GapBridge: Connecting Missing Domains

• GapBridge is a family of task-specific bridge mechanisms that explicitly model missing links across separated representations, domains, geometries, or inference stages.
• In engineering design, it employs a graph-guided, diffusion-based imputation model that leverages cross-attention and graph neural networks to complete partial CAD specifications.
• GapBridge also extends to domains like computational pathology and generative modeling, where cyclic registration-synthesis and bridging frameworks address misalignments and missing data.

GapBridge denotes a family of task-specific “bridge” mechanisms that connect separated representations, domains, geometries, or stages of inference. In one formal usage, it is a graph-guided, diffusion-based parametric data completion system for engineering/CAD design that maps an incomplete parametric specification to a completed design (Zhou et al., 2024). In another, it is a cyclic registration-synthesis framework that bridges weakly paired H&E and IHC consecutive sections through deformable structural alignment (Yuan et al., 1 Sep 2025). Earlier mathematical work also introduced a gap function as a scalar indicator of torsional instability for partially hinged bridge-deck plates (Berchio et al., 2017). The collected usage suggests that “GapBridge” is not a single canonical architecture, but a recurring label for mechanisms that explicitly model a missing link rather than ignoring it.

1. Literal bridge mechanics and the gap function

A mathematically precise precursor to the GapBridge idea appears in the study of torsional instability for suspension-bridge decks modeled as partially hinged rectangular plates (Berchio et al., 2017). The deck is represented as a thin, long, narrow rectangular plate

$$\Omega=(0,\pi)\times(-\ell,\ell),\qquad 2\ell\ll \pi,$$

with hinged short edges $\{0,\pi\}\times(-\ell,\ell)$ and free long edges $y=\pm\ell$. The vertical deformation $u$ is governed by the Kirchhoff–Love plate energy

$$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$

with admissible space

$$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$

The central functional is the gap function

$G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$

and its maximum magnitude

$$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$

This quantity measures the difference in vertical displacement between the two free edges. If the two edges move very differently, the deck is twisting strongly; if the gap is small, the deck is behaving more symmetrically and is less prone to dangerous torsion.

Two load families were used to test whether $G^\infty$ behaves as a torsional “meter.” For loads concentrated near one free edge,

$$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$

the special midpoint-load case

$\{0,\pi\}\times(-\ell,\ell)$0

yields

$\{0,\pi\}\times(-\ell,\ell)$1

As $\{0,\pi\}\times(-\ell,\ell)$2,

$\{0,\pi\}\times(-\ell,\ell)$3

uniformly on $\{0,\pi\}\times(-\ell,\ell)$4, with

$\{0,\pi\}\times(-\ell,\ell)$5

The asymptotic expansion

$\{0,\pi\}\times(-\ell,\ell)$6

shows that the closer the same total load is pushed toward the free edge, the larger the gap becomes. The paper also observes numerically that $\{0,\pi\}\times(-\ell,\ell)$7 appears strictly increasing.

For resonant loads proportional to torsional eigenmodes,

$\{0,\pi\}\times(-\ell,\ell)$8

the gap takes the explicit form

$\{0,\pi\}\times(-\ell,\ell)$9

with

$y=\pm\ell$0

The estimate

$y=\pm\ell$1

shows that the torsional gap vanishes like $y=\pm\ell$2 as the plate becomes narrower. The paper further shows that even longitudinal eigenfunctions give zero gap identically, whereas the first torsional mode $y=\pm\ell$3 gives the largest gap among the modes tested. In bridge interpretation, this establishes a direct analytic link between PDE plate theory and the engineering notion of torsional bridge safety.

2. GapBridge as graph-guided parametric data completion

In engineering design, GapBridge is proposed as a graph-guided, diffusion-based parametric data completion system that bridges incomplete user-provided design intent and a fully specified parametric CAD design (Zhou et al., 2024). The motivation is that engineering designs are rarely complete at the moment of ideation, while CAD parameters are interdependent and classical imputers usually treat missingness as a tabular prediction problem and ignore structural relationships among parts.

The pipeline has five conceptual stages: input a partial parametric design and an assembly graph; encode tabular parameters using a Feature Tokenizer and Positional Tokenizer inspired by TabCSDI; encode design structure with a Graph Neural Network over the assembly graph; fuse graph, feature, and positional embeddings with cross-attention; and use a diffusion denoising model to impute the missing parameters and generate a completed design. The method is therefore a multimodal conditional imputation model in which tabular encoders capture parameter values and position, the graph encoder captures design relationships, and the diffusion model generates missing values conditioned on all of the above.

The bicycle case study makes the structural role of the assembly graph explicit. The 221 bike features are grouped into 11 components such as seat tube, head tube, top tube, wheel, handlebar, and BB. Nodes correspond to components, and edges represent physical connection or interaction between components. Missing values are encoded as zeros in node features so the graph encoder preserves input dimensionality while still handling absent data. The paper compares a vanilla GCN encoder with GATv2, and reports that the attention-based graph encoder performs better.

The diffusion module follows a TabCSDI-style conditional denoising objective,

$y=\pm\ell$4

where $y=\pm\ell$5 is the conditioning signal formed from observed parameters plus graph/tabular embeddings. The task is framed as conditional completion,

$y=\pm\ell$6

and as estimation of the missing-given-observed conditional distribution,

$y=\pm\ell$7

Training uses a bicycle CAD dataset derived from BIKED with 4,500 bicycles augmented to 12,506 samples, a 90/10 train/test split, and 10% of features randomly masked. At inference, the diffusion sampler generates multiple possible completions, which can be ranked, explored, or rendered into final CAD outputs. This is why the system is described as an AI design copilot rather than a deterministic imputer.

Evaluation includes RMSE, Error Rate, Diversity Score, and KL divergence or distribution comparisons. In the reported generative comparison, Ours (GATv2) achieves RMSE 0.916, $y=\pm\ell$8 0.161, MAE 0.335, Error Rate 0.184, and Diversity 3.10; Ours (Vanilla GCN) achieves RMSE 0.924 and Diversity 2.16; and TabCSDI achieves RMSE 0.950, $y=\pm\ell$9 0.098, MAE 0.36, Error Rate 0.213, and Diversity 1.47. The bicycle study also reports that the model preserves dataset-like feature distributions, better matches conditional means than TabCSDI, handles strongly correlated features like stem angle well, still produces plausible values for weakly correlated features like water bottle on down tube, and can generate multiple coherent design variants for the same incomplete bicycle.

3. GapBridge as cyclic registration-synthesis in virtual IHC staining

In computational pathology, GapBridge is a cross-modal bridge between weakly paired H&E and IHC consecutive sections (Yuan et al., 1 Sep 2025). The problem is that adjacent histological slices are not perfectly aligned: they differ by a few microns in cutting position, can deform during sectioning or staining, and therefore exhibit local shape shifts, missing tissue fragments, or different cellular arrangements. That misalignment creates a domain gap that makes pixel-level supervision unreliable and can force the generator to learn geometry instead of the actual IHC staining pattern.

GapBridge is described as a cyclic alignment-synthesis framework with two main learnable parts: a Generator $u$0 that synthesizes a virtual IHC image $u$1 from the H&E source $u$2, and a Registration network $u$3, a VoxelMorph-style deformable registration model that estimates a deformation field $u$4 to warp the synthesized image toward the target IHC image $u$5: $u$6 Registration is not treated as post-processing. The registered output $u$7 is fed into the adversarial learning loop, so synthesis and registration continuously influence one another.

The adversarial objective is

$u$8

and the paper explicitly gives the registration gradient through the adversarial pathway,

$u$9

The alignment terms combine pixel, perceptual, and pyramid-scale constraints: $$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$0 while the registration regularizer is

$$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$1

The total registration objective is

$$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$2

with all default weights set to 1 in the experiments.

GapBridge is coupled to the other two pillars of PRINTER: prototype-driven content/style decoupling and deformation-aware adversarial learning. The paper states that prototypes solve “what stain pattern to render,” while GapBridge solves “where that pattern should land in tissue space.” Ablations isolate this role. The alignment network “outperforms the unaligned scheme in all evaluation metrics,” removing NMI hurts the deformation constraint, and removing adversarial learning weakens joint optimization of synthesis and registration. In the registration-quality table, Gen-Registration achieves SSIM 0.4877, PSNR 19.8522, LPIPS 0.2259, and FID 82.2434, while the final model (“Ours”) reports SSIM 0.4763, PSNR 19.8431, LPIPS 0.2315, and FID 79.2665. Experiments use the weakly paired adjacent-section datasets HIT (H&E–CD3 and H&E–PAX5), BCI (H&E–HER2), and MIST (H&E–ER), with all images resized to $$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$3 and training for 200 epochs.

