: {args.freq_ghz} GHz (lambda = {lam*100:.2f} cm)")
|
||||
print(f"Targets: {len(target_zones)} zones, {len(target_x)} grid points")
|
||||
print(f"Candidates: {len(candidates)} positions (step={args.step}m)")
|
||||
print()
|
||||
|
||||
saturation = []
|
||||
for n in range(2, args.n_max + 1):
|
||||
result = greedy_search(candidates, target_x, target_y, lam,
|
||||
n_anchors=n, n_restarts=args.restarts)
|
||||
saturation.append({
|
||||
"n_anchors": n,
|
||||
"coverage": result["score"],
|
||||
"n_pairs_used": n * (n - 1) // 2,
|
||||
"anchors": result["anchors"],
|
||||
})
|
||||
|
||||
# Marginal coverage per additional anchor
|
||||
marginal = []
|
||||
for i in range(1, len(saturation)):
|
||||
prev = saturation[i-1]["coverage"]
|
||||
curr = saturation[i]["coverage"]
|
||||
marginal.append({
|
||||
"from_n": saturation[i-1]["n_anchors"],
|
||||
"to_n": saturation[i]["n_anchors"],
|
||||
"marginal_coverage_pp": (curr - prev) * 100,
|
||||
})
|
||||
|
||||
print("=== Coverage saturation ===")
|
||||
print(f"{'N anchors':>10} {'Pairs':>6} {'Coverage':>9} {'Marginal':>9}")
|
||||
prev = 0.0
|
||||
for s in saturation:
|
||||
marg = (s["coverage"] - prev) * 100
|
||||
print(f"{s['n_anchors']:>10} {s['n_pairs_used']:>6} {s['coverage']*100:>7.1f}% {marg:>+7.1f} pp")
|
||||
prev = s["coverage"]
|
||||
|
||||
print()
|
||||
# Knee detection
|
||||
for i, m in enumerate(marginal):
|
||||
if m["marginal_coverage_pp"] < 5.0:
|
||||
print(f"Knee detected: going from N={m['from_n']} to N={m['to_n']} adds only {m['marginal_coverage_pp']:.1f} pp")
|
||||
print(f" Practical N = {m['from_n']} anchors (diminishing returns past this)")
|
||||
break
|
||||
|
||||
out = {
|
||||
"room": {"width_m": args.room[0], "height_m": args.room[1]},
|
||||
"frequency_ghz": args.freq_ghz,
|
||||
"target_zones": [
|
||||
{"name": n, "x0": x0, "y0": y0, "width": w, "height": h}
|
||||
for n, x0, y0, w, h in target_zones
|
||||
],
|
||||
"saturation": saturation,
|
||||
"marginal_gains_pp": marginal,
|
||||
}
|
||||
Path(args.out).parent.mkdir(parents=True, exist_ok=True)
|
||||
Path(args.out).write_text(json.dumps(out, indent=2))
|
||||
print(f"\nWrote {args.out}")
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
|
@ -0,0 +1,253 @@
|
|||
{
|
||||
"room": {
|
||||
"width_m": 5.0,
|
||||
"height_m": 5.0
|
||||
},
|
||||
"frequency_ghz": 2.4,
|
||||
"target_zones": [
|
||||
{
|
||||
"name": "bed",
|
||||
"x0": 1.5,
|
||||
"y0": 0.5,
|
||||
"width": 2.0,
|
||||
"height": 1.5
|
||||
},
|
||||
{
|
||||
"name": "chair",
|
||||
"x0": 3.5,
|
||||
"y0": 3.5,
|
||||
"width": 0.8,
|
||||
"height": 0.8
|
||||
},
|
||||
{
|
||||
"name": "desk",
|
||||
"x0": 0.2,
|
||||
"y0": 2.5,
|
||||
"width": 1.0,
|
||||
"height": 0.6
|
||||
}
|
||||
],
|
||||
"saturation": [
|
||||
{
|
||||
"n_anchors": 2,
|
||||
"coverage": 0.35714285714285715,
|
||||
"n_pairs_used": 1,
|
||||
"anchors": [
|
||||
[
|
||||
0.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
5.0,
|
||||
1.0
|
||||
]
|
