Knowledge Base

# https://github.com/westandskif/rate-mirrors#usage
export TMPFILE="$(mktemp)"; \
sudo true; \
rate-mirrors --save=$TMPFILE arch --max-delay=21600 \
    && sudo mv /etc/pacman.d/mirrorlist /etc/pacman.d/mirrorlist-backup \
    && sudo mv $TMPFILE /etc/pacman.d/mirrorlist

• Pacman Mirrorlist Generator
• Reflector: retrieve, filter, sort by speed, and overwrite mirror list

If you're sure that pacman is not running in another shell, you can remove the lock by hand.

sudo rm /var/lib/pacman/db.lck

Source:

• "Pacman is currently in use, please wait." / Pacman & Package Upgrade Issues …

#!/bin/bash
doit=0

for i in {1..3}; do
echo -n ${i}
done

echo "---"

for i in {1..3}; do
((doit))&&(echo -n ${i})
done

echo "---"

for i in {1..3}; do
((doit))&&echo -n ${i}
done

echo "---"

((doit))&&for i in {1..3}; do
echo -n ${i}
done

echo "---"

((doit))&&
for i in {1..3}; do
    echo -n ${i}
done

echo "---"

Also ((dontdoit))!!echo "something"

emacs $(/bin/ls */* --sort=time | tail -n 5)

Cast a string to integer in bash by adding 0. It works well if the string is NULL.

NUM="99"
NUM=$(($NUM+0))

NUM=""
NUM=$(($NUM+0))

Source:

• Bash: comparing a string as an integer - Stack Overflow

## Assign "string-true" to VAR if VARTOCHECK is equal to "string-cond"
[ $VARTOCHECK == "string-cond" ] && VAR="string-true" || VAR="string-false"

Source:

• bash - Conditional assignment based on environment variable

Use the following expression if the assignment is numerical.

## Assign 20 if true, or 10 if false
variable=$(( 1 > 0 ? 20 : 10 ))

Source:

• How to build a conditional assignment in bash? - Stack Overflow

Use explainshell to match command-line arguments to their help text.

Use shellcheck for warnings and suggestions for shell scripts. It can be used online in ShellCheck.net.

Use bluetoothctl to turn the bluetooth controller off and on

echo -e 'show\npower off\npower on\nquit' | bluetoothctl

Source: https://unix.stackexchange.com/a/533782/88701

Don't forget to add --user if it's a user service. Also, -b is short for -b-0 (Ghosthree3 at libera.chat)

journalctl --user -u servicename -b

Consider removing the fallback initramfs to make temporary space. A definite solution is to expand the boot folder. Edit the linux.preset in /etc/mkinitcpio.d to disable generating a new fallback image. Helpful when pacman throws Partition /boot too full.

ls -sh /boot/initramfs-linux-fallback.img

ps -p $$

Source: How to determine the current shell I'm working on

Check that there is a desktop file in /usr/share/applications/firefox.desktop. If there isn't, create one:

Then, update the corresponding xdg entry xdg-settings set default-web-browser firefox.desktop. Test by running xdg-open "www.mozilla.org".

Use rsync --parent to keep the folder structure.

find -iname '*.rds' -exec cp {} . \;
find -iname '*.rds' -exec rsync --parent {} . \;

## any file extension
find . -iname '*.*' -exec basename {} \; | sort | uniq
## a specific file extension, e.g., rds files
find . -iname '*.rds' -exec basename {} \; | sort | uniq

Source:

• tldr/find.md at master · tldr-pages/tldr

Use xev to look for the keycode and keysym in the KeyPress or KeyRelease event

Run xwininfo on a console and click on the target window.

1920 (1080p) is often a good size

# TODO

Source: Convert every pdf in the current directory to png

To switch between US and Greek (polytonic) keyboard layouts using Alt + Caps Locks. Add to ~/.xinitrc, or possibly ~/.config/i3/config, to make it persistent.

setxkbmap 'us,gr' -variant ',polytonic' -option grp:'alt_caps_toggle'

• To list them all man xkeyboard-config Other than Alt + Shift to switch keyboard layout, any other Xorg key
• To list the toggle keys only grep "grp:.*toggle" /usr/share/X11/xkb/rules/base.lst Xorg/Keyboard configuration

Use a Compose key. Here's my .XCompose, below there are many more

• Xorg/Keyboard configuration - ArchWiki
• xcompose/.XCompose at master · exaexa/xcompose · GitHub
• XCompose/.XCompose at master · svinota/XCompose · GitHub
• xcompose/math.conf at master · nshepperd/xcompose · GitHub
• xcompose/superscripts.conf at master · nshepperd/xcompose · GitHub
• dotfiles/.XCompose at master · Wafelack/dotfiles · GitHub

• To list all compose key options grep "compose:" /usr/share/X11/xkb/rules/base.lst
• To set a compose key setxkbmap -option compose:rctrl
• Xorg/Keyboard configuration - ArchWiki

• Unicode subscripts and superscripts

• Filesystem Hierarchy Standard

find . -name "*.log" | xargs ls -lt

Source:

• How to display modified date time with 'find' command?

A PulseAudio source works as an input device (microphone, monitor) sink works as an output device (speaker).

To redirect video from OBS to a new virtual camera input

• Install the linux headers if you don't have them, e.g, sudo pacman -S linux-headers
• Install v4l2loopback-dkms, e.g., sudo pacman -S v4l2loopback-dkms
• Load the kernel module sudo modprobe v4l2loopback
• Select Dummy video device as video source in the meeting app, e.g., in Zoom Settings > Video > Camera
• Source: Open Broadcaster Software - ArchWiki

To redirect audio from OBS to a new virtual sound input

• Create a null output device

  pulsemodule=$(pactl load-module module-null-sink sink_name=obs_audio
        sink_properties=device.description=obs_audio_sink_for_mic)
  

• In pavucontrol, Playback tab, change the output of OBS-monitor to Null output
• In pavucontrol, Recording tab, change the input of Zoom to Null output
• Source:
  • MacGyver at libera.chat,
  • PulseAudio/Examples - ArchWiki
  • Redirecting Pulseaudio sink to a virtual source

• /etc/X11/xorg.conf.d/ (preferred place for host-specific configurations)
• /usr/share/X11/xorg.conf.d/
• /etc/X11/xorg.conf (deprecated)
• /etc/xorg.conf (deprecated)

1. Remove nouveau: sudo pacman -R xf86-video-nouveau
2. Remove all xorg.conf files that might still refer to nouveau drivers (check in /etc/X11/xorg.conf.d/ and /usr/share/X11/xorg.conf.d/)
3. Install the NVIDIA drivers: AUR (en) - nvidia-470xx-utils

• Fork and change https://github.com/SV-97/Math-Layout/blob/master/gm

• Type an equation in UTF8?

[…] at the core of Git is a simple key-value data store [..,] you can insert any kind of content into a Git repository, for which Git will hand you back a unique key you can use later to retrieve that content.

Source: Git - Git Objects

git branch -m newname

After the merge, it's safe to delete the branch

git branch -d branch1

Source: what to do with branch after merge?

diff <(git diff --name-only)  <(git ls-files -- sub/dir) | grep "^>" | cut -b3-

Source: is there any way to list the unmodified files in Git?

git clean -d -x -f

Source: how do I clear my local working directory in git?

