The latest blog posts to take off on Hacker News. 216 posts.
As discussed in Pattern Matching and Recursion , a well-known programming puzzle is to write a function that determines whether a string of parentheses is “balanced,” i.e. each opening parenthesis has a corresponding closing parenthesis, and the parentheses are properly nested.
A common example of recursion is the function to calculate the $n$-th Fibonacci number: def naive_fib(n): if n < 2: return n else: return naive_fib(n-1) + naive_fib(n-2) This follows the mathematical definition very closely but it’s performance is terrible: roughly $\mathcal{O}(2^n)$. This is commonly patched up with…
The why and how of nonnegative matrix factorization Gillis, arXiv 2014 from: ‘Regularization, Optimization, Kernels, and Support Vector Machines.’ Last week we looked at the paper ‘Beyond news cont…
Once upon a time, my computer architecture professor mentioned that using a random eviction policy for caches really isn't so bad. That random eviction isn't bad can be surprising — if your cache fills up and you have to get rid of something, choosing the least recently used (LRU) is an obvious choice, since you're…
See also other posts tagged Single Rotation . In the previous post I have presented the Reversible Cellular Automata simulator , along ...
Last time we talked about free will, superintelligent predictors, and Dr. Evil planning to destroy the earth from his moon base. Today I'd like to talk about a more down-to-earth topic: time travel. The first point I have to make is one that Carl Sagan made: we're all time travelers—at the rate of one second per…
Many people are surprised to learn that `sed`, a seemingly simple text filtering program, is actually Turing complete. This realization prompts the question: how can a text processing utility achieve such computational power? The answer lies in sed's fundamental operations. Essentially, sed functions as a miniature...
A perfect hash function is one that is collision-free. By implication, the hash must be at least as many bytes as the key and the function is theoretically reversible, though not always tractably so. In other words, perfect hashing is a special case of encryption. Because the hash is no smaller than the key, the…
You may be interested in my new arXiv paper, joint work with Xi Cheng, an undergraduate at UC Davis (now heading to Cornell for grad school); Bohdan Khomtchouk, a post doc in biology at Stanford; a…
Hash tables are the most popular probabilistic data structure, by quite a margin. You compute some hash code then compute an array index from that hash code. If you’re using open addressing-c…
Not all instructions on modern processors cost the same. Additions and subtractions are cheaper than multiplications which are themselves cheaper than divisions. For this reason, compilers frequently replace division instructions by multiplications. Roughly speaking, it works in this manner. Suppose that you want to…
Physicist Lev Landau used to play a mental game with Soviet license plates [1]. The plates had the form of two digits, a dash, two more digits, and some letters. Rules of the game His game was to apply high school math operators to the numbers on both side of the dash so that the
Tim Rocktäschel — Co-Founder and Chief Scientist of Recursive; Professor of AI at UCL. Artificial General Intelligence, Open-Endedness, and Recursive Self-Improvement.
A much-abused result in mathematical logic , supposed by many authors who don't understand it to support their own favored brand of rubbish, and even subjected to surprisingly rough handling by some who really should know better.
A 100 lines of Python code that substitute the compiler front-end for a specific computation. This shows that you don't need a “fast” compiling language to write efficient code. In fact, a compilation is only one of the multiple ways to achieve speed.
What is the 🐞(n) of your API?
The math behind how people wait in line
In this blogpost I explore how ODE’s can be used to solve data modelling problems. I take a deep dive into the data modelling problem at hand and present ODE...
1. Introduction Shortly after the death of E.W. Dijkstra (1930-2002), K.R. Apt wrote an obituary under the title Portrait of a Genius [1]. At the time it seemed to me a bit over the top. Now, with …
RSA encryption allows for anyone to send me messages that only I can decode. To set this up, I select two large random primes $latex p$ and $latex q$ (each of which is hundreds of bits long), and r…
Discover the secrets behind hit music with our popular song chords analysis from 1300 tracks. Your songwriting journey begins here!
By Michael Nielsen, January 2019
We are very sorry to hear of the death of Michael Atiyah. Michael was a giant of mathematics. He held many positions including Savilian Professor of Geometry here in Oxford, President of the Royal Society, Master of Trinity College, Cambridge, the founding Directorship of the Isaac Newton Institute and Chancellor of…
We've been speculating for a long time that hash-based keyword lookup ought to be faster than binary search, but up to now we hadn't found a suitable tool for generating the hash function. Joerg Sonnenberger provided the inspiration, and sample code, to show us that rolling our own generator wasn't a ridiculous idea…
The purpose of this article is to show you step-by-step examples of how to use the Fourier transform algorithm to multiply two numbers. The primary advantage of using fourier transforms to multiply numbers is that you can use the asymptotically much faster 'Fast Fourier Transform algorithm', to achieve better…
Judea Pearl and Dana Mackenzie sent me a copy of their new book, “The book of why: The new science of cause and effect.”
When an experimental study states "The group with treatment X had significantly less disease ( p = 1%)", many people interpret this statement as being equivalent to "there is a 99% chance that if I do treatment X it will prevent disease." This essay explains why these statements are not equivalent. For such an…
Note that some of the wrong answers can be fixed with various workarounds. For example Common–Lisp gives the correct answer for:
