Compare lineage appearance timing and its regulators on a precomputed `dynamo` vector-field `AnnData` using topography, graph potentials, Jacobian, and vector-calculus outputs. Use when checking whether one lineage appears earlier than its peers, curating fixed points, analyzing regulator pairs on a downstream-ready vector field, or adapting `400_tutorial_hsc_dynamo_megakaryocytes_appearance.ipynb`.
Compare lineage appearance timing and its regulators on a precomputed `dynamo` vector-field `AnnData` using topography, graph potentials, Jacobian, and vector-calculus outputs. Use when checking whether one lineage appears earlier than its peers, curating fixed points, analyzing regulator pairs on a downstream-ready vector field, or adapting `400_tutorial_hsc_dynamo_megakaryocytes_appearance.ipynb`.
Dynamo Lineage Appearance Analysis
Goal
Analyze whether one lineage appears earlier than related lineages in a precomputed dynamo dataset by combining fixed-point curation, transition-graph potentials, regulator-pair Jacobian analysis, and vector-calculus quantities such as speed, divergence, acceleration, and curvature.
Quick Workflow
Inspect whether the AnnData already contains the vector-field and transition-graph outputs this workflow depends on.
Choose the stage or stages you actually need: topography curation, appearance-order comparison, regulator-pair Jacobian, or vector-calculus follow-up.
Use build_graph(...), div(...), and potential(...) on the relevant transition matrix instead of inferring lineage order from plots alone.
Run dyn.vf.jacobian(...) on the regulator and effector genes of interest before interpreting lineage-specific interactions.
Compute speed, divergence, acceleration, and curvature in the same basis you want to compare across cells.
Validate output keys and return types before treating the analysis as complete.
Interface Summary
dyn.sample_data.hematopoiesis(url='https://figshare.com/ndownloader/files/47439635', filename='hematopoiesis.h5ad') loads the worked example used in this notebook family.
dyn.vf.topography(adata, basis='umap', layer=None, X=None, dims=None, n=25, VecFld=None, show_progress=False, **kwargs) maps fixed points onto the current vector field when they are missing or need remapping.
dyn.pl.topography(..., basis='umap', fps_basis='umap', terms=['streamline', 'fixed_points'], quiver_source='raw', fate='both', n=25, ...) is the main visualization entrypoint.
build_graph(adj_mat), div(g), and potential(g, div_neg=None) are the graph-operator primitives behind the notebook's appearance-order comparison.
dyn.vf.jacobian(..., sampling=None, sample_ncells=1000, basis='pca', method='analytical') computes cell-wise Jacobians from the reconstructed vector field.
dyn.pl.jacobian(..., basis='umap', jkey='jacobian', j_basis='pca', layer='M_s', cmap='bwr') visualizes selected Jacobian entries on an embedding.
dyn.vf.speed(..., method='analytical'), dyn.vf.divergence(..., sampling=None, basis='pca', method='analytical'), dyn.vf.acceleration(..., basis='umap', method='analytical'), and dyn.vf.curvature(..., basis='pca', formula=2, method='analytical') provide the main dynamical quantities used in the notebook.
Read references/source-grounding.md before documenting narrower parameter behavior than the current source supports.
Stage Selection
Use the fixed-point stage when the task is to inspect or curate candidate attractors and saddles before downstream interpretation.
Use the graph-potential stage when the task is to compare appearance timing across related lineages with cosine_transition_matrix or fp_transition_rate.
Use the Jacobian stage when the task is to test a specific regulator pair, not when the user only wants a lineage-order figure.
Use the vector-calculus stage when the task is to compare speed_pca, divergence_pca, acceleration_pca, or curvature_pca across cell states.
Keep basis='umap' for notebook-style plotting and basis='pca' for Jacobian, divergence, and other quantities that rely on the PCA vector field.
Read references/stage-selection.md before choosing non-default method, formula, fate, terms, or worked-example gene and lineage labels.
Input Contract
Expect a processed AnnData that already contains a reconstructed vector field, not raw counts alone.
Expect adata.uns['VecFld_umap'] and usually adata.uns['VecFld_pca'].
Expect adata.obsm['X_umap'] for plotting and adata.uns['PCs'] for PCA-space back-projection.
Expect adata.obsp['cosine_transition_matrix'] for the notebook's first potential comparison.
Expect adata.obsp['fp_transition_rate'] if you want the Fokker-Planck-style potential branch.
Expect adata.var.use_for_dynamics and adata.var.use_for_pca when using Jacobian or PCA-basis vector calculus.
