Ciro Santilli @cirosantilli 37

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Discrete Fourier transform Updated 2025-07-16

N

complex numbers

x_{k}

Output: another sequence of

N

complex numbers

X_{k}

such that:

x_{n} = \frac{1}{N} \sum_{k = 0}^{N - 1} X_{k} e^{i 2 π \frac{kn}{N}}

(1)

Intuitively, this means that we are braking up the complex signal into

N

sinusoidal frequencies:

$X_{0}$ : is kind of magic and ends up being a constant added to the signal because $e^{i 2 π \frac{kn}{N}} = e^{0} = 1$
$X_{1}$ : sinusoidal that completes one cycle over the signal. The larger the $N$ , the larger the resolution of that sinusoidal. But it completes one cycle regardless.
$X_{2}$ : sinusoidal that completes two cycles over the signal
...
$X_{N - 1}$ : sinusoidal that completes $N - 1$ cycles over the signal

and is the amplitude of each sine.

We use Zero-based numbering in our definitions because it just makes every formula simpler.

Motivation: similar to the Fourier transform:

compression: a sine would use N points in the time domain, but in the frequency domain just one, so we can throw the rest away. A sum of two sines, only two. So if your signal has periodicity, in general you can compress it with the transform
noise removal: many systems add noise only at certain frequencies, which are hopefully different from the main frequencies of the actual signal. By doing the transform, we can remove those frequencies to attain a better signal-to-noise

In particular, the discrete Fourier transform is used in signal processing after a analog-to-digital converter. Digital signal processing historically likely grew more and more over analog processing as digital processors got faster and faster as it gives more flexibility in algorithm design.

Sample software implementations:

numpy.fft, notably see the example: numpy/fft.py

Figure 1.
DFT of $2 sin (t) + cos (4 t)$ with 25 points
. This is a simple example of a discrete Fourier transform for a real input signal. It illustrates how the DFT takes N complex numbers as input, and produces N complex numbers as output. It also illustrates how the discrete Fourier transform of a real signal is symmetric around the center point.

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Display manager Updated 2025-07-16

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Check which you you have:

systemctl status display-manager.service

Tested on Ubuntu 23.10 I see:

● gdm.service - GNOME Display Manager
     Loaded: loaded (/lib/systemd/system/gdm.service; static)
     Active: active (running) since Sun 2023-12-24 10:34:50 GMT; 23min ago
    Process: 1827 ExecStartPre=/usr/share/gdm/generate-config (code=exited, status=0/SUCCESS)
   Main PID: 1850 (gdm3)
      Tasks: 4 (limit: 71817)
     Memory: 6.8M
        CPU: 119ms
     CGroup: /system.slice/gdm.service
             └─1850 /usr/sbin/gdm3

which means I have GNOME Display Manager.

Bibliography:

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Django (web-framework) Updated 2025-07-16

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React setups:

One problem with Django is that it does not expose its ORM as an external library: stackoverflow.com/questions/33170016/how-to-use-django-1-8-5-orm-without-creating-a-django-project which is wasteful of development time.

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DNA detection Updated 2025-07-16

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DNA detection means determining if a specific DNA sequence is present in a sample.

This can be used to detect if a given species of microorganism is present in a sample, and is therefore a widely used diagnostics technique to see if someone is infected with a virus.

You could of course do full DNA Sequencing to see everything that is there, but since it is as a more generic procedure, sequencing is more expensive and slow.

The alternative is to use a DNA amplification technique.

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DNA microarray Updated 2025-07-16

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Can be seen as a cheap form of DNA sequencing that only test for a few hits. Some major applications:

gene expression profiling
single-nucleotide polymorphism: specificity is high enough to detect snips

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DNA repair Updated 2025-07-16

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DNA sequencing milestone Updated 2025-07-16

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Most of these are going to be Whole-genome sequencing of some model organism:

1975 by Sanger et al.: 5 kbp of the single-stranded bacteriophage ΦX174 using Sanger's radiolabelling method
1981 by Sanger et al.: 17 kbp of human mitochondrial DNA via Sanger method, known as the Cambridge Reference Sequence
2003: Human Genome Project (3 Gbp)

en.wikipedia.org/wiki/Whole_genome_sequencing#History lists them all. Basically th big "firsts" all happened in the 1990s and early 2000s.

