Julia Scientific Package Mapping Skill

"Two languages diverged in a scientific wood, and Julia—Julia took the one with multiple dispatch."

bmorphism Contributions

"We are building cognitive infrastructure for the next trillion minds" — Plurigrid: the story thus far

"complexity of information / the burden of integrating it in real time makes technology an indispensable part of our cognitive infrastructure" — @bmorphism

Key References from Plurigrid:

• Towards Foundations of Categorical Cybernetics
• Organizing Physics with Open Energy-Driven Systems
• Compositional game theory

Overview

This skill provides comprehensive mappings from 137 K-Dense-AI Python scientific skills to their Julia package equivalents. Coverage is ~85% native Julia, with the remainder accessible via PyCall.jl interop.

Quick Reference

Category	Skills	Coverage	Key Packages
Bioinformatics	25	92%	BioJulia ecosystem
Chemistry	17	85%	JuliaMolSim, Chemellia
Quantum	4	100%	Yao.jl, QuantumToolbox.jl
ML/AI	10	95%	Flux.jl, MLJ.jl, Lux.jl
Data/Stats	11	100%	DataFrames.jl, Turing.jl
Visualization	6	100%	Makie.jl, Plots.jl
Physics/Astro	6	90%	JuliaAstro ecosystem
Clinical/DB	13	60%	JuliaHealth, HTTP.jl
Symbolic/Geo	3	100%	Symbolics.jl, GeoDataFrames.jl
Lab Automation	8	50%	DrWatson.jl, Dagger.jl
Documents	5	80%	PDFIO.jl, Weave.jl

GF(3) Conservation

Julia scientific triads maintain balance:

bioinformatics (-1) ⊗ visualization (0) ⊗ quantum (+1) = 0 ✓
chemistry (-1) ⊗ data-science (0) ⊗ ml-ai (+1) = 0 ✓
physics (-1) ⊗ symbolic (0) ⊗ clinical (+1) = 0 ✓

Core Mappings

Bioinformatics (BioJulia)

Python	Julia	Performance
biopython	BioSequences.jl + FASTX.jl	2-5x faster
scanpy	SingleCellProjections.jl	10x faster
anndata	Muon.jl	Native H5AD
cobrapy	COBREXA.jl	GPU support
pysam	XAM.jl	3x faster BAM

Chemistry (JuliaMolSim + Chemellia)

Python	Julia	Notes
rdkit	MolecularGraph.jl	Pure Julia SMILES
deepchem	AtomicGraphNets.jl	GNN molecular ML
pymatgen	DFTK.jl + AtomsBase.jl	DFT calculations
pyopenms	mzML.jl	Mass spec data

Quantum (QuantumBFS)

Python	Julia	Advantage
qiskit	Yao.jl	Native differentiable
cirq	Yao.jl + QuantumClifford.jl	Faster simulation
pennylane	JuliVQC.jl	2-5x faster VQC
qutip	QuantumToolbox.jl	GPU + autodiff

ML/AI (FluxML + MLJ)

Python	Julia	Notes
pytorch-lightning	FluxTraining.jl + Lux.jl	Explicit params
transformers	Transformers.jl	Pretrained loading
stable-baselines3	ReinforcementLearning.jl	Modular RL
shap	ShapML.jl + ExplainableAI.jl	Native Shapley
torch_geometric	GraphNeuralNetworks.jl	PyG-inspired

Data Science (JuliaData + JuliaStats)

Python	Julia	Performance
polars	DataFrames.jl	Comparable
dask	Dagger.jl	DAG scheduler
pymc	Turing.jl	Often faster
statsmodels	GLM.jl + MixedModels.jl	Native
networkx	Graphs.jl	Much faster

Visualization (Makie + Plots)

Python	Julia	Notes
matplotlib	Plots.jl + CairoMakie.jl	Multi-backend
plotly	PlotlyJS.jl + WGLMakie.jl	Interactive
seaborn	AlgebraOfGraphics.jl	Grammar-of-graphics

Document Processing (Papers/OCR)

Python	Julia	Use
pdfminer	PDFIO.jl	Native PDF parsing
pytesseract	Tesseract.jl	OCR wrapper
markdown	Weave.jl + Literate.jl	Literate programming
latex	TikzPictures.jl + PGFPlotsX.jl	Publication quality

