dnd 5e – Can players choose specific points in space, down to the inch, to cast a spell so as to avoid hitting a prone character?

Say there is a character that is prone, such as if they were unconscious, and they are surrounded on all 8 square grids (assuming that a grid is being used) by other creatures. Can a player cast a spell that has a sphere effect such as fireball or shatter such that only the 8 creatures surrounding the one that is prone be hit?

Would this potentially have any adverse effects with potentially breaking or having any unintended consequences for any other spells/effects down the line if this were allowed?

Obviously when it comes to casting some spells, the caster has the option to “choose a point in space”, but when playing with the understanding of a grid system that works in chunks of a given dimension does is it feasible to have spells cast in such a way so that a body lying prone won’t be affected by a spell cast just overhead?

Free disk space under APFS

I upgraded today from Sierra to High Sierra (yes I know it’s old but I have audio hardware that won’t work on newer systems).

As part of the migration, it changes the HFS+ partition to APFS. I have Time Machine backups set to external USB disks, but this is not automatic and I do it once a week/month manually.

I am aware that there is now a local snapshot mechanism in High Sierra, but how on earth do I discover what real free disk space I have??

On the desktop it said 54.91 and in Disk Utility it said 25.18:
first examination

I tried tidying away the invisible snapshots, even though Time Machine is disabled:

tmutil listlocalsnapshots /
com.apple.TimeMachine.2020-09-23-124636

sudo tmutil deletelocalsnapshots 2020-09-23-124636
Deleted local snapshot '2020-09-23-124636'

Now I look and it shows the following, 54.41 on the desktop, 33.66 in Disk Utility:
after deleting snapshots

If I enquire on the free space using df in the console, it reports approximately the same as the desktop:

df -h
Filesystem                    Size   Used  Avail Capacity    iused               ifree %iused  Mounted on
/dev/disk1s1                 838Gi  781Gi   54Gi    94%    1772094 9223372036853003713    0%   /

How can I get an accurate indication of free disk space???? It’s madness.

EDIT: Whilst writing this, the desktop now believes it is 59.32 GB free…

javascript – Multiple audio player – arrow keys & space

I am creating a Vue component of an audio player.

And I am having some difficulties in finding the ideal way to get the arrow keys and space to work.

I have found a solution, however I think it is not the best, nor the most effective. I’ve added a listener to the DOM in the component, but the problem is that I will have multiple players along the page, so I will have multiple DOM listeners.

Is it a good solution or is there a better one?

    // component code
    ...

     document.addEventListener( 'keydown', event => {
        if ( !state.isPlaying )
            return;

        switch ( event.keyCode ) {
            case 32:
                pause();
                break;
            case 37:
                audio.currentTime -= 2;
                break;
            case 39:
                audio.currentTime += 2;
                break;
            default:
                break;
        }
    });
```

Is run-length encoding possible in O(1) space given that the output is shorter than the input?

This is inspired by a problem from here. This is the approximate form of the problem:

Given a string like “aaaa777cbb” (10 symbols long), run length encode it in-place to a string like “a473c1b2” (8 symbols long). You are guaranteed that the input will always be longer than the output.

The precise form of the problem is:

  • There is a set S of symbols containing all the positive integers and also some other symbols (so the set contains both a and 1000000000).
  • You are given an ordered list of symbols from S. Any symbol from S may appear in the list.
  • You can
    • Replace one symbol in the list with another
    • Trim the list to a length of your choice by removing symbols from the end
  • You cannot
    • Insert symbols
    • Remove symbols from the middle or the beginning
  • You must overwrite the list of symbols with it’s run-length-encoding representation and trim it to length so that it includes only the run-length-encoding representation.
    • The run-length-encoding representation replaces each series of 1 or more of the same symbol in the input with that symbol followed by the symbol representing the number of occurrences of the previous symbol.
      • For example: (A, A, A, A, A, A, A, A, A, A, 7) becomes (A, 10, 7, 1) meaning “A ten times followed by 7 one time”
      • () becomes ()
      • Note that the length of the output list is always even
    • You are guaranteed that the length of the input list is always larger than the length of the output list
  • You must do this in O(1) space

Intuitively I don’t think this is possible. The solutions provided on the original site seem to break on strings like “abccccc” (length 7) where the output should be “a1b1c5” (length 6), since they start by overwriting “b” with the “1” from “a1” before they have even checked which symbol is in the 2nd position.

I have thought about trying to start by finding the compressible runs of letters (2 or more of the same letter), but I don’t know how to tell which symbols are already processed and which are from the original input without using some sort of memory that which would grow with the size of the input (like a bitmap of processed areas) and therefore put me in violation of the O(1) space requirement.

I consider acceptable answers to be proofs that this problem either is or is not solvable in O(1) space.

Can quotient space be isomorphically isometric to some closed subspace of original one?

Suppose $mathcal{B}$ is a Banach space which is not isomorphic to a Hilbert space. And $mathcal{M}$ is the closed subspace of $mathcal{B}$. What condition should I pose on $mathcal{B}$ such that the quotient space $mathcal{B}/mathcal{M}$ is isomorphically isometric to some closed subspace of $mathcal{B}$?

whitespace – Distributing vertical space in Word

If I have a page in Word with several paragraphs, is it possible to automatically space them apart according to some proportions? For example, if the page is roughly:

pagebreak
paragraph
paragraph
paragraph
pagebreak

Can I put something after each paragraph that automatically takes up certain percents of the whitespace? For example:

pagebreak
paragraph
20% of whitespace
paragraph
50% of whitespace
paragraph
30% of whitespace
pagebreak

I know ways to manually adjust spacing until the percentages are just right. I’m wondering if I can just declare the percentages somehow (maybe using frames?). And even if, for example, one paragraph’s text is edited to make it have more lines, the percentages on the white space will still hold.

time complexity – A genral turing model with one tape to define sublinear space (L,NL,..)

A genral turing model with one tape to define sublinear space (L,NL,..)

Normally to define sub-linear space complexity we need special Turing models with many tapes, at least two: a read-only tape and a work tape; or often three: with an additional output tape. (We do this because the reading of the input would cost us linear space.)

I’m looking for a general Turing model with just one tape and one consistent definition for space and for complexity that works in all the cases, inclusively the sub-linear case of L (Logspace), NL (NLogspace).. and the more famous P, NP, PSPACE etc.

For this purpose obviously we must change the space definition – but how best?

No space left on device – Fedora 23

/tmp directory does not have enough space as package size around 700MB

pip downloads files to temporary directory, environment variable TMPDIR specifies that directory, also pip puts files into cache thus --cache-dir specification, --no-cache-dir should work too. --build specifies directory where wheel will be built, so its specification is also useful.

try below code

TMPDIR=/data/somedir / pip install --cache-dir=/data/somedir / --build /data/somedir/ torch