Call the garbage collector

git gc

For binary files that change often

git repack -a -d --depth=250 --window=250

Source: how to shrink the .git folder?

git commit -a

Source: using git commit -a

git ls-files --deleted -z | xargs -r0 git rm

Source: staging deleted files

To revert all changes since last commit

git reset --hard HEAD

To revert some changes

git reset
git checkout <file-name>

Source: how to revert git rm -r

The path to the key has to be unique. Requires x-clip.

# Generate a new key
ssh-keygen -t ed25519 -C "your_email@example.com"
# Add key to the ssh-agent in your local machine
eval "$(ssh-agent -s)"
ssh-add ~/.ssh/id_ed25519
# Copy key to clipboard
xclip -selection clipboard < ~/.ssh/id_ed25519.pub

Use ControlMaster in .ssh/config

ControlMaster auto
ControlPath ~/.ssh/%r@%h:%p

Configure the host in .ssh/config once and do ssh shortname

Host shortname
User username
HostName hostname
Port 22
ServerAliveInterval 60

• ssh/config preconfigurations for shortening the ssh and sshfs invocations (see ssh_config)
• autosf
• lazy mount for sshfs via systemd

To match foo in any conex except when enclosed by brackets {foo}, use negative lookarounds but be careful to match {foo and foo}. Alternatively, use PCRE with (*SKIP)(*F)|} (OnlineCop at libera.chat). Other use cases for this pattern: exclude foo in comment lines (#foo, //foo, /*foo*/), quotes ("foo", 'foo').

grep "(?<!\{)foo(?!\})"
grep -P "\{foo\}(*SKIP)(*F)|foo"

Source:

• https://regex101.com/r/9j9BVZ/1
• https://regex101.com/r/gP0oMS/1

Note the need to use single quotes around the regex and to double-escape the function call parenthesis to match, for example, library(capturethis)

grep -Poh -r '(\w+)(?=::)|(?:library|require(?:Namespace)?)\\("?(\w+)"?\\)' --include="*\.R" | sort | uniq

Source:

• https://regex101.com/r/XDsxbU/1

grep -Poh '(http|ftp|https):\/\/([\w_-]+(?:(?:\.[\w_-]+)+))([\w.,@?^=%&:\/~+#-]*[\w@?^=%&\/~+#-])' myfile.txt | sort | uniq

Source:

• Regular expression to find URLs within a string

I typically separate my file in labeled sections using this pattern: comment separator (one or more), space, label (can include space), space, at least four dash lines but typically enough to fill the column space. This can be matched with \S+\s(.+?)\s-{4,}

;; Speed bar -------------------------------------------------------------------

%% Introduction ----------------------------------------------------------------

## Read data -------------------------------------------------------------------

^(?:\d|\d?\.\d+|10(?:\.0+)?)$

Source: https://regex101.com/r/kk8SIF/1/

A regex to string kind of situation.

• onlinestringtools: string from regex generator

• Best practices for regular expressions

Populate the all target programatically. For each file with extension ext1, build a file with the same name but extension ext2.

all : $(patsubst %.ext1, %.ext2, $(wildcard *.ext1))

all : $(patsubst %.tex, %.pdf, $(wildcard *.tex))

Source:

• c++ - Makefile that compiles all cpp files in a directory into separate execu…

Use pdftotext to extract the content of a PDF file and write it into a text file.

pdftotext document.pdf document.txt

Use pdffonts to list all the fonts used in a PDF

pdffonts document.pdf

Use pdfimages to extract images from a PDF file

pdfimages -list document.pdf
pdfimages -png -f 1 -l 10 document.pdf

Use pdfunite to merge input1.pdf and input2.pdf into merged_document.pdf.

pdfunite input1.pdf input2.pdf merged_document.pdf

Use Ghostscript to merge input1.pdf and input2.pdf into merged_document.pdf.

gs -sDEVICE=pdfwrite dNOPAUSE -dBATCH -dSAFER -dQUIET  \
   -dAutoRotatePages=/None \
   -sOutputFile="merged_document.pdf" input1.pdf input2.pdf

Source: How to merge several PDF files?

Use pdfseparate to extract page by page as sample-1.pdf, sample-2.pdf, sample-3.pdf.

pdfseparate sample.pdf sample-%d.pdf

Use Ghostscript to extract pages 12-15 from input.pdf into extracted_document.pdf.

gs -sDEVICE=pdfwrite dNOPAUSE -dBATCH -dSAFER -dQUIET  \
     -dFirstPage=12 \
     -dLastPage=15 \
     -sOutputFile="extracted_document.pdf" \
     input.pdf

Source: How can I extract a page range / a part of a PDF?

Use Ghostscript to compress input.pdf and write into compressed_document.pdf using a distiller preset

• -dPDFSETTINGS=/screen lower quality, smaller size (72 dpi)
• -dPDFSETTINGS=/ebook better quality, slightly larger size (150 dpi)
• -dPDFSETTINGS=/prepress prepress optimized (300 dpi)
• -dPDFSETTINGS=/printer print optimized (300 dpi)
• -dPDFSETTINGS=/default wide variety of uses, larger size

gs -sDEVICE=pdfwrite dNOPAUSE -dBATCH -dSAFER -dQUIET  \
   -dCompatibilityLevel=1.4 \
   -dPDFSETTINGS=/ebook \
   -sOutputFile="compressed_document.pdf" input.pdf

Source: How can I reduce the file size of a scanned PDF file?

Use pdfcrop to automatically crop margins from a PDF file

pdfcrop document.pdf

Use exiftool for reading and manipulating PDF metadata.

exiftool -all:all  file.pdf ## read all the tags
exiftool -all:all= file.pdf ## remove all the tags

Source:

• exiftool(1p) — Arch manual pages
• tldr | simplified, community driven man pages

Use qpdf, or the older and sometimes deprecated pdftk. Use single quotes when including special characters. The user password is mandatory. The user and owner passwords cannot be the same.

## 128 and 256 bit encryption available in qpdf
qpdf --encrypt 'pass1' 'pass2' 256 -- input.pdf output.pdf
## 128 bit or lower encryption available in pdftk
pdftk input.pdf output output.pdf owner_pw 'pass1' user_pw 'pass2' encrypt_128bit

Source:

• How to set password for pdf files? - Unix & Linux Stack Exchange

mkdir -p layouts/_default/_markup/render-link.html
echo '<a href="{{ .Destination | safeURL }}"{{ with .Title}} title="{{ . }}"{{ end }}{{ if strings.HasPrefix .Destination "http" }} target="_blank"{{ end }}>{{ .Text }}</a>' > layouts/_default/_markup/render-link.html

Source: How to Open Link in New Tab with Hugo's new Goldmark Markdown Renderer

Show contentname as landing or home page

mkdir -p layouts
echo '{{ with .GetPage "/contentname" }}{{.Render}}{{end}}' > layouts/index.html

Source: I want to redirect my Homepage to a content page

• TeX FAQ: The TeX Frequently Asked Question List
• nug: Package that warns the user about the use of obsolete things
• l2tabu: Practical usage guide with mistakes, obsolete packages and commands

Elements are in order recommended in The Chicago Manual of Style

Short document

• myclass.cls
• wrapper.tex
• frontmatter.tex
  • title page, table of contents, list of illustrations, list of tables, list of abbreviations
• mainmatter.tex
  • introduction
  • rest of the content
• backmatter.tex
  • appendices, bibliography, index

Full book

• myclass.cls
• wrapper.tex
• frontmatter.tex
  • half title (main title sans subtitle), series title or frontispiece, title page, copyright page, dedication, epigraph, table of contents, list of illustrations, list of tables, foreword, preface, acknowledgements, list of abbreviations, second half title
• mainmatter.tex
  • introduction
  • rest of the content
• backmatter.tex
  • epilogue, appendices, glossary, bibliography, index, and colophon

Run latexmk -pdf -pvc --interaction=nonstopmode file.tex to compile the TeX document every time the file changes on disk.