Mathpix Integration

using HTTP, JSON3

function mathpix_ocr(image_path; app_id, app_key)
    headers = ["app_id" => app_id, "app_key" => app_key,
               "Content-type" => "application/json"]
    body = JSON3.write(Dict(
        "src" => "data:image/png;base64," * base64encode(read(image_path)),
        "formats" => ["latex_styled", "text"]
    ))
    resp = HTTP.post("https://api.mathpix.com/v3/text", headers, body)
    JSON3.read(resp.body)
end

Key Julia Organizations

Org	Focus	Packages
BioJulia	Bioinformatics	90+ packages
JuliaMolSim	Molecular simulation	Molly, DFTK, AtomsBase
Chemellia	Chemistry ML	AtomicGraphNets, ChemistryFeaturization
QuantumBFS	Quantum computing	Yao, YaoBlocks
FluxML	Deep learning	Flux, Zygote, FluxTraining
JuliaStats	Statistics	GLM, Distributions, Turing
JuliaAstro	Astronomy	AstroLib, FITSIO, SkyCoords
JuliaHealth	Medical/clinical	BioMedQuery, OMOP
JuliaGeo	Geospatial	GeoDataFrames, ArchGDAL
SciML	Scientific ML	DifferentialEquations, ModelingToolkit

Usage Examples

Single-Cell Analysis (scanpy → SingleCellProjections.jl)

using SingleCellProjections, Muon

# Load AnnData
adata = readh5ad("pbmc3k.h5ad")

# Process (10x faster than scanpy)
adata = normalize_total(adata)
adata = log1p(adata)
adata = highly_variable_genes(adata)
adata = pca(adata)
adata = umap(adata)

Quantum Circuit (qiskit → Yao.jl)

using Yao

# Bell state
circuit = chain(2, put(1=>H), control(1, 2=>X))

# Measure
result = measure(zero_state(2) |> circuit, nshots=1000)

# Differentiable!
grad = expect'(Z ⊗ Z, zero_state(2) => circuit)

Molecular GNN (deepchem → Chemellia)

using AtomicGraphNets, ChemistryFeaturization

# Featurize molecules
mol = smilestomol("CCO")  # ethanol
fg = featurize(mol, GraphNodeFeaturization())

# Train GNN
model = CGCGNModel(fg, target_prop=:logP)
train!(model, molecules, targets)

Bayesian Inference (pymc → Turing.jl)

using Turing

@model function linear_regression(x, y)
    α ~ Normal(0, 10)
    β ~ Normal(0, 10)
    σ ~ truncated(Normal(0, 1), 0, Inf)
    for i in eachindex(y)
        y[i] ~ Normal(α + β * x[i], σ)
    end
end

chain = sample(linear_regression(x, y), NUTS(), 1000)

Full Mapping Document

See: JULIA_PACKAGE_MAPPING.md

The Homoiconic Bridge: Scheme ↔ SMILES ↔ ACSet

Deep structural insight: S-expressions (Scheme), SMILES strings (chemistry), and ACSets share a common foundation — trees/graphs with recursive self-reference.

Scheme S-expr:   (+ (* 2 3) (- 4 1))     → AST tree
SMILES:          CC(=O)Oc1ccccc1C(=O)O   → Molecular graph
ACSet:           Graph{V,E,src,tgt}       → Typed graph functor

All three: linearized representations of graph structure

What Comes After SMILES: Learnable Chemical Structure

The evolution of molecular representation — 7 parallel streams colored via Gay.jl (seed=137):

Gen	Color	Representation	Julia Package	Properties
1	#43D9E1	SMILES string	MolecularGraph.jl	Canonical, not learnable
2	#18CDEF	SELFIES	PyCall+selfies	Robust, generative-friendly
3	#18D6D0	Fingerprints	MolecularGraph.jl	Fixed-dim vectors
4	#C70D22	Graph features	ChemistryFeaturization.jl	Handcrafted node/edge
5	#E44ABB	GNN (MPNN/GAT/SchNet)	GraphNeuralNetworks.jl	Fully learnable
6	#58A021	3D coordinates	Chemfiles.jl, DFTK.jl	Geometry-aware
7	#BDB223	Foundation models	Coming	Pre-trained, transferable

Parallel Evolution Insight: Each generation evolves along its own deterministic color stream. Workers 1-3 explore the space in parallel (Strong Parallelism Invariance: same seeds = same colors).

