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<title>Harmonic number and Zeta functions explained in Julia (part 2) - You don't need to prove this</title>
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<h1>Harmonic number and Zeta functions explained in Julia (part 2)</h1>
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<span> Posted on Wed 15 April 2020 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<p><em>This is part 2 of a series explaining what is Harmonic number and it's connection with Zeta
functions. The post is written as a Jupyter notebook with Julia kernel. You can download it
<a href="https://newptcai.github.io/notebook/2020-04-14-harmonic-2.ipynb">here</a>.</em></p>
<hr>
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<h2 id="Lottery-in-a-pandemic">Lottery in a pandemic<a class="anchor-link" href="#Lottery-in-a-pandemic">¶</a></h2><p>In the last post we have seen how to compute and approximate the $m$-th harmonic number, i.e.,
$$
H_m = \sum_{i=1}^m \frac{1}{i}
$$</p>
<p>This number appears in the famous <a href="https://en.wikipedia.org/wiki/Coupon_collector%27s_problem">coupon collection problem</a>. But today let me give you another place where it is useful.</p>
<p>Imaging a place called Path Town which has $10$ residents, which, for some mysterious reasons, has a social network that looks like this</p>
<pre><code>😀️ -- 😀️ -- 😀️ -- 😀️ -- 😀️ -- 😀️ -- 😀️ -- 😀️ -- 😀️ -- 😀️
</code></pre>
<p>In other words, person 1 (from the left) knows only person 2, person 2 knows only person 1 and 3, person 3 only knows person 2 and 4, and so on.
So their social network is just a path of $10$ people.</p>
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<p>Now suppose that person 1 sadly contracted corona virus 🤧️. But instead of putting him in isolation, the town decided to do social distancing more "fairly". Every day, among all the people who may still contract the virus through the social network, one is chosen <strong>uniformly at random</strong> through lottery to be put into quarantine. (What is fairer than a lottery?) This goes on until person 🤧️ is also in quarantine.</p>
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" alt="dylan-nolte-RSsqjpezn6o-unsplash.jpg"></p>
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Photo by dylan nolte on Unsplash
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<p>For example, by the end of day 1, maybe person 6 won the lottery and the network becomes like this</p>
<pre><code>🤧️️ -- 😀️ -- 😀️ -- 😀️ -- 😀️ 😭️ ( 😀️ -- 😀️ -- 😀️ -- 😀️ )
</code></pre>
<p>Then on day 2, among the 5 people who are still connected to person 1, person 3 got lucky. The network becomes</p>
<pre><code>🤧️️ -- 😀️ 😭️ ( 😀️ -- 😀️ ) 😭️ ( 😀️ -- 😀️ -- 😀️ -- 😀️ )
</code></pre>
<p>Finally on day 3, person 1 wons the lottery and he is finally in isolation.</p>
<pre><code>🤧️️ ( 😀️ ) 😭️ ( 😀️ -- 😀️ ) 😭️ ( 😀️ -- 😀️ -- 😀️ -- 😀️ )
</code></pre>
<p>Now the question is, on average, how many days does it take, or equivalently, how many people need to be isolated, for person 🤧️️ to go into isolation?</p>
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<h2 id="Lottery-by-playing-cards">Lottery by playing cards<a class="anchor-link" href="#Lottery-by-playing-cards">¶</a></h2>
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<p>Instead of doing a lottery each day, a more efficient but equivalent way to do this is to uniformly randomly shuffle a deck of playing card of $1,.., 10$ and give each person a card.</p>
<p>Then in day one, the person has card with the lowest number is chosen. On day two, the person among the remaining ones with a card of lowest number is chosen. This goes on until eventual until eventual Mr 🤧️️ is chosen.</p>
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" 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<p>This may sounds surprising 😱️. But think about it for a minute. On the first day, who has better chance to draw the smallest card?
Everyone has the same change.
