#ConradMitzenmacher-6
"In this paper, we begin by reviewing the fascinating history of this fundamental problem. Then, we use methods from #ComplexAnalysis to prove that Miller’s random monkey experiment yields power laws for [the] rank-frequency distribution
>
>with probability assignments to keys satisfying a rationality assumption on log-ratios of pairs of probabilities.
We use analytic methods to establish a simple explicit power law in cases with rational log-ratios for pairs of probabilities; more specifically,
> Image
>we use generalized Dirichlet series and an elementary identity established by means of Fourier series. Passing to a limit on these formulas predicts an analogous result in the remaining “irrational” cases, and this prediction agrees with an unpublished theorem..by Montgomery;
>
>in Section VI, we provide Montgomery’s argument, that uses methods that are standard in analytic number theory.
The use of analytic techniques to study problems of this type is not in itself novel (see [8]–[10], for example), and it is also a well-known phenomenon that
>
>rationality issues can lead to cases that behave in a manner somewhat different from generic cases.
The novelty of this paper is, therefore, not in the consideration of analytic techniques but rather in the application of these techniques to an interesting nontrivial problem
>

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More from @LGcommaI

Jul 18
Nationale Notenbanken haben um 2010 HEIMLICH Geld 'gedruckt'. Aufgedeckt hat es v.a. #DanielHoffmann/#TUBerlin.
archive.ph/SbKJT("EZB sieht tatenlos zu
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Erstmals [sagte] die #EZB.., wie viel Geld sie in die Finanzmärkte zu pumpen gedachte,
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>um die lahme Konjunktur und die äußerst niedrige Inflation anzukurbeln.

..1,14 Billionen #Euro schweres Anleihenkaufprogramm..
neue geldpolitische Ära..

Tatsächlich hat diese Ära schon Jahre zuvor begonnen – nur hat das so gut wie niemand mitbekommen[!].
>
>
Die Notenbanken des #Euro-Systems kaufen schon längst in großem Stil Wertpapiere auf. Und dabei macht das erste kleine Staatsanleihen-Programm der EZB aus dem Jahr 2010 nur den kleinsten Teil aus. Denn zusätzlich haben die nationalen Zentralbanken in Frankreich, #Italien
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Jul 18
"Der Typ, der die #InternetExplorer-bugs verwaltet..war..30..sah aus wie..60 und meinte: Es kommen..so viele #bugs hier rein! Wir kommen gar nicht dazu, irgendwelche [davon] zu schließen; wir verwalten die nur noch." (21m20s )

#Rot
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Jul 18
#Empfehlenswert:#Recommendable
#Frankreich:#France
#Franzoesisch:#French:#Francais
#Neuigkeiten:#NEWS:#NOUVELLES
#TVL ["Le Journal" of 2022-07-18]

("la situation en #Ukraine. Le président a décidé de limoger plusieurs hauts responsables tout en réclamant
>
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Nous évoquerons ensuite l’arrivée du texte de loi sur le pouvoir d’achat à l’Assemblée nationale, un nouveau test pour la majorité mais aussi pour les oppositions.
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Et puis nous reviendrons sur les violents incendies qui ravagent le sud-ouest de la #France."
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Jul 18
#ConradMitzenmacher-7

"A. Notation and Terminology

Throughout this paper, the phrase ›log-ratio‹ for a pair of positive real numbers refers to the ratio of their logarithms (to a common base, the choice of which cancels out)..

All logarithms without an indicated base
>
>are understood to be taken to the base 𝑒..

II. Review of Definitions and History
Our treatment here is based on a recent survey by Mitzenmacher [#Internet #Mathematics 1(2), 226‒251 (2004)], to which we refer the reader for more information.[ Footnote: For instance,
> Image
>this survey describes another argument that leads to a #PowerLaw of word frequency based on preferential attachment, originally due to Simon [Biometrika 42(3/4), 425–440 (1955)]. We do not present this argument here.]
In what follows, we let 𝑓ⱼ be the (asymptotic) fraction of>
Read 9 tweets
Jul 16
quarks.de/technik/energi…

Trotzdem sind..Forschungsexpertise und neue Ideen gefragt, wie man langlebige radioaktive Spaltprodukte entschärfen kann.

[Z.B.] mit laserbasierten Verfahren.
..Experimente dazu gibt es..von Gérard #Mourou und #DonnaStrickland, den Nobelpreisträgern aus>
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Relevanter Kontext: connectiv.events/gerard-mourou-…("Physiker #GerardMourou [sagt], dass Laser die Lebensdauer von Atommüll von „einer Million Jahre auf 30 Minuten“ senken könnten, ..")
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„Die Kernenergie ist vielleicht der beste Kandidat für die Zukunft“, sagte der Nobelpreisträger, „aber wir haben immer noch viel gefährlichen Müll. Die Idee ist,
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