| Mathematics | |
|---|---|
| Numerical analysis and scientific computing | A 2012 thesis studied the stability of space–time discretizations for parabolic equations. Later work combined wavelets in time with multigrid in space and developed numerical methods for computing the second moments of stochastic differential equations. 2012 thesis · Corrections · Parallel C++ implementation · Stochastic ODEs |
| Inverse problems and regularization | A 2015 paper uses interpolation spaces to characterize the convergence rates of Tikhonov regularization and Landweber iteration. Paper · Corrections |
| Optimization, mean-field games, and optimal transport | An augmented Lagrangian solver computes equilibria in mean-field games with diffusion. Later notes explore how individual choices relate to collective outcomes and optimal transport. Solver · Mathematical notes |
| Probability, statistics, and causal inference | Study notes cover Bayesian regression, Gaussian processes, and Monte Carlo methods. Applied studies examine how confounding affects estimates of booking cancellations and how to compare conversion rates in an A/B test. Probabilistic AI · Booking simulation · Conversion analysis |
| Public transport and operations research | A study of Taiwanese bus services matched GPS traces to roads and reconstructed timetables. A later Manhattan study used taxi-trip records to estimate how many dynamically routed minibuses could serve the same demand. Taiwan transit · Manhattan study |
| Mathematical finance and decision analysis | A Black–Scholes derivation, an interactive net-present-value decision tree, and exercises in bond valuation, duration, and currency risk. Black–Scholes notes · Decision tree · Portfolio exercises |
| Quantum information and algorithms | Python and Q# exercises reproduce Bell-state correlations, quantum teleportation, Simon’s algorithm, and period finding. Code and exercises |
| Biology and chemistry | |
|---|---|
| Computational neuroscience and topology | Graphs of the C. elegans connectome and a rat cortical microcircuit support experiments on how removing connections changes cliques and the topological features measured by Betti numbers. Connectome experiments |
| Cancer genomics and single-cell transcriptomics | A breast-cancer subtype classifier trained on bulk TCGA gene-expression data was applied to individual tumour cells. PAM50 study |
| Neurodegeneration and brain transcriptomics | A joint course project compared methods for estimating cell-type proportions in mixed brain tissue. Subsequent ALS work examined fibroblast activation, APOE expression, and genotypes. Deconvolution project · Source · ALS analysis · Source · Genotype analysis |
| Bioinformatics and cell signalling | Projects cover sequence alignment, genome assembly, phylogenetics, RNA folding, and case–control variant discovery. Gene-expression analyses examine how human lung cells respond to infection, signalling molecules, and small-molecule inhibitors. Bioinformatics studies · Team project · Fibroblast response |
| Cell biophysics and synthetic biology | A kinetic model developed with L. Kapinos and R. Y. H. Lim predicts how strongly cargo concentrates in the nucleus relative to the cytoplasm. A separate project with H. Hu simulated genetic circuits for E. coli to play the game of 15 sticks. Nuclear transport · Report · Source · Genetic-circuit report · Source |
| Public-health informatics | Counter-Resistance is a platform proposal for sharing antimicrobial-resistance data across research, healthcare, and agriculture while preserving the origin of each contribution. Counter-Resistance |
| NMR spectroscopy and molecular machine learning | The 2025 ETH Zürich MSc thesis explored how a language model can rank structures from NMR annotations. Subsequent models learn a shared representation of molecular graphs and experimental peak lists. Integrations of published models support both structure prediction from peaks and prediction of atom-specific ¹H and ¹³C shifts from 3D coordinates. Thesis and predictions · NMRPeak integration · NMRNet++ integration |
| Cheminformatics and chemical data | One molecular graph can have many valid SMILES strings. GRIMACE determines which tokens can follow a given prefix for a specified molecule. Related work uses graph decomposition to enumerate those strings and collects experimental measurements from ChemRxiv papers for testing structure-prediction methods. GRIMACE · Code · Graph decomposition · ChemRxiv data |
| Molecular dynamics and quantum chemistry | A simulation pipeline samples molecular conformations in explicit solvent, clusters the conformers, and uses density functional theory to calculate NMR shieldings and spin–spin couplings. Simulation and calculations |
| Software systems | |
|---|---|
| Scientific platforms and model deployment | A common API connects a browser workspace to independently operated NMR methods. Each provider supplies its scientific code. Shared tools handle jobs and save finished results for delivery when the API is available again. Provider tools · SECS integration |
| Smart contracts, payments, and blockchain indexing | In dapp32, a contract describes the actions that a generic viewer can present. Examples include bicycle ownership and workshop permissions, escrow, and payment channels with signed vouchers. Work on the rindexer fork addresses PostgreSQL recovery when a chain reorganization replaces previously indexed blocks. dapp32 · Source · Payment protocol documentation · Source · Indexer recovery |
| AI agents and local inference | Projects include a GPT-3 explainer for Python errors, web retrieval for a custom GPT, inbound email for agents, and support for custom tool calls in local model inference. Python error explainer · Web crawler · Local inference change |
| Linux, security, and reliability | Tools isolate coding agents in disposable containers, inspect Linux user and group ID mappings, and monitor host and container health. A companion collection documents practices for maintaining software over time. Agent sandbox · Container tools · Host monitoring · Development practices |
| Misc | |
|---|---|
| Cycling, cartography, and navigation | A route generator finds long rides with little backtracking in Nairobi’s Karura and Sigiria forests. An Android app detects departures from a GPX route, and an OpenStreetMap editor extension aligns reference images for tracing. Forest routes · Source · Android navigation · Map editor extension |
| Mechanical design and parametric CAD | Models of metric threaded fasteners and a T25 socket use drawings and reference meshes to check dimensions before STEP or STL export. Interactive CAD viewer · Source |
| Writing systems, sound, and human–computer interaction | Experiments test whether the shape of a Chinese character predicts its Mandarin tone, whether a laptop microphone can recognize digits traced on the chassis, and how character frequencies sound when mapped to a melody. Hanzi classifier · Acoustic input · Text sonification |
| Computer vision and federated learning | A remote-sensing exercise identifies rooftops in satellite images using OpenStreetMap labels. A separate experiment trains a model across two clients using federated averaging. Roof segmentation · Federated learning |
| Photography, consent, and digital licensing | PhotoVeto lets people specify how photographs may be used and share those terms through a QR code. PhotoVeto |
| Teaching, scientific writing, and translation | Materials include differential-equation exercises, Octave labs, GRE mathematics sessions, and workshops on scientific writing. A German-to-English translation of Frobenius’s 1895 paper on Sylow’s theorem preserves the original pagination. Teaching materials · Frobenius translation |