Source: What You See is What You Get (WYSIWYG) for PGF/TikZ?

Sometimes, we have one or two words hanging on the last line of a paragraph.

• Globally, set a large penalty for creating a club line at bottom of page adding \clubpenalty=10000 (source)
• Add \looseness=-1 immediately before the paragraph (source)
• Adjust badness limits
• \parfillskip controls the length at the end of a paragraph

%% Add prefix S to label names
\renewcommand{\thepage}{S\arabic{page}}
\renewcommand{\thesection}{S\arabic{section}}
\renewcommand{\thetable}{S\arabic{table}}
\renewcommand{\thefigure}{S\arabic{figure}}
%% Modify the text used at the start of the caption
\renewcommand{\figurename}{Supplemental Material, Figure}

• adding prefix to figure caption in LaTeX?

• When should I use non-breaking space?
• What is the right way to use of non-breakable space before math expressions?

• Footnotes without numbering

Use upright d followed by math x, and possibly add a space \, before the differential operator

\begin{equation}
  \int_0^1 x^2 \, \mathrm{d}x
\end{equation}

• Should I \mathrm the d in my integrals?
• What's the proper way to typeset a differential operator?

Use \mathop, or \DeclareMathOperator if amsopn or amsmath are loaded to create operators such as trace, diag, argmax, and argmin.

\newcommand{\diag}{\mathop{\mathrm{diag}}}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\trsym}{tr}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator{\evsym}{E}
\DeclareMathOperator{\vsym}{V}
\DeclareMathOperator{\corsym}{Cor}
\DeclareMathOperator{\covsym}{Cov}
\DeclareMathOperator{\sesym}{SE}

Source:

• Defining a new log-like function in LaTeX | The TeX FAQ

• Punctuation
  • add to an inline and displayed equation the punctuation required by conventional rules, e.g., question mark, comma, semicolon, period
  • add punctuation inside the math mode scope to avoid orphans
• Fractions
  • prefer horizontal bar or forward slash over precomposed fractions for accessibility reasons.
  • metric units are given in decimal fractions, non-metric units can be either type of fraction
• Upright (Roman) versus italic
  • prefer upright over italic for operators, e.g., \(\mathrm{d}x\) over \(dx\)
  • but prefer italic over upright for standard universal constants, e.g., \(e\) over \(\mathrm{e}\) and \(\pi\) over \(\mathrm{\pi}\)
  • prefer italic for variable and function names,
  • but prefer upright for multi-letter names, e.g., \(\mathrm{log}(x)\) over \(log(x)\) and \(\mathrm{sin}(x)\) over \(sin(x)\)
  • prefer upper case italics for sets
• Blackboard bold: standard number system and some certain mathematical objects
• Linear algebra:
  • prefer lowercase bold for vectors, uppercase bold for matrices
  • transpose: prefer \top for a superscript non-italic capital letter T
  • scalar or dot product: prefer center dot \cdot over juxtaposition
  • inner product: use angle brackets \langle and \rangle, e.g., \(\langle \mathbf{a}, \mathbf{b} \rangle\) (How to define an inner product argument in LaTeX)
  • matrix product
  • this is some text followed by a link (This is the helpful and descriptive page title)

Source: Manual of Style/Mathematics - Wikipedia

• The Comprehensive LaTeX Symbol List
• List of LaTeX mathematical symbols: all predefined mathematical symbols

• Detexify: draw symbol by hand or use the symbol table

Use \coloneqq and \vcoloneqq from the mathtools package.

• Source: Symbol for definition :=

• lua-visual-debug: it looks gorgeous

Body width:  \the\textwidth
Body height: \the\textheight

• How to interpret the page layout in LaTeX using layout package?
• Page layour visual guide

• \textfloatsep — distance between floats on the top or the bottom and the text;
• \floatsep — distance between two floats;
• \intextsep — distance between floats inserted inside the page text
• (using h) and the text proper.
• \dbltextfloatsep — distance between a float spanning both columns and the text;
• \dblfloatsep — distance between two floats spanning both columns.

• \captionsetup{font=footnotesize}

  % Reduced margins
  \usepackage{geometry}
  \geometry{left=0.75in,right=0.75in,bottom=1in,top=1in}
  
  % Minimal spacing around captions and floats
  \setlength{\abovecaptionskip}{2pt plus 1pt minus 2pt}
  \setlength{\belowcaptionskip}{2pt plus 1pt minus 2pt}
  \setlength{\textfloatsep}{2pt plus 1pt minus 2pt}
  \setlength{\intextsep}{2pt plus 1pt minus 2pt}
  \setlength{\floatsep}{2pt plus 1pt minus 2pt}
  
  % Minimal spacing around equations
  \setlength{\abovedisplayskip}{0pt}
  \setlength{\belowdisplayskip}{0pt}
  \setlength{\abovedisplayshortskip}{0pt}
  \setlength{\belowdisplayshortskip}{0pt}
  

Source:

• How to change the spacing between figures/tables and text?
• How to reduce the size of captions in all figures?
• How can I modify vertical space between figure and caption?
• Reducing spacing after headings
• Layouts package: enable the display of various elements of a document's layout

Use the adjustbox package to

\adjustbox{trim={.05\width} {.2\height} {0.1\width} {.15\height}, clip}%
{\includegraphics[width=0.5cm]{cupdot.png}}

Source:

• Cropping/Trimming an image with includegraphics by specifying perce…

• Use the \proof environment from the amsthm package (source)
  • Add some text, if needed
  • Begin a align environment
    • Use the aligned subenvironment within align, possibly with a [t] option, or similar subenvinroments to break long lines (source)
    • Use the \shortintertext command from the mathtools package to write short text between lines, or \intertext if you prefer larger space above and below the math line (source)
    • Use the \tag command if you want to refer to a line by a name instead of a number

There is a strong argument for increasing the linespread to accomodate for $Y^{(0)}$ if you need to use smash too often. If you insist, though, use \setlength{\lineskiplimit}{-100pt}

• How does one stop automatic line spacing increases when typesetting tall math

• Low-effort approach: load \usepackage[section]{placeins} and set h! for placement specifiers. It adds a \FloatBarrier (more) at the end of a section to avoid mixing floats and sections.
• How to influence the position of float environments like figure and table in LATEX?

https://paste.xinu.at/m-QzacZr/ https://paste.xinu.at/m-sHDc/

\makeatletter
\def\input@path{{/path/to/folder/}}
% or: \def\input@path{{/path/to/folder/}{/path/to/another/folder/}}
\makeatother

Source: \input and absolute paths

Say you want to align the first column to the left and the rest to the right without needing to figure out how many columns the table has. You can specify more columns than used, but not vice-versa, as in l*9r or l*{99}. Use brackets for more than one digit.

\begin{tabular}{l*{99}r}
  col1 & col2 \\
\end{tabular}

This macro was shared by [exa] at libera.chat.

Long story short, you can't call \input{filename} before \multicolumn.

\csname @@input\endcsname filename

Source:

• ! Misplaced \omit error when inputting table with multicolumn

Use latemk file.tex -pdf and that's it. No need to run multiple commands or figure out the right order. Put in a makefile if that's your workflow.

Source: how to properly 'make' a latex project?

