: Is the following piece of text comprehensible and written in good style? I am a PhD candidate and I am having difficulty in communicating effectively in writing. Specifically, this post is a

If it weren't for the fact that your links were Wikipedia links I would have thought your post was spam. I see what you are trying to accomplish; However writing a piece of work that asks a question about a questions seems a bit off. Maybe try something more declarative for a critique.

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I have a small contribution to the excellent advice already offered....

When possible, read your work aloud. If you stumble over a phrase or sentence, so will your readers. Reading aloud reinforces where the pauses should be, for clarity and emphasis, because you'll need to take a breath occasionally, unlike when you read silently. Best of luck!

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I'll offer some blunt advice that I've given my own grad students over the years.
Be direct. Make it easy for readers to see the main points you're trying to convey. (I think the main parts of your question are that you're a Ph.D. student whose advisor thinks your writing needs improvement, and you're asking for comments about style and understandability.)
Prefer shorter, simpler sentences. (The sentences beginning with "I thought that..." and "My supervisor..." could be shortened a lot.)
Avoid jargon, vague words and phrases, and superfluous words. ("my writing work" should be "my writing"; "the readers would get a glimpse of my ability to communicate" is superfluous.)
Avoid intrusive parenthetical phrases. ("and, in addition, explains" breaks the flow of the sentence.)
Avoid superfluous modifiers. (You suggest that readers could offer "insightful comments", but that's a bit of unneeded flattery.)
Here's how I'd rewrite your question, retaining a semi-academic style:

I am a PhD candidate and I would like to improve my writing. My
supervisor believes that if my writing were easier to understand, we
could work together more productively. I have two questions: Is my
writing understandable? Could the style be improved? A sample is given
below.
...
I hope that my question is appropriate for this forum.

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(Note: The current edit of this post fixes some of these issues.)

Clarity of objectives

It's unclear, exactly, what you want people to critique; the way the post is written implies that there will be text other than the question and the question's title, and that this text is what you want people to critique. The body of your question is laying the groundwork for why you're seeking a critique and the sorts of problems you're looking at - all this is good information - but there's an implication that the question is just background.

I'm harping on this point because it illustrates point of writing that far too many people ignore: Know your audience. On this site, people generally post a critique question with a specific question (in this case, is your text comprehensible), and format the post so there's either specific text they want a critique on, or a link to that text. A few minutes' research could have saved us this confusion. (But perhaps this is a lesson you needed to learn?)

White space

Your original post was all one paragraph; the edit that John performed helped split the text up into three paragraphs, which helps readability. (Edit: Using a double return will give one paragraphs with white space in between them.)

Spending a little more time on organization (outlining what you meant to write, and in what order you will present the issues) will only help you do this upfront.

Organization is particularly important in academic writing.

Clarity

Even if it does ramble a little, your writing is clear. However, there's a certain style in academic writing that you may want to learn to emulate; stylistic departures are not well tolerated in academic writing.

I suggest reading documents similar to the ones you'll be generating - journal articles, dissertations - to learn about this. Your advisor may be able to suggest a few for you to read. (Remember, the best kind of writing for you to produce is what your advisor thinks is good.)

References

Strunk and White is a good guide to simple, clear style. It's a short book, and well worth reading.

The Chicago Manual of Style is a large tome that very few people read cover to cover. Perhaps your advisor means for you to use it as a reference; it's a good one.

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Well, let's start...

Specifically, this post

You just lost us. "This post" often means "an external piece to which I am linking" or "some text which is going to follow shortly," rather than "this question you're reading."

is a piece of text submitted for critique and, in addition, explains what I am trying to achieve.

Redundant, but okay in context.

This situation was driving down our productivity rate and so he established a formal approach to deal with the problem.

Which is? and relates to us and this post how?

Here also I feel like something's missing. It reads like you're building up to asking something specific, or presenting a chunk of text, and then you overshoot it completely and move on to the footnotes (the reference material). So you've described a problem but you haven't actually showed us what it is.

Your writing seems to be reasonably clear in general. You might have to post something else for us to look at, or give us an example of something your advisor balked at.

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