This was so hot (no pun intended) and reproducible that the prize was awarded one year after discovery. Quite rare in those days already.
In graph theory, an **independent set** (also known as a stable set) is a set of vertices in a graph, none of which are adjacent to each other. In other words, a set of vertices \( S \) is called an independent set if for every pair of vertices \( u \) and \( v \) in \( S \), there is no edge connecting \( u \) and \( v \) in the graph.
N. David Mermin is a prominent American physicist known for his work in theoretical condensed matter physics, quantum mechanics, and the philosophy of science. He is particularly well-known for his contributions to quantum theory, including the interpretation of quantum mechanics and research on the foundations of quantum physics. Mermin is also recognized for his clear and engaging writing style, which he has used to communicate complex scientific concepts to a broader audience. He has held academic positions at several prestigious institutions, including Cornell University.
The induced subgraph isomorphism problem is a computational problem in graph theory and computer science. It involves determining whether a specific graph (often referred to as the "target graph") can be found as an induced subgraph within another graph (often referred to as the "host graph"). ### Definitions: 1. **Graph:** A graph \( G \) consists of a set of vertices (or nodes) and a set of edges (connections between pairs of vertices).
x86 Paging Tutorial K-ary trees to the rescue by 
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01The algorithmically minded will have noticed that paging requires associative array (like Java
Map of Python dict()) abstract data structure where:The single level paging scheme uses a simple array implementation of the associative array:and in C pseudo-code it looks like this:
- the keys are the array index
- this implementation is very fast in time
- but it is too inefficient in memory
linear_address[0] = physical_address_0
linear_address[1] = physical_address_1
linear_address[2] = physical_address_2
...
linear_address[2^20-1] = physical_address_NBut there another simple associative array implementation that overcomes the memory problem: an (unbalanced) k-ary tree.
Using a K-ary tree instead of an array implementation has the following trade-offs:
In C-pseudo code, a 2-level K-ary tree with and we have the following arrays:
K = 2^10 looks like this:level0[0] = &level1_0[0]
level1_0[0] = physical_address_0_0
level1_0[1] = physical_address_0_1
...
level1_0[2^10-1] = physical_address_0_N
level0[1] = &level1_1[0]
level1_1[0] = physical_address_1_0
level1_1[1] = physical_address_1_1
...
level1_1[2^10-1] = physical_address_1_N
...
level0[N] = &level1_N[0]
level1_N[0] = physical_address_N_0
level1_N[1] = physical_address_N_1
...
level1_N[2^10-1] = physical_address_N_Nand it still contains
2^10 * 2^10 = 2^20 possible keys.K-ary trees can save up a lot of space, because if we only have one key, then we only need the following arrays:
The key initial quantum electrodynamics experiments:
The longest uncrossed knight's path refers to a path traced by a knight on a chessboard where the knight visits each square without revisiting any square (i.e., without crossing over itself or visiting the same square more than once). This kind of problem is often explored in the context of graph theory and combinatorial optimization.
In graph theory, a **matching** is a set of edges in a graph such that no two edges share a common vertex. In other words, it is a way of pairing the vertices of a graph such that each vertex is included in at most one edge of the matching. Here's a more detailed explanation: 1. **Vertices and Edges**: A graph consists of a set of vertices (nodes) and a set of edges (connections between pairs of vertices).
The Maximum Cut (Max Cut) problem is a well-known problem in combinatorial optimization and graph theory. It involves a given undirected graph, where the goal is to partition the set of vertices into two disjoint subsets in such a way that the number of edges between the two subsets is maximized.
Early electron diffraction experiment from 1927 that drastically confirmed the matter wave hypothesis.
The maximum flow problem is a classic optimization problem in network flow theory, which aims to find the maximum flow that can be sent from a source node (often referred to as the "source") to a sink node (often referred to as the "sink" or "target") in a flow network. A flow network is a directed graph where each edge has a capacity representing the maximum allowable flow that can pass through that edge.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact