Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018: > How thick is a three-sided coin? Translated into mathematician-ese, this means > What aspect ratio of a flipped coin leads to the chance of landing on…
Shamir's Secret Sharing Scheme
The Latest News from Research at Kudelski Security
Ramanujan came up with an approximation for factorial that resembles Stirling's famous approximation but is much more accurate. As with Stirling's approximation, the relative error in Ramanujan's approximation decreases as n gets larger. Typically these approximations are not useful for small values of n. For n = 5…
Some friends of mine play the board game Settlers Of Catan . In this game, each player rolls two ordinary dice on their turn, and the number which comes up determines what resources people get for the turn. When a seven is rolled, something special happens: no resources are generated, and instead a robber moves on the…
If I were to design a computer algebra system (CAS) from scratch today, I would try to achieve the following goals. Several ideas have already been implemented in one system or another, but certainly not all at once. Some ideas could be adopted by existing CASes; others would require fundamentally different designs or…
It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.
Background Backpropagation is a common method for training a neural network. There is no shortage of papers online that attempt to explain how backpropagation works, but few that include an example…
Let’s play a game. I’m thinking of a number from 1 to 100. You guess, and I tell you whether my number is higher or lower.
the forgotten data structure (not really)
Casual introduction to the uncertainty principle from quantum mechanics and how it leads to neutron stars and superfluids
About six weeks ago, on May 19, 2022, GitHub released Math support on Markdown. At the time of the release, it received criticism for being ill-designed and buggy. I, too, wrote a blog post about it.
In this post we take a look a how the mathematical idea of a convolution is used in probability. In probability a convolution is a way to add two random variables. Using a slightly ridiculous, mad-science, example we walk through multiple way to compute a convolution and ultimate arrive at the formu
In 1986, Eugene Myers published An O(ND) Difference Algorithm and Its Variations , which unified the problems of finding the longest common subsequence of two sequences (the LCS of "driftwood" and "artwork" is "two") and finding the shortest edit script for transforming one sequence into another. Myers showed that…
A sure foundation for Computational Complexity source—wonderful 2015 CACM interview Juris Hartmanis passed away this morning. He was a professor in Cornell’s computer science department…
Bayesianism, the doctrine that it's always rational to represent our beliefs in terms of probabilities, dominates the intellectual world, from decision theory to the philosophy of science. But does it make sense to quantify our beliefs about such ineffable things as scientific theories or the future? And what separates
This post describes the implementation of pysmtgcc. See “GCC Translation Validation” for background information.
In this post we'll work our way towards an algorithm that can compute convex polygon intersections. We'll also explore a method for intersections between axis-aligned rectangles, a function that can determine the intersection of two line segments, as well as a point in polygon test.
https://thetab.com/uk/2020/05/20/this-is-how-the-nobel-prize-winning-hinge-algorithm-actually-works-157740
Researchers have calculated the quantum computer size necessary to break 256-bit elliptic curve public-key cryptography: Finally, we calculate the number of physical qubits required to break the 256-bit elliptic curve encryption of keys in the Bitcoin network within the small available time frame in which it would…
You have heard your grandmother tell you many times: parallel programming is hard. In 2022, does it still have to be? Back in grandma’s heyday, they knew a cool and breezy way to do paralleli…
In our paper, published today in Nature, we introduce AlphaTensor, the first artificial intelligence (AI) system for discovering novel, efficient, and provably correct algorithms for fundamental tasks such as matrix multiplication. This sheds light on a 50-year-old open question in mathematics about finding the…
Milton Friedman’s interest rate fallacy is one of the most mystifying and counterintuitive facts in modern finance.
Binary lambda calculus ( BLC ) is a minimal, pure functional programming language invented by John Tromp in 2004, 1 based on a binary encoding of the untyped lambda calculus in De Bruijn index notation.
Now available for preorder.
Audio Link With the arrival of summer weather in many parts of the U.S., it’s time to think again about various outdoor activities. Wat...
How does set theory help to understand type assignability and resolution in TypeScript?
