**Cross-layer interaction** and **service mapping** are concepts often discussed in the context of network management, system architecture, and distributed systems. Here’s a brief overview of each: ### Cross-layer Interaction 1. **Definition**: Cross-layer interaction refers to the communication and collaboration between different layers of a system or architecture. This is particularly important in network protocols, where layers (like the application, transport, network, and link layers) typically operate independently.
The rich-club coefficient is a measure used in network science to analyze the organization and connectivity patterns within a network, especially in relation to the nodes with high degrees (i.e., nodes that have a large number of connections). The concept is based on the observation that nodes with many connections (often referred to as "rich" nodes) tend to be more interconnected than would be expected in a random network.
Peak Information Rate (PIR) refers to the maximum rate at which data can be transmitted over a network or communication channel. It is generally defined in bits per second (bps) and represents the highest data transfer rate achievable under optimal conditions. In the context of networking and telecommunications, PIR is often used to describe the capabilities of various technologies, including broadband services, where it indicates the maximum speed available to users.
PyTorch model by Ciro Santilli 40 Updated 2025-08-08
This section lists specific models that have been implemented in PyTorch.
Sinusoidal by Ciro Santilli 40 Updated 2025-07-16
A function that is either a sine or cosine, i.e. we don't know or care where the origin is exactly.
This is particularly relevant in electronics, where the oscilloscope's time origin is set to match the wave.
Hanford site by Ciro Santilli 40 Updated 2025-07-16
The B Reactor of the facility produced the plutonium used for Trinity and Fat Man, and then for many more thousand bombs during the Cold War. More precisely, this was done at
Located in Washington, in a dry place the middle of the mountainous areas of the Western United States, where basically no one lives. The Columbia river is however nearby, that river is quite large, and provided the water needed by their activities, notably for cooling the nuclear reactors. It is worth it having look on Google Maps to get a feel for the region.
Unlike many other such laboratories, this one did not become a United States Department of Energy national laboratories. It was likely just too polluted.
Figure 1.
Aerial image of the Hanford site in 1960
. Source.
Curl (mathematics) by Ciro Santilli 40 Updated 2025-07-16
Points in the direction in which a wind spinner spins fastest.
Del by Ciro Santilli 40 Updated 2025-07-16
Oh, and if it weren't enough, mathematicians have a separate name for the damned nabla symbol : "del" instead of "nabla".
TODO why is it called "Del"? Is is because it is an inverted uppercase delta?
Divergence by Ciro Santilli 40 Updated 2025-07-16
Takes a vector field as input and produces a scalar field.
Mnemonic: it gives out the amount of fluid that is going in or out of a given volume per unit of time.
Therefore, if you take a cubic volume:
  • the input has to be the 6 flows across each face, therefore 3 derivatives
  • the output is the variation of the quantity of fluid, and therefore a scalar
Gradient by Ciro Santilli 40 Updated 2025-07-16
Takes a scalar field as input and produces a vector field.
Mnemonic: the gradient shows the direction in which the function increases fastest.
Think of a color gradient going from white to black from left to right.
Therefore, it has to:
  • take a scalar field as input. Otherwise, how do you decide which vector is larger than the other?
  • output a vector field that contains the direction in which the scalar increases fastest locally at each point. This has to give out vectors, since we are talking about directions

Pinned article: 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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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