htmx ~ Yes, and...
In this essay, Carson Gross discusses his advice to young people interested in computer science worried about the future given the advancements in AI.
algorithms-math
Building Faster Prefix Search With the Trie Data Structure
Returning suggestions after every keystroke is expensive when a system stores millions of entries. Find out how the trie data structure narrows each search and the most effective ways to build a working implementation in Java.
Researchers Discover the Optimal Way To Optimize | Quanta Magazine
The leading approach to the simplex method, a widely used technique for balancing complex logistical constraints, can’t get any better.
In response, he invented the simplex method,
mathematicians proved that the time it takes to complete a task could rise exponentially with the number of constraints
Reversing Factorio's RNG
This post details how Factorio's random number generation works, how it can be reversed and how I used that knowledge to predict and manipulate the RNG with pure in‑game mechanics.
How is it possible for a deterministic game like Factorio to have a random mechanic?
PRNG
Curvature Beziers
Improving on a timeless recipe
Backpropagation Explained for Beginners (Part 3): How Backpropagation Really Works
From one gradient to every gradient
Compression is prediction | ngrok blog
Compression and LLMs are trying to solve the exact same problem: predicting what comes next. Learn the fundamentals of compression and how better prediction leads to better shrinkage.
Beyond Enumerable: Testing Membership with Bloom Filters
Checking whether you've seen something before usually means storing everything you've seen. A Bloom filter does it in about ten bits per item and can only be wrong in one direction. This post builds from a single bit to the structure RocksDB and Cassandra use to skip disk reads.
Terezija Semenski (@terezijasemenski)
Nobody understood function composition from my whiteboard. Everybody understands it from this pizza. #mathematics #math #meme #fridayhumor
Polynomial Regression: How to Fit and Interpret Curved Relationships
Learn what polynomial regression is, when to use it, and how to interpret curved model results correctly.
Meet Flash-KMeans: An IO-Aware, Exact K-Means That Runs Over 200× Faster Than FAISS on GPUs - MarkTechPost
Flash-KMeans is an IO-aware, exact K-Means that uses FlashAssign and Sort-Inverse Update to outperform FAISS by over 200×.
Biological Evolution and Information Acquisition
A few weeks ago we looked at a simulation of technological evolution by economist Brian Arthur, in which he was able to start with simple building blocks (such as a NAND gate) and evolve surprisingly complex circuits (such as a 12-way AND gate or a 4-bit adder) by randomly…
The thing that makes 4-bit AI work is a grid of nothing but +1s and -1s called a Hadamard matrix. Here's how a 159 year old matrix ended up…
The thing that makes 4-bit AI work is a grid of nothing but +1s and -1s called a Hadamard matrix. Here's how a 159 year old matrix ended up rescuing modern AI model performance: In 1867 James Joseph Sylvester was studying how to color tiles. He found you could build square grids…
Two Researchers Are Rebuilding Mathematics From the Ground Up | Quanta Magazine
By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.
Bash Arithmetic: Integer and Floating-Point Math
How to do arithmetic in Bash with the (( )) operator, $(( )) expansion, the let builtin, and bc or awk for floating-point math the shell cannot do natively.
I spent 31 hours on the math behind TurboQuant so you don't have to
A deep dive by Baseten's research team breaking down the math behind TurboQuant
Book Review: The Mind-Boggling Science of Enormous Numbers
In "Huge Numbers," mathematician Richard Elwes spotlights some of the largest numbers humans have ever contemplated.
Culture Explorer (@cultureexplorer)
Beauty in mathematics is not only in solving problems. It is in seeing structure, symmetry, and quiet unity where most people only see numbers.
Kalman Filter Explained Through Examples
Easy and intuitive Kalman Filter tutorial
Wireless Network Turns Interference Into Computation
Sensor networks could improve capacity faster than they grow
Think Labyrinth: Maze Algorithms
Modular: Software Pipelining for GPU Kernels: Part 1 - The Pipeline Problem
Flash Attention is a simple algorithm: tiled back-to-back matmuls with an online softmax algorithm in between. The algorithm fits in a few dozen lines of pseudocode. Yet Flash Attention 4's production kernel is 2,875 lines, and the hardest part to get right isn't the math. It's…
How BM25 and RAG Retrieve Information Differently? - MarkTechPost
When you type a query into a search engine, something has to decide which documents are actually relevant — and how to rank them. BM25 (Best Matching 25), the algorithm powering search engines like Elasticsearch and Lucene, has been the dominant answer to that question for…
The clever part is that BM25 doesn’t reward keyword stuffing
saturation
An interactive intro to Elliptic Curve Cryptography (ECC)
A hands-on introduction to elliptic curve cryptography. Start with curve geometry, build point addition and scalar multiplication, see why ECDLP is hard, and then use that math in ECDH, ECDSA, and ECIES.
