Graph theory

Pseudorandom graph

In graph theory, a graph is said to be a pseudorandom graph if it obeys certain properties that random graphs obey with high probability. There is no concrete definition of graph pseudorandomness, but there are many reasonable characterizations of pseudorandomness one can consider. Pseudorandom properties were first formally considered by Andrew Thomason in 1987. He defined a condition called "jumbledness": a graph is said to be -jumbled for real and with if for every subset of the vertex set , where is the number of edges among (equivalently, the number of edges in the subgraph induced by the vertex set ). It can be shown that the Erdős–Rényi random graph is almost surely -jumbled. However, graphs with less uniformly distributed edges, for example a graph on vertices consisting of an -vertex complete graph and completely independent vertices, are not -jumbled for any small , making jumbledness a reasonable quantifier for "random-like" properties of a graph's edge distribution. (Wikipedia).

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Pseudorandom Number Generation and Stream Ciphers

Fundamental concepts of Pseudorandom Number Generation are discussed. Pseudorandom Number Generation using a Block Cipher is explained. Stream Cipher & RC4 are presented.

From playlist Network Security

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Pseudorandom Generators for Regular Branching Programs - Amir Yehudayoff

Amir Yehudayoff Institute for Advanced Study March 16, 2010 We shall discuss new pseudorandom generators for regular read-once branching programs of small width. A branching program is regular if the in-degree of every vertex in it is (either 0 or) 2. For every width d and length n, the p

From playlist Mathematics

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How to Generate Pseudorandom Numbers | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What is a the difference between a random and a pseudorandom number? And what can pseudo random numbers allow us to do that random numbers can't? Tweet at us! @pbsinfi

From playlist Probability

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Patrick Morris - Triangle factors in pseudorandom graphs (CMSA Combinatorics Seminar)

Patrick Morris presents "Triangle factors in pseudorandom graphs," 31st March 2021 (CMSA Combinatorics Seminar) http://combinatorics-australasia.org/seminars.html

From playlist CMSA Combinatorics Seminar

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Determine if a set of points is a parallelogram using the distance formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determining if a set of points makes a parallelogram or not

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Better Pseudorandom Generators from Milder Pseudorandom Restrictions - Parikshit Gopalan

Parikshit Gopalan Microsoft Research Silicon Valley, Mountain View, CA April 3, 2012 We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for

From playlist Mathematics

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Pseudorandom Generators for Read-Once ACC^0 - Srikanth Srinivasan

Srikanth Srinivasan DIMACS April 24, 2012 We consider the problem of constructing pseudorandom generators for read-once circuits. We give an explicit construction of a pseudorandom generator for the class of read-once constant depth circuits with unbounded fan-in AND, OR, NOT and generaliz

From playlist Mathematics

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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

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11. Pseudorandom graphs I: quasirandomness

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao discusses a classic result of Chung, Graham, a

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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Solving Laplacian Systems of Directed Graphs - John Peebles

Computer Science/Discrete Mathematics Seminar II Topic: Solving Laplacian Systems of Directed Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: March 02, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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The Green-Tao theorem and a relative Szemeredi theorem - Yufei Zhao

Slides for this talk: https://drive.google.com/file/d/1RdgY6N869MN5lJwl2jv1HwIgWky6aW5C/view?usp=sharing The Green-Tao theorem and a relative Szemeredi theorem - Yufei Zhao Abstract: The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the p

From playlist Mathematics

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The Abel Prize announcement 2021 - Avi Wigderson and László Lovász

0:49 The Abel Prize announced by Hans Petter Graver, President of The Norwegian Academy of Science and Letters 1:38 Citation by Hans Munthe-Kaas, Chair of the Abel committee 10:22 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 17:43

From playlist The Abel Prize announcements

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The Search for Randomness | Jean Bourgain

March 25, 2009 Jean Bourgain, IBM von Neumann Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/bourgain Although the concept of randomness is ubiquitous, it turns out to be difficult to generate a truly random sequence of events

From playlist Mathematics

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The Green - TAO Theorem (Lecture 5) by Gyan Prakash

Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod

From playlist Workshop on Additive Combinatorics 2020

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Using a set of points determine if the figure is a parallelogram using the midpoint formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Jonathan Katz - Introduction to Cryptography Part 1 of 3 - IPAM at UCLA

Recorded 25 July 2022. Jonathan Katz of the University of Maryland presents "Introduction to Cryptography I" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This lecture will serve as a "crash course" in modern cryptography for those with no prior exposure

From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography

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26C3: Privacy-Enhanced Event Scheduling 4/6

Clip 4/6 Speaker: Benjamin Kellermann Event schedulers, well-known from groupware and social software, typically share the problem that they disclose detailed availability patterns of their users. This talk distinguishes event scheduling from electronic voting and proposes a privacy-e

From playlist 26C3: Here be dragons day 3

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12. Pseudorandom graphs II: second eigenvalue

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX What can be inferred about a graph from its second eigenv

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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Terence Tao (UCLA): Pseudorandomness of the Liouville function

The Liouville pseudorandomness principle (a close cousin of the Mobius pseudorandomness principle) asserts that the Liouville function λ(n), which is the completely multiplicative function that equals −1 at every prime, should be "pseudorandom" in the sense that it behaves statistically li

From playlist TP Harmonic Analysis and Analytic Number Theory: Opening Day

Related pages

Graph removal lemma | Green–Tao theorem | K-vertex-connected graph | Cauchy–Schwarz inequality | Almost surely | Ramanujan graph | With high probability | Regular graph | Szemerédi regularity lemma | Erdős–Rényi model | Graph theory | Adjacency matrix | Induced subgraph | Complete graph | K-edge-connected graph | Cayley graph | Natural density | Independent set (graph theory) | Chromatic number | Szemerédi's theorem | Expander mixing lemma | Min-max theorem | Maximum cut | Grothendieck inequality