As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.
Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix which encodes the value for each possible pair of basis vectors.
The following aspects of Maxwell's equations make no sense without special relativity:
- the Lorentz force would be different observers have different speeds, see e.g.: charged particle moving at the same speed of electrons thought experiment
- Maxwell's equations imply that the speed of light is the same for all inertial reference frames
When charged particle though experiment are seen from the point of view of special relativity, it becomes clear that magnetism is just a direct side effect of charges being viewed in special relativity. One is philosophically reminded of how spin is the consequence of quantum mechanics + special relativity.
Experiments that involve sequencing bulk DNA found in a sample to determine what species are present, as opposed to sequencing just a single specific specimen. Examples of samples that are often used:
- river water to determine which bacteria are present, notably to determine if the water is free of dangerous bacteria. A concrete example is shown at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it".
- sea water biodiversity: ocean-microbiome.embl.de/companion.html
- food, including searching for desirable microorganisms such as in cheese or bread yeast
- poo, e.g. to study how the human microbiome influences health. There are companies actively working on this, e.g.: www.microbiotica.com/
One related application which most people would not consider metagenomics, is that of finding circulating tumor DNA in blood to detect tumors.
Metric space vs normed vector space vs inner product space Updated 2025-05-21 +Created 1970-01-01
TODO examples:
- metric space that is not a normed vector space
- norm vs metric: a norm gives size of one element. A metric is the distance between two elements. Given a norm in a space with subtraction, we can obtain a distance function: the metric induced by a norm.
Hierarchy of topological, metric, normed and inner product spaces
. Source. 
Bluetooth support: not enough RAM for it, though in principle its chip/transceiver could support it! microbit-micropython.readthedocs.io/en/v1.0.1/ble.html
Supported editors: microbit.org/code/
Bibliography:
The Nobel Prize of mathematics!
Microwave only found applications into the 1940s and 1950s, much later than radio, because good enough sources were harder to develop.
One notable development was the cavity magnetron in 1940, which was the basis for the original radar systems of World War II.
This is notably what the United States emerged to be after World War II. But it was likely what Nazi Germany also was, and many other superpowers.
Ciro Santilli feels that much more relevant would be to also include academia as in "military-industrial-academic" complex, the Wikipedia page actually mentions precedents to this idea.
The addition of congress/politicians is also relevant.
It is basically in this context that American science and technology flourished after World War II, including notably the development of quantum electrodynamics, Richard Feynman being a prototypical example, having previously worked on the Manhattan Project.
CIA 2010 covert communication websites Wayback Machine crawl date search Updated 2025-05-21 +Created 1970-01-01
Computer science course of the University of Oxford variant Updated 2025-05-21 +Created 1970-01-01
The "greatest common divisor" of two integers and , denoted is the largest natural number that divides both of the integers.
Because the Minkowski inner product product is not positive definite, the norm induced by an inner product is a norm, and the space is not a metric space strictly speaking.
E.g., as of 2020, their help login help.openstreetmap.org/ shows MyOpenID as an option, which was discontinued in 2014, and not Google OAuth.
They do still seem to have a bit more activity than gis.stackexchange.com/questions/tagged/openstreetmap on Stack Exchange.
Complaints:
- Transliteration is off by default!...... wiki.openstreetmap.org/wiki/Translation You just have to learn all scripts ever. Good luck with the Chinese characters. Genius.
- In order to see information about places, you have to click "Query features" on the toolbar first. Who made such a terrible UI? Direct click is a much, and so easy to implement?
- It is impossible to discern different types of paths and other walking path symbols, the symbols are too small, and just scale down to a line no matter how much you zoom in.
- Power lines are way too visible. While that is kind of cool, it is useless and distracting to most people most of the time.
- No street-level imagery...: help.openstreetmap.org/questions/1178/adding-photos
- No aerial imagery: help.openstreetmap.org/questions/6849/how-can-i-see-the-aerial-imagery-without-editing-the-map But that is kind of understandable, as that one might not be free.
- No restaurant ratings: help.openstreetmap.org/questions/64852/ratings-for-pois because it is "Subjective". OMG those people, such a huge value powerhouse wasted.
Terrible name, but very interesting dataset:
GitHub describes the input quite well:
The model takes as input a RGB image from the robot workspace camera and a task string describing the task that the robot is supposed to perform.What task the model should perform is communicated to the model purely through the task string. The image communicates to the model the current state of the world, i.e. assuming the model runs at three hertz, every 333 milliseconds, we feed the latest RGB image from a robot workspace camera into the model to obtain the next action to take.
TODO: how is the scenario specified?
TODO: any simulation integration to it?
There are unlisted articles, also show them or only show them.