Markov chains are mathematical systems that model transitions between different states with associated probabilities, represented through transition matrices or diagrams. The concept finds practical applications in various fields, from weather prediction to Google's PageRank algorithm, with the ability to simulate real-world phenomena by incorporating probabilistic state transitions.
TigerBeetle rebuilt their documentation site from scratch, moving away from Docusaurus to achieve better performance, simplicity, and integration with their zero-dependency philosophy. The new implementation uses Zig and Pandoc, resulting in a 10x reduction in footprint while maintaining functionality and adding features like integrated search and offline capabilities.
Geometric Algebra provides a unified mathematical framework for understanding vector spaces and geometric transformations across multiple dimensions. The framework encompasses vectors, bivectors, and higher-dimensional elements, with practical applications in 2D and 3D rotations. Complex numbers, quaternions, and dual quaternions emerge naturally as subalgebras, enabling powerful geometric operations.
A novel encoding format for real numbers on computers is presented, using a sequence of sign bits to represent values through iterative logarithms. The format efficiently handles both very large and very small numbers, utilizing a Gray code pattern and lexicographic ordering.
A personal account details the development of the XB-70 Valkyrie supersonic bomber through the lens of a father's career at General Electric during the Cold War. The ambitious aircraft project, despite its technological advances, was ultimately reduced from a strategic bomber program to a research vehicle due to the rise of ballistic missiles. The narrative weaves together family history, technological innovation, and Cold War politics while following the father's professional evolution from farm boy to engineer.
David E. Weisberg chronicles the 80-year evolution of Computer-Aided Design (CAD) through extensive interviews with industry pioneers and detailed company histories. The comprehensive 650-page document covers CAD's development from its 1950s origins through the early 2000s, offering insights into the technology, companies, and individuals who revolutionized engineering design.
Mathematical advances in 'landscape function' theory have significantly improved LED light bulb efficiency, leading to substantial energy savings in US households. The technology enables more accurate simulation of LED designs, particularly helping solve the 'green gap' problem through V-shaped defects in semiconductor layers. US consumers are projected to save $890 billion by 2035 through LED adoption.
An accessible introduction to stochastic calculus and Brownian motion, focusing on physical intuition and calculus-based derivations rather than formal probability theory, covering key concepts from discrete random walks to Itô calculus and stochastic differential equations.
A database tracks comprehensive K-12 school shooting incidents, including all instances of guns being fired, brandished, or bullets hitting school property. The database encompasses various scenarios like gang violence, domestic incidents, sports event shootings, and accidents, documenting the full scope of gun-related incidents on school grounds.
Princeton Engineering researchers demonstrated AI's ability to design complex wireless chips in hours instead of weeks, creating more efficient designs that humans find difficult to comprehend. The AI-generated chips, focusing on millimeter-wave technology, achieved superior performance by taking unconventional approaches and discarding traditional templates. While promising, the process still requires human oversight to address potential design failures.