4. Bridging observation, training, and utility gaps in generative modeling

Several recent works use closely related bridge mechanisms to handle missing views, train–test mismatch, or the utility gap between synthetic and real data. In GLADOS, the task is Generative Reconstruction from Disjoint Views, where the input images have zero visual overlap and thus cannot be aligned by standard geometric methods (Wilczynski et al., 8 May 2026). The framework operates through Generative Spatial Bridging, Robust Coarse 3D Reconstruction, and Iterative Context Expansion and Consistency Optimization, followed by Generative 3D Refinement via Anchored Grid Inpainting. Stage 1 synthesizes an intermediate “anchor” image $$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$4 so that $$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$5 contains adjacent pairs with non-empty overlap. Stage 2 uses Dust3R-like dense pointmap regression as a spatial low-pass filter to absorb local contradictions from the generated bridge. Stage 3 repeatedly renders, inpaints, predicts depth, aligns it to the current scene, and adds Gaussian primitives, while multiview consistency sampling reduces drift. On the two-view disjoint benchmark, GLADOS reports CLIP 23.559, FID 234.560, MET3R 0.032, GeCo$$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$6 0.012, GeCo$$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$7 0.045, GeCo$$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$8 0.032, Photo 0.097, and Rec. Fail 0. The paper also notes that augmenting baselines with the synthetic midpoint can propagate hallucinated geometry.

In GapDiff, the bridge is between learning and inference in diffusion-based 3D molecule generation (Liu et al., 2024). The paper argues that standard diffusion training conditions on true intermediate states, whereas inference repeatedly conditions on the model’s own imperfect predictions, creating exposure bias. GapDiff therefore probabilistically replaces the true intermediate state with a model-predicted pseudo state during training. If $$\mathbb E(u)=\int_\Omega \left(\frac12(\Delta u)^2+(1-\sigma)(u_{xy}^2-u_{xx}u_{yy})-fu\right)\,dx\,dy,$$9 is the true noisy state and $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$0 is the pseudo state obtained by predicting the clean molecule and re-noising it, the training condition $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$1 is chosen by

$$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$2

The loss remains a reconstruction objective,

$$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$3

but the conditioning distribution becomes closer to inference. The paper studies original OR-style, linear, and arc annealing schedules for $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$4, and reports that arc annealing with $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$5 is strongest. On CrossDocked2020, BindDM+Ours achieves Vina Score avg $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$6, med $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$7; Vina Min avg $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$8, med $$H^2_*=\Big\{w\in H^2(\Omega): w=0 \text{ on } \{0,\pi\}\times(-\ell,\ell)\Big\}.$$9; Vina Dock avg $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$0, med $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$1; High Affinity avg $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$2, med $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$3; and all-atom pair distance JSD 0.065.

The synthetic-data literature uses a different but conceptually related notion of gap. Gap Filler (GaFi) is a post-processing pipeline intended to reduce the utility gap between synthetic data and real data in classification (Lampis et al., 2023). Its three techniques are Dynamic Sample Filtering, Dynamic Dataset Recycle, and Expansion Trick. Dynamic Sample Filtering uses a real-data-trained classifier for label-consistency filtering and confidence-threshold filtering, with thresholds from $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$4 to $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$5. Dynamic Dataset Recycle regenerates the full synthetic dataset every $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$6 epochs. Expansion Trick samples latent noise from a wider distribution than used in training, increasing diversity but lowering per-image quality unless paired with filtering. The full GaFi pipeline performs checkpoint optimization, stddev optimization over $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$7 with step $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$8, threshold optimization over $G(x):=u(x,\ell)-u(x,-\ell),\qquad x\in(0,\pi),$9 with step $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$0, and final training with recycle period $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$1. The remaining gaps to real-data accuracy are reduced to 2.03% on Fashion-MNIST, 1.78% on CIFAR-10, and 3.99% on CIFAR-100.

5. Bridge mechanisms in code, graphs, sequences, and systems

A substantial part of the recent literature uses “bridge” language for intermediate structured representations that restore information lost by a naive formulation. CodeGRAG is a retrieval-augmented code generation framework that bridges the gap between natural language and programming language by converting code into a composed syntax graph built from AST, DFG, CFG, and read/write flow (Du et al., 2024). Given a code pool entry $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$2, the framework stores $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$3 in a knowledge base. A query embedding $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$4 is compared with candidate representations $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$5 using cosine distance,

$$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$6

Graph encoding is done with a GNN and attention-based message passing. On HumanEval-X with GPT-3.5-Turbo, the reported Pass@1 results include baseline: 57.93 C++, 71.95 Python; + Code-RAG: 60.37 C++, 72.56 Python; + CodeGRAG: 62.20 C++, 72.56 Python; + Cross-Lingual Code-RAG: 62.20 C++, 70.12 Python; and + Cross-Lingual CodeGRAG: 64.02 C++, 77.44 Python. The paper states that graph retrieval helps more than raw code retrieval, and that the graph captures shared program semantics beyond language-specific vocabulary.

