Alex Raichev

Do the Math

youtube~IsIfokifwSo

And join the movement to solve the climate crisis at 350.org.

Video sourced from YouTube here.

Author: Alex Raichev
Date: 2013-07-13
Tags: global warming, video, 350
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PRISM Break

Opt out of PRISM, the NSA’s global data surveillance program. For software tips, see http://prism-break.org/.

Author: Alex Raichev
Date: 2013-07-05
Tags: website, PRISM, security
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Brahma

If the red slayer think he slays,
Or if the slain think he is slain,
They know not well the subtle ways
I keep, and pass, and turn again.

Far or forgot to me is near;
Shadow and sunlight are the same;
The vanished gods to me appear;
And one to me are shame and fame.

They reckon ill who leave me out;
When me they fly, I am the wings;
I am the doubter and the doubt,
I am the hymn the Brahmin sings.

The strong gods pine for my abode,
And pine in vain the sacred Seven;
But thou, meek lover of the good!
Find me, and turn thy back on heaven.

~ Ralph Waldo Emerson, 1857

Apparently Emerson should have titled this poem 'Brahman' instead of 'Brahma'. For why and more insighful commentary, see Emerson's Brahma: An Indian Interpretation, K. R. Chandrasekharan, The New England Quarterly, Vol. 33, No. 4 (Dec., 1960), pp. 506-512.

Author: Alex Raichev
Date: 2013-06-04
Tags: poem, Emerson
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Flow

youtube~jE1j5Om7g0U

Judson Brewer, an addiction psychiatrist and neuroscientist at Yale University, describes flow and his research findings on the topic.

Video sourced from YouTube here.

Author: Alex Raichev
Date: 2013-05-25
Tags: nonduality, video, neuroscience
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The New World of Sales

youtube~O1bSwewzyjQ

Author Daniel H. Pink answers seven questions about pitching, selling, and closing for the 21st Century workforce.

Video sourced from YouTube here.

Author: Alex Raichev
Date: 2013-05-25
Tags: sales, video
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Blohg to Pelican

Over the past few days i moved this website's backend from Blohg to Pelican, both of which are RST-capable website generators. I did so, because i don't need the dynamic Flask-application capabilities of Blohg and because Pelican is more mature and equally simple to use.

The transition was mostly smooth, but i did encounter a few issues that required me to search beyond Pelican's documentation to resolve. To save new Pelicaneers the effort, here are those issues and resolutions.

Issue 1: Custom paginated templates.

I wanted a separate landing page and blog page, and the Pelican docs don't elaborate on this point. Querying the Pelican developers through the project's Github page, i received instructions from justinmayer. First, he said, i needed to make a custom template to house my blog, which i called blog.html. It contains the code

{% extends "base.html" %}
{% set active_page = "blog" %}
{% block title %}{{ SITENAME }} - Blog{% endblock %}
{% block content %}
{% for article in (articles_page.object_list if articles_page else articles) %}
    <div class="blogItem">
    <h1><a href="{{ SITEURL }}/{{ article.url }}">{{ article.title }}</a></h1>
    {{ article.content }}

    <div class="blogMeta">
    Author: <a href="mailto: {{ AUTHOR_EMAIL }}">{{ article.author }}</a><br>
    Date: {{ article.locale_date }}<br>
    {% if article.tags %}
        Tags:
        {% for tag in article.tags %}
            <a href="{{ SITEURL }}/{{ tag.url }}">
            {{ tag }}</a>{% if not loop.last %}, {% endif %}
        {% endfor %}<br />
    {% endif %}
    <a href="{{ SITEURL }}/{{ article.url }}#disqus_thread">Comments</a> -
    <a href="{{ SITEURL }}/{{ article.url }}">Permalink</a>
    </div>
    </div><!-- end #blogItem -->
{% endfor %}
{% include 'pagination.html' %}
{% endblock content %}

By the way, here's the code for the pagination template pagination.html:

{% if articles_page and articles_paginator.num_pages > 1 %}
    <div class="pagination">
    <ul>
    {% if articles_page.has_previous() %}
        {% set num = articles_page.previous_page_number() %}
        <li class="prev"><a href="
            {{ SITEURL }}/{{ page_name }}{{ num if num > 1 else ''}}.html"
            >&laquo;</a></li>
    {% endif %}
    {% for num in range( 1, 1 + articles_paginator.num_pages ) %}
        <li><a href="
            {{ SITEURL }}/{{ page_name }}{{ num if num > 1 else '' }}.html"
            class="{{ 'active' if num == articles_page.number else '' }}"
            >{{ num }}</a></li>
    {% endfor %}
    {% if articles_page.has_next() %}
        <li class="next"><a href="
            {{ SITEURL }}/{{ page_name }}{{
               articles_page.next_page_number() }}.html"
            >&raquo;</a></li>
    {% endif %}
    </ul>
    </div>
{% endif %}

I got it from the tuxlit_tbs Pelican theme and modified it to my liking.

Second, i had to add the following lines to my pelicanconf.py.

