Clean up rudiments from the template

Author: nomad-vagabond

papers/vadym_pasko/main.md

@@ -83,7 +83,7 @@ B_{i,k}(t) =
 \frac{t_{i+k+1} - t}{t_{i+k+1} - t_{i+1}} B_{i+1,k-1}(t)
 ```
 
-In {ref}`cox-de-boor` possible divisions by zero are resolved by the convention that ‘anything divided by zero is zero’.
+In {ref}`cox-de-boor` possible divisions by zero are resolved by the convention that ‘anything divided by zero is zero’ [@lyche-morken].
 
 This formulation separates geometry (control points) from basis functions, allowing flexible manipulation and efficient computation of spline curves.
 
@@ -102,9 +102,7 @@ Parametric splines are widely used in computer graphics, computer-aided desig (C
 These properties make parametric splines ideal for applications in: 3D modeling and animation, font and character design, surface generation (via tensor product surfaces), and industrial design (automotive, aerospace, etc.).
 
 
-An intuitive visual explanation of splines, different forms of their representation and unique properties is given in the video by Freya Holmér: 
-
-[📺 The Continuity of Splines](https://www.youtube.com/watch?v=jvPPXbo87ds)
+An intuitive visual explanation of splines, different forms of their representation and unique properties is given in the video by Freya Holmér [@holmer-continuity-of-splines].
 
 Despite their geometric advantages, parametric splines are rarely used in statistical data fitting and regression analysis. The primary limitation is the parameterization problem: for observed data points $(x_i, y_i)$, there is no natural way to assign parameter values $t_i$ that correspond meaningfully to the underlying data relationship. Additionally, parametric splines do not provide the direct functional relationship $y = f(x)$ that is typically required for prediction and statistical inference in data analysis contexts. This is why spline functions are often a more popular choice. 
 
@@ -238,7 +236,7 @@ A mathematical representation of B-splines as a linear combination of basis func
 
 From a mathematical standpoint, manual editing of curves breaks the strict formulation of the optimization problem solved by the automatic fitting algorithms. From the user’s perspective, manual fitting can produce better results -  smoother curves with smaller residuals (better accuracy).
 
-In SciPy, the spline fitting process is encapsulated in automatic, hardcoded optimization routines such as `UnivariateSpline` or `LSQUnivariateSpline`, described in the previos section. While this programmatic design serves well for deterministic batch processing or scriptable pipelines, it limits the native adjustability of spline shapes limiting ability to modify the control polygon and knot vector with visual feedback. Of course, there is always an option to adjust these values in code manually, but as described in [(Pasko 2015)](http://vadym-pasko.com/blog/2015/03/06/spline-approx-scipy.html), such an approach can be inefficient and time-consuming. Another option - write custom scripts for optimizing fitting process selecting different strategie, but this adds a level of complexity to the curve fitting process, not afordable for all users and all cases.
+In SciPy, the spline fitting process is encapsulated in automatic, hardcoded optimization routines such as `UnivariateSpline` or `LSQUnivariateSpline`, described in the previos section. While this programmatic design serves well for deterministic batch processing or scriptable pipelines, it limits the native adjustability of spline shapes limiting ability to modify the control polygon and knot vector with visual feedback. Of course, there is always an option to adjust these values in code manually, but as described in [@pasko-blog-post-2015], such an approach can be inefficient and time-consuming. Another option - write custom scripts for optimizing fitting process selecting different strategie, but this adds a level of complexity to the curve fitting process, not afordable for all users and all cases.
 
 Another significant limitation lies in the lack of model portability and reproducibility. Spline objects created in SciPy are tightly coupled with the Python runtime and the local environment. There is, however, an option to export splines as a set of its defining objects: order (int), knot vector (1D array), and coefficients (1D array) or control points (2D array), but recreation of them as objects in code will require users a knowledge of the process and basic understanding of B-spline structure. Another option - serialization of spline objects, may also not be convenient for all cases.
 
@@ -728,239 +726,3 @@ Despite this limitation, SplineCloud introduces the novel capability of building
 
 ## Summary and Future Directions (TODO)
 
-
-## Bibliographies, citations and block quotes (WIP)
-
-Bibliography files and DOIs are automatically included and picked up by `mystmd`.
-These can be added using pandoc-style citations `[@doi:10.1109/MCSE.2007.55]`
-which fetches the citation information automatically and creates: [@doi:10.1109/MCSE.2007.55].
-Additionally, you can use any key in the BibTeX file using `[@citation-key]`,
-as in [@hume48] (which literally is `[@hume48]` in accordance with
-the `hume48` cite-key in the associated `mybib.bib` file).