• GitHub workflow yaml file by exaexa

• Consider building a class
  • LATEX2e for class and package writers Sec 2.3
  • Example manurxiv/manurxiv.cls at exaexa/manurxiv
  • documentclass writing - cls file - multiple files

Mix and match (suggestions for a research paper style):

• Search for accessibility guidelines
• A base template for inspiration, e.g., ICML2021 Template
• Layout, e.g., two columns
• Portrait pages need to be easy to set up
• Line numbering
• Author affiliation need to be easy to set up
• Short title in header/footer
• Page number in header/footer
• Headings need to be easy to spot
• Text font, e.g., libertinus, palladios, see also The LaTeX Font Catalogue
• Math font
• Load AMS packages
• Reasonably minimal page margins
• Reasonably minimal fig/table caption margins
• Allow for fig/table extending over both columns
• Appendix need to be easy to set up
• Appendix fig/table numbering should start with A, e.g., Table A.1
• Option to hide names and acknowledgments
• Option for a short table of content on front page
• Have some basic editing commands
  • Logical markup, see CTAN: Package soul (Manual, Sec 5.1)
  • Note box, see How to highlight an entire paragraph?
• Recall that not everyone types in English

• Author commands
  • typically short, lower case names
  • e.g. \section, \emph, \times
• Class and package writer commands
  • typically long, CamelCase names
  • e.g., \InputIfFileExists, \RequirePackage, \PassOptionsToClass
• Internal commands
  • typically contain an @ in their name
  • e.g., \@tempcnta, \@ifnextchar and \@eha
• Exceptions:
  • \hbox is internal
  • \m@ne, the constant -1, is for class and package writers

• Issue: when using {\color{green} text}, color is restored after the final }
  • e.g., \setbox0=\hbox{\color{green} ⟨text⟩}
• Use LaTeX box commands rather than TeX primites
  • \sbox rather than \setbox
  • \mbox rather than \hbox
  • \parbox or a minipage environment rather than \vbox
• Use \normalcolor to set regions to main document color rather like \normalfont

• Use the doc software which comes with LaTeX (see The LaTeX companion)

The path of the local folder, and many others, are defined in /etc/texmf/web2c/texmf.cnf. The default path for local files is ~/texmf. Packages, .tex and .sty files go in ~/texmf/tex/latex, bibtex style files .bst go in ~/texmf/bibtex/bst/. Finally, run texhash ~/texmf/ to update the database.

• Source: Where can I put local latex style files and packages?

Use beamerposter (possibly with the Gemini template) or tikzposter.

• The Not So Short Introduction to LaTeX2e: LaTeX2e in 139 minutes
• The TeXbook: an example of the business of writing a book in TeX
• TeXbyTopic: covers the way TeX works in as much detail as most ordinary programmers will ever need to know
• AMS Author Handbook: include package recommendation, structure, and checklist

%% references
\usepackage[
backend=bibtex,            % Use legacy bibtex backend (biber is better)
natbib=true,               % Load aliases for citation commands
citestyle=authoryear-comp, % Inline: Author year, compressed
maxcitenames=1,            % Inline: max 1 author name
bibstyle=authoryear,       % Bibliography: Author year
giveninits=true,           % Bibliography: first and middle name initials
dashed=false,              % Bibliography: no dash for recurrent authors
abbreviate=true,           % Bibliography: abbreviate
maxbibnames=100,           % Bibliography: all author names
sorting=nyt,               % Bibliography: sort by name, year, title
isbn=true,                 % Bibliography: print ISBN
url=false,                 % Bibliography: don't print URL
doi=true,                  % Bibliography: print DOI
eprint=false               % Bibliography: don't print eprint information
]{biblatex}

% Bibliography: print authors as "last name, first name"
\DeclareNameAlias{sortname}{family-given}

Source:

• Guidelines for customizing biblatex styles - TeX - LaTeX Stack Exchange

This will bold YOURFAMILYNAME in the bibliography but not in the citations.

% Bibliography: bold last name
\usepackage{ifthen}
\AtBeginBibliography{%
\renewcommand*{\mkbibnamefamily}[1]{%
  \ifthenelse{\equal{#1}{YOURFAMILYNAM}}{\textbf{#1}}{#1}}
}

Source:

• Make author names bold in bibliography only - TeX - LaTeX Stack Ex…

Use AtBeginSection and AtBeginSubsection respectively to add a frame when a section or a subsection is created. Beamer has the built-in templates sectionpage and subsectionpage for section slides. You may modify them or simply create a new template.

\AtBeginSection{\frame{\sectionpage}}
\AtBeginSubsection{\frame{\subsectionpage}}

Source:

• sectioning - Automatically generate section title slides in beamer?

Use <beamer:0> to hide it in the presentation, use <handout:0> to hide it in the handout, use <handout:0|beamer:0> or simply <all:0> to hide it in both beamer and handout mode.

\begin{frame}<beamer:0>
  \frametitle{This frame won't be visible}
  Lorem ipsum
\end{frame}

Source:

• How to exclude certain slides from handout

Use \usepackage{appendixnumberbeamer} to automatically reset the frame counter when the \appendix command is called. No need to do this by hand :)

• CTAN: Package appendixnumberbeamer
• Don't count backup slides - TeX - LaTeX Stack Exchange
• Beamer frame numbering in appendix - TeX - LaTeX Stack Exchange

Load \usepckage{hyperref}. Use \label{somename} or \hypertarget{somename} to set a target. Use \hyperlink{somename}{text to show} or \hyperlink{somename}{\beamerbutton{text to show}} to print a text or button linking to the target.

• CTAN: Package beamer
• Beamer: Hyperlink to specific slide in frame? - TeX - LaTeX Stack …

Mix and match:

• A base template
• Text font, e.g., https://tug.org/FontCatalogue/mathfonts.html
  • Latin Modern, Stix2, XITS, Asana, Fira Math, TeX Gyre {Pagella,Bonum,Schola,Termes,Heros}, Libertinus, Euler, Lucida Bright, and Minion Pro
• Math font, e.g., Libertinus
  • Mono math? https://tug.org/FontCatalogue/computerconcrete/
  • Suggest a "nice" font family for my basic LaTeX template (text and math)
• Color palette, e.g., https://lvjr.bitbucket.io/contrast.html
• Accessibility guidelines
• Good presentation guidelines
• List of slide layouts

• Engine: graphviz, mostly DOT
• Editor online: Edotor

Typically requires a bit more of work, but it's more flexible and allows for neater graphs

• Use the graphdrawing tikz library for automated graph layout
• TikZ & PGF manual

• C-\ RET TeX, then C-u C-\ to change it back (parsnip at Libera.chat)
• latex-input: Enter Unicode characters using LaTeX notation (grym at Libera.chat)

• Highlighting by Word, Line and Regexp

• The Emacs StartUp Profiler (ESUP)

• Save point in register r C-x r SPC r (point-to-register), jump to position in register r C-x r j r (jump-to-register) (rpav at Libera.Chat)
• Set a mark C-SPC C-SPC, then jump back C-u C-SPC (Desertcoffee at Libera.Chat)

• GNU ELPA - crdt
• Collaborative editing with Emacs
• EmacsConf - 2021 - talks - Emacs Research Group, Season Zero

• Use tree-sitter if your expression is a programming language identifier
• Use origami for general purpose folding, i.e., GitHub - gregsexton/origami.el: A folding minor mode for Emacs
• Change imenu's regular expressions, e.g., see imenu-generic-expression in Imenu (GNU Emacs Lisp Reference Manual)
• See more information about category folding EmacsWiki: Category Outline

bpalmer at Libera.chat

• GitHub - caisah/emacs.dz: Awesome emacs config files

• GitHub - emacs-tw/awesome-emacs: A community driven list of useful Emacs pack…
• ripgrep
• eshell
• dired
• mu4e
• org-publish: for a website
• org-roam

• AucTex reference card

See Tables 1 and 2 in Babel: Languages.