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DNS Census 2013 Updated 2025-07-16

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dnscensus2013.neocities.org/

Data format overview: opendata.stackexchange.com/questions/1951/dataset-of-domain-names/21077#21077

TODO was this data also obtained illegally like the Carna botnet

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NIST Atomic Spectra Database Updated 2025-07-16

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NIST database for spectral line: physics.nist.gov/PhysRefData/ASD/lines_form.html

Let's do a sanity check.

Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on

From there we can see for example the 1 to 2 lines:

1s to 2p: 121.5673644608 nm
1s to 2: 121.56701 nm TODO what does that $2$ mean?
1s to 2s: 121.5673123130200 TODO what does that mean?

We see that the table is sorted from lower from level first and then by upper level second.

So it is good to see that we are in the same 121nm ballpark as mentioned at hydrogen spectral line.

TODO why I can't see 2s to 2p transitions there to get the fine structure?

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DNS configuration of Ciro Santilli's website Updated 2025-07-16

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AKA how this GitHub page gets served under the domain: cirosantilli.com

Ciro only touches this very rarely, and always forgets and go into great pain whenever a change needs to done, so it is important to document it.

The last change was of 2019-07-07, when Ciro moved from the www subdomain www.cirosantilli.com to the APEX cirosantilli.com. A redirect is setup from the www subdomain to APEX.

GoDaddy DNS entries:

Type    Name    Value                   TTL
A       @       185.199.108.153         1 Hour
A       @       185.199.109.153         1 Hour
A       @       185.199.110.153         1 Hour
A       @       185.199.111.153         1 Hour
CNAME   www     cirosantilli.github.io  1 Hour

Moved cirosantilli.com to Porkbun 2022-02, unfortunatly records were not automatically updated and domain went down for a bit, upadded to new entries for IPv6 as well which are not documented by GitHub:

TYPE 	HOST	ANSWER	TTL	PRIORITY	OPTIONS
A	cirosantilli.com	185.199.108.153	600
A	cirosantilli.com	185.199.109.153	600
A	cirosantilli.com	185.199.110.153	600
A	cirosantilli.com	185.199.111.153	600
AAAA	cirosantilli.com	2606:50c0:8000::153	600
AAAA	cirosantilli.com	2606:50c0:8001::153	600
AAAA	cirosantilli.com	2606:50c0:8002::153	600
AAAA	cirosantilli.com	2606:50c0:8003::153	600
CNAME	www.cirosantilli.com	cirosantilli.github.io	600

where the IPs are obtained from: help.github.com/en/articles/setting-up-an-apex-domain#configuring-a-records-with-your-dns-provider (archive).

Under github.com/cirosantilli/cirosantilli.github.io/settings

Custom domain: cirosantilli.com
Enforce HTTPS: checked

And the CNAME file is tracked in this repository: CNAME.

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Integer factorization algorithms better than Shor's algorithm Updated 2025-07-16

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2023 www.schneier.com/blog/archives/2023/01/breaking-rsa-with-a-quantum-computer.html comments on "Factoring integers with sublinear resources on a superconducting quantum processor” arxiv.org/pdf/2212.12372.pdf

A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong.
We have long known from Shor’s algorithm that factoring with a quantum computer is easy. But it takes a big quantum computer, on the orders of millions of qbits, to factor anything resembling the key sizes we use today. What the researchers have done is combine classical lattice reduction factoring techniques with a quantum approximate optimization algorithm. This means that they only need a quantum computer with 372 qbits, which is well within what’s possible today. (The IBM Osprey is a 433-qbit quantum computer, for example. Others are on their way as well.)

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Interesting members of the Santilli family Updated 2025-07-16

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Found through Google with no direct relation known to Ciro Santilli:

en.wikipedia.org/wiki/Santilli: Wikipedia page of the glorious family, Santillis with their own Wikipedia page:
- Ruggero Santilli: "fringe science guy", by far dominates Google as of 2019. Created the respectable R.M. Santilli Foundation
- Ray Santilli made a fake 1995 alien autopsy movie, YouTube sample: www.youtube.com/watch?v=sVcaT2QnoDs
- Ivana Santilli: Canadian singer, pop-electric-chill: www.youtube.com/watch?v=hQRuVN0H8dM
accounts on important websites
- github.com/santilli anonymous GitHub as of 2019
- santilli.com/ for rent by realnames.com/ (wiki page) as of 2019
- twitter.com/santilli is Marcel Santilli the guy who took the Twitter handle of the family
  www.linkedin.com/in/marcelsantilli
  Also Brazilian and tech related like Ciro Santilli.
- www.youtube.com/user/TheOverthrowShow thepetesantillishow.com/ Pete Santilli, American Conservative news commentator show, makes Ciro cringe of boredom. At least he has a passion.