DIRECT_TEMPLATES = (('index', 'blog', 'tags', 'categories', 'archives'))
PAGINATED_DIRECT_TEMPLATES = (('blog',))

Issue 2: Disqus comments.

This is another topic the Pelican docs don't elaborate on. To embed Disqus comments in my blog pages, i read Disqus's help article on embedding comments and Disqus's help article on adding comment counts and did the following.

First, i made the template disqus_comments.html which contains the code

{% if DISQUS_SITENAME %}
    <div class="blogItem">
    <h2>Comments</h2>
    <div id="disqus_thread"></div>
    <script type="text/javascript">
        var disqus_shortname = '{{ DISQUS_SITENAME }}';
        (function() {
            var dsq = document.createElement('script');
            dsq.type = 'text/javascript';
            dsq.async = true;
            dsq.src = 'http://' + disqus_shortname + '.disqus.com/embed.js';
            (document.getElementsByTagName('head')[0] ||
             document.getElementsByTagName('body')[0]).appendChild(dsq);
        })();
    </script>
    <noscript>
        Please enable JavaScript to view the
        <a href="http://disqus.com/?ref_noscript={{ DISQUS_SITENAME }}">
            comments powered by Disqus.
        </a>
    </noscript>
    <a href="http://disqus.com" class="dsq-brlink">
        blog comments powered by <span class="logo-disqus">Disqus</span>
    </a>
    </div>
{% endif %}

and in my article.html template added the line {% include 'disqus_comments.html' %} before the line {% endblock %}. Doing so embeds Disqus comments for each blog post (article).

Second, i made the template disqus_comment_counts.html which contains the code

{% if DISQUS_SITENAME %}
    <script type="text/javascript">
        var disqus_shortname = '{{ DISQUS_SITENAME }}';
        (function () {
            var s = document.createElement('script'); s.async = true;
            s.type = 'text/javascript';
            s.src = 'http://' + disqus_shortname + '.disqus.com/count.js';
            (document.getElementsByTagName('HEAD')[0] ||
             document.getElementsByTagName('BODY')[0]).appendChild(s);
        }());
    </script>
{% endif %}

and in my base.html template added the line {% include 'disqus_comment_counts.html' %} before the </body> tag. That enables blog post comment counts via the tags <a href="{{ SITEURL }}/{{ article.url }}#disqus_thread">Comments</a>.

Issue 3: Typesetting math.

I wanted to use MathJax to typeset math on this site. Pelican has a LaTeX plugin, which uses MathJax, but doesn't work properly at present. It didn't typeset math in the list view of my blog posts, only in the detail view of each post. So i searched the web for an alternative and found this helpful blog post from another Pelican user. Following its instructions, i added this Javascript code into the <head> section of my base.html template:

<!-- Using MathJax, with the delimiters $ -->
<!-- Conflict with pygments for the .mo and .mi -->
<script type="text/x-mathjax-config">
    MathJax.Hub.Config({
    "HTML-CSS": {
    styles: {
    ".MathJax .mo, .MathJax .mi": {color: "black ! important"}}
    },
    tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']],processEscapes: true}
    });
    MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () {
    var VARIANT = MathJax.OutputJax["HTML-CSS"].FONTDATA.VARIANT;
    VARIANT["normal"].fonts.unshift("MathJax_SansSerif");
    VARIANT["bold"].fonts.unshift("MathJax_SansSerif-bold");
    VARIANT["italic"].fonts.unshift("MathJax_SansSerif-italic");
    VARIANT["-tex-mathit"].fonts.unshift("MathJax_SansSerif-italic");
    });
    MathJax.Hub.Register.StartupHook("SVG Jax Ready",function () {
    var VARIANT = MathJax.OutputJax.SVG.FONTDATA.VARIANT;
    VARIANT["normal"].fonts.unshift("MathJax_SansSerif");
    VARIANT["bold"].fonts.unshift("MathJax_SansSerif-bold");
    VARIANT["italic"].fonts.unshift("MathJax_SansSerif-italic");
    VARIANT["-tex-mathit"].fonts.unshift("MathJax_SansSerif-italic");
    });
</script>

<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
</script>

I removed the ['$','$'] item which allows dollar signs to delimit math text, as is standard in LaTeX documents, but it requires escaping every backslash in the math text with an additional backslash. For now i'll stick with the standard RST role :math: for inline math and the standard RST directive .. math:: for block math display. The area of a circle is Ac = (π ⁄ 4)d2, that is,

Ac = (π)/(4)d2.
Author: Alex Raichev
Date: 2013-05-11
Tags: tip, software
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Delicious Dal

Ingredients

  • 1.5 C green or brown lentils
  • 5 C water
  • 2 T coconut oil
  • 1 400mL can chopped tomatoes
  • 1 onion chopped
  • 2 cloves garlic chopped
  • 1 T shredded ginger
  • 1 t ground turmeric
  • 1 hot chili
  • 1 red capsicum chopped
  • 1 t salt
  • 1 t cumin seeds
  • 2 t black mustard seeds
  • some coriander leaf for garnish

Directions

  1. Except for 1 T coconut oil, the cumin seeds, and the mustard seeds, put everything into a pressure cooker, and cook at high pressure for 11 minutes.
  2. Fry the reserved coconut oil, cumin seeds, and mustard seeds until the mustard seeds begin to pop.
  3. Add the fried seeds and oil to the soup, garnish with coriander leaf, and serve.

