Algorithmic information theory | Randomness
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free or not) universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet (e.g. decimal digits). Random sequences are key objects of study in algorithmic information theory. As different types of algorithms are sometimes considered, ranging from algorithms with specific bounds on their running time to algorithms which may ask questions of an oracle machine, there are different notions of randomness. The most common of these is known as Martin-Löf randomness (K-randomness or 1-randomness), but stronger and weaker forms of randomness also exist. When the term "algorithmically random" is used to refer to a particular single (finite or infinite) sequence without clarification, it is usually taken to mean "incompressible" or, in the case the sequence is infinite and prefix algorithmically random (i.e., K-incompressible), "Martin-Löf–Chaitin random". It is important to disambiguate between algorithmic randomness and stochastic randomness. Unlike algorithmic randomness, which is defined for computable (and thus deterministic) processes, stochastic randomness is usually said to be a property of a sequence that is a priori known to be generated by (or is the outcome of) an independent identically distributed equiprobable stochastic process. Because infinite sequences of binary digits can be identified with real numbers in the unit interval, random binary sequences are often called (algorithmically) random real numbers. Additionally, infinite binary sequences correspond to characteristic functions of sets of natural numbers; therefore those sequences might be seen as sets of natural numbers. The class of all Martin-Löf random (binary) sequences is denoted by RAND or MLR. (Wikipedia).
Randomness Quiz Solution - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
What is the recursive formula and how do we use it
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the alternate in sign sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the definition of an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the formula for the rule for the nth term of a arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What are the formulas for arithmetic and geometric sequences
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Randomness - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Introduction to Sequences (Discrete Math)
This video introduces sequences for a discrete math class. mathispower4u.com
From playlist Sequences (Discrete Math)
Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist Computer - Cryptography and Network Security
Lecture 20 | Machine Learning (Stanford)
Lecture by Professor Andrew Ng for Machine Learning (CS 229) in the Stanford Computer Science department. Professor Ng discusses POMDPs, policy search, and Pegasus in the context of reinforcement learning. This course provides a broad introduction to machine learning and statistical p
From playlist Lecture Collection | Machine Learning
Avi Wigderson: Randomness and pseudorandomness
Abstract: The talk is aimed at a general audience, and no particular background will be assumed. Is the universe inherently deterministic or probabilistic? Perhaps more importantly - can we tell the difference between the two? Humanity has pondered the meaning and utility of randomness fo
From playlist Abel Lectures
High-Confidence Predictions under Adversarial Uncertainty - Andrew Drucker
Andrew Drucker Massachusetts Institute of Technology February 13, 2012 We study the setting in which the bits of an unknown infinite binary sequence x are revealed sequentially to an observer. We show that very limited assumptions about x allow one to make successful predictions about unse
From playlist Mathematics
9. Modeling and Discovery of Sequence Motifs
MIT 7.91J Foundations of Computational and Systems Biology, Spring 2014 View the complete course: http://ocw.mit.edu/7-91JS14 Instructor: Christopher Burge This lecture by Prof. Christopher Burge covers modeling and discovery of sequence motifs. He gives the example of the Gibbs sampling
From playlist MIT 7.91J Foundations of Computational and Systems Biology
Giray Ökten: Derivative pricing, simulation from non-uniform distributions - lecture 3
The models of Bachelier and Samuelson will be introduced. Methods for generating number sequences from non-uniform distributions, such as inverse transformation and acceptance rejection, as well as generation of stochastic processes will be discussed. Applications to pricing options via re
From playlist Probability and Statistics
Randomness in Algorithms: Understanding It, Eliminating It
Short Talks by Postdoctoral Members Topic: Randomness in Algorithms: Understanding It, Eliminating It Speaker: Roei Tell Affiliation: Member, School of Mathematics September 30, 2022
From playlist Short Talks by Postdoctoral Members
Kharkov, Universal approach to β-matrix models - Valerie King
Valerie King University of Victoria; Member, School of Mathematics April 1, 2014
From playlist Mathematics
Algorithmic Stochastic Localization for the Sherrington-Kirkpatrick Model - Mark Sellke
Computer Science/Discrete Mathematics Seminar I Topic: Algorithmic Stochastic Localization for the Sherrington-Kirkpatrick Model Speaker: Mark Sellke Affiliation: Member, School of Mathematics Date: November 28, 2022 Sampling from high-dimensional, multimodal distributions is a computat
From playlist Mathematics
Giray Ökten: Number sequences for simulation - lecture 1
After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiter’s uniform point sets will be discussed. We will then present randomized q
From playlist Probability and Statistics
Finding the rule of the sequence using multiplication and addition
👉 Learn how to write the explicit formula for the nth term of an arithmetic sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. An arithmetic sequence is a sequence in which each term of the sequence
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