Possibly related variants:

Santillo:
- Will Santillo who makes somewhat artistic porn photos. His website with several free demos: santillophotography.com/
- www.linkedin.com/in/ciro-santillo-2025a6ba/ a "Ciro Santillo", github.com/Ciruxx, also a programmer
Santilly, a town in Saône-et-Loire department, France
- santilly.com/ redirects to www.pompes-funebres-santilly.com/fr/, a French funerary service

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Interests Updated 2025-07-16

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The key content previously on this page was moved to the following sections:

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Interface Message Processor Updated 2025-07-16

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NIST Post-Quantum Cryptography Standardization Updated 2025-07-16

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This post-quantum cryptography competition by NIST is a huge milestone of the field.

It was mind blowing when in 2022, after several years of selection, one of the 7 finalists was broken on a classical computer, not even in a quantum computer! news.ycombinator.com/item?id=30466063 | eprint.iacr.org/2022/214 Breaking Rainbow Takes a Weekend on a Laptop by Ward Beullens. Dude announced he had a break a few days before submission: twitter.com/WardBeullens/status/1492780462028300290 On Twitter. He's so young. Epic.

Edit: and then, after the third round, things were a bit unclear, so they made a fourth round with 4 choices out of the 7 from round 3, and in August 2022 one of the four was broken again on a classic CPU!!! OMG: arstechnica.com/information-technology/2022/08/sike-once-a-post-quantum-encryption-contender-is-koed-in-nist-smackdown/

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OpenShot Updated 2025-07-16

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Ubuntu 20.10 crash...:

  exceptions:ERROR Unhandled Exception
Traceback (most recent call last):
  File "/usr/bin/openshot-qt", line 11, in <module>
    load_entry_point('openshot-qt==2.5.1', 'gui_scripts', 'openshot-qt')()
  File "/usr/lib/python3/dist-packages/openshot_qt/launch.py", line 97, in main
    app = OpenShotApp(argv)
  File "/usr/lib/python3/dist-packages/openshot_qt/classes/app.py", line 218, in __init__
    from windows.main_window import MainWindow
  File "/usr/lib/python3/dist-packages/openshot_qt/windows/main_window.py", line 45, in <module>
    from windows.views.timeline_webview import TimelineWebView
  File "/usr/lib/python3/dist-packages/openshot_qt/windows/views/timeline_webview.py", line 42, in <module>
    from PyQt5.QtWebKitWidgets import QWebView
ImportError: /usr/lib/x86_64-linux-gnu/libQt5Quick.so.5: undefined symbol: _ZN4QRhi10newSamplerEN11QRhiSampler6FilterES1_S1_NS0_11AddressModeES2_, version Qt_5_PRIVATE_API

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Optical fiber Updated 2025-07-16

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Video 1.

The Story of Light by Bell Labs (2015)

Source. Gives some ideas of the history of fiber optics. Features: Herwig Kogelnik.

Video 2.

Fiber optic cables by EngineerGuy

. Source.

Video 3.

Fiber optics fundamentals by Shaoul Ezekiel

. Source. 2008 at MIT. Theory and demonstration.

youtu.be/0DCrIAxEv_Y?t=560:
- on smaller wavelengths, loss is due to Rayleigh scattering
- on longer wavelengths, loss is due to material absorption
Terefore, the 1.5 micrometer window truly is the minimum.

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Optics Updated 2025-07-16

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The science and engineering of light!

When dealing more specifically with individual photons, we usually call it photonics.

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Orange Papers Updated 2025-07-16

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See: cirosantilli.com/china-dictatorship/orange-papers

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Ordered pair Updated 2025-07-16

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Sets are unordered, but we can use them to create ordered objects, which are of fundamental importance. Notably, they are used in the definition of functions.

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