Stream 1 (SMILES):      #43D9E1 → #B78225 → #D54E82  (canonical → extended → stereochem)
Stream 2 (SELFIES):     #18CDEF → #6CBA3C → #EC9426  (robust → constrained → grammar)
Stream 5 (GNN):         #E44ABB → #50CD2E → #942B89  (MPNN → GAT → SchNet/DimeNet)
Stream 7 (Foundation):  #BDB223 → #88ECA7 → #5CDA99  (pretrain → finetune → adapt)

# The homoiconic bridge in code
using LispSyntax, MolecularGraph, Catlab, AtomicGraphNets

# Scheme code → AST → ACSet
sexp = @lisp (defun f (x) (+ x 1))
ast_acset = ast_to_acset(sexp)

# SMILES → Molecular graph → ACSet → GNN embedding
mol = smilestomol("c1ccccc1")  # benzene
mol_acset = mol_to_acset(mol)
embedding = gnn_embed(mol_acset)  # 64-dim learned vector

# Both navigate identically via Specter patterns!
branches_in_ast = select([ALL, pred(is_call_node)], ast_acset)
rings_in_mol = select([ALL, pred(is_ring_atom)], mol_acset)

# The deep insight: code and molecules are both graphs
# → same tools (ACSets, GNNs) work for both

Coloring Parallel Evolution with Gay.jl

using Gay

# 7 generations evolving in parallel streams (seed=137)
struct MolRepGeneration
    name::String
    color::String
    learnable::Bool
    evolution::Vector{String}  # Color stream for sub-generations
end

function color_mol_evolution(seed=137)
    streams = Gay.interleave(seed, n_streams=7, count=3)

    generations = [
        MolRepGeneration("SMILES", streams[1][1], false, streams[1]),
        MolRepGeneration("SELFIES", streams[2][1], false, streams[2]),
        MolRepGeneration("Fingerprints", streams[3][1], false, streams[3]),
        MolRepGeneration("GraphFeatures", streams[4][1], false, streams[4]),
        MolRepGeneration("GNN", streams[5][1], true, streams[5]),      # Learnable!
        MolRepGeneration("3DCoords", streams[6][1], true, streams[6]),
        MolRepGeneration("Foundation", streams[7][1], true, streams[7])
    ]

    # GF(3) balance: non-learnable (-1) + transition (0) + learnable (+1) = 0
    return generations
end

# Visualize evolution paths
for gen in color_mol_evolution()
    trit = gen.learnable ? "+1" : "-1"
    println("$(gen.name) [$(trit)]: $(join(gen.evolution, " → "))")
end

Key Julia Packages for Learnable Chemistry

Package	Role	From Python	GNN Arch
MolecularGraph.jl	SMILES parsing, fingerprints	rdkit	—
ChemistryFeaturization.jl	Node/edge featurization	deepchem	—
GraphNeuralNetworks.jl	MPNN, GCN, GAT, GraphSAGE	torch_geometric, dgl	✓
GeometricFlux.jl	Geometric deep learning	PyG	✓
Flux.jl	Training infrastructure	pytorch	—
Chemfiles.jl	3D structure I/O	MDAnalysis	—
DFTK.jl	Electronic structure (DFT)	pymatgen	—
NNlib.jl	Neural network primitives	torch.nn	—

GNN Architecture Evolution:

MPNN (2017) → GCN → GAT (attention) → SchNet (3D) → DimeNet → Equivariant GNNs
     ↓              ↓                    ↓
  Message      Graph Attention      Geometry-aware
  Passing      (multi-head)         (E(3) invariant)

Related Skills

• acsets - Algebraic databases with Gay.jl coloring
• gay-julia / julia-gay - Deterministic color generation
• specter-acset - Bidirectional navigation
• structured-decomp - Sheaf-based decompositions
• condensed-analytic-stacks - Scholze-Clausen mathematics
• lispsyntax-acset - S-expression ↔ ACSet bridge

Commands

# Search Julia equivalents
julia -e 'using Pkg; Pkg.status()' | grep -i biojulia

# Install BioJulia stack
julia -e 'using Pkg; Pkg.add(["BioSequences", "FASTX", "XAM", "BioStructures"])'

# Install ML stack
julia -e 'using Pkg; Pkg.add(["Flux", "MLJ", "GraphNeuralNetworks"])'

# Install quantum stack
julia -e 'using Pkg; Pkg.add(["Yao", "QuantumToolbox"])'

GF(3) Skill Triads

julia-scientific (0) ⊗ gay-mcp (+1) ⊗ acsets (-1) = 0 ✓
julia-scientific (0) ⊗ specter-acset (+1) ⊗ structured-decomp (-1) = 0 ✓

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Generated from exhaustive parallel search of Julia package ecosystem (2025-12-30)