New Commentary E-Journal on Comp. Mat. Sci.

The other day I came across a new electronic journal aimed at providing expert opinion and commentary on important papers within the field of computational materials science. The name of the electronic publication is called KIM REVIEW and has the following aim and scope:

"... publishes commentaries on important articles related to classical molecular simulations of hard and soft matter materials. The objectives are to inform practitioners in the field of key contributions, both new developments and foundational work, that they should be aware of, and to provide a forum for community discussion of such innovations."

If this venture proves to be fruitful and gets traction, I think it's going to greatly aid newcomers to the field. This is particularly the case in computational materials science and materials informatics where the explosion of research papers and new tools is far too difficult to keep up with. The one thing though is this is just an opinion/commentary journal so it won't provide the "how-to" part of a research paper. 

The one thing I'm curious about is whether or not the editors of the journal will get enough contributing authors to make the electronic publication be productive. I would guess that only senior, well-established, researchers are going to be willing to contribute given that if their commentary indicates that a paper is "not that impactful" it may be seen as "risky" for a young researcher. The solution is probably just to focus on papers that are known to advance the field of computational materials science and then just focus on providing "spark" notes/commentary. 

Overall, I hope this electronic publication takes off as it will make it much easier to figure out what papers I should read to stay up-to-date. If you are interested,  you can submit recommendations for articles to be reviewed here. Best of luck to the editors and future authors.

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0.9999.... = 1 ?

I saw this quick video the other day with the title "Simple proof for $0.999... = 1$" and thought, "can I do this on my own" without watching. The fortunate result was pretty much yes, but my approach was using the concept of limits and was involved compared to the algebra approach shown in the video after I watched it. So I want to document the proof using the algebraic method in the video so I can remember that there are sometimes more straightforward ways to do the same thing. The idea is that we can start with the variable $x$ which we say is:

$$ x = 0.999\cdots $$

Then if we multiply $x$ by $10$, we have

$$ 10x = 10*0.999\cdots$$

which can be rewritten as

$$ 10x = 9 + 0.999\cdots$$

and substituting $x$ back-in on the right hand side,

$$ \begin{aligned} 10x &= 9 + x \\ 10x - x &= 9 \\ 9x &= 9 \\ \therefore x &= 1 \end{aligned} $$

The one thing that I questioned immediately though, is this is a valid mathematical proof or more of a conceptual demonstration of infinite decimal numbers. It most certainly looks to be the latter as discussed on the Wikipedia page. Since I'm not a professional mathematician I can't say why this algebraic approach is most likely not a rigorous proof, but again seems like a nice reminder that there are different ways to convey relations.

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Thoughts on note taking and presentations

Lately I've been thinking a lot about my process of taking notes and preparing presentations. In the last 10 years I've tried to explore many different kinds of techniques and approaches. Like most, I tried to get the most out of MS word and powerpoint throughout the years; I quickly abandoned MS word after writing my masters thesis, which was sheer frustration. As for PowerPoint, this was a more difficult, its not that I didn't want to part-ways with PowerPoint its just there are many "natural operations" that make it a more desirable experience. I guess it comes down to the acroynym, WYSIWYG, which is What You See Is What You Get, where as with something like Beamer $\LaTeX$ , you have WYSIWYW, where the G  is changed to W for "want". 

For presentation format, I find it much less natural to go with WYSIWYW approach since the layout of slides is very much a visual and aesthetic preference so one needs to play around with placement of figures and text to get the best kind of "feel". Also, I have noticed many use PowerPoint slides as a way to put down there research notes and create a record or timeline of their results and analysis. This then becomes the draft for conference presentations and final an outline for research articles. This process flow once again seems very natural and easy, in other words, it doesn't require doing much other than updating your slide deck as you progress. However, this of course this is error prone because it won't track provenance information for graphs or figures you insert and the version control of your slides in PowerPoint is less ideal git, for example. 

So you may ask "I don't see any major issues here? just use PowerPoint"... well that is fair but I think PowerPoint does have some significant issues for individual science and engineering researchers. For one Microsoft still abides by the draconian approach of charging for basic software, its clear the Microsoft isn't making their money from single user office products anymore but from cloud services and enterprise package purchases. But putting that aside, I significantly think the following are some headaches for many:

• The equation editor is cumbersome and frustrating. The only viable workaround is IguanaTeX.
• No support for Zotero or Mendeley reference managers. Adding references to slides in beamer  is easy. 
• The pptx format/standard should be open or more specifically, easy to support. There should be a free MS PowerPoint viewer that allows for PDF export as well.
• "In-file" code generated figures. I've used pythontex in the past to create code generated figures on a beamer slide.
• Version control for individual slides. If you use $\LaTeX$ or Markdown, you can create separate files for each slide and then using git for version control. This makes reverting a specific slide back to a previous version straightforward; although the main issue is you can't do this in a WYSIWYG manner.

There are some other things that can be frustrating with PowerPoint, for example it will crash frequently if the slide deck gets to large. One thing to point out is I don't think Google Slides has done that much of a better job other than they don't charge for the service.

