What happens when a True Polymorphed Simulacrum is affected by Dispel magic, but only the Simulacrum spell is dispelled?

Something very weird happened last Sunday night in my Tier 4 gaming session : a player had a simulacrum that was True Polymorphed (into a Red Abishai) for more than an hour (became “permanent”). A foe casted Dispel Magic at 3rd level on the True Polymorphed Simulacrum, and succeeded the DC17 check for Simulacrum, but failed the DC19 check for True Polymorph.

I ruled that it became an actual, real, independent (free-will) creature (here, a Red Abishai), but I’m not sure if that was correct.

What happens when a True Polymorphed Simulacrum is affected by Dispel magic, but only the Simulacrum spell is dispelled ?

is it always true that the depth of BFS is $\leq$ DFS?

I have a simple theoretical question in very basic algorithms, as the title mentions, is it always true that the depth of BFS is $ \leq$ DFS?

From what I understand, the tricky part here is the possible cycles in the graph. Even though that I believe that the depth of BFS will always be less or equal to the depth of DFS.

In each iteration of BFS, from what I understand, the depth might grow by one, but DFS’s grows in each vertex it can not reach, sometimes above the maximal value of BFS.

So, is it always true that the depth of BFS is $ \leq$ DFS?

True Error of a binary classifier

For a given classifier h, How is the true error over a distribution D defined? \begin{align*} L_D(h) &= \sideset{\mathbb{E}}{}{}_{x,y \sim D} \Pr[h(x) \neq y] \ &= \sideset{\mathbb{E}}{}{}_{x,y \sim D} \begin{cases} \Pr[y \neq 0|x] & \text{if } h(x) = 0, \ \Pr[y \neq 1|x] & \text{if } h(x) = 1. \end{cases} \end{align*}

I saw these two formulae here Showing that Bayes classifier is optimal Are these two equivalent?

Bash, if more commands true then ok

is possible to do samothing like this?

if rsync $  folder/coopshop/prod $  folder2/coopshop rsync $  folder/coopweb/prod $  folder2/coopweb rsync $  folder/unihobbyshop/shop $  folder2/unihobbyshop rsync $  folder/unnihobbyweb/web $  folder2/unihobbyweb then   echo "OK! rsync done!" else   echo "Error! rsync crashed!" fi 

I know there is possibility to do with \ character at the end of line, but this is not quite elegant solution. Is better way to do this?

Thank you.

Как получить из массива ниже перечисленного member_id, когда is_owner = true

array(4) { [“items”]=> array(36) { [0]=> array(5) { [“member_id”]=> int(454598412) [“invited_by”]=> int(454598412) [“join_date”]=> int(1559166975) [“is_admin”]=> bool(true) [“is_owner”]=> bool(true) } [1]=> array(4) { [“member_id”]=> int(-158645511) [“invited_by”]=> int(134582877) [“join_date”]=> int(1534238649) [“is_admin”]=> bool(true) } [2]=> array(4) { [“member_id”]=> и тд..

Prove that $T(n) \leq 8n^2$ or find value of $n$ when statement is not true (reccurence relation)

We have a function $ T: \mathbb{N}\to\mathbb{N}$ defined recurrently:

$ $ T(n)=\begin{cases} 0 &\text{ if } n=0,\ 3T(\lfloor{n/2}\rfloor) + 2n^2 &\text{otherwise.} \end{cases}$ $

Prove that for each $ n\in\mathbb{N}_0$ : $ T(n) \leq 8n^2$

How can I prove such statement? I was thinking of using the Master Theorem to get asymptotically tight bounds of the recurrence but I think that is not a right approach. Any help appreciated