Treat notebook-specific obs['cell_type'] labels such as HSC, MEP-like, Meg, Ery, and Bas, and genes such as FLI1 and KLF1, as worked-example defaults rather than hard requirements.
If the user only has raw counts or only wants upstream preprocessing or velocity fitting, route to a more appropriate skill instead of forcing this downstream analysis workflow.
Minimal Execution Patterns
For the worked example load and appearance-order comparison:
import dynamo as dyn
from dynamo.tools.graph_operators import build_graph, div, potential
adata = dyn.sample_data.hematopoiesis()
g = build_graph(adata.obsp["cosine_transition_matrix"])
cosine_div = div(g)
adata.obs["cosine_potential"] = potential(g, -cosine_div)
g_fp = build_graph(adata.obsp["fp_transition_rate"])
fp_div = div(g_fp)
adata.obs["potential_fp"] = potential(g_fp, fp_div)
adata.obs["pseudotime_fp"] = -adata.obs["potential_fp"]
For fixed-point remapping or manual curation:
dyn.vf.topography(adata, n=750, basis="umap")
Xss = adata.uns["VecFld_umap"]["Xss"]
ftype = adata.uns["VecFld_umap"]["ftype"]
# choose the subset after inspecting the remapped fixed points for this dataset
keep_idx = [...]
adata.uns["VecFld_umap"]["Xss"] = Xss[keep_idx]
adata.uns["VecFld_umap"]["ftype"] = ftype[keep_idx]
dyn.pl.topography(
adata,
basis="umap",
fps_basis="umap",
color=["cell_type"],
streamline_alpha=0.9,
save_show_or_return="return",
)
For regulator-pair Jacobian analysis and notebook-style plotting:
For a bounded worked-example smoke check, use the command recorded in assets/acceptance.json.
Validation
Before analysis, check these items:
VecFld_umap exists in adata.uns
X_umap exists in adata.obsm
cosine_transition_matrix exists in adata.obsp
fp_transition_rate exists in adata.obsp if the Fokker-Planck branch is needed
After graph-potential comparison, check these items:
cosine_potential or your renamed cosine-potential column exists in adata.obs
potential_fp exists in adata.obs when you run the fp_transition_rate branch
pseudotime_fp exists and is the sign-flipped version used for notebook-style time interpretation
After Jacobian analysis, check these items:
jacobian_pca exists in adata.uns
adata.uns['jacobian_pca'] includes jacobian, cell_idx, regulators, and effectors
dyn.pl.jacobian(..., save_show_or_return='return') returns a GridSpec
After vector-calculus analysis, check these items:
speed_pca exists in adata.obs
divergence_pca exists in adata.obs
acceleration_pca exists in adata.obs
curvature_pca exists in adata.obs
acceleration and curvature layers are created for the pca branch
After topography plotting, check these items:
adata.uns['VecFld_umap']['Xss'] and adata.uns['VecFld_umap']['ftype'] still align after any manual curation
dyn.pl.topography(..., save_show_or_return='return') returns an Axes
Constraints
Do not treat the notebook's fixed-point indices as reusable defaults. They depend on the exact remapped topography, n, and current vector-field fit.
Do not use this skill as a raw-data preprocessing recipe. It assumes a downstream-ready dynamo object with vector-field outputs already present.
Do not recommend curvature(..., formula=1) as a normal branch in the current runtime. Source-grounded reviewer execution hit a runtime failure when that branch tried to write a missing matrix into obsm.
Do not recommend dyn.pl.topography(..., quiver_source='reconstructed') as a normal branch in the current runtime. Reviewer execution hit an ImportError in that branch.
Prefer the default topography terms=['streamline', 'fixed_points'] unless the user explicitly needs additional overlays and you have checked the current source behavior.
Keep notebook cosmetics such as dyn.pl.style(font_path='Arial') out of the reusable workflow.
Resource Map
Read references/stage-selection.md when choosing between topography, appearance-order, Jacobian, and vector-calculus stages.
Read references/worked-example.md when the user specifically wants the HSC / MEP-like / Meg / Ery / Bas and FLI1 / KLF1 setup from the notebook.
Read references/source-notebook-map.md to trace notebook sections into this reusable skill.
Read references/source-grounding.md for inspected signatures, source-level branch behavior, empirical checks, and known runtime traps.
Read references/compatibility.md when notebook prose, parameter names, or current runtime behavior diverge.
Use assets/acceptance.json for the bounded worked-example smoke path used by local validation.
