Generalize function to allow adding some useful things which people wanted to be classical functions but which are not,
It therefore requires you to redefine and reprove all of calculus.
For this reason, most people are tempted to assume that all the hand wavy intuitive arguments undergrad teachers give are true and just move on with life. And they generally are.
One notable example where distributions pop up are the eigenvectors of the position operator in quantum mechanics, which are given by Dirac delta functions, which is most commonly rigorously defined in terms of distribution.
Distributions are also defined in a way that allows you to do calculus on them. Notably, you can define a derivative, and the derivative of the Heaviside step function is the Dirac delta function.
Publishes through the Fermilab YouTube channel under the playlist "Fermilab - Videos by Don Lincoln"
Some insights, but too much on the popular science side of things.
Is this exact sentence really from UNIX philosophy? en.wikipedia.org/wiki/Unix_philosophy#Do_One_Thing_and_Do_It_Well
Of course, it has precedents, e.g. jack of all trades, master of none
No, see: superconductor I-V curve.
Bibliography:
- physics.stackexchange.com/questions/62664/how-can-ohms-law-be-correct-if-superconductors-have-0-resistivity on Physics Stack Exchange
- physics.stackexchange.com/questions/69222/how-can-i-put-a-permanent-current-into-a-superconducting-loop
- www.quora.com/Do-superconductors-produce-infinite-current-I-V-R-R-0-How-do-they-fit-into-quantum-theory
- www.reddit.com/r/askscience/comments/dcgdf/does_superconductivity_imply_infinite_current/
- www.reddit.com/r/askscience/comments/7xhb46/what_would_happen_if_a_voltage_was_applied_to_a/
Amazingly confirms the wave particle duality of quantum mechanics.
The effect is even more remarkable when done with individual particles such individual photons or electrons.
Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.
The dual space of a vector space , sometimes denoted , is the vector space of all linear forms over with the obvious addition and scalar multiplication operations defined.
Since a linear form is completely determined by how it acts on a basis, and since for each basis element it is specified by a scalar, at least in finite dimension, the dimension of the dual space is the same as the , and so they are isomorphic because all vector spaces of the same dimension on a given field are isomorphic, and so the dual is quite a boring concept in the context of finite dimension.
Infinite dimension seems more interesting however, see: en.wikipedia.org/w/index.php?title=Dual_space&oldid=1046421278#Infinite-dimensional_case
It can be seen as the limit case of an Einstein solid at high temperatures. At lower temperatures, the heat capacity depends on temperature.
This website is really cool! crawl.akrasiac.org:8080/#lobby You can spectate players live and chat! Also has statistics.
Devs of this game are smart, they have one good in-tree tileset, unlike some other text-based games that didn't have an in-tree option...
Build on Ubuntu 21.10:
sudo apt install build-essential libncursesw5-dev bison flex liblua5.1-0-dev \
libsqlite3-dev libz-dev pkg-config python3-yaml binutils-gold python-is-python3 \
libsdl2-image-dev libsdl2-mixer-dev libsdl2-dev libfreetype6-dev libpng-dev \
fonts-dejavu-core advancecomp pngcrush
git clone --depth 1 --branch 0.28.0 https://github.com/crawl/crawl
cd crawl/crawl-ref/source
echo 0.28-a > util/release_ver
make -j`nproc` TILES=y
./crawlThis launches the UI version already for you.
The first gene in the E. Coli K-12 MG1655 genome. Remember however that bacterial chromosome is circular, so being the first doesn't mean much, how the choice was made: Section "E. Coli genome starting point".
Part of E. Coli K-12 MG1655 operon thrLABC.
At only 65 bp, this gene is quite small and boring. For a more interesting gene, have a look at the next gene, e. Coli K-12 MG1655 gene thrA.
Does something to do with threonine.
This is the first in the sequence thrL, thrA, thrB, thrC. This type of naming convention is quite common on related adjacent proteins, all of which must be getting transcribed into a single RNA by the same promoter. As mentioned in the analysis of the KEGG entry for e. Coli K-12 MG1655 gene thrA, those A, B and C are actually directly functionally linked in a direct metabolic pathway.
We can see that thrL, A, B, and C are in the same transcription unit by browsing the list of promoter at: biocyc.org/group?id=:ALL-PROMOTERS&orgid=ECOLI. By finding the first one by position we reach; biocyc.org/ECOLI/NEW-IMAGE?object=TU0-42486.
Contains the genes: e. Coli K-12 MG1655 gene thrL, e. Coli K-12 MG1655 gene thrA, e. Coli K-12 MG1655 gene thrB and e. Coli K-12 MG1655 gene thrC, all of which have directly linked functionality.
We can find it by searching for the species in the BioCyc promoter database. This leads to: biocyc.org/group?id=:ALL-PROMOTERS&orgid=ECOLI.
That page lists several components of the promoter, which we should try to understand!
Some of the transcription factors are proteins:
After the first gene in the codon, thrL, there is a rho-independent termination. By comparing:we understand that the presence of threonine or isoleucine variants, L-threonyl and L-isoleucyl, makes the rho-independent termination become more efficient, so the control loop is quite direct! Not sure why it cares about isoleucine as well though.
E. Coli Whole Cell Model by Covert Lab Default run variant Updated 2025-07-01 +Created 1970-01-01
The default run variant, if you don't pass any options, just has the minimal growth conditions set. What this means can be seen at condition.
Notably, this implies a growth medium that includes glucose and salt. It also includes oxygen, which is not strictly required, but greatly benefits cell growth, and is of course easier to have than not have as it is part of the atmosphere!
But the medium does not include amino acids, which the bacteria will have to produce by itself.
E. Coli Whole Cell Model by Covert Lab Other run variants Updated 2025-07-01 +Created 1970-01-01
Besides time series run variants, conditions can also be selected directly without a time series as in:which select row indices from so
python runscripts/manual/runSim.py --variant condition 1 1reconstruction/ecoli/flat/condition/condition_defs.tsv. The above 1 1 would mean the second line of that file which starts with:"condition" "nutrients" "genotype perturbations" "doubling time (units.min)" "active TFs"
"basal" "minimal" {} 44.0 []
"no_oxygen" "minimal_minus_oxygen" {} 100.0 []
"with_aa" "minimal_plus_amino_acids" {} 25.0 ["CPLX-125", "MONOMER0-162", "CPLX0-7671", "CPLX0-228", "MONOMER0-155"]1 means no_oxygen.Unfortunately, due to lack of one page to rule them all, the on-Git tree publication list is meager, some of the most relevant ones seems to be:
- 2021 open access review paper: journals.asm.org/doi/full/10.1128/ecosalplus.ESP-0001-2020 "The E. coli Whole-Cell Modeling Project". They should just past that stuff in a README :-) The article mentions that it is a follow up to the previous M. genitalium whole cell model by Covert lab. Only 43% of known genes modelled at this point however, a shame.
- 2020 under Science paywall: www.science.org/doi/10.1126/science.aav3751 "Simultaneous cross-evaluation of heterogeneous E. coli datasets via mechanistic simulation"
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