Functional ultrasound imaging, often referred to as functional ultrasound or fUS, is a non-invasive imaging technique used to assess and visualize physiological processes within the body in real-time. Unlike traditional ultrasound, which primarily focuses on anatomical structures, functional ultrasound provides insights into the functionality of tissues and organs by monitoring their physiological activity. Key features of functional ultrasound imaging: 1. **Real-time Monitoring**: It allows for real-time assessment of blood flow, tissue movement, and other dynamic physiological processes.
Ultrasound-switchable fluorescence imaging is an advanced imaging technique that combines ultrasonography and fluorescence microscopy to enhance imaging capabilities in various biological and medical applications. This method exploits the unique properties of ultrasound waves to modulate or switch on/off fluorescence signals from specific markers or probes within tissues. ### Key Concepts: 1. **Fluorescence Imaging**: This involves the use of fluorescent dyes or proteins that emit light upon excitation.
An inverse function is a function that reverses the action of the original function. If you have a function \( f(x) \), the inverse function, denoted as \( f^{-1}(x) \), will take the output of \( f \) and return the original input.
The term "sixth power" refers to raising a number to the exponent of six. In mathematical terms, if \( x \) is a number, then the sixth power of \( x \) is expressed as \( x^6 \).
A "Blue Hole" is a marine geological phenomenon characterized by a large, underwater sinkhole or vertical cave that has a deep blue color due to its considerable depth. These formations are typically found in tropical and subtropical regions and are often associated with coral reef formations. The depth and clarity of the water in blue holes create striking visual contrasts, making them popular among divers and tourists. One of the most famous blue holes is the Great Blue Hole in Belize, which is part of the Belize Barrier Reef.
A Registered Professional Liability Underwriter (RPLU) is a designation awarded to professionals who specialize in underwriting professional liability insurance. This type of insurance provides protection to professionals against claims of negligence, errors, or omissions in the services they provide. The RPLU designation indicates that the individual has attained a certain level of expertise and knowledge in this specialized area of insurance.
Bidirectional text refers to text that contains both left-to-right (LTR) and right-to-left (RTL) writing systems within the same document or piece of content. This phenomenon is common in languages such as Arabic and Hebrew, which are written from right to left, while languages like English, French, and Spanish are written from left to right. In bidirectional text, the layout and reading order can become complex as the languages interact.
In Unified Modeling Language (UML), a **Classifier** is a fundamental concept that represents a general kind of thing in the model. Classifiers are used to define the structure and behavior of a system. They can encapsulate attributes (data) and operations (methods), and they are an essential part of object-oriented design. ### Types of Classifiers in UML 1. **Class**: The most common type of classifier.
Clock Constraints Specification Language (CCSL) is a formal language used for specifying temporal constraints in systems that involve timing and synchronization. It is particularly relevant in contexts like real-time systems, embedded systems, and event-driven systems where timing behavior is critical. CCSL provides a way to describe: 1. **Temporal Events**: These are events that occur at specific points in time or over specific intervals.
A software analysis pattern is a reusable solution to a recurring design problem in software analysis and design. These patterns provide a template or guideline for addressing specific issues or challenges that developers and architects may encounter during the analysis phase of software development. They embody best practices, reflecting the collective experience of software practitioners and helping to improve the efficiency, quality, and manageability of software systems.
The unit of electrical inductance is the henry (symbol: H). One henry is defined as the amount of inductance in a circuit in which a change in current of one ampere per second induces an electromotive force of one volt. Mathematically, this can be expressed as: 1 H = 1 V·s/A Where: - V is volts, - s is seconds, - A is amperes.
The approach many courses take to physics, specially "modern Physics" is really bad, this is how it should be taught:
This is likely because at some point, experiments get more and more complicated, and so people are tempted to say "this is the truth" instead of "this is why we think this is the truth", which is much harder.
But we can't be lazy, there is no replacement to the why.
Related:
Everyone is beginner when the field is new, and there is value in tutorials written by beginners.
For example, Ciro Santilli felt it shocking how direct and satisfying Richard Feynman's scientific vulgarization of quantum electrodynamics were, e.g. at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), and that if he had just assumed minimal knowledge of mathematics, he was about to give a full satisfactory picture in just a few hours.
Other supporters of this:
Compton scattering by Ciro Santilli 40 Updated 2025-07-16
Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.
The formula is exactly that of two relativistic billiard balls colliding.
Therefore this is evidence that photons exist and have momentum.
Video 2.
L3.3 Compton Scattering by Barton Zwiebach (2017)
Source.
System of units by Ciro Santilli 40 Updated 2025-07-16
The key thing in a good system of units is to define units in a way that depends only on physical properties of nature.
Ideally (or basically necessarily?) the starting point generally has to be discrete phenomena, e.g.
What we don't want is to have macroscopic measurement artifacts, (or even worse, the size of body parts! Inset dick joke) as you can always make a bar slightly more or less wide. And even metals evaporate over time! Though the mad people of the Avogadro project still attempted otherwise well into the 2010s!
Standards of measure that don't depend on artifacts are known as intrinsic standards.
Electromagnetism by Ciro Santilli 40 Updated 2025-07-16
As of the 20th century, this can be described well as "the phenomena described by Maxwell's equations".
Back through its history however, that was not at all clear. This highlights how big of an achievement Maxwell's equations are.

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