Argument from authority Updated +Created
Carbon-14 Updated +Created
Crystal oscillator Updated +Created
Histone Updated +Created
These are apparenty an important part of transcriptional regulation given the number of modifications they can undergo! Quite exciting.
Project to explain each Nobel Prize better Updated +Created
Understand and explain amazingly every single Nobel Prize in physics, chemistry and biology. Since in particular the Nobel Foundation is unable to do that for any at all, especially of the key old ones, e.g. www.nobelprize.org/prizes/physics/1965/summary/. Hopeless.
To be fair, those in theoretical physics at least basically come down to reading a bunch of books. But perhaps anything slightly more experimental could have
Term of the University of Oxford Updated +Created
Each term has 8 weeks, and the week number is often used to denote the time at which something happens.
Week 0 is also often used to denote the week before classes officially start. This is especially important in the first term of the year (Michaelmas term) where people are coming back to school and meeting old and new friends.
At the end of the year, after Trinity term, students have exams. These basically account for all of the grades. In certain courses such as the Physics course of the University of Oxford, there is only new material on Michaelmas term and Hilary term, Trinity term being revision-only. So you can imagine that during Trinity term, students are going to be on edge.
Bibliography:
D Updated +Created
qiskit/qft.py Updated +Created
This is an example of the qiskit.circuit.library.QFT implementation of the Quantum Fourier transform function which is documented at: docs.quantum.ibm.com/api/qiskit/0.44/qiskit.circuit.library.QFT
Output:
init: [1, 0, 0, 0, 0, 0, 0, 0]
qc
     ┌──────────────────────────────┐┌──────┐
q_0: ┤0                             ├┤0     ├
     │                              ││      │
q_1: ┤1 Initialize(1,0,0,0,0,0,0,0) ├┤1 QFT ├
     │                              ││      │
q_2: ┤2                             ├┤2     ├
     └──────────────────────────────┘└──────┘
transpiled qc
     ┌──────────────────────────────┐                                     ┌───┐   
q_0: ┤0                             ├────────────────────■────────■───────┤ H ├─X─
     │                              │              ┌───┐ │        │P(π/2) └───┘ │ 
q_1: ┤1 Initialize(1,0,0,0,0,0,0,0) ├──────■───────┤ H ├─┼────────■─────────────┼─
     │                              │┌───┐ │P(π/2) └───┘ │P(π/4)                │ 
q_2: ┤2                             ├┤ H ├─■─────────────■──────────────────────X─
     └──────────────────────────────┘└───┘
Statevector([0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
             0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
             0.35355339+0.j, 0.35355339+0.j],
            dims=(2, 2, 2))

init: [0.0, 0.35355339059327373, 0.5, 0.3535533905932738, 6.123233995736766e-17, -0.35355339059327373, -0.5, -0.35355339059327384]
Statevector([ 7.71600526e-17+5.22650714e-17j,
              1.86749130e-16+7.07106781e-01j,
             -6.10667421e-18+6.10667421e-18j,
              1.13711443e-16-1.11022302e-16j,
              2.16489014e-17-8.96726857e-18j,
             -5.68557215e-17-1.11022302e-16j,
             -6.10667421e-18-4.94044770e-17j,
             -3.30200457e-16-7.07106781e-01j],
            dims=(2, 2, 2))
So this also serves as a more interesting example of quantum compilation, mapping the QFT gate to Qiskit Aer primitives.
If we don't transpile in this example, then running blows up with:
qiskit_aer.aererror.AerError: 'unknown instruction: QFT'
The second input is:
and the output of that approximately:
[0, 1j/sqrt(2), 0, 0, 0, 0, 0, 1j/sqrt(2)]
which can be defined simply as the normalized DFT of the input quantum state vector.
test_executables.js Updated +Created
This script tests all executables under a selected directory.
Ciro Santilli has been writing scripts of that type for a long time in order to test his programming self-learning setups with asserts.
The most advanced of those being the test system of Linux Kernel Module Cheat.
But had too much stuff that would be specific to that project, so Ciro decided to start this new one in Node.js, hopefully it will also be the last he ever writes.
A sample usage of the test library can be seen at: nodejs/sequelize/test.
Wooden spoon (award) Updated +Created
x86 Paging Tutorial / Intel manual Updated +Created
Although it is impossible to understand without examples in mind, try to get familiar with the manuals as soon as possible.
Specially interesting is Figure 4-4 "Formats of CR3 and Paging-Structure Entries with 32-Bit Paging", which gives the key data structures.
Fishers of men Updated +Created
Gospel of Matthew 4 King James Version:
18 And Jesus, walking by the sea of Galilee, saw two brethren, Simon called Peter, and andrew the Apostle his brother, casting a net into the sea: for they were fishers.
19 And he saith unto them, Follow me, and I will make you fishers of men.
Formal system Updated +Created
Lie algebra of Updated +Created
This is a good first concrete example of a Lie algebra. Shown at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" has an example.
We can use use the following parametrization of the special linear group on variables , and :
Every element with this parametrization has determinant 1:
Furthermore, any element can be reached, because by independently settting , and , , and can have any value, and once those three are set, is fixed by the determinant.
To find the elements of the Lie algebra, we evaluate the derivative on each parameter at 0:
Remembering that the Lie bracket of a matrix Lie group is really simple, we can then observe the following Lie bracket relations between them:
One key thing to note is that the specific matrices , and are not really fundamental: we could easily have had different matrices if we had chosen any other parametrization of the group.
TODO confirm: however, no matter which parametrization we choose, the Lie bracket relations between the three elements would always be the same, since it is the number of elements, and the definition of the Lie bracket, that is truly fundamental.
Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" then calculates the exponential map of the vector as:
with:
TODO now the natural question is: can we cover the entire Lie group with this exponential? Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation" explains why not.
Lie group Updated +Created
The key and central motivation for studying Lie groups and their Lie algebras appears to be to characterize symmetry in Lagrangian mechanics through Noether's theorem, just start from there.
Notably local symmetries appear to map to forces, and local means "around the identity", notably: local symmetries of the Lagrangian imply conserved currents.
The fact that there are elements arbitrarily close to the identity, which is only possible due to the group being continuous, is the key factor that simplifies the treatment of Lie groups, and follows the philosophy of continuous problems are simpler than discrete ones.
Bibliography:
Video 1.
What is Lie theory? by Mathemaniac 2023
. Source.
Senior Wrangler Updated +Created

There are unlisted articles, also show them or only show them.