NB: --batch implies -q, hence initialization files are no loaded. Add -l ~/.emacs, -l ~/.config/emacs/init.el or similar.

echo 'type emacs > /dev/null 2>&1 &&
emacs README.org --batch -f org-md-export-to-markdown --kill &&
git add README.md' >> .git/hooks/pre-commit && chmod +x .git/hooks/pre-commit

• ~mplscorwin/org-git-hooks: automatically render code and documentation from org when you git commit
• bug#12791: 24.2; An option to load user init file with -batch

Set up a custom font lock format by calling the function font-lock-add-keywords.

(add-hook 'org-mode-hook
     (lambda ()
       (font-lock-add-keywords
        nil
        '(("^-\\{5,\\}"  0 '(:foreground "green" :weight bold))))))

Source:

• How can I color horizontal lines in org mode? - Emacs Stack Exchange
• Font Lock (GNU Emacs Manual)

Use org-modern for a modern style via font locking and text properties. Consider also org-superstar, which has a reduced scope for headings and plain lists only.

Source:

• GitHub - minad/org-modern: Modern Org Style
• GitHub - integral-dw/org-superstar-mode: Make org-mode stars a little more super

• Use cases of org-mode as a scientific productivity tool for academics
• Org-mode reference card

• What is the difference between currying and partial application?

• Requirements:

  • Referential transparecy: always returns the same result if given the same arguments
    • Rely on their own arguments and immutable values only, e.g.,

  a string

  • No dependence on random number generation, data files
  • Must have no side effects
    • No need to worry if used in multiple places, or down a deep

  call chain

  • No uncertainty about what an object name refers to
  • Easier to trace and debug
• Immutable data structures
  • Recursion instead of for/while loops
  • Function composition instead of attribute mutation

A program is chain of monoids (which is a chain of continuations (which is a chain of partial applications (which is a chain of compositions (which is a chain of one-argument functions))))

• Functions all the way down!
  • Function as inputs
  • Functions as outputs
  • Function as arguments
    • Hard-coded data, e.g., for i in 1:10
    • Hard-coded behavior, e.g., print
    • Decouple behavior from data, i.e., any behavior times any data
    • Collection functions, e.g., fold, map, reduce, collect
• Composition pattern: chain low-level operations
  • e.g., apple -> cherry = apple -> banana + banana -> cherry
  • Low-level operation: e.g., string -> string
  • Service: chained low level operations, e.g., Address -> Validation
  • Use-case: chained services, e.g., ChangeProfileRequest -> ChangeProfileResult
  • Application: chained use-cases, e.g., Request -> Response
  • Composition is fractal
  • Works for functions with one parameter only (see next)

• Partial application

  • Write a two-parameter function as a one-parameter function that returns a one parameter function, e.g., a + b = function(b) { a + b }).
  • Uses:
    • When working with vectorized applications, e.g., lapply, Map,

  Filter.

  • To inject dependencies, e.g., on a database or file

  connection.

• Continuations: chain partial applications

  • Bad: nested checks (pyramid of doom)
  • Good:
    • Start with an abstract if_ function -> returnType
    • Chain them:

  if_(doA) else doNestedActionLevel1
  if_(doB) else doNestedActionLevel2
  if_(doC) else doNestedActionLevel3
  

• Monoids: chain continuations
  • Closure: combining two things always returns another one thing.
    • Readily vectorized!
  • Associativity: when combining more than two things, pairwise combination order does not matter
    • Readily parallelized!
    • Easy for incremental accumulation
  • Identity: a special thing called "zero" that returns the same thing that was combined with it
    • Use as initial value for empty or missing data
• Two-track model for error handling:
  • Use a switch function for error handling, e.g., validate(input) calls sucessFun(input) or failure(error)

From Functional Programming Patterns (NDC London 2014) by Scott Wlaschin.

• Functional Programming Design Patterns: design pattern overview and some demonstrations
• Where are all the functional programming design patterns?
• Origami programming: natural patterns for computation over recursive datatypes
• Functional Programming, Simplified: large free preview available
  • The proper way to handle exceptions and null values
  • Many lessons on for-expressions, which lead naturally into monads
• To know good vs bad Scala style
• Functional Programming | Clojure for the Brave and True

• NSEs are like super duper macros

• Functions as arguments
• Functions as ?
• Functions as output

Or something like that for functions, check

x <- unlist(replicate(10, rep(sample(LETTERS, 1), rpois(1, 4))))
sequence(rle(x)$lengths)                  # if ordered
unlist(sapply(unname(table(x)), seq.int)) # doesn't need ordering

Source: generate sequence within group in R

x <- unlist(replicate(10, rep(sample(LETTERS, 1), rpois(1, 4))))
head(cumsum(rle(x)$lengths)+1, -1)

Source: Identifying where value changes in R data.frame column

Note that as.numeric(as.factor(x)) does not work if x contains numbers. Also, the match-unique combo scales better with large vectors.

x <- c(4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 1, 1, 1, 5, 5, 5, 5)
match(x, unique(x))
## [1] 1 1 1 2 2 2 2 3 3 3 3 4 4 4 5 5 5 5

Source: how to create a consecutive group number

If x is a data.frame, which is a list with attributes, use x[] to preserve all attributes.

x[] = lapply(x, type.convert)

Source: Jiří Moravec

Use base::asplit for efficiency, where asplit(X, 1) and asplit(X, 2) return a list of rows and columns respectively.

## I just learned about asplit
asplit(X, 1)

## Original note
X <- matrix(rnorm(100), nrow = 20)
l <- as.list(as.data.frame(t(X)))

The workhorse of any labeling function

l <- list(key1 = "value1", key2 = NA, key3 = 022)
lookup <- function(x, l) { unlist(l[x]) }

Source: benchmark unlist versus do.call(c, list) for list lookup in R

General approach with Base R only

Filter(function(x)!all(is.na(x)), df)

Via data.table for general time and memory efficiency (40% faster in example)

DT[, which(unlist(lapply(DT, function(x)!all(is.na(x))))), with = FALSE]

Source: remove columns from dataframe where ALL values are NA

Use unlist(lapply(split(x, f), FUN)) for speed, but consider tapply(x, f, FUN) for readibility maybe?

## Unit: microseconds
##     expr      min        lq      mean    median        uq       max neval
## f0(x, f)  409.578  415.5165  426.9041  418.9500  424.3400  4237.466 10000
## f1(x, f)  411.208  418.3095  430.4231  421.8645  427.4155  5550.120 10000
## f2(x, f)  474.681  487.1265  498.8509  492.6960  497.6360  2552.075 10000
## f3(x, f) 1395.582 1442.3785 1494.0197 1459.3515 1472.5205 28121.379 10000
set.seed(1)

x <- rnorm(10000)
f <- factor(rpois(10000, 5))

tapply_ <- function(x, f, FUN) { unlist(lapply(split(x, f), FUN)) }

f0 <- function(x, f) { unlist(lapply(split(x, f), mean)) }
f1 <- function(x, f) { tapply_(x, f, mean) }
f2 <- function(x, f) { tapply(x, f, mean) }
f3 <- function(x, f) { by(x, f, mean) }

bench <- microbenchmark::microbenchmark(
           f0(x, f), f1(x, f), f2(x, f), f3(x, f),
           times = 1E4)

print(bench)

## Row with maximum `g` for each group `id` in the `bdt` data.table
bdt[bdt[, .I[g == max(g)], by = id]$V1]

Source: subset rows corresponding to max value by group using data.table

out <- setNames(c("value1", "value2"), c("name1", "name2"))

Source: create a numeric vector with names in one statement?

Including ellipsis also!

f <- function(a, b = 2, ...) { c(as.list(environment()), list(...)) }

Source: get all Parameters as List

options(error = recover, show.error.locations = TRUE, warn = 2)

Source: debugging unexpected errors in R – how can I find where the error occurred?

SMA <- function(x, K) {
  if(!(K %% 2)) stop("K is not even")
  rowMeans(embed(c(rep(NA, K / 2), x, rep(NA, K / 2)),  K), na.rm = TRUE)
}

Source:

• Centered moving average in R (without using packages)

Note: this needs validation.

myfun <- function(seed) {
  old  <- .Random.seed
  on.exit({assign(".Random.seed", old, envir = .GlobalEnv)})
  set.seed(seed)
}

Thanks to fendur on #R at libera.chat

• Client-side, precomputed dashboard like document:
  • Idea: one chapter contains an image plus some comments
  • Start with html_document
  • Use .tabset-pills to organize chapters
  • Use .tabset-fade to make switching smoother
• Pimp my RMD: a few tips for R Markdown

Below is a quick template I prepared.

---
title: "Barebone dashboard"
date: "`r Sys.Date()`"
output: html_document
---

<style type="text/css">
.main-container {
   max-width: 100% !important;
}
.title, .author, .date {
  display:inline!important;
}
.nav-pills {
  line-height: 0px !important;
}
.h1 {
 font-size: 16px !important;
}
</style>

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  echo       = FALSE,
  fig.align  = "center",
  fig.width  = 16,
  fig.height = 8.1,
  out.height = "80%"
)
```

# {.tabset .tabset-fade .tabset-pills}

## Precipitation per year

```{r}
plot(Nile, col = "darkgreen", lwd = 2, log = "y")
title(main = "Annual flow of the river", adj = 1, line = .5)
```

1. This is a full-page wide picture
2. Line 2
3. Line 3
4. Line 4
5. Line 5

## MPG explained

```{r}
par(mfrow = c(1, 2))
plot(mtcars$mpg, mtcars$drat)
plot(mtcars$mpg, mtcars$wt)
```

1. This is a full-page side-by-side picture
2. Line 2
3. Line 3
4. Line 4
5. Line 5

## Species and width

