Julia Scientific

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

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)

Chemistry (JuliaMolSim + Chemellia)

Quantum (QuantumBFS)

ML/AI (FluxML + MLJ)

Data Science (JuliaData + JuliaStats)

Visualization (Makie + Plots)

Document Processing (Papers/OCR)

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

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):

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

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 ✓

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

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 3. Variations on an Arithmetic Theme

Concepts: generic arithmetic, coercion, symbolic, numeric

GF(3) Balanced Triad

julia-scientific (+) + SDF.Ch3 (○) + [balancer] (−) = 0

Skill Trit: 1 (PLUS - generation)

Secondary Chapters

• Ch9: Generic Procedures
• Ch8: Degeneracy
• Ch7: Propagators
• Ch4: Pattern Matching
• Ch2: Domain-Specific Languages
• Ch10: Adventure Game Example

Connection Pattern

Generic arithmetic crosses type boundaries. This skill handles heterogeneous data.