On day two, among the remaining ones, who has better chance? No one! Everyone again has the same chance. What happens on day one does not change this fact.</p>
<p>Let's write a Julia function to simulate how this works.</p>
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<div class="prompt input_prompt">In [1]:</div>
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<div class=" highlight hl-julia"><pre><span></span><span class="k">using</span> <span class="n">Random</span><span class="o">:</span> <span class="n">randperm</span>
<span class="k">function</span> <span class="n">corona_lottery</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">X1</span> <span class="o">=</span> <span class="n">randperm</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X1</span>
<span class="k">while</span> <span class="n">length</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">1</span>
<span class="n">println</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">pos</span> <span class="o">=</span> <span class="n">findmin</span><span class="p">(</span><span class="n">X</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="n">pos</span><span class="p">]</span>
<span class="k">end</span>
<span class="k">return</span> <span class="n">X1</span>
<span class="k">end</span>
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<pre>corona_lottery (generic function with 1 method)</pre>
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<p>So the lottery may go like this</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">corona_lottery</span><span class="p">(</span><span class="mi">10</span><span class="p">);</span>
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<pre>[1, 2, 3, 7, 10, 5, 4, 8, 9, 6]
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<p>or this</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">corona_lottery</span><span class="p">(</span><span class="mi">10</span><span class="p">);</span>
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<pre>[10, 5, 4, 1, 2, 6, 3, 7, 8, 9]
[10, 5, 4]
[10, 5]
[10]
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<h2 id="The-records">The records<a class="anchor-link" href="#The-records">¶</a></h2>
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<p>Let's look at an example closer. (I will seed the random number generator so we will get the same example every time.)</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="k">import</span> <span class="n">Random</span>
<span class="n">Random</span><span class="o">.</span><span class="n">seed!</span><span class="p">(</span><span class="mi">1001</span><span class="p">)</span>
<span class="n">cards</span> <span class="o">=</span> <span class="n">corona_lottery</span><span class="p">(</span><span class="mi">10</span><span class="p">);</span>
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<pre>[8, 9, 4, 6, 1, 10, 5, 3, 2, 7]
[8, 9, 4, 6]
[8, 9]
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<p>In this example, the first person goes to isolation is at position $5$. Because he got the card <code>1</code> which is smaller than all cards.</p>
<p>The, the second one who won the lottery is at position $3$, because his card <code>4</code> is smallest among all the four people who survived 😱️ till day 2.</p>
<p>Then on day three, only two people left and Mr 🤧️ who is at position $1$ won with a card <code>8</code>, so the whole process ends.</p>
<p>Stare into this list of numbers a little longer,</p>
<pre><code>[(((8), 9, 4), 6, 1), 10, 5, 3, 2, 7]
</code></pre>
<p>you will notice that <code>8</code>, <code>4</code>, <code>1</code> are all smaller than every number before them 🤔️.</p>
<p>Given a list of numbers $X_1, \cdots, X_{10}$, we say that $X_i$ is a <strong>record</strong> it smaller than every number before it.</p>
<p>So it looks like that the number of records in the deck of cards
are the same as the number of people who have to go into isolation.</p>
<p>Let's do another lottery and see if this is still true.</p>
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<p>First a function to print out where the records are with red color.</p>
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<p>Another lottery</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">cards1</span> <span class="o">=</span> <span class="n">corona_lottery</span><span class="p">(</span><span class="mi">10</span><span class="p">);</span>
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<pre>[9, 2, 3, 5, 6, 4, 10, 7, 8, 1]
[9, 2, 3, 5, 6, 4, 10, 7, 8]
[9]
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<p>Let's color where the records are</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="k">function</span> <span class="n">print_records</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="kp">in</span> <span class="mi">1</span><span class="o">:</span><span class="n">length</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">if</span> <span class="n">all</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">.></span> <span class="n">v</span><span class="p">)</span>
<span class="n">printstyled</span><span class="p">(</span><span class="s">"</span><span class="si">$v</span><span class="s"> "</span><span class="p">,</span> <span class="n">color</span><span class="o">=:</span><span class="n">red</span><span class="p">)</span>
<span class="k">else</span>