PromptGCN addresses the information gaps created by subgraph sampling in lightweight GCN training (Ji et al., 2024). The graph is partitioned into subgraphs $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$7, and a shared prompt matrix

$$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$8

stores compact global information. For a node feature $$G^\infty:=\max_{x\in[0,\pi]} |u(x,\ell)-u(x,-\ell)|.$$9, the model selects the most relevant prompt through

$G^\infty$0

then fuses the prompt with the node feature, with concatenation reported as best. The same prompt parameters are updated and passed across sequentially trained subgraphs, so later subgraphs benefit from information learned earlier. On Flickr, PromptGCN improves accuracy by up to 5.48% over subgraph sampling baselines; on ogbl-collab, it improves the backbone by 2.02%; and on large graphs memory can be reduced by up to 28× relative to full-batch GCN.

BRIDGE studies datasets in which each node has both a personal event sequence $G^\infty$1 and a graph relation $G^\infty$2 (Chen et al., 29 Oct 2025). The model couples a sequence encoder and a graph message-passing module under a single task objective, with residual updates

$G^\infty$3

Its distinctive layer, TokenXAttn, performs token-level cross-attention across neighboring sequences: $G^\infty$4

$G^\infty$5

On Brightkite friendship prediction, Bridge-TokenXAttn reports MRR 92.9, H@1 90.7, H@3 94.2, H@5 95.4, and H@10 96.7. On Amazon fraud detection, Bridge variants outperform graph-only, temporal graph, and SBERT baselines, with Bridge-TokenXAttn best on Amazon-Electronics at Max F1 49.2 and PR-AUC 51.6.

At the systems level, “Bridging the Gap Between Domain-specific Frameworks and Multiple Hardware Devices” proposes a compiler-style bridge from domain-specific frameworks to heterogeneous hardware (Wen et al., 2024). The argument is that case-by-case porting has complexity $G^\infty$6, while a multi-layer abstraction pipeline reduces this to $G^\infty$7. Applications in Deep Learning, Classical Machine Learning, and Data Analysis are first mapped to domain-specific abstractions, then to a unified DAG-based abstraction, then to about 80 primitive operators, and finally to hardware backends including X86, ARM, RISC-V, IoT devices, and GPU. Reported speedups include 1.1x to 3.83x on X86 servers, 1.06x to 4.33x on ARM IoT devices, 1.25x to 3.72x on RISC-V IoT devices, and 1.93x on GPU.

6. Geometric gap coupling and the broader interpretation

A mathematically rigorous example of “bridging a gap” in the literal geometric sense appears in discontinuous Galerkin isogeometric analysis for diffusion problems on segmentations with non-matching interfaces (Hofer et al., 2015). The computational domain is decomposed into two physical subdomains plus a gap region,

$G^\infty$8

where the two gap faces satisfy

$G^\infty$9

The method does not solve inside $$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$0. Instead, it uses Taylor expansions along line segments connecting opposite points on $$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$1 and $$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$2 to approximate the missing interface fluxes. For example,

$$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$3

This produces a modified variational formulation posed only on $$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$4, together with a special dG IgA discretization and an error estimate in which the gap size $$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$5 explicitly controls the additional remainder term. If the gap satisfies $$f_\alpha(x,y)=K_\alpha e^{\alpha y}g(x),\qquad K_\alpha:=\frac{\alpha}{2\sinh(\alpha \ell)\int_0^\pi |g(x)|\,dx},$$6, the method quantifies how the convergence rate degrades or recovers as the gap shrinks relative to the mesh.

The collected usage across bridge-deck plate theory, CAD completion, pathology, disjoint-view reconstruction, diffusion-based molecule generation, retrieval-augmented code generation, lightweight GCNs, sequence-graph learning, heterogeneous compilation, and dG IgA suggests a common pattern: the “bridge” is an explicitly modeled intermediary that carries information across a discontinuity that would otherwise be ignored. A common misconception would be to treat GapBridge as a single standardized method. The literature instead presents domain-specific mechanisms: a scalar torsional indicator in a partially hinged plate (Berchio et al., 2017), a graph-guided diffusion imputer for incomplete CAD designs (Zhou et al., 2024), a cyclic deformable registration-synthesis loop for weakly paired histology (Yuan et al., 1 Sep 2025), prompt embeddings that transfer global context across sampled subgraphs (Ji et al., 2024), or synthetic midpoint views that convert zero-overlap inputs into weak-overlap reconstruction problems (Wilczynski et al., 8 May 2026). The limitations are similarly domain-specific: some conclusions are derived for idealized models, as in the rectangular, linearly elastic plate; some monotonicity claims are supported numerically rather than proved; some bridge signals can propagate hallucinated geometry; and some methods depend strongly on annealing schedules or structural priors. What unifies them is not a shared implementation, but a shared methodological stance: gaps are treated as first-class objects of modeling, optimization, or analysis rather than as nuisance artifacts.