NeuroSky is a company that specializes in the development of brainwave monitoring technology and applications. Founded in 2004, NeuroSky focuses on creating consumer and medical devices that utilize electroencephalography (EEG) to measure brain activity. Their technology often involves the use of lightweight and affordable headsets or sensors that can detect brainwave patterns and convert them into data that can be used for various applications, such as gaming, meditation, and cognitive training.
The Maurer–Cartan form is a fundamental concept in the theory of Lie groups and differential geometry, particularly in the study of Lie group representations and the geometry of principal bundles. Given a Lie group \( G \), the Maurer–Cartan form is a differential 1-form on the Lie group that captures information about the group structure in terms of its tangent space.
A "moving frame" can refer to different concepts depending on the context, including mathematics, physics, and engineering. Here are a few interpretations: 1. **Mathematics (Differential Geometry)**: In the context of differential geometry, a moving frame is often used to describe a set of vectors that vary along a curve or surface.
In music, a "key" refers to the tonal center around which a piece of music is organized. It is defined by a specific scale that serves as the foundation for melodies and harmonies within a composition. Each key is typically associated with a specific note (the tonic) and a set of pitches that can be used in the music. Keys are categorized as major or minor: 1. **Major Key**: Associated with a bright and happy sound.
GHDL by Ciro Santilli 37 Updated 2025-07-16
Examples under vhdl.
First install GHDL. On Ubuntu:
sudo apt install verilator
Tested on Verilator 1.0.0, Ubuntu 22.04.
Run all examples, which have assertions in them:
cd vhdl
./run
RISC-V by Ciro Santilli 37 Updated 2025-07-16
The leading no-royalties options as of 2020.
China has been a major RISC-V potential user in the late 2010s, since the country is trying to increase its semiconductor industry independence, especially given economic sanctions imposed by the USA.
E.g. a result of this, the RISC-V Foundation moved its legal headquarters to Switzerland in 2019 to try and overcome some of the sanctions.
Paging is implemented by the CPU hardware itself.
Paging could be implemented in software, but that would be too slow, because every single RAM memory access uses it!
Operating systems must setup and control paging by communicating to the CPU hardware. This is done mostly via:
Processes can however make requests to the OS that cause the page tables to be modified, notably:
The kernel then decides if the request will be granted or not in a controlled manner.
Natural pseudodistance is a concept used in mathematical biology and ecology, particularly in the study of population genetics and evolutionary theory. It is typically used to quantify the genetic differences or relationships between populations or individuals based on genetic data. In general, a pseudodistance is a metric that measures how "far apart" two entities are within a particular space or context, but it may not fulfill all the properties of a true distance metric (such as the triangle inequality).
FFFFF 000 points to its own physical address FFFFF 000. This kind of translation is called an "identity mapping", and can be very convenient for OS-level debugging.
When TLB is filled up, older addresses are overwritten. Just like CPU cache, the replacement policy is a potentially complex operation, but a simple and reasonable heuristic is to remove the least recently used entry (LRU).
With LRU, starting from state:
  valid  linear  physical
  -----  ------  --------
> 1      00003   00005
  1      00007   00009
  1      00009   00001
  1      0000B   00003
adding 0000D -> 0000A would give:
  valid  linear  physical
  -----  ------  --------
  1      0000D   0000A
> 1      00007   00009
  1      00009   00001
  1      0000B   00003
The Linux Kernel reserves two zones of virtual memory:
  • one for kernel memory
  • one for programs
The exact split is configured by CONFIG_VMSPLIT_.... By default:
  • on 32-bit:
    • the bottom 3/4 is program space: 00000000 to BFFFFFFF
    • the top 1/4 is kernel memory: C0000000 to FFFFFFFF, like this:
      ------------------ FFFFFFFF
      Kernel
      ------------------ C0000000
      ------------------ BFFFFFFF
      
      
      Process
      
      
      ------------------ 00000000
  • on 64-bit: currently only 48-bits are actually used, split into two equally sized disjoint spaces. The Linux kernel just assigns:
    • the bottom part to processes 00000000 00000000 to 008FFFFF FFFFFFFF
    • the top part to the kernel: FFFF8000 00000000 to FFFFFFFF FFFFFFFF, like this:
      ------------------ FFFFFFFF
      Kernel
      ------------------ C0000000
      
      
      (not addressable)
      
      
      ------------------ BFFFFFFF
      Process
      ------------------ 00000000
Kernel memory is also paged.
Now, there are two ways to go about this.
The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.
The second is the much celebrated ladder operator method.
It basically replaces a bunch of discrete digital components with a single chip. So you don't have to wire things manually.
Particularly fundamental if you would be putting those chips up a thousand cell towers for signal processing, and ever felt the need to reprogram them! Resoldering would be fun, would it? So you just do a over the wire update of everything.
Vs a microcontroller: same reason why you would want to use discrete components: speed. Especially when you want to do a bunch of things in parallel fast.
One limitation is that it only handles digital electronics: electronics.stackexchange.com/questions/25525/are-there-any-analog-fpgas There are some analog analogs, but they are much more restricted due to signal loss, which is exactly what digital electronics is very good at mitigating.
Video 1.
First FPGA experiences with a Digilent Cora Z7 Xilinx Zynq by Marco Reps (2018)
Source. Good video, actually gives some rationale of a use case that a microcontroller wouldn't handle because it is not fast enough.
Video 2.
FPGA Dev Board Tutorial by Ben Heck (2016)
Source.
Video 3.
The History of the FPGA by Asianometry (2022)
Source.

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