Notes

Serves about 6. C = cup, T = tablespoon, t = teaspoon.

Author: Alex Raichev
Date: 2013-04-27
Tags: recipe
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Store Credit

Here's the store credit problem from Google Code Jam Qualification Round Africa 2010, which i discovered via Programming Praxis:

You receive a credit C at a local store and would like to buy two items. You first walk through the store and create a list L of all available items. From this list you would like to buy two items that add up to the entire value of the credit. The solution you provide will consist of the two integers indicating the positions of the items in your list (smaller number first). For instance, with C=100 and L={5,75,25} the solution is 2,3; with C=200 and L={150,24,79,50,88,345,3} the solution is 1,4; and with C=8 and L={2,1,9,4,4,56,90,3} the solution is 4,5.

Algorithm 1

Brute force. Test all pairs in the list. O(n^2) time and O(n) space.

Algorithm 2

Sort the list and then iterate over the list, at each step looking for the complementary price of the current price via binary search. O(n lg n) time and O(n) space.

Algorithm 3

Store the prices and indices in a dictionary and then iterate over the dictionary, at each step looking for the complementary price. Since dictionary look-up is constant time on average, this is an O(n) time (in the average case) and O(n) space algorithm. Hooray!

Here's a Python 2.7 implementation:

def find_pair(credit, prices):
    # Make a dictionary with items of the form
    # (price, set of indices of items with that price).
    # Note that the price list could contain duplicate prices.
    d = dict()
    for (i, p) in enumerate(prices):
        d[p] = d.get(p, set())
        d[p].add(i + 1)  # + 1 to index from 1 instead of 0.
    for price in d.keys():
        if price <= credit:
            # Remove price index from d.
            i = d[price].pop()
            # Check whether there's a complementary price in d.
            if credit - price in d:
                # This works even if price == credit - price.
                j = d[credit - price].pop()
                return min(i, j), max(i, j)
            # Reinsert price index into d.
            d[price].add(i)
    return "Sorry, no pair of item costs sum to %s" % credit
Author: Alex Raichev
Date: 2013-04-11
Tags: algorithm, puzzle
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Cat Vs. Dog

Updated for clarity 23 Sep 2013.

A friend of mine recently pointed me to Spotify's Cat vs. Dog puzzle. The question is long, and so i'll summarize it without its motivating context.

You are given n votes, each of which is a pair of strings of the form (Ci, Dj) (a cat-lover vote) or (Dj, Ci) (a dog-lover) for some integers 1 ≤ i, j ≤ n. This collection of votes can contain repeats. Two votes (a, b) and (c, d) are said to conflict if a = d or b = c. So a conflict can only occur between a cat-lover vote and a dog-lover vote. Your job is to find the size of a maximal subcollection of the votes in which no two votes conflict.

Algorithm 1

Brute-force. Run through all possible subcollections of votes and test each for conflicts. Choose the biggest non-conflicting subcollection.

This procedure would take O(2n) time in the worst case, because there are 2n subcollections to check. That's very slow. Can we be more clever?

Algorithm 2

Yes, model the problem with a graph.

  1. Distinguish the votes by tagging each with a unique identifier, such as an integer between 1 and n. This takes O(n) time.
  2. Build the following undirected graph G. Make each vote a vertex, and add the edge {u, v} if u and v are conflicting votes. This takes O(n2) time. Notice that G is bipartite, because every edge connects a cat-lover vote to a dog-lover vote and no vertex is both a cat-lover vote and a dog-lover vote.
  3. Notice that every maximal subset of nonconflicting votes is the complement of a minimum vertex cover for G. So find the size k of a minimum vertex cover for G and return n − k. Now, finding the size of a minimum vertex cover in an arbitrary undirected graph is an NP-complete problem, and there's no known sub-exponential time way to do that. However, our graph is bipartite, and so by Koenig's theorem, the size of a minimum vertex cover of G equals the size of a maximum matching for G, the latter of which can be found by the Hopcroft-Karp algorithm in O(|E|(n)) time, where |E| is the number of edges in G. In the worst case, |E| = n2 and running Hopcroft-Karp takes O(n2.5) time.

So all up, Algorithm 2 takes O(n2.5) time in the worst case.

Author: Alex Raichev
Date: 2013-04-02
Tags: algorithm, puzzle
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Contours: A Mathematical Coloring Book

Here is a mathematical coloring book I recently made. It contains black and white pictures generated by mathematical formulas which you color in for fun. Best printed on size A4 paper or bigger. Enjoy and share!

Author: Alex Raichev
Date: 2013-04-02
Tags: math, art, book
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Why no comments? I used to do public comments but found that moderating and maintaining them took too much time in front of the computer, time better spent playing outdoors. So these days I only do private comments, that is, you can email me comments regarding a post by clicking the 'Comment' link at the bottom of the post.