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Cold Days Still Belong in a Warming Climate
A warmer climate can still produce a freezing morning. The question is how the range and frequency of temperatures change, rather than whether cold weather h...
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Advanced Sequential Change-Point Detection for Univariate Models
Derive the Gaussian CUSUM from likelihood ratios, distinguish alarm time from change location, and run a complete reproducible monitoring example.
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Paths of Combinatorics and Probability
Dive into the intersection of combinatorics and probability, exploring how these fields work together to solve problems in mathematics, data science, and bey...
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Ethics of AI and Sensing in Older-Adult Care
Ethical technology for older adults requires consent, privacy, proportional monitoring, accessibility, contestability, and attention to decision-making capac...
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Combinatorics with Python: Count Before You Enumerate
Python can enumerate combinatorial objects, but combinatorics is primarily about counting without enumeration and understanding computational explosion.
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Ergodicity: Time Averages, Invariant Sets, and Mixing
Ergodicity is a precise property of a measure-preserving dynamical system. It is not merely a temporary regime, nor is chaos sufficient for ergodicity.
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The Pigeonhole Principle: Counting Forces Existence
The pigeonhole principle turns finite counting constraints into existence proofs. Its power lies in choosing the right objects and boxes.
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Spectral Clustering: The Graph Is the Model
Spectral clustering converts a similarity graph into an eigenvector embedding and then clusters that embedding. The graph construction is the model.
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Clustering Is a Model of Similarity
Clustering does not discover a unique hidden partition of data. It produces groups relative to a representation, similarity measure, algorithm, and scale.
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Topological Data Analysis: Shape Across Scales
Topological data analysis summarizes multiscale shape through constructions such as persistent homology and Mapper, but topology does not make high-dimension...
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