Published on: 2025-04-29 14:54:51
Monte Carlo Crash Course Sampling In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? Pseudo-Random Numbers Fortunately, Monte Carlo methods don’t need truly random numbers. Instead, we can use a pseudo-random number generator (PRNG). A PRNG produces a deterministic stream of numbers that look uniformly random: By “look uniformly random,”
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Find related items on AmazonPublished on: 2025-05-08 22:29:29
Analytic Combinatorics -- A Worked Example 08 Apr 2025 - Tags: sage Another day, another blog post that starts with “I was on mse the other day…”. This time, someone asked an interesting question amounting to “how many unordered rooted ternary trees with $n$ nodes are there, up to isomorphism?”. I’m a sucker for these kinds of combinatorial problems, and after finding a generating function solution I wanted to push myself to get an asymptotic approximation using Flajolet–Sedgewick style analyt
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Find related items on AmazonPublished on: 2025-07-10 11:00:06
Omega-3s have several benefits for your health. Not only are they good for your heart, but recent research has linked omega-3 consumption with decreasing the risk of age-related hearing conditions. The best part? Omega-3s are found in many food sources, but you can also choose from over-the-counter omega-3 supplements. But like any trendy health food, omega-3 fatty acids are surrounded by hype. Which benefits are backed by science, and are there any downsides to omega-3s or their supplements? W
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Find related items on AmazonPublished on: 2025-07-12 06:00:03
In this article: Omega-3s have several health benefits. They play essential roles in the body, like decreasing inflammation, keeping our brain healthy and immune system functioning. And don't forget about the role they play in heart health and fetal development. Unlike other nutrients, our bodies can't naturally produce omega-3s. If you're an avid fish eater, you likely get enough omega-3s from your diet. But if you don't eat fish, have a history of heart attacks or have elevated levels of tri
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