```{r fig.width = 8.1, fig.height = 8.1}
pairs(iris[, 1:3], col = iris$Species, bg = iris$Species, pch = 21)
```

1. This is a full-page square picture
2. Line 2
3. Line 3
4. Line 4
5. Line 5

Check GitHub - daattali/addinslist to discover and install useful RStudio addins. You can install the addinslist package to browse the list from RStudio.

Here are some suggestions:

• GitHub - seasmith/AlignAssign: Align the assignment operators within a highli…
• GitHub - petermeissner/assignparams: RStudio Addin to evaluate comma separate…
• GitHub - dcomtois/sortLines: Adds "Sort Selected Lines" to RStudio's Addins menu

• Rtips
• A Collection of Simple R Shortcuts
• Efficient R programming
• erikgahner/awesome-ggplot2: A curated list of awesome ggplot2 tutorials, packages, etc.

RStudio general recommendation is to include .Rproj file in the repository, i.e., do not ignore it

Source: should *.Rproj files be added to .gitignore?

?

• AlignAssign

Use ess-build-tags-for-directory (C-c C-e t and C-c C-e C-t) to build the tags, then xref-find-definitions (M-.) to look up a definition via Xref.

Source: How to jump to R source code with ESS?

• ESS – Emacs Speaks Statistics
• https://ess-intro.github.io/

• Variables in the transformed parameters blocks

  1. Can have constraints for error checking
  2. Are global
  1. can be accessed from the generated quantities block
  2. are part of the output by default

• List of datasets for machine-learning research - Wikipedia

• NCSU Functional Data Analysis Lab
• CRAN - Package refund
• Tecator dataset

• IBEX: Interstellar Boundary Explorer
  • Main paper: 10.3847/1538-4365/aa66d8

• Borg: Deduplicating archiver with compression and encryption

• Cache Directory Tagging Specification: avoid backing up, archiving, or otherwise unnecessarily copying directories

• Minimal make file
• Passing arguments to make
• Rules with grouped targets: when one script produces more than one target
• Automatic variables: handy to write recipes
• Automation and make: for analysis, visualization and papers
• Self-documenting makefiles

• Automating data-analysis pipelines
• Awesome pipeline: curated list of awesome pipeline toolkits

• Tabular data pager: works fine with CSV files too!
• VisiData: lightning fast tabular data exploring, arranging, plotting

• Data Organization in Spreadsheets

1. Cycle initiation
2. Build reference data
3. Extract (from sources)
4. Validate
5. Transform (clean, apply business rules, check for data integrity, create aggregates or disaggregates)
6. Stage (load into staging tables, if used)
7. Audit reports (for example, on compliance with business rules. Also, in case of failure, helps to diagnose/repair)
8. Publish (to target tables)
9. Archive

Source: Real-life ETL cycle

• Workflow for statistical analysis and report writing
• What is a research compendium for reproducible research
• Drake documentation

• 1 color:
  • for points: black #000000
  • for lines: either black #000000 or honolulu blue #2271B2
  • for filled areas: summer sky #3DB7E9
  • for surfaces: TBD
• 2 colors:
  • for points: TBD
  • for lines: honolulu blue #2271B2 and gamboge #E69F001
  • for filled area: honolulu blue #2271B2 and gamboge #E69F001
• 3 colors:
  • for points: TBD
  • for lines: TBD
  • for filled areas: TBD

Source:

• Color-palette for color blindness: maintain perceptual luminance uniformity in color blind space

• Color Palette for All types of Color Blindness
• Color-palette for color blindness: maintain perceptual luminance uniformity in color blind space
• Color Universal Design: set of colors that is unambiguous both to colorblinds and non-colorblinds

• What to consider when choosing colors for data visualization
• Data-to-viz: visualization decision tree guide

Use the sacct command, possibly with -S starttime and -E endtime arguments. It also accepts the --format argument.

sacct -S now-1days

Source:

• Slurm Workload Manager - sacct

Use seff jobid after the job has finished. Use sacct -s r jobid or sstat jobid for jobs in progress.

Source:

• Find out the CPU time and memory usage of a slurm job

Short answer: you can't if you're using #SBATCH tokens. Consider creating a command called via sbatch instead, where you can pass modifiers and arguments to the sbatch as needed (e.g., sbatch --mem=$mymem).

Source:

• Use Bash variable within SLURM sbatch script

Alternatively, you can pass the script through stdin replacing the position arguments.

Source:

• Sbatch: pass job name as input argument

This is an excellent guide: Introducing Slurm | Princeton Research Computing. It covers how to submit serial jobs, multithreaded jobs, multinode or parallel MPI jobs, multinode, multithreaded jobs, job arrays, running multiple jobs in parallel as a single job, and running a sequence of jobs (job dependencies).

• Name things mainly for their role, sometimes for their type
• Variable names follow mathematical notation only in low-level functions, use meaningful name for user facing variables
• Use unabbreviated verbs for function names
• Keep abbreviations between 3 and 4 chars

Modeling

Cross-validation

Object types

Transformations

Other

Statistics

Measurement units

Let \(X_t\), \(t\in[a,b]\) be a centered stochastic process with \(\mathrm{E}[X_t] = 0\) for \(t\in[a,b]\) Assume the process satifies a technical continuity condition. Then, we have

where \(Z_k\) are pairwise uncorrelated rando mvariables and \(e_k\) are continuous real-valued functions on \([a,b]\) that are pariwise orthogonal in \(L^2([a,b])\). If the process is Gaussian, then \(Z_k\) are Gaussian and stochastically indepenedent.

Given any orthonormal basis \(e_k(t)\) of \(L^2([a,b])\), we can approximate the stochastic process with

The Karhunen–Loève expansion minimizes the total mean square error resulting of its truncation.

Source: Kosambi–Karhunen–Loève theorem - Wikipedia

Let \(W_t\) be a Wiener process, i.e., a center standard Gaussian process with covariance function \(K_{W}(t,s)=\operatorname {cov} (W_{t},W_{s})=\min(s,t)\). Then, the expansion consists of sinusoidal functions

Source: Kosambi–Karhunen–Loève theorem - Wikipedia

Let \(\mathbf{T} = \mathbf{X} \mathbf{W}\) for principal component score matrix \(\mathbf{T}\) and loading matrix \(\mathbf{W}\). Set the models \(Y = \mathbf{X} \mathbf{\beta} + \mathbf{\varepsilon}\) and \(Y = \mathbf{T} \mathbf{\beta}_T + \mathbf{\varepsilon}\). Then, \(\mathbf{X} \mathbf{\beta} = \mathbf{T} \mathbf{\beta}_T \iff \mathbf{\beta} = \mathbf{W} \mathbf{\beta}_T\).

• How to reverse PCA and reconstruct original variables from several principal components?
• Relationship between SVD and PCA. How to use SVD to perform PCA?

Look at the tail of the QR decomposition pivot vector (rickyrick at libera.chat)

• How to identify which variables are collinear in a singul…
• QR decomposition - Column pivoting

• Conditional random field: considers the context (neighborhood) of an observation when predicting a label
• Markov random field: finite or infinite undirected graphical model that can do cyclic dependencies but can't do induced dependencies

Cressie and Hawkins (1980) found that the fourth-root of χ1 has a skewness of 0.08 and a kurtosis of 2.48 (compared with 0 and 3 for the Gaussian distribution). Estimates of location, such as the mean and the median, can then be applied to sqrt(X). Finally, these estimates can be raised to the 4th power and adjusted for bias. Consider the square-root-differences cloud for visualization.

• Source: 10.1002/9781119115151 eq. (2.2.8)

Some heuristics that I have heard here and there.

• Recall that linearity, additivity, and constant variance are key assumptions for a linear model
• Are you analyzing multiple responses separately? Do some responses benefit from the log transformation? Do you want to apply the same transformation to all the responses to avoid "p-hacking"?
• Are the changes on the responses happening on a relative scale?
• "Log transform, kids. And don’t listen to people who tell you otherwise."

Source:

• You should (usually) log transform your positive data
• Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge university press.

• If the range(x) = max(x) - min(x) is equal to or larger than 10 (Jarad)
• Similarly, if the ratio(x) = max(x) / min(x) is equal to or larger than 10
• If plot is more loaded to the left of 1 than to the right (Jarad), especially for ratios.

Consider a covariate (AKA independent variable, regressor, predictor) with true zeroes observed.

• \(log(x+1)\) which maps 0 to 0
• \(log(x+c)\) where \(c\) is either estimated or set to be some small positive value
  • Model sensitivity rule of thumb
• inverse hyperbolic sine, which behaves like a log for large values
• replace with two variables: a binary indicator for zero, and \(log(x)\) for if \(x\) is nonzero or zero otherwise (see Hosmer & Lemeshow's book)
  • probability plots of the positive part of the original variable are useful for identifying an appropriate re-expression
• Box-Cox
• Square root, or cube root, for something quick and dirty to get you going
• Source
  • How should I transform non-negative data including zeros?
  • Transforming data with zeros | Rob J Hyndman

For hierarchical models, WAIC estimates predictive performance for a new observation from an existing group whereas cross-validation estimates the predictive performance for a new observation from a new group.

• Source: WAIC and cross-validation in Stan! | Statistical Modeling, Causal Inference, …

• Splines with Nonnegative $B$-Spline Coefficients
• How can I find a non-negative interpolation function? (positivity-preserving interpolation is hard)

Here is some general guidance, which of course may not be the best fit for some specific situations

• Clarify the research question
• Focus on estimates, confidence intervals, and clinical relevance
• Carefully account for missing data
• Do not dichotomise continuous variables
• Consider non-linear relationships
• Quantify differences in subgroup results
• Consider accounting for clustering
• Interpret I2 and meta-regression appropriately
• Assess calibration of model predictions
• Carefully consider the variable selection approach
• Assess the impact of any assumptions
• Use reporting guidelines and avoid overinterpretation

Source

• On the 12th Day of Christmas, a Statistician Sent to Me . . . | The BMJ

• A Catalog of Noninformative Priors

• One long run in MCMC: If you can't get a good answer with one long run, then you can't get a good answer with many short runs either.

• A mostly complete chart of Neural Networks by Fjodor van Veen at the Asimov Institute

• Universal kernels should be able to approximate any continuous functions on a compact subset, making a mean function nonessential
