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Clara Xiao

Mathematician and computer scientist

Formatting test

Here is a post with all kinds of crazy formatting so that I can test out my CSS.

Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

Make sure the keyboard element Ctrl + Alt + Delete doesn’t mess up the spacing.

Heading bravo

Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

A graph showing the number of college degrees granted in various fields of study between the years 2000 and 2017. The number of degrees granted in health professions and related programs and business has increased steadily, wile the number in the social sciences and history has increased before beginning to drop.A graph showing the number of college degrees granted in various fields of study between the years 2000 and 2017. The number of degrees granted in health professions and related programs and business has increased steadily, wile the number in the social sciences and history has increased before beginning to drop.

What a figure!

An expandable section Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

Heading charlie the first

Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

Heading charlie the second

Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

A blockquote:

Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

Ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

Things I like to eat:

Items on my desk:

  1. Computer
  2. Speakers
  3. Coffee
  4. Notepad

Code

I’ve been using the following fish alias fzl (“fuzzy list”) to run fzf (“fuzzy find”) in the current directory with a bat preview. It’s just a couple of light tweaks to the examples listed in the fzf readme.

~/.config/fish/functions/fzl.fish:

function fzl
    # `bat` is aliased to `batcat` on Debian
    if type -q batcat
        set -f bat_command "batcat"
    else
        set -f bat_command "bat"
    end

    # Set the overall width of the `bat` preview to
    # 50% the width of the current terminal
    set -l bat_width $(math ceil $COLUMNS x 0.5)

    # My preferred `bat` options
    set -f bat_command \
        $bat_command \
        --style numbers \
        --color always \
        --italic-text always \
        --wrap auto \
        --terminal-width $bat_width

    fzf \
        --preview "$bat_command {}" \
        --preview-window right,$bat_width,nowrap
end

Example below.

Python example

https://github.com/maxkapur/cronjobs/blob/main/backup_nextcloud_contacts.py

def get_connection_parameters():
    parser = ArgumentParser(
        description="Create backups of Nextcloud calendar and contacts files"
    )
    parser.add_argument(
        "url", help="Nextcloud base URL (https://nextcloud.example.com)"
    )
    parser.add_argument("username", help="Nextcloud username (admin)")
    parser.add_argument(
        "keyfile", help="Path to file containing password (~/nextcloud_key)"
    )
    args = parser.parse_args()

    # Enforce HTTPS and allow some typical variants
    url = "https://" + args.url.rstrip("/").lstrip("http://").lstrip("https://")
    username = args.username

    with open(args.keyfile) as file:
        password = file.read()
        file.close()

    return url, username, password

def raise_an_error():
    x = 5
    if x > 4:
        raise ValueError(f"{x = } > 4")

class ClassExample:
    """A docstring.

    Has multiple lines.
    """

    def some_method(self, x: int) -> None:
        "Docstring."

        # Print it
        print(x)

Julia example

# Main purpose of creating this was to see "special" strings (symbol, regex) in
# action, but rouge doesn't parse them as anything special :(

if 5 < 6
    @assert match(r"\d", "hello2")
end

(string(:hello) == "hello" ? 5 : 6) |> sqrt

Math

In this post, we will show that functions of the form

f(X)1ˉiΩX(1pi)iX(1qi)f(X)=1prodiinOmegasetminusX(1pi)prodiinX(1qi)f(X)1ˉiΩX(1pi)iX(1qi)

are submodular for pi,qi∈[0,1]p_i, q_i \in [0, 1]pi​,qi​∈[0,1] where each pi≤qi,p_i \leq q_i,pi​≤qi​, and examine an application of this small result that demonstrates its practical value.1

  1. Lorem ipsum dolor sit amet consectetur adipisicing elit. Aliquam ipsa ducimus laudantium, ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi!

    Ab numquam optio cumque perspiciatis voluptatum quis accusantium, atque excepturi, laboriosam similique! Laboriosam sed dignissimos quasi non animi! ↩︎