Explore rigorous expositions on asymptotic analysis, optimization theory, and computational methods — crafted for seasoned mathematicians seeking deeper structural insights.
Spectral optimization sounds neat on paper: shift eigenvalues, smooth signals, boost cluster separability. But pick a graph that's a scale-free mess o...
I've spent more nights than I'd like chasing phantom solutions in inverse problems. You fit a model, the numbers look clean, but the result is junk. T...
So you've got an inverse problem on your hands. Maybe you're reconstructing an image from noisy projections, or estimating subsurface properties from ...
You've probably seen an MRI scan that looks impossibly clear, or watched a blurry photo get sharpened by an app. Those aren't magic—they're inverse pr...
You've built a beautiful forward model. Maxwell's equations, Navier-Stokes, acoustic wave propagation—the physics is clean, the discretization is stab...
You spend weeks polishing your inverse problem solver. The data's noisy, but your regularization prior is 'well-known'—TV norm, maybe L1 wavelet spars...
So you've got a point cloud, a distance matrix, maybe a graph. You want to find loops, holes, clusters that persist across scales—the usual persistenc...
You've got a point cloud that looks like a Swiss cheese—lots of holes, maybe a tunnel or two. Persistent homology is supposed to find those features. ...
Persistence landscapes are a staple in topological data analysis. But when a landscape looks too jagged or too flat, the first instinct is to tweak ei...
Witness complexes promised a cure for the curse of dimensionality. Instead of building a simplicial complex on every point, you pick a few landmarks a...
Persistent homology is a gift to data scientists who think topologically. It takes a point cloud, builds a simplicial complex at multiple scales, and ...
You're staring at a model that should work—but doesn't. The math is correct, the code compiles, and yet the predictions drift, the residuals scream, a...