• The mean function may not live in the space of functions being modeled
• A mean function can help with extrapolation when using a nonperiodic kernel

Source: Why is the mean function in Gaussian Process uninteresting?

Since differentiation is a linear operator, the derivative of a Gaussian process is another Gaussian process.

Source:

• Rasmussen and Williams (2006, section 9.4)
• Derivative of a Gaussian Process

If all finite linear combinations \(\sum_i a_i X_{t_i}\) are Gaussian and the process is continuous, \(Y_t = \int_0^t X_s \, \mathrm{d}s\) is a Gaussian process.

• Integral of a Gaussian process (this result is more general)
• Integral of Brownian motion is Gaussian?

The convolution of a Gaussian process, as a linear combination of Gaussia nrandom variables, remains a Gaussian process.

• 10.1109/TSP.2011.2119315
• Sparse Convolved Gaussian Processes for Multi-output Regression

• Computationally impractical for large data sets: inference requires the inversion of an \(N\times{}N\) covariance matrix, which is \(O(N^3)\)
  • Use a large data approximation: When Gaussian Process Meets Big Data: A Review of Scalable GPs
• Covariance function is commonly assumed to be stationary, limiting modeling flexiblity (e.g., noise variance is different in differents parts of the input space, the function has a discontinuity)

• Multi-Output GP Emulator: fit, predict, optimize, tools for experimental design, dimension reduction, and calibration.

• Gaussian Process Summer Schoool Lectures

• big list - A good book of functional analysis - MathOverflow

• The Matrix Cookbook: collection of linear algebra facts
• Matrix calculus: symbolic vector and matrix derivatives
• The Matrix Reference Manual: reference information about linear algebra and the properties of real and complex matrices.
• Old and New Matrix Algebra Useful for Statistics: large number of matrix identities.
• Useful Matrix and Gaussian formulae: reference sheets of useful matrix and Gaussian formulae.

• GENO: optimization solver code generator

An orthonormal basis for \(L^2([0,1], \mathcal{R})\) is \(1, 2\sqrt{cos(2\pi nx)},2–\sqrt{sin(2\pi nx)}\) for \(x\in[0, 1]\) and \(n = 1,2,\dots\)

Source:

• Fourier basis functions - Mathematics Stack Exchange
• For interval \([-\pi,\pi]\) Are Fourier series a basis for \(L^2((-\pi,\pi)^m)\)?
• For arbitrary \([a, b]\) Orthonormal set of basis functions in \(L^2({a,b})\)

As with any software, for Computer Assisted Algebra I try to use open source software as much as possible. I keep the use of Wolfram Alpha and Wolfram Mathematica to a minimum.

• List of computer algebra systems - Wikipedia
• SymPy (documentation): Python library for symbolic mathematics
• Yacas: (documentation) can be access via R using the Ryacas package
• Wolfram Mathematica (proprietary, paid) and Wolfram Alpha (proprietary, free in some cases)

• The Elements of Style by Strunk, W., Jr. and White, E.B. An opinionated style guide.
• The Chicago Manual of Style (15th ed.), Chicago: University of Chicago Press.
• Garner's Modern American Usage by Bryan A. Garner.
• English for Writing Research Papers by Adrian Wallwork
• proselint: whisper suggestions on how to improve your prose, see what it looks for.

• academic-phrases Emacs package
• 600 academic phrases from English for Writing Research Papers

• Good, best, better: in what sense?
• Difficult: what are you trying to say more precisely? What's the complexity?

• List of technical names used frequently and short sentences
• Emulator, surrogate, meta-model, statistical model versus computer experiment, computer model, mechanistic model, physical model, climate model, what have you
• Significant(ly) has a technical connotation, use considerable or considerably if one want to avoid such connotation
• A vector/scalar(-valued) function of a vector/scalar variable (greenbagels at Libera.Chat). A function of a vector variable, associated with multivariate calculus, depends on the domain of the function. A vector-valued or scalar-valued function, associated with vector calculus, depends on the range of the function.

• Prefer repeating a technical term in the same sentence, or a sequence of sentences, rather than using synonyms that are not defined.

Yeah, it sounds weird to be repetitive and I sometimes feel that I keep repeting myself too much. As a reader, though, I sometimes wish the writter would be more precise even at the price of repetition. Even thought a section might be about a specific density function (e.g., predictive density), make sure that in every sentence it is obvious that you are referring to that density and not to any of the dozen densities that a model have and are highly connected to the density you are talking about.

They are tough to beat. In most situations, I prefer an extensive use of attributive nouns. Be ware they grow too big too often; I sometimes break a really long chain of nouns into two smaller attribute noun clauses.

Compare the benefit of the parametrization that we propose for this model versus the proposed model parametrization benefit.

• multiple instead of more than one

• List of English determiners: Positive paucal determiners
• The Cambridge Grammar of the English Language. DOI: 10.1017/9781316423530

Litotes help moderate an adjective, e.g., not unlike vs like, not uncommon vs common, non-trivial vs complex. "Not unlike" is slightly different than saying "like" much like saying "I love apples" is not the same thing as saying "I don't hate apples."

Source:

• Litotes - Wikipedia
• "Like" versus "not unlike" - English Language & Usage Stack Exchange

I sometimes doubt about the right verb tense for a sentence. When I read, I often see authors changing tenses often, perhaps with a good reason. Here a few thoughts.

• Active voice
  • I don't have a reference to use, but I've seen a pushback against the traditional use of passive voice. It's probably a good idea to stick to either active or passive voice throughout the manuscript.
• Present tense
  • Facts that are always true, e.g., a Gaussian process is a probabilistic model
• Present perfect
  • Things that have been done recently, e.g., Author (year) has recently introduced a novel framework
• Past tense
  • Things that were done in the past, e.g., Author (year) built a parametric function

• Hyphens are used when two or more adjectives or an adjective and a noun together modify another noun; for example, goodness-of-fit test is the equivalent of test for goodness of fit.
• Most words with prefixes such as sub, non, pre, post are not hyphenated, for example: subtable, nonnormal, nonlinear, premultiply, postgraduate.
• No dash when using the wise suffix, e.g., elementwise instead of element-wise, subspace instead of sub-space
• Closed compound nouns, e.g., metadata instead of meta data
• Prefer "Considering/As/Since subject verb" over "Considering that subject verb" (mdogg at libera.chat)
• squared exponential is grammatical, square exponential is not
• y is quadratic in x or y is a quadratic function of x, but never y is quadratic on x

• Use "respectively" at the end of the sentence, preferably, or in the middle. Use comma.
• Prefer "and is thus" over "and thus is" (187M vs 24M matches). Consider "therefore" or "thence" instead of "thus", which is becoming archaic, for causation.
• Don't be unnecessarily indirect, don't be fluffy. E.g., "Consider"
• Can/could/may: can expresses certainty, could expresses uncertainty or a conditional statement, may expresses a possibility or a permission, may not expresses a denial of permission. (The Chicago manual of style, 2017, 5.250).

• Use bold for (i) make the core of the message as salient as possible, (ii) in-line headings at the start of the line
• Use emph, or italic if emph is not available, to mark format names or definition concepts
• Use underline for editing comments that won't make it to the final version
• Use verbatim for programming-like keywords, e.g., gemv
• Use code for in-line code snippets

• A sentence is better than a paragraph. A phrase is better than a sentence. A word is better than a phrase. An image is better than a word.
• Have you noticed how hard it is to convey a technical detail while giving an oral presentation? Now imagine how hard it is for the audience to understand anything too technical. Be a nice speaker instead :)

• Research Statement: Cornll University Graduate School

• Research proposal template (published by the SML group for an opening)

You probably want a LaTeX command for these.

• Citation needed: when you are inclined to accept the statement, but still need to pin-point the best reference
• Verification needed: when you want to double-check that something is as stated
• Revision needed: when you want to review the math or, more generally, the logic of the statement
• Further research needed: when you make a broad statement, typically outside the scope of the current writing, that seems worth exploring by you or anyone else
• Discussion needed: when you want to have others opinion

Automatic differentiation can decrease runtime at large over numeric differentiation with little effort. In some (typically surprising) cases, automatic differentiation can yield better runtimes than analytical differentiation. A key aspect about analytical differentiation is that, besides the math work needed to obtain the analytical form, their implementation typically requires a non-trivial amount of work to beat automatic differentiation. Numerical differentiation is almost always the least performant.

Source: Analytic Derivatives — Ceres Solver

To optimize a function of \(m\) parameters, L-BFGS-B spends per step roughly \(2m\) calls on calculating a tangent plane (derivatives) plus a further call at each newly chosen location, which is typically at a short distance. L-BFGS-B can be more robust in higher dimension settings than Nelder-Mead.

Source: Surrogates - Robert Gramacy

In absence of problem-specific information, use the square root of machine epsilon for forward difference, and the cubic root of machine epsilon for centered difference. Finding a minimum gets the square root of epsilon while finding a root gets epsilon.

Source: Choosing epsilon

Use the dot product

X  <- iris3[,,1]

M  <- tcrossprod(X)
m  <- diag(M)
o  <- rep(1, nrow(M)) # column vector
h2 <- m %*% t(o)      # outer(m, o) = m %*% t(o)

D2 <- -2 * M + h2 + t(h2)

all.equal(D2, unname(as.matrix(dist(X))^2))

def compute_distances_no_loops(self, X):
  dists = -2 * np.dot(X, self.X_train.T) +
  np.sum(self.X_train**2, axis=1) + np.sum(X**2, axis=1)[:, np.newaxis]
  return dists

Source: Dot Product and Distance Matrix