Modular arithmetic | Pseudorandom number generators
A permuted congruential generator (PCG) is a pseudorandom number generation algorithm developed in 2014 which applies an output permutation function to improve the statistical properties of a modulo-2n linear congruential generator. It achieves excellent statistical performance with small and fast code, and small state size. A PCG differs from a classical linear congruential generator (LCG) in three ways: * the LCG modulus and state is larger, usually twice the size of the desired output, * it uses a power-of-2 modulus, which results in a particularly efficient implementation with a full period generator and unbiased output bits, and * the state is not output directly, but rather the most significant bits of the state are used to select a bitwise rotation or shift which is applied to the state to produce the output. It is the variable rotation which eliminates the problem of a short period in the low-order bits that power-of-2 LCGs suffer from. (Wikipedia).
Stanford Seminar - PCG: A Family of Better Random Number Generators
"PCG: A Family of Better Random Number Generators" - Melissa O'Neill of Harvey Mudd College Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to operat
From playlist Engineering
How to multiply two exponents when they do not have same base and fraction powers
👉 Learn how to multiply with rational powers. To multiply two or more numbers/expressions with rational exponents, we apply the basic rules of exponents. If the two numbers/expressions are the same, we simply take one of the number and raise it to the power of the sum of the exponents. If
From playlist Multiply Fractional Exponents
How do we multiply polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Science & Technology Q&A for Kids (and others) [Part 55]
Stephen Wolfram hosts a live and unscripted Ask Me Anything about science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram Outline of Q&A 0:00 Stream starts 2:25 Stephen begins the s
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
Multiplying Two Binomials - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying Two Binomials - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiply Two Binomials Using FOIL - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying Two Binomials - Math Tutorial - Polynomial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying Polynomials - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying Two Binomials Using Box Method - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Lecture 9 - Random Walk Models
This is Lecture 9 of the COMP510 (Computational Finance) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Hong Kong University of Science and Technology in 2008. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/computationalfinance/pdf
From playlist COMP510 - Computational Finance - 2007 HKUST
How Do Computers Produce Random Numbers?
The first in a series of videos on noise; in this premiere we tackle the idea of white noise and pseudo-random number generators. Twitter: https://twitter.com/Acerola_t Twitch: https://www.twitch.tv/acerola_t Discord: https://discord.gg/FxGQvbfm6Y Code: https://github.com/GarrettGunnell/L
From playlist Noise
Discrete Structures: Random number generators, checksums, hashing
Learn about random number generators, checksums, and hashing. We'll start with the von Neumann random number generator and the contemporary linear congruential generator. Then we'll go over the Luhn algorithm used for credit card number validation and then introduce hash functions such as
From playlist Discrete Structures, Spring 2022
Applications of thin orbits - Alex Kontorovich
Members' Seminar Topic: Applications of thin orbits Speaker:Alex Kontorovich Date: Monday, April 11 We will discuss some natural problems in arithmetic that can be reformulated in terms of orbits of certain "thin" (semi)groups of integer matrix groups. For more videos, visit http://v
From playlist Mathematics
What We've Learned from NKS Chapter 7: Mechanisms in Programs and Nature
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Periodic Random Function Generation using Matplotlib and Python
In signal processing, for certain applications, periodic random signals might be needed. In this micro-tutorial we show how such a periodic random function can be generated. This is achieved by looping a 2d random noise onto itself to create a 1 dimensional random noise. The algorithm is i
From playlist Engineering Animations
How to Simplify an Expression Using Distributive Property - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials