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MathML in Chromium
A joint effort to add native MathML-Core support to web browsers.
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Loop invariants can give you coding superpowers
A loop invariant is a simple yet powerful tool for designing, testing, modifying, documenting and proving code correct.
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Alpha Compositing
Interactive article explaining alpha compositing concepts.
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Dungeon Generation in Enter The Gungeon
I’ve been playing a lot of Enter The Gungeon recently. It’s a great, brutally hard, twin stick bullet hell that reminded me a lot of Binding of Isaac. But as I’ve been playing it …
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Notes on Weight Initialization for Deep Neural Networks
Neural networks involve long sequence of multiplications, usually between a matrix and a vector, say \(a*x\). The result of this sequence of multiplications will either have a huge magnitude or be reduced to 0. We can divide \(a\) by a number ( scaling_factor ) to scale down its magnitude to the right level. Proper…
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The Riemann Hypothesis (Part 2)
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Solving a linear optimization problem on incentive allocation
At Lyft, scientists solve all kinds of optimization problems. While solvers can come in handy, there are times when complicated or…
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A fast alternative to the modulo reduction (2016)
Suppose you want to pick an integer at random in a set of N elements. Your computer has functions to generate random 32-bit integers, how do you transform such numbers into indexes no larger than N? Suppose you have a hash table with a capacity N. Again, you need to transform your hash values (typically 32-bit ……
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Towards a Better Pythagorean Cup
There was an article on Hacker News the other day by David Richeson entitled Make Your Own Pythagorean Cup . A Pythagorean cup is a cup with a built-in siphon. Supposedly invented by Pythagoras, the cup functions just like an ordinary cup as long as it is only filled to a certain level. If anyone gets greedy and tries…
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RSA: Theory and Implementation
RSA has been a staple of public key cryptography for over 40 years, and is still being used today for some tasks in the newest TLS 1.3 standard. This post describes the theory behind RSA - the math that makes it work, as well as some practical considerations; it also presents a complete implementation of RSA key…
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The Single Rotation rule: simple and rich reversible cellular automaton (2013)
See also other posts tagged Single Rotation . In the previous post I have presented the Reversible Cellular Automata simulator , along ...
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Mathematical Jargon Failures
From the highly eclectic blog of Mark Dominus
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Curve fitting A: Linear Least Squares
The graph on the left shows a third example, taken from analytical chemistry: a straight-line calibration data set where X = concentration and Y = instrument reading (Y = a + b X). Click to download that data . The blue dots are the data points. They don't all fall in a perfect straight line because of random noise…
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Gaussian Processes Are Not So Fancy
Gaussian Processes have a mystique related to the dense probabilistic terminology that's already evident in their name. But Gaussian Processes are just models, and they're much more like k-nearest neighbors and linear regression than may at first be apparent.
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Linguistics Using Category Theory (2018)
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Understanding “Deep Double Descent”
Double descent is a puzzling phenomenon in machine learning where increasing model size/training time/data can initially hurt performance, but then i…
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Information Theory with TensorFlow
Redirecting to https://www.mukeshmithrakumar.com/blog/deep-learning-with-tf2-probability-and-information-theory/ .
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Quantum transitions take time – the news is its experimental demonstration
A number of people have asked me to weigh in on this story in Quanta Magazine (based on this paper [ PDF version ] and also reported in t...
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Warning Signs in Experimental Design and Interpretation (2007)
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…
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Predicting When P=NP Is Resolved
Has it outlasted the ability to estimate when? Composite of src1, src2 Ryohei Hisano and Didier Sornette wrote in 2012 a paper titled, “On the distribution of time-to-proof of mathematical co…
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A Visual Introduction to Morse Theory
In a previous article , I already introduced manifolds and their, ahem, manifold ways. Among the many interesting comments I received about this article, some were dealing with a basic question, namely how to measure the properties of a manifold. In this article, I want to present a few concepts from Morse theory …
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Cache tables
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…
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Time to Abolish "Statistical Significance"?
The idea of "statistical significance" has been a basic concept in introductory statistics courses for decades. If you spend any time lookin...
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Measuring the size of the Earth by watching a shadow on a wall
Recently I've been discussing the details of measuring the size of the Earth by watching a shadow descending a wall at sunrise, or ascending at sunset. The sums are easy enough if you do it at either Equinox, and at the Equator, and you can read about it here:
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Stock Option Pricing Inference
I’m a stock market enthusiast 📈, so lately I have spent my spare time on the topic of stock option pricing, and I was curious to find out whether or not I could build a script that accurately reflected real market option prices. It turns out I came close, and learned a lot along the way, which I share in this article.