📊 It's Thursday, time for our weekly (but weakly so) quiz! This week: integers, and remarkable sequences.

See this as an extended ad for the OEIS, if you will. Also, if you don't know the OEIS: go check it out (and come back)! oeis.org

1/
Let's start with a "fun" one. To be unhelpful, let's say as a hint that I'm expanding exp(e^x-1) as a series around 0, and am interested in the coefficients

Q1: Guess what number comes next—maybe this sequence will ring a bell? [There might be a trap]
1, 1, 2, 5, 15, 52, ??

2/
We won't do too many of those "guess what's next" games though, since they are mostly meaningless. But let's mention that, of course, @xkcdComic has a comic about integer sequences, because XKCD is basically Borges' library for the Internet.
xkcd.com/2016/
3/
Next question: a lot of integer sequences have a combinatorial or interesting raison d'être, and many are named after their "discoverer" or at least have an interesting name.
Q2: which one of those did I make up?

4/
We're going to get back to that at the end, but first, a look at prime numbers.

There are a lot of "types" of prime numbers. For instance, the set of even prime numbers is pretty small.

Q3: Which one of those sets is known to contain infinitely many prime numbers?

5/
Now, let's see. We have all those strange sequences—they are all infinite, there are too many to even consider, so let's focus on a few interesting ones.

Q4: which one of the below sequences grows the fastest?

5/
And as promised, to conclude... other funny names. There are so many of them. So. Many.

Q5: Which one of the names below did I make up?

6/
That's all for today! Of course, we didn't even scratch the surface of all the bizarre, interesting, or boring things I could have asked.

As usual, answers and discussions tomorrow. In the meantime, feel free to comment (and/or give your favourite integer sequence) below!

7/end

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More from @ccanonne_

4 Dec
📊 Answers and discussion for yesterday's quiz on sequences (and their names).

Before we go to the first question, again: if you haven't, bookmark oeis.org. It's useful: the solution to some of your problems may be recorded there!

1/
So, the first question... was a trap. All three answers were valid...

I was personally thinking of 203, since that corresponds to the next Bell number (en.wikipedia.org/wiki/Bell_numb…).

But maybe your were thinking of something else? Maybe the number of...

2/
... ascent sequences avoiding the pattern 201 (oeis.org/A202062)? Or the number of set partitions of [n] that avoid 3-crossings (oeis.org/A108304)? Who am I to judge?

(I prefer Bell numbers.)

3/
Read 10 tweets
3 Dec
A paper with a broken and ill-defined "solution" to privacy in ML gets a $50k prize?! While said solution was already fully broken at the time of the award—on a challenge chosen by the authors?🤦‍♂️

The presentation slides must have been hella convincing.
Will Carlini et al. get a share of the prize money for breaking the system prior to the award ceremony? arxiv.org/abs/2011.05315
Disclaimer: I am in no way affiliated w/ any of the authors of the attack, nor w/ the authors of the original paper, nor w/ basically anyone involved. I'm just dismayed at the signal sent, & the overall waste—so much good work done elsewhere, and this is what gets the highlight.
Read 5 tweets
27 Aug
📊 It's Thursday for many, time for this week's quiz! As alluded earlier, we're going to flip coins. Like, a lot.

Today: you have a biased coin which lands heads with some probability p∊(0,1), and you can toss it as many times as you want. You don't know p, though...

1/10
... which is a real shame, since you want to simulate *another* biased coin which lands heads w/ proba exactly f(p), where f: (0,1)→(0,1) is fixed.
(Also, you'd like to do this efficiently, thank you very much.)

Let's start with a simple function: f(p)=1/2.

Q1: Can you?

2/10
OK, so that was the warmup. Let's formalize a bit more what "efficiently" means here. For us, it will mean (1) with a number of coins finite almost surely (no infinite sequence of tosses), and (2) with a finite automaton.

Ha.

A finite automaton.

3/10
Read 10 tweets
6 Aug
📊 It's Thursday [reference needed], time for a weᵄekly quiz! Given some recent events about randomized polynomial time (RP), it feels like a short discussion about 🎲 is topical.

So, let's go: Las Vegas, Monte Carlo, and... Bellagio (?) algorithms!

1/8
Let's start with some definitions—because that's fun, right. We'll discuss 3 types of decision algorithms: BPP (Monte Carlo), ZPP (Las Vegas), and RP (the... other) algorithms.

All three are randomized 🎲. What's the difference? The type of errors they allow.

2/8
↬BPP: efficient (run in poly time), can make mistakes but only w/ probability ≤¼

↬RP: efficient, can make mistakes but only when they say "no", and even then w/ probability ≤½

↬ZPP: efficient *in expectation* (yet could run forever sometimes), but never make mistakes.

3/8
Read 9 tweets
30 Jul
📊 Today, (weakly|weekly) quiz will be about graphs. The ones with nodes and edges, not those plotting against you.

Specifically, *planar* graphs. The nice ones.

1/7
What's an (undirected) graph here? Just a pair G=(V,E) of n=|V| vertices (nodes) and m=|E| edges, where E ⊆ V×V and each edge in E is a pair (v₁,v₂) indicating if the two nodes v₁ and v₂ are connected.
If E=V×V (all possible edges), G is the complete graph, Kₙ.

2/7
(above, that's K₇, also very cool on t-shirts.). A graph G is *planar* if you can draw it on a sheet of paper w/o crossing edges ("can be embedded in the plane"). Kₙ, for instance, is not planar.

Leading us to Q1: I give you G. How hard is it to decide if it's planar?

3/7
Read 7 tweets
23 Jul
📊 It's Thursday: time for our wÆkly quiz! I'll build a little bit on last week's statistics/algorithms thread (see below for a recap), and ask you two 2️⃣ questions.

General topic: testing distributions, "leaky" measurements, and adaptivity. 🔍

1/6
Suppose you have the following type of measurements: at each time step, you get to specify a subset S⊆[k], your "question"; and *try* to observe a fresh sample x from the unknown distribution p (over [k]). With probability η, you get to see x: it's leaked to you 🎁...

2/6
... but with probability 1-η, you only get to know if x is in S. (Think of it as yes/no ❓, but w/ an η chance to get full info 🎁.)

We'll fix η=1/√k: you don't win 🎁. often. Your goal: test if p is uniform, or at large statistical distance (TV) from uniform, say 1/100.

3/6
Read 6 tweets

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