<span class="n">print</span><span class="p">(</span><span class="s">"</span><span class="si">$v</span><span class="s"> "</span><span class="p">)</span>
<span class="k">end</span>
<span class="k">end</span>
<span class="k">end</span>
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<pre>print_records (generic function with 1 method)</pre>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">print_records</span><span class="p">(</span><span class="n">cards1</span><span class="p">)</span>
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<pre><span class="ansi-red-fg">9 </span><span class="ansi-red-fg">2 </span>3 5 6 4 10 7 8 <span class="ansi-red-fg">1 </span></pre>
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<p>You can run this as many times you want. The number of isolation is always the same as the number of records. This is because if you get a record card, no one on your left you will be isolated before you. So you are guaranteed to go to self-isolation 😭️.</p>
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<h2 id="Back-to-harmonic-number">Back to harmonic number<a class="anchor-link" href="#Back-to-harmonic-number">¶</a></h2>
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<p>So what is the chance that the person at position $1$, i.e., Mr 🤧️ being a record? Well, he will always be one.</p>
<p>What is the chance of the person at position $2$ to be a record? Well, since he is only competing with one person, he has $1/2$ of chance to win. So on average, he contributes $1/2$ records.</p>
<p>By this argument, the person at position $i$ contributes on average $1/i$ records. Adding this up, and we have our old friend 😍️, the harmonic number
$$
H_m = \sum_{i=1}^m \frac{1}{m}.
$$
So on average there are $H_m$ records among a uniform random permutations of $m$ people. In terms of pandemic, there are on average $H_m$ people of the Path Town have to go into isolation.</p>
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<h2 id="Simulation-with-Julia">Simulation with Julia<a class="anchor-link" href="#Simulation-with-Julia">¶</a></h2>
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<p>In case I have not convinced you that harmonic number is the right answer. Let's do some simulation.</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="k">function</span> <span class="n">corona_lottery_winner_num</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">winner</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">X1</span> <span class="o">=</span> <span class="n">randperm</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X1</span>
<span class="k">while</span> <span class="n">length</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">1</span>
<span class="c"># println(X)</span>
<span class="n">pos</span> <span class="o">=</span> <span class="n">findmin</span><span class="p">(</span><span class="n">X</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="n">pos</span><span class="p">]</span>
<span class="n">winner</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">end</span>
<span class="k">return</span> <span class="n">winner</span>
<span class="k">end</span>
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<pre>corona_lottery_winner_num (generic function with 1 method)</pre>
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<p>Let run the lotter for $10$ people $10000$ times.</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">lottery_data</span> <span class="o">=</span> <span class="n">map</span><span class="p">(</span><span class="n">i</span><span class="o">-></span><span class="n">corona_lottery_winner_num</span><span class="p">(</span><span class="mi">10</span><span class="p">),</span> <span class="mi">1</span><span class="o">:</span><span class="mi">10</span><span class="o">^</span><span class="mi">4</span><span class="p">);</span>
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<p>And the average is</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="k">using</span> <span class="n">Statistics</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">mean_isolation</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">lottery_data</span><span class="p">)</span>
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<pre>2.9275</pre>
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<p>While the $H_{10}$ is</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">harmonic</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">=</span> <span class="n">sum</span><span class="p">(</span><span class="n">i</span><span class="o">-></span><span class="mi">1</span><span class="o">/</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="o">:</span><span class="n">m</span><span class="p">);</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">h10</span> <span class="o">=</span> <span class="n">harmonic</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
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<pre>2.9289682539682538</pre>
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<p>And the difference is</p>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">h10</span> <span class="o">-</span> <span class="n">mean_isolation</span>
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<pre>0.0014682539682535634</pre>
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<p>Do you believe me now? 😀️</p>
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