Introduction to Laplace transforms
A Laplace transform is a type of integral transform that acts on functions.
Probabilistic Nearest Neighbor Search: The Swiss Army Knife of GenAI
ANN — Approximate Nearest Neighbors — is at the core of fast vector search, itself central to GenAI, especially GPT and LLM. My new methodology, abbreviated as PANN, has many other app…
A Behavior-Centric Taxonomy for Swarm Intelligence: Reclassifying Algorithms Based on Bio-Inspired Mechanisms
Swarm Intelligence (SI) represents a significant paradigm within artificial intelligence, drawing inspiration from the collective behaviors of natural systems to solve complex computational problems. However, the conventional classification of SI algorithms often groups them…
k-anonymity, the parent of all privacy definitions - Ted is writing things
How a privacy researcher proved a politician wrong, and how she created the first ever definition of anonymity in the process.
In this article, I'll describe and analyze Sweeney's successful reidentification attack,
these factors appear to be necessary: remove one of them and suddenly, the attack no longer works.
The Perils of Algorithmic Pricing
Hotels and landlords can mitigate legal risks by choosing decentralized revenue management systems that use public data.
How Drone Swarms Actually Work and What Industries Should Care
True drone swarms can cut costs and boost efficiency in agriculture, logistics and humanitarian demining, but software remains a hurdle.
Image Dithering: Eleven Algorithms and Source Code
Dithering is still a surprisingly applicable technique, not just for practical reasons (such as preparing a full-color image for output on a non-color printer), but for artistic reasons as well. Dithering also has applications in web design, where it is a useful technique for…
Dithering Sticky notes:Adding white noise to reduce errors from spurious signals
dithering is fundamentally about error diffusion.
The Game Theory of How Algorithms Can Drive Up Prices | Quanta Magazine
Recent findings reveal that even simple pricing algorithms can make things more expensive.
An Introduction to Multisets
Multisets are sets that allow repetition of elements. As such, multisets pave the way to a number of interesting possibilities of theoretical and applied nature. In the present work, after revising the main aspects of traditional sets, we introduce some of the main concepts and…
Multisets are sets that allow repetition of elements.
generalization to take into account vectors and matrices
Ethereum’s consensus layer elliptic curve
Introduction to the BLS12-381 curve used in Ethereum's consensus layer. Focus on concrete calculations to make the curve more tangible.
Generate random points inside a sphere
Generating random points inside a sphere of any dimension.
The customary way to generate points on a sphere in n dimensions is to generate points from an n-dimensional normal (Gaussian) distribution and normalize by dividing by the length. And the way to generate samples from an n-dimensional normal is simply to generate a list of n one-dimensional normals…
Instead, the thing to do is to set
5 Physics Equations Everyone Should Know
Our physics expert picks his top-five equations, plus a scheme to supply US power needs with a bucket of baseballs. Thanks, Einstein!
5 More Physics Equations Everyone Should Know
These five equations should be part of your mental toolkit. They might even improve your bowling score.
Maze generation algorithm - Wikipedia
Hilbert space: treating functions as vectors - Eli Bendersky's website
Bland, easy to follow, for fans of everything: what has the Netflix algorithm done to our films?
When the streaming giant began making films guided by data that aimed to please a vast audience, the results were often generic, forgettable, artless affairs. But is there a happy ending?
Derivatives, Gradients, Jacobians and Hessians – Oh My!
This article explains how these four things fit together and shows some examples of what they are used for. Derivatives Derivatives are the most fundamental concept in calculus. If you have a funct…
Raft Consensus Algorithm
Raft is a consensus algorithm that is designed to be easy to understand.
Note: https://chatgpt.com/share/68a1ca09-9bc8-8008-a635-e55bd9e4d4c9
Bezier-rs Interactive Documentation
What Is the Luhn Algorithm? The Math Behind Secure Credit Card Numbers
Find out how this simple algorithm from the 1960s keeps your wallet safe
New Sphere-Packing Record Stems From an Unexpected Source | Quanta Magazine
After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.
The Impossible Calculator—Asterisk
Google Android’s calculator is (probably) the most widely used calculator in the world. It’s also the most advanced.
The biggest perturbation of satellite orbits
The most important factor left out of the two body problem is the J2 effect, due to the fact that the earth is not a sphere of uniform density.
Cloud quantum computing: A trillion-dollar opportunity with dangerous hidden risks
Guest Join the event trusted by enterprise leaders for nearly two decades. VB Transform brings together the people building real enterprise AI strategy. Learn more Quantum computing (QC) brings with it a mix of groundbreaking possibilities and significant risks. Major tech…
How Cursor Indexes Codebases Fast
Merkle Trees in the real world
Bloom Filters
A visual, interactive guide to what bloom filters are, when you would use them, and how they work.