-Read more about [citations in the MyST documentation](https://mystmd.org/guide/citations).
-
-If you wish to have a block quote, you can just indent the text, as in:
-
-> When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, experience. But if we still carry on our sifting humor, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication.
->
-> -- @hume48
-
-Other typography information can be found in the [MyST documentation](https://mystmd.org/guide/typography).
-
-
-Tom Lyche and Knut Mørken, Spline Methods (University of Oslo, 2008)
-
-### DOIs in bibliographies
-
-In order to include a DOI in your bibliography, add the DOI to your bibliography
-entry as a string. For example:
-
-```{code-block} bibtex
-:emphasize-lines: 7
-:linenos:
-@book{hume48,
-  author    =  "David Hume",
-  year      = {1748},
-  title     = "An enquiry concerning human understanding",
-  address   = "Indianapolis, IN",
-  publisher = "Hackett",
-  doi       = "10.1017/CBO9780511808432",
-}
-```
-
-### Citing software and websites
-
-Any paper relying on open-source software would surely want to include citations.
-Often you can find a citation in BibTeX format via a web search.
-Authors of software packages may even publish guidelines on how to cite their work.
-
-For convenience, citations to common packages such as
-Jupyter [@jupyter],
-Matplotlib [@matplotlib],
-NumPy [@numpy],
-pandas [@pandas1; @pandas2],
-scikit-learn [@sklearn1; @sklearn2], and
-SciPy [@scipy]
-are included in this paper's `.bib` file.
-
-In this paper we not only terraform a desert using the package terradesert [@terradesert], we also catch a sandworm with it.
-To cite a website, the following BibTeX format plus any additional tags necessary for specifying the referenced content is recommended.
-If you are citing a team, ensure that the author name is wrapped in additional braces `{Team Name}`, so it is not treated as an author's first and last names.
-
-```{code-block} bibtex
-:emphasize-lines: 2
-:linenos:
-@misc{terradesert,
-  author = {{TerraDesert Team}},
-  title  = {Code for terraforming a desert},
-  year   = {2000},
-  url    = {https://terradesert.com/code/},
-  note   = {Accessed 1 Jan. 2000}
-}
-```
-
-## Source code examples
-
-No paper would be complete without some source code.
-Code highlighting is completed if the name is given:
-
-```python
-def sum(a, b):
-    """Sum two numbers."""
-
-    return a + b
-```
-
-Use the `{code-block}` directive if you are getting fancy with line numbers or emphasis. For example, line-numbers in `C` looks like:
-
-```{code-block} c
-:linenos: true
-
-int main() {
-    for (int i = 0; i < 10; i++) {
-        /* do something */
-    }
-    return 0;
-}
-```
-
-Or a snippet from the above code, starting at the correct line number, and emphasizing a line:
-
-```{code-block} c
-:linenos: true
-:lineno-start: 2
-:emphasize-lines: 3
-    for (int i = 0; i < 10; i++) {
-        /* do something */
-    }
-```
-
-You can read more about code formatting in the [MyST documentation](https://mystmd.org/guide/code).
-
-## Figures, Equations and Tables
-
-It is well known that Spice grows on the planet Dune [@Atr03].
-Test some maths, for example $e^{\pi i} + 3 \delta$.
-Or maybe an equation on a separate line:
-
-```{math}
-g(x) = \int_0^\infty f(x) dx
-```
-
-or on multiple, aligned lines:
-
-```{math}
-\begin{aligned}
-g(x) &= \int_0^\infty f(x) dx \\
-     &= \ldots
-\end{aligned}
-```
-
-The area of a circle and volume of a sphere are given as
-
-```{math}
-:label: circarea
-
-A(r) = \pi r^2.
-```
-
-```{math}
-:label: spherevol
-
-V(r) = \frac{4}{3} \pi r^3
-```
-
-We can then refer back to Equation {ref}`circarea` or
-{ref}`spherevol` later.
-The `{ref}` role is another way to cross-reference in your document, which may be familiar to users of Sphinx.
-See complete documentation on [cross-references](https://mystmd.org/guide/cross-references).