Thus in light of this thinking my approach lately has been to starting exploring new approaches to note taking and presentation making. What I've decided to experiment with is the use of Quarto, which is a document preparation environment. What I like is you can create several different formats all from the same source files. The source files are written in simple markdown and extra capabilities are provided through extended syntax (e.g. code can be placed in an execution environment with {} around the language name). I've started with this mainly for making presentations using the revealjs framework and I'll see how it works. What I like so far is I can begin the presentations more similar to how I might take digital notes and then just use the content I want for slides. One potentially exciting capability of Quarto, is that because it uses Pandoc to export different format documents, it is possible to render a pptx file version of a presentation. I'm hesitant that this will be successful though.

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Nice presentation on AI/ML in materials science

I came across this slide deck from Prof. Shyue Ping Ong at UCSD. He leads a really exciting group that focuses on computational materials science and materials informatics. Many of his papers are outstanding and this particular slide provides a nice review of different use cases for AI/ML. I will note though that in many scenarios trying to replicate or implement similar research is a fairly hefty endevour unless your working with others who have done it before. 

 

A*STAR Webinar on The AI Revolution in Materials Science from Shyue Ping Ong

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Symmetries

What is Symmetry?

This is an interesting question, namely, because when I ask myself this my mind immediately starts thinking in terms of spatial symmetries. For example, putting my hands in front of me, I see mirror symmetry. This isn't entirely correct because my hands have immutable chirality that don't allow me to turn a left hand into a right hand or vica-versa ( I'd have to remove my fingers and reposition them, something I'm interested in doing). The reason that I think in terms of spatial symmetries is because my experience occurs in a 3D spatial world and my brain and eyes have evolved to identify objects with symmetries to characterize and label. For example faces have a high-degree of symmetry and it would make sense if I could remember faces. The truth however, is symmetry is much more ubiquitus in the construct of our universe. That is to say, we see symmetries in the most abstract of concepts.

So how does one understand symmetries in an abstract sense? The most fundamental place to start is of course mathematics, specifically within group theory. This branch of mathematics is primarily concerned with the grouping (hence the name) of structures for different algebras. For example what groups exist in a structure that makes up vector spaces¹.  The groups we are talking about contain internal symmetries whereby when they act on a object in a structure leave it invariant with respect to the operation. Let me try with a simple example. We start with a vector in a unit circle, $\mathbf{v} = \frac{1}{\sqrt{2}} \mathbf{x} + \frac{1}{\sqrt{2}} \mathbf{y}$ with magnitude $\lvert \mathbf{v} \rvert = 1$, now if I rotate²  the vector by any angle but do so such that the magnitude says the same the vector will always be relatable or transferable back to the original vector by some rotation that conserves the magnitude. This is what constitutes a symmetry. For our vector in the unit circle it has an continuous symmetry operation, i.e., I can define an infinitely small rotation angle and then sum up an infinite number of those rotations to get back to the original state. But there are other groups where the symmetry is discrete, which show up in physical systems such as crystals or shapes.

Group Theory in Science

The areas of discrete and continuous symmetry groups is called Lie theory and finite group theory, respectively. Lie theory is the mathematics that leads to modern quantum physics, in the context of what our universe "consist" of, it provides the language to discuss/represent internal symmetries. These internal symmetries are associated with fundamental fields that are consistent with the principals of quantum mechanics and special relativity. At the moment this is all I can say about Lie theory since I only have a limited understanding. It is a very powerful approach in quantum physics. 

Intuitively its much easier to think about finite symmetry groups, these are every so familiar to use as I described in the first paragraph. Think of a geometric shape like an equilateral triangle or square. For the triangle, which is a 2D object, we can ask what operations leave the appearance of the system invariant? Well there is a grouping of 6 operations. There are 2 rotation operators, counter and clockwise rotations by 120 degrees about the axis perpendicular to the center, that leave leave the appearance of the triangle the same. Although if we were to add some kind of "label" to the sides or corners we could then say that the appearance is invariant but the system has been reoriented. This is how I think of the laws of physics and the quantities we observe in nature. The laws of physics are always invariant, they are the same and fully encompassing within our universe. However, the quantities energy, matter, spacetime, etc.  that we measure or relate one another to can differ depending on how we are "oriented". In addition to the rotations there are mirror/reflection operations, 3 of them, that would leave the appearance of the triangle the same but produce unique orientations if we labeled the corners or sides. There is also the operation that does nothing, the identity operation, this can literally be though of as doing nothing such as multiplying a number by one does nothing, or can be thought of as the operation that brings the object back onto itself. For our triangle that would be the rotation of 180 degrees. 

The operations described above are called a set which has the unique property that is is closed under any combination of operators in the set, this is what is referred to as a group. To discuss this more specifically, think of the identity operation. We could write this as the combination of 3 clockwise 90-degree rotations.  $^\dagger$

 

$^{\dagger}$ This post is incomplete.     

¹I want to be a bit clear here, the term vector spaces is used in the most abstract way possible. We shouldn't think of a spatial vector in 3D, we should think of a vector in some N-dimensional space that can represent essentially anything

² The rotation of a vector in a unit circle can be done using a matrix, $\mathbf{M} = \begin{bmatrix} \cos{\theta} & \sin{\theta} \\ -\sin{\theta} & \cos{\theta} \end{bmatrix}$ where the $\mathbf{x}$ and $\mathbf{y}$ components are adjusted based on the angle $\theta$. The magnitude will be unchanged and therefore this type of matrix acting on this this 2D vector space is refereed to an orthogonal matrix.

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