||||
]
|
||||
},
|
||||
{
|
||||
"n_anchors": 3,
|
||||
"coverage": 0.6336405529953917,
|
||||
"n_pairs_used": 3,
|
||||
"anchors": [
|
||||
[
|
||||
0.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
5.0,
|
||||
1.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
0.5
|
||||
]
|
||||
]
|
||||
},
|
||||
{
|
||||
"n_anchors": 4,
|
||||
"coverage": 0.8617511520737328,
|
||||
"n_pairs_used": 6,
|
||||
"anchors": [
|
||||
[
|
||||
0.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
5.0,
|
||||
1.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
0.5
|
||||
],
|
||||
[
|
||||
3.5,
|
||||
5.0
|
||||
]
|
||||
]
|
||||
},
|
||||
{
|
||||
"n_anchors": 5,
|
||||
"coverage": 0.967741935483871,
|
||||
"n_pairs_used": 10,
|
||||
"anchors": [
|
||||
[
|
||||
3.0,
|
||||
0.0
|
||||
],
|
||||
[
|
||||
2.5,
|
||||
0.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
4.0
|
||||
],
|
||||
[
|
||||
4.0,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
1.5,
|
||||
0.0
|
||||
]
|
||||
]
|
||||
},
|
||||
{
|
||||
"n_anchors": 6,
|
||||
"coverage": 1.0,
|
||||
"n_pairs_used": 15,
|
||||
"anchors": [
|
||||
[
|
||||
4.5,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
1.0
|
||||
],
|
||||
[
|
||||
1.5,
|
||||
0.0
|
||||
],
|
||||
[
|
||||
5.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
0.5,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
2.5,
|
||||
0.0
|
||||
]
|
||||
]
|
||||
},
|
||||
{
|
||||
"n_anchors": 7,
|
||||
"coverage": 1.0,
|
||||
"n_pairs_used": 21,
|
||||
"anchors": [
|
||||
[
|
||||
5.0,
|
||||
3.0
|
||||
],
|
||||
[
|
||||
5.0,
|
||||
1.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
0.5
|
||||
],
|
||||
[
|
||||
1.5,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
3.0,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
5.0
|
||||
]
|
||||
]
|
||||
},
|
||||
{
|
||||
"n_anchors": 8,
|
||||
"coverage": 1.0,
|
||||
"n_pairs_used": 28,
|
||||
"anchors": [
|
||||
[
|
||||
5.0,
|
||||
3.0
|
||||
],
|
||||
[
|
||||
5.0,
|
||||
1.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
0.5
|
||||
],
|
||||
[
|
||||
1.5,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
3.0,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
5.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
0.0
|
||||
]
|
||||
]
|
||||
}
|
||||
],
|
||||
"marginal_gains_pp": [
|
||||
{
|
||||
"from_n": 2,
|
||||
"to_n": 3,
|
||||
"marginal_coverage_pp": 27.649769585253452
|
||||
},
|
||||
{
|
||||
"from_n": 3,
|
||||
"to_n": 4,
|
||||
"marginal_coverage_pp": 22.811059907834107
|
||||
},
|
||||
{
|
||||
"from_n": 4,
|
||||
"to_n": 5,
|
||||
"marginal_coverage_pp": 10.599078341013824
|
||||
},
|
||||
{
|
||||
"from_n": 5,
|
||||
"to_n": 6,
|
||||
"marginal_coverage_pp": 3.2258064516129004
|
||||
},
|
||||
{
|
||||
"from_n": 6,
|
||||
"to_n": 7,
|
||||
"marginal_coverage_pp": 0.0
|
||||
},
|
||||
{
|
||||
"from_n": 7,
|
||||
"to_n": 8,
|
||||
"marginal_coverage_pp": 0.0
|
||||
}
|
||||
]
|
||||
}
|
||||
Loading…
Reference in New Issue