intermittent thoughts
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When you shouldn't trust einsum
There's no substitute for looking at exactly what your code is doing.
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Conditions for the existence of approximations to the constant sheaf
A result I never got around to publishing
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Representational limitations of knowledge graph embeddings
Turns out linear models just aren't very expressive.
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Something perplexing about UMAP
n_neighbors may not mean what you think it does.
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Sheaves and Probability, Part 3
A topological perspective on message passing.
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Sheaves and Probability, Part 2
A first try at using sheaves to solve marginalization problems in graphical models.
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Sheaves and Probability, Part 1
How to represent some structures from statistics and probability using cellular sheaves and cosheaves.
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Hybrid Systems and Homotopy Theory
Doing topology and engineering at the same time can be tricky.
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Homology via Matrix Reduction 2: The Long Exact Sequence of a Pair
Algebraic topology is really just matrix algorithms.
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Homology via Matrix Reduction
Algebraic topology is just matrix algorithms.
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Buridan's Principle
Making decisions is actually impossible.
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Hodge theory and persistent homology
Connections between two sorts of approximate topology through the singular value decomposition.
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Flow-coloring duality
A discussion of an interesting interplay between algebraic topology and the combinatorics of graphs.
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UMAP
My attempt to understand a new algorithm for low-dimensional visualization of point cloud data.
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A topologist's proof of the matrix-tree theorem
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Spectral Sheaves
A summary of my thesis proposal.
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Mapper and cosheaves
Some notes on a couple of papers fleshing out the connections between Mapper, Reeb graphs, and cosheaves.
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Some less-than-intuitive examples with cellular sheaves
A few weird things I discovered while building intuition for cellular sheaves.
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