Blog

Analytic Combinatorics: The Symbolic Method, Generating Functions, and Average-Case Algorithm Analysis

A rigorous exploration of analytic combinatorics—the symbolic method for deriving generating functions, singularity analysis, saddle-point asymptotics, and applications to average-case analysis of algorithms and random structures.

From Lru To Arc: A Technical Survey Of Cache Eviction Policies And Their Performance In Web Scale Distributed Caches

A comprehensive technical exploration of cache eviction policies, from LRU to ARC, covering their performance in web-scale distributed caches, key concepts, practical implementations, and real-world applications.

Additive Combinatorics: Szemerédi's Theorem, Sumset Inequalities, and Applications in Property Testing

A rigorous exploration of additive combinatorics—Szemerédi's theorem on arithmetic progressions, Plünnecke-Ruzsa inequalities, the Balog-Szemerédi-Gowers theorem, and their applications in property testing and pseudorandomness.

Combinatorial Designs and Coding Theory: Block Designs, Steiner Systems, and Finite Geometry

An exploration of combinatorial design theory—block designs, Steiner systems, finite projective planes—and their deep connections to error-correcting codes and experimental design.

Tropical Geometry: Algorithmic Applications in Optimization, Phylogenetics, and Deep Learning

A rigorous exploration of tropical geometry—the min-plus semiring, tropical varieties, and the unexpected connections between algebraic geometry and combinatorial algorithms.

Timeouts, Retries, and Idempotency Keys: A Practical Guide

Make your distributed calls safe under partial failure. How to budget timeouts, avoid retry storms, and use idempotency keys without shooting yourself in the foot.

Teaching GraphQL to Cache at the Edge

A deep dive into making GraphQL play nicely with edge caches without breaking declarative APIs.

Algebraic Geometry in Computer Science: Gröbner Bases, the Nullstellensatz, and Applications in Cryptography and Coding Theory

A rigorous exploration of how algebraic geometry—Gröbner bases, Hilbert's Nullstellensatz, and elliptic curves—powers modern cryptography, error-correcting codes, and complexity theory.

Designing CRDT-Powered Collaboration Platforms that Stay Consistent

Deep dive into how conflict-free replicated data types underpin realtime editors, whiteboards, and multiplayer apps without sacrificing UX.

CPU Caches and Cache Coherence: The Memory Hierarchy That Makes Modern Computing Fast

A comprehensive exploration of how CPU caches bridge the processor-memory speed gap. Learn about cache architecture, replacement policies, coherence protocols, and how to write cache-friendly code for maximum performance.

Information Geometry: Statistical Manifolds, the Fisher Information Metric, and Natural Gradient Descent

A rigorous journey through information geometry—the Riemannian geometry of statistical models, the Fisher metric as the unique invariant metric, natural gradient, and the dually flat structure of exponential families.

Designing A Conflict Free Replicated Data Type (Crdt) For Real Time Collaborative Text Editing: Merging Operational Transform And Rga With Vector Clocks And Tombstone Management

Virtual Memory and Page Tables: How Modern Systems Manage Memory

A comprehensive exploration of virtual memory, page tables, and address translation. Learn how operating systems provide memory isolation, enable overcommitment, and optimize performance with TLBs and huge pages.

Process Scheduling and Context Switching: How Operating Systems Share the CPU

A deep dive into how operating systems decide which process runs next and how they switch between processes. Understand scheduling algorithms, context switches, and the trade-offs that shape system responsiveness.

Software Supply Chain Security: SBOMs, Sigstore, Reproducible Builds, and Attestation

An in-depth guide to securing the software supply chain: SBOMs, provenance, Sigstore, SLSA, reproducible builds, code signing, and operational best practices.

Online Learning: Regret Minimization, the Multiplicative Weights Algorithm, and Adversarial Bandits

A rigorous treatment of online learning—regret minimization, multiplicative weights, EXP3 for adversarial bandits, and the deep connections to game theory and boosting.

Statistical Learning Theory: PAC Learning, VC Dimension, and the Bias-Complexity Tradeoff

A rigorous development of statistical learning theory—the PAC framework, VC dimension and Sauer's lemma, the fundamental theorem, Rademacher complexity, and the mathematical limits of learning from data.

Large Deviations Theory: Cramér's Theorem, Importance Sampling, and Rare Event Simulation

A rigorous exploration of large deviations—the theory of exponentially rare events—from Cramér's theorem to Sanov's theorem, and their application to importance sampling for reliable networks.

Renewal Theory for Computer Science: The Renewal Equation, Key Renewal Theorem, and Applications in Cache Analysis and Failure Recovery

A rigorous journey through renewal theory—the mathematics of recurring events—from the renewal equation and key renewal theorem to applications in garbage collection, cache replacement, and fault-tolerant system analysis.

Stochastic Processes for Computer Science: Poisson, Brownian Motion, Queueing and Reliability

A rigorous treatment of continuous-time stochastic processes—Poisson processes, CTMCs, Brownian motion with the reflection principle—and their applications in queueing theory, reliability engineering, and network performance.

Markov Chains for Computer Science: MCMC, Mixing Times, and Randomized Algorithms

A rigorous treatment of Markov chains from a computer science perspective—Metropolis-Hastings, coupling bounds, spectral gaps, and the role of rapid mixing in modern randomized algorithms.

Abstract Interpretation: The Cousot Framework, Galois Connections, and Sound Static Analysis by Construction

A rigorous exploration of abstract interpretation—Patrick and Radhia Cousot's unifying framework for static program analysis, from Galois connections to widening operators and the soundness proofs that guarantee analysis correctness.

Domain Theory: Scott's D∞ Construction, Denotational Semantics, and the Mathematics of Recursive Types

A rigorous exploration of domain theory—Scott's D∞ construction, continuous lattices, the fixpoint theorem, and how domains provide the mathematical foundation for denotational semantics of programming languages.

Process Calculi: Milner's CCS, the π-Calculus, Bisimulation, and Session Types for Protocol Correctness

A rigorous exploration of process calculi—from CCS to the π-calculus, the theory of bisimulation, and the Curry-Howard line connecting session types to linear logic.