-
-Mauris purus enim, volutpat non dapibus et, gravida sit amet sapien. In at
-consectetur lacus. Praesent orci nulla, blandit eu egestas nec, facilisis vel
-lacus. Fusce non ante vitae justo faucibus facilisis. Nam venenatis lacinia
-turpis. Donec eu ultrices mauris. Ut pulvinar viverra rhoncus. Vivamus
-adipiscing faucibus ligula, in porta orci vehicula in. Suspendisse quis augue
-arcu, sit amet accumsan diam. Vestibulum lacinia luctus dui. Aliquam odio arcu,
-faucibus non laoreet ac, condimentum eu quam. Quisque et nunc non diam
-consequat iaculis ut quis leo. Integer suscipit accumsan ligula. Sed nec eros a
-orci aliquam dictum sed ac felis. Suspendisse sit amet dui ut ligula iaculis
-sollicitudin vel id velit. Pellentesque hendrerit sapien ac ante facilisis
-lacinia. Nunc sit amet sem sem. In tellus metus, elementum vitae tincidunt ac,
-volutpat sit amet mauris. Maecenas[^footnote-1] diam turpis, placerat[^footnote-2] at adipiscing ac,
-pulvinar id metus.
-
-[^footnote-1]: On the one hand, a footnote.
-[^footnote-2]: On the other hand, another footnote.
-
-:::{figure} figure1.png
-:label: fig:stream
-This is the caption, sandworm vorticity based on storm location in a pleasing stream plot. Based on example in [matplotlib](https://matplotlib.org/stable/plot_types/arrays/streamplot.html).
-:::
-
-:::{figure} figure2.png
-:label: fig:em
-This is the caption, electromagnetic signature of the sandworm based on remote sensing techniques. Based on example in [matplotlib](https://matplotlib.org/stable/plot_types/stats/hist2d.html).
-:::
-
-As you can see in @fig:stream and @fig:em, this is how you reference auto-numbered figures.
-To refer to a sub figure use the syntax `@label [a]` in text or `[@label a]` for a parenhetical citation (i.e. @fig:stream [a] vs [@fig:stream a]).
-For even more control, you can simply link to figures using `[Figure %s](#label)`, the `%s` will get filled in with the number, for example [Figure %s](#fig:stream).
-See complete documentation on [cross-references](https://mystmd.org/guide/cross-references).
-
-```{list-table} This is the caption for the materials table.
-:label: tbl:materials
-:header-rows: 1
-* - Material
-  - Units
-* - Stone
-  - 3
-* - Water
-  - 12
-* - Cement
-  - {math}`\alpha`
-```
-
-We show the different quantities of materials required in
-@tbl:materials.
-
-Unfortunately, markdown can be difficult for defining tables, so if your table is more complex you can try embedding HTML:
-
-:::{table} Area Comparisons (written in html)
-:label: tbl:areas-html
-
-<table>
-<tr><th rowspan="2">Projection</th><th colspan="3" align="center">Area in square miles</th></tr>
-<tr><th align="right">Large Horizontal Area</th><th align="right">Large Vertical Area</th><th align="right">Smaller Square Area<th></tr>
-<tr><td>Albers Equal Area   </td><td align="right"> 7,498.7   </td><td align="right"> 10,847.3  </td><td align="right">35.8</td></tr>
-<tr><td>Web Mercator        </td><td align="right"> 13,410.0  </td><td align="right"> 18,271.4  </td><td align="right">63.0</td></tr>
-<tr><td>Difference          </td><td align="right"> 5,911.3   </td><td align="right"> 7,424.1   </td><td align="right">27.2</td></tr>
-<tr><td>Percent Difference  </td><td align="right"> 44%       </td><td align="right"> 41%       </td><td align="right">43%</td></tr>
-</table>
-:::
-
-or if you prefer LaTeX you can try `tabular` or `longtable` environments:
-
-```{raw} latex
-\begin{table*}
-  \begin{longtable*}{|l|r|r|r|}
-  \hline
-  \multirow{2}{*}{\bf Projection} & \multicolumn{3}{c|}{\bf Area in square miles} \\
-  \cline{2-4}
-   & \textbf{Large Horizontal Area} & \textbf{Large Vertical Area} & \textbf{Smaller Square Area} \\
-  \hline
-  Albers Equal Area   & 7,498.7   & 10,847.3  & 35.8  \\
-  Web Mercator        & 13,410.0  & 18,271.4  & 63.0  \\
-  Difference          & 5,911.3   & 7,424.1   & 27.2  \\
-  Percent Difference  & 44\%      & 41\%      & 43\%  \\
-  \hline
-  \end{longtable*}
-
-  \caption{Area Comparisons (written in LaTeX) \label{tbl:areas-tex}}
-\end{table*}
-```
-
-Perhaps we want to end off with a quote by Lao Tse[^footnote-3]:
-
-> Muddy water, let stand, becomes clear.
-
-[^footnote-3]: $\mathrm{e^{-i\pi}}$