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ProtonMail now offers elliptic curve cryptography
Proton Mail has become the first and only encrypted email provider to support elliptic curve cryptography (ECC), providing more security and performance.
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Faster remainders when the divisor is a constant: beating compilers & libdivide
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…
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What's the difference between 0/0 and 1/0?
From the highly eclectic blog of Mark Dominus
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How Fair Is My D20? (2015)
An automatic system for rolling a polyhedral die and taking photos of the rolls; extracting the image of just the die from those images; clustering the images of the die by which face is shown; and analyzing the results.
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A Short Intro to Constraints
The essence of constraint is projection.
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Fundamental Algorithms III
Three more fundamental algorithms in the series. Today, recursive permutations, subsets of the given set and variations with repetitions. Th...
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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
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Exploring Weight Agnostic Neural Networks
Posted by Adam Gaier, Student Researcher and David Ha, Staff Research Scientist, Google Research, Tokyo When training a neural network to accompl...
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Principal component analysis: pictures, code and proofs (2018)
The code used to generate the plots for this post can be found here.
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Swift Numerics
I’m excited to announce a new open-source project for the Swift ecosystem, Swift Numerics! Swift Numerics will provide the building blocks of numerical computing in Swift, as a set of fine-grained modules bundled together into a single Swift package. My hope is that we can quickly fill some important gaps in the…
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A sane introduction to maximum likelihood estimation and maximum a posteriori
It is frustrating to learn about principles such as maximum likelihood estimation (MLE), maximum a posteriori (MAP) and Bayesian inference in general. The main reason behind this difficulty, in my opinion, is that many tutorials assume previous knowledge, use implicit or inconsistent notation, or are even addressing a…
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Neural Networks Are Essentially Polynomial Regression (2018)
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…
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Reed Solomon codes are cool
thoughts
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A Million Digits of Pi in 9 Lines of JavaScript
"Big integers" have landed in Javascript, at least in Firefox and Chrome. One of my favorite things to do with high precision arithmetic is to calculate digits of π. From scratch, that is, using only addition, subtraction, multiplication, and division.
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Neural ODE's: Understanding how they model data
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...
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The Soviet license plate game and Kolmogorov complexity
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
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‘A Swiss cheese-like material’ that can solve equations
Engineering professor Nader Engheta and his team have demonstrated a metamaterial device that can function as an analog computer, validating an earlier theory about ‘photonic calculus.’
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A Good Year for “A Programmer’s Introduction to Mathematics”
A year ago today I self-published “A Programmer’s Introduction to Mathematics” (PIM). In this short note I want to describe the success it’s had, summarize the complaints of some readers and the praise of others, and outline what’s next. Since publication PIM has sold over 11,000 copies. A rough chart showing the…
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Introduction to Bayesian Filter
Restate Some Basic Concepts and Math in Bayesian Filter
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Everything Is Correlated
Anthology of sociology, statistical, or psychological papers discussing the observation that all real-world variables have non-zero correlations and the implications for statistical theory such as ‘null hypothesis testing’.
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L2 Regularization and Batch Norm
This blog post is about an interesting detail about machine learning that I came across as a researcher at Jane Street - that of the interaction between L2 r...