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Algorithms

Computational Chemistry
Protein folding energy landscape funnel showing high-energy unfolded states converging to the native state

How to Fold Graciously: The Levinthal Paradox

A perspective paper defining the Grand Challenge of protein folding: distinguishing kinetic pathways from thermodynamic …...

Computational Chemistry
Log-scale plot showing exponential growth of alkane isomer counts from C1 to C40

The Number of Isomeric Hydrocarbons of the Methane Series

Henze and Blair's 1931 JACS paper deriving exact recursive formulas for counting alkane isomers up to C₄₀.

Scientific Computing
Comparison of exponential sampling methods showing histograms from both inverse transform and von Neumann methods overlaid with the theoretical exponential distribution

Exponential Random Number Generation: Two Classic Algorithms Compared

Compare inverse transform sampling and von Neumann's rejection method for exponential random numbers with Python …

Computational Chemistry

Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling

Torrie and Valleau's 1977 paper introducing Umbrella Sampling, an importance sampling technique for Monte Carlo …...

Natural Language Processing
Huffman Tree visualization for the input 'beep boop beer!' showing internal nodes with frequency counts and leaf nodes with characters

Vectorizing the Tree: High-Performance Word2Vec in Pure PyTorch

Production-grade Word2Vec in PyTorch with vectorized Hierarchical Softmax, Negative Sampling, and torch.compile support....

Scientific Computing
Molecular structure alignment showing protein conformations and RMSD calculation

Kabsch Algorithm: NumPy, PyTorch, TensorFlow, and JAX

Learn about the Kabsch algorithm for optimal point alignment with implementations in NumPy, PyTorch, TensorFlow, and JAX …

Scientific Computing
Comparison of IQCRNN (Our Method) vs standard Policy Gradient showing training curves, phase portraits, and state trajectories for control tasks

IQCRNN: Certified Stability for Neural Networks

PyTorch IQCRNN enforcing stability guarantees on RNNs via Integral Quadratic Constraints and semidefinite programming....

Natural Language Processing
Information Quality Ratio plot showing statistical dependencies decay as window size increases

Analytical Solution to Word2Vec Softmax & Corpus Bias Probing

Analytical derivation of Word2Vec's softmax objective factorization and a new framework for detecting semantic bias in …...

Machine Learning Fundamentals
Vintage slot machine with multiple arms representing the multi-arm bandit problem in machine learning

A Framework for Multi-Arm Bandit Problems

Framework for understanding multi-arm bandit algorithms through five dimensions. Covers exploration vs exploitation and …

Machine Learning Fundamentals
Various symmetric and repetitive patterns generated by Compositional Pattern Producing Networks

HyperNEAT: Scaling Neuroevolution with Geometric Patterns

How HyperNEAT uses indirect encoding and geometric patterns to evolve large-scale neural networks with biological …

Machine Learning Fundamentals
NEAT genome encoding diagram showing node genes and connection genes with innovation numbers

NEAT: Evolving Neural Network Topologies

Learn about NEAT's approach to evolving neural networks: automatic topology design, historical markings, and speciation …

Machine Learning Fundamentals
Diagram showing the three main types of machine learning: supervised, unsupervised, and reinforcement learning

Breaking Down Machine Learning for the Average Person

Discover how machine learning actually works through three fundamental approaches, explained with everyday examples you …