#bernoulli — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #bernoulli, aggregated by home.social.
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This was my weekend project... Last year I got an external 5.25" #iomega #Bernoulli disk drive (the 90/150 MB variant). Sadly, those "portable" drives had an SCSI enclosure made out of plastic and due to the way it was handled, the case was badly broken with missing parts - hence beyond repair.
Took me quite some time to find a fitting replacement enclosure. I wanted one with no audio-out ports on the back, as that is not a CD-ROM and I did not want unused ports. Second, the face plate is non-standard and ever so slightly larger than a normal one, so the drive did not fit in any of the SCSI cases I had. However, a few weeks ago, I finally found a perfect one - or so I thought...
After installing the drive and hook up all cables, powering it up did nothing. Of course, the PSU in this enclosure was broken - who had guessed. So I spend three days creating a new one incl. a mounting plate, fitting connectors etc.
Only have to wire up the SCSI ID selector switch and then it's done.
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However, this comes with plenty of caveats and blind spots.
xG assumes that shots are independent Bernoulli trials.
In reality, shots within a match are correlated.
A team that's behind on the scoreboard tends to generate more chances, but often of lower quality.
The model also doesn't account for how good (or bad) the goalkeeper is. Nor does it capture the pressure or motivation players feel when taking a shot.
It also fails to capture the tactical context of a match.
In the end, there are moments when it's like modeling market correlations with a Pearson correlation matrix during a financial panic. The dependence structure changes. You need copulas!
Even with its limitations, though, xG remains one of the best metrics we have for characterizing a football match.
The scoreboard tells you who won.
xG tells you who was more likely to have won based on the chances they created.
#ExpectedGoals #xG #FootballAnalytics #SoccerAnalytics #DataScience #SportsAnalytics #Probability #Statistics #MachineLearning #LogisticRegression #GradientBoosting #Bernoulli #ExpectedValue #Football #Soccer #WorldCup #FIFA #TacticalAnalysis #PerformanceAnalysis #SportsData #DataVisualization #Analytics #QuantitativeAnalysis #Mathematics #PredictiveModeling #FootballStats #xGA #Mbappe #Spain #Argentina
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Bernoulli Disk Goes “Wii!” When Plugged Into WiiU
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My custom ecosystem for watching #Dexter on a laptop while saving battery:
1️⃣ Thermal Physics: Designed a 3D-printed case for a #Raspberry #Pi 4 #VPN #gateway (WireGuard + ProtonVPN). Passive cooling via chimney effect clears heat with a 2-3 cm/s airflow (Bernoulli).
2️⃣ Client Side: Booting BashCoreGee live in RAM. Privacy via Mullvad Browser, zero local crypto overhead, massive battery life.
Built step by step 👊🦾
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Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.
Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).
Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.
One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.
But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.
**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**
2/3
#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz
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Look what I found on a regional flea market. #iomega #bernoulli #vintagecomputing #retrocomputing
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One day, one decomposition
A000928: Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Irregular_primes.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/Irregular_primes.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Irregular_primes.html#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #irregular #primes #PrimeNumbers #graph #threejs #webGL
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One day, one decomposition
A249134: Numbers k such that Bernoulli number B_k has denominator 27303D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A249134.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A249134.html#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #denominator #graph #threejs #webGL
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I'll probably never own a drive to read those, but these are some very impressive floppy disk cartridges. Also, 20 megs in 1984 - that's more than a typical hard disk had at that time. 😲
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Ok, nix explodiert und das Laufwerk meldet "ready", wenn die Disk eingelegt ist. 🙂 Richtig testen kann ich erst später, wenn das Laufwerk wieder in einem externen SCSI-Gehäuse verbaut ist und ich einen Mac mit SCSI aufgebaut habe.
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Keine Ahnung, ob das eine gute Idee ist/war, aber da ich für das #Bernoulli-Laufwerk nur eine einzige, ziemlich verdreckte, 150 MB-Disk hatte, habe ich die mal zerlegt und gereinigt. Sehr interessanter Aufbau. Sind zwei Scheiben direkt übereinander. Dazwischen ist ein Flies. Vermute, die Köpfe werden zwischen die beiden Scheiben gefahren, da der Shutter nur die Oberseite freigibt.
In dem Video ist das Flies zwischen den Scheiben entfernt, daher sieht man nicht so gut, dass es zwei sind...
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Zur Abwechselung etwas #SCSI-Zeugs: zwei 4/8 GB DAT-Streamer, der linke vom Design her definitiv für alte Macs gedacht.
Ein 150 MB #IOMEGA #Bernoulli-Laufwerk. Gehäuse ist leider aus Plastik und an etlichen Stellen gebrochen. Laufwerk scheint, zumindest mechanisch, aber ok zu sein.
Und noch ein schöner SCSI-Tower. 🥳
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Let \(\varpi=\dfrac{\Gamma^2\left(\frac14\right)}{2\sqrt{2\pi}}=2.62205755\ldots\) be the lemniscate constant. Then,
\[\Large\displaystyle\sum_{n=1}^\infty\dfrac{1}{\sinh^4(\pi n)}=\dfrac{\varpi^4}{30\pi^4}+\dfrac{1}{3\pi}-\dfrac{11}{90}\]#Series #Sum #InfiniteSum #LemniscateConstant #GammaFunction #Lemniscate #LemniscateOfBernoulli #Bernoulli #Math #Maths #InfiniteSeries #HyperbolicSines
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Buen día, miserables.
Hace trescientos veintiséis años don Isaac Newton tuvo un momento de someone is wrong on the Internet (https://en.wikipedia.org/wiki/Later_life_of_Isaac_Newton#Bernoulli's_mathematical_challenge) y gracias a eso tenemos no sólo un bello resultado matemático, sino una frase que le ha complicado la vida a los filólogos durante siglos:
https://www.nature.com/articles/333592c0.pdf
¡Sean vuestros conflictos por lo menos tan productivos como éste!
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Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons - Any student new to the principles of fluid dynamics will be familiar with Bernoull... - https://hackaday.com/2023/10/19/variable-nozzle-ducted-fan-provides-fluid-dynamics-lessons/ #variablenozzle #fluiddynamics #remotecontrol #dronehacks #bernoulli #brushless #ductedfan #jetengine #venturi #drone #motor
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In the mood to prove a conjecture about Bernoulli polynomials? This way:
a(n) is the positive integer k such that the k-th derivative of the n-th Bernoulli polynomial B(n, x) contains only integer coefficients but no lower derivative of B(n, x) has this property.
More generally:
The 'integral index' k of a rational polynomial p(x) is the smallest integer k such that p^[k](x) is an integer polynomial, where p^[k](x) denotes the k-th derivative of p. (Integer polynomials have integral index 0.)
Using this way of speaking, the a(n) are the integral indices of the Bernoulli polynomials.
Conjecture: Every integer appears in the sequence a only a finite number of times.
a(n) = https://oeis.org/A366189
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To the attention of the #EDOC2023 and #CoopIS2023 Early Birds and Authors https://www.rug.nl/research/bernoulli/conf/edoc-2023/registration-form?lang=en
🗓️Authors' registration is open until September 3rd❗️❗️❗️
🗓️Early Bird registration until September 11th 📌Tutorial-only participants - use the tutorial-only option.We are looking forward to welcoming you at the #Bernoulli Institute in #Groningen this year!
@academicchatter #conference #InformationSystems @edutooters -
To the attention of the #EDOC2023 and #CoopIS2023 Early Birds and Authors
https://rug.nl/research/bernoulli/conf/edoc-2023/registration-form
🗓️Authors' registration is open until September 3rd❗️❗️❗️
🗓️Early Bird registration until September 11th
📌Tutorial-only participants - use the tutorial-only option
We are looking forward to welcoming you at the #Bernoulli Institute in #Groningen this year!
@academicchatter #conference #InformationSystems @edutooters -
Spectral learning of Bernoulli linear dynamical systems models for decision-making
Iris R Stone, Yotam Sagiv, Il Memming Park, Jonathan W. Pillow
Action editor: Shinichi Nakajima.
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In 1738, Daniel Bernoulli discovered the principle that increasing the flow of a gas or liquid decreases its pressure. #Poetry #Science #History #Hydrodynamics #Bernoulli (https://sharpgiving.com/thebookofscience/items/p1738.html)
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In 1683, Jacob Bernoulli discovered the third irrational constant, Euler’s number. #Poetry #Science #History #Mathematics #EulersNumber #Bernoulli (https://sharpgiving.com/thebookofscience/items/p1683.html)
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In 1683, Jacob Bernoulli discovered the third irrational constant, Euler’s number. #Poetry #Science #History #Mathematics #EulersNumber #Bernoulli (https://sharpgiving.com/thebookofscience/items/p1683.html)
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History of the Picard scheme by Steven L Kleiman
#lemniscate
#Bernoulli
#Fagnano
#Euler -
Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.
- Augusta Ada King, Countess of Lovelace
#science #math #mathematics #mathematician #ada #lovelace #language #life #bernoulli
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I've been thinking about implementing an algorithm for computing #Bernoulli numbers that Henri Cohen loosely describes in one of his books. Funnily enough, the first computer program intended to run on actual hardware was written by #AdaLovelace :lovelace: and was also intended for Bernoulli numbers.
Now I kind of want to understand her program and implement it too. I bet someone already has done it. Maybe I should go find what others have written on this.