1171
Can you be sure to clear a line at Tetris?
Summary: it is possible to play Tetris and guarantee that you will score at least one line, no matter which pieces are given to you, i.e., even assuming they are chosen adversarially.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
1172
Zero Knowledge Proofs: An illustrated primer
One of the best things about modern cryptography is the beautiful terminology. You could start any number of punk bands (or Tumblrs) named after cryptography terms like ‘hard-core predicate&#…
1173
A Short Intro to Constraints
The essence of constraint is projection.
1174
Fundamental Algorithms III
Three more fundamental algorithms in the series. Today, recursive permutations, subsets of the given set and variations with repetitions. Th...
1175
The control group is out of control (2014)
I. Allan Crossman calls parapsychology the control group for science. That is, in let’s say a drug testing experiment, you give some people the drug and they recover. That doesn’t tell …
1176
Death by hockey sticks
You may be familiar with the term “hockey stick curve,” used describe a trend that has been flat/stable for a very long time, but shoots up at the end of the series in dramatic fashion, resembling the shape of a hockey stick. Hockey can be a violent sport, and it’s easy to get hurt by even one well-aimed swing…
1177
Why Bayesian Stats Needs Monte-Carlo Methods
Bayesian statistics rely heavily on Monte-Carlo methods. A common question that arises is “isn’t there an easier, analytical solution?” This post explores a bit more why this is by breaking down the analysis of a Bayesian A/B test and showing how tricky the analytical path is and exploring more of t
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1179
Elsevier journals – some facts
Update: figures now in from Imperial. See below. Further update: figures in from Nottingham too. Further update: figures now in from Oxford. Final update: figures in from LSE. A little over two yea…
1180
An Algebra of Graphs
Graph theory is my favourite topic in mathematics and computing science and in this blog post I’ll introduce an algebra of graphs that I’ve been working on for a while. The algebra has become my go-to tool for manipulating graphs and I hope you will find it useful too.
1181
Hopfield Networks Is All You Need
Blog post
1182
Playing with Wolfram Playing Cards
A few weeks ago, I knocked my favorite mug off the counter and it shattered. RIP:
1183
Logistic Regression from Bayes’ Theorem
In this post we’ll explore how we can derive logistic regression from Bayes’ Theorem. Starting with Bayes’ Theorem we’ll work our way to computing the log odds of our problem and the arrive at the inverse logit function. After reading this post you’ll have a much stronger intuition for how logistic
1184
Rendering a Buddhabrot at 4K and Other Bad Ideas
Benedikt Bitterli's Portfolio
1185
A Detailed Elliptic Curve Cryptography Tutorial
When adding two integers i and j of bitlength b, the result will be of bitlength b + 1 in the worst case. This means they can easily be naively added. If the result is larger or equal to F p one has only to subtract p from the result, i.e.:
1186
Why Quantum Mechanics?
In the past few months, I’ve twice injured the same ankle while playing with my kids. This, perhaps combined with covid, led me to several indisputable realizations: I am mortal.Despite my se…
1187
Using Euro coins as weights (2004)
Here is a cheap way to obtain a set of standard weights, for measuring weights up to about 100 gram, to an accuracy of about 0.5 gram : Use the coins of the currency of your country. Thus one can make use of the fact that these coins are fabricated in mass production, and because of that have not only a constant shape…
1188
How does cosine similarity work?
Cosine similarity measures the angle between two vectors — the dot product divided by the product of their magnitudes. Here's what each part of the formula does.
1189
The main trick in machine learning
I have been irritated that many recent introductions to machine learning/neural networks/whatever that fail to emphasise the most import trick in machine learning. Many internet resources don’t mention it, and even good textbooks often don’t drill it in to the reader the absolute criticality to success the trick is…
1190
Mandelbrot deep zoom theory and practice (2021)
Perturbation and rescaling for efficient rendering of fractal images.
1191
How inevitable is the concept of numbers?
Stephen Wolfram considers if numbers are actually required, the use of symbolics and the potential for the growing role of computational irreducibility.
1192
What is the Axiom of Choice?
One of the easiest ways to start a (friendly) fight in a group of mathematicians is to bring up the axiom of choice. I'll explain what it is, why it's so controversial, and hopefully shed some light on how we choose axiomatic systems and what that means for the math we do.
1193
How long does music stardom last? A statistical analysis
When do music stars achieve fame, and how long does fame typically last?
1194
How to explain infinity to kids
From the highly eclectic blog of Mark Dominus
1195
Why Does Integer Addition Approximate Float Multiplication?
Here is a rough approximation of float multiplication (source): float rough_float_multiply(float a, float b) { constexpr uint32_t bias = 0x3f76d000; return bit_cast<float>(bit_cast<uint32_…
1196
Compressing a flag to 11 bits
I recently saw an interesting YouTube video by “Physics for the Birds”. The main video is about matrixes, but he used flags to explain some of the operations on matrixes:
1197
The Limits of the CAP Theorem
This post explains how CAP-Consistent systems can be highly available, how the CAP theorem applies to CockroachDB, and why consistency is the better choice.
1198
Money Stuff is Linear-ish
What was once a pre-market morning newsletter became an afternoon newsletter, 12 seconds at a time
1199
Levels of Excellence
Over on Google+, a computer scientist at McGill named Artem Kaznatcheev passed on this great description of what it’s like to learn math, written by someone who calls himself ‘man aft…
1200
