Data synchronization | Distributed computing problems | Logical clock algorithms
A version vector is a mechanism for tracking changes to data in a distributed system, where multiple agents might update the data at different times. The version vector allows the participants to determine if one update preceded another (happened-before), followed it, or if the two updates happened concurrently (and therefore might conflict with each other). In this way, version vectors enable causality tracking among data replicas and are a basic mechanism for optimistic replication. In mathematical terms, the version vector generates a preorder that tracks the events that precede, and may therefore influence, later updates. Version vectors maintain state identical to that in a vector clock, but the update rules differ slightly; in this example, replicas can either experience local updates (e.g., the user editing a file on the local node), or can synchronize with another replica: * Initially all vector counters are zero. * Each time a replica experiences a local update event, it increments its own counter in the vector by one. * Each time two replicas a and b synchronize, they both set the elements in their copy of the vector to the maximum of the element across both counters: . After synchronization, the two replicas have identical version vectors. Pairs of replicas, a, b, can be compared by inspecting their version vectors and determined to be either: identical, concurrent, or ordered ( or ). The ordered relation is defined as: Vector if and only if every element of is less than or equal to its corresponding element in , and at least one of the elements is strictly less than. If neither or , but the vectors are not identical, then the two vectors must be concurrent. Version vectors or variants are used to track updates in many distributed file systems, such as Coda (file system) and Ficus, and are the main data structure behind optimistic replication. (Wikipedia).
What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh
From playlist Introduction to Vectors
A short refresher on vectors. Before I introduce vector-based functions, it's important to look at vectors themselves and how they are represented in python™ and the IPython Notebook using SymPy.
From playlist Life Science Math: Vectors
Vectors: Addition and Scalar Multiplication
This is the first video of a series from the Worldwide Center of Mathematics explaining the basics of vectors. This video deals with vector notation, vector addition, and scalar multiplication. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Vectors
This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
Vector Calculus 1: What Is a Vector?
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
How to compute the length and direction of a vector. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/0hPXc99Ql9
From playlist Introduction to Vectors
Calculus 3: Vector Calculus in 2D (17 of 39) What is the Position Vector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the position vector. The position vector indicates the position of a particle relative to the origin. The position usually depends on, or is a function of, a parametric variable (ex. t
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
Linear Algebra for Computer Scientists. 1. Introducing Vectors
This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of f
From playlist Linear Algebra for Computer Scientists
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
This video explores changes to the StyleGAN architecture to remove certain artifacts, increase training speed, and achieve a much smoother latent space interpolation! This paper also presents an interesting Deepfake detection algorithm enabled by their improvements to latent space interpol
From playlist Generative Adversarial Networks
Linear Algebra - Part 22 - Linear Independence (Definition) [dark version]
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From playlist Linear Algebra [dark version]
Live CEOing Ep 191: Language Design in Wolfram Language
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From playlist Behind the Scenes in Real-Life Software Design
Multivariable Calculus | Vector forms of Green's Theorem.
We present two vector forms of Green's Theorem. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus | Line Integrals
Complex Brunn–Minkowski theory and positivity of vector bundles – Bo Berndtsson – ICM2018
Geometry | Analysis and Operator Algebras Invited Lecture 5.2 | 8.2 Complex Brunn–Minkowski theory and positivity of vector bundles Bo Berndtsson Abstract: This is a survey of results on positivity of vector bundles, inspired by the Brunn–Minkowski and Prékopa theorems. Applications to c
From playlist Geometry
2D Rotations and Complex Exponentials
In this video, we will discover how to rotate any vector in two dimensions with the help of the complex numbers, especially the complex exponential. We will eventually derive a general formula which I claim, with some modifications, can be used to understand the more complex problem of 3D
From playlist Complex Numbers
Linear Algebra - Part 25 - Coordinates with respect to a Basis [dark version]
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From playlist Linear Algebra [dark version]
Linear Algebra - Part 26 - Steinitz Exchange Lemma [dark version]
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From playlist Linear Algebra [dark version]
Exploring Rapier2d part 1 - Getting set up
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From playlist Exploring Rapier2d
Linear Algebra - Part 23 - Linear Independence (Examples) [dark version]
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From playlist Linear Algebra [dark version]
What is the projection of one vector on another one and how is it useful? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/CpZUX1mFLS
From playlist Introduction to Vectors