How dangerous is this modified exhaustion compared to other harmful conditions?

In this question, I asked about the ramifications of monsters causing exhaustion:

How dangerous is exhaustion?

The answers concluded, that this would generally be very risky and dangerous.

I therefore decided to limit myself to a reduced threat version for the time being, which has the following modifications:

1. Limited effect

A target only gains exhaustion levels this way up to three levels. Any excess levels that would be caused this way are not applied.

And

2. Easy recovery

Taking a short rest or casting lesser restoration removes one level of exhaustion gained this way. Taking a long rest or casting greater restoration removes all levels of exhaustion gained this way.

How does this compare to other harmful conditions, such as stunned or paralyzed? Could I replace a stun or paralyze effect with one level of this reduced threat exhaustion and maintain a similar power level of the monster?

Unlisted effects of Conditions

In a game I DM’d, a PC had cast a spell with a Concentration requirement and was subsequently Paralyzed. I quickly checked the description of the Paralyzed condition, which said nothing about Concentration but did say that the character was Incapacitated. I checked Incapacitated, which also says nothing about Concentration. I thus ruled in-game that the PC could maintain concentration on the spell even while Paralyzed.

However, post-game, I read the description of Concentration, where it clearly says that you lose Concentration when you are Incapacitated. It seems (in my opinion) like that is an important enough consequence of the Incapacitated condition that it should be listed with the description of the condition.

So now I wonder – are there other instances of Conditions which have consequences that are not listed in the description of the Condition itself, but are found somewhere else?

Related: What would be the implications of ignoring the incapacitated condition tied to the paralyzed condition?

Find number of ways to create sequence $A$ of length $n$ satisfying $m$ conditions

Find number of ways to create sequence $ A$ of length $ n$ satisfying $ m$ conditions. This sequence $ A$ should consist of only non negative numbers. Each condition is described by three integers $ i,j,k$ signifying $ max$ ($ A_{i}$ ,$ A_{j}$ )=$ k$ .
It is guaranteed that each index of the sequence will be there in at least one condition i.e. there will be finite number of such sequences.
The maximum value of $ n$ will not exceed $ 18$ and maximum value of $ k$ will not exceed $ 2*10^4$ .
I tried it using dynamic programming but the time complexity came out to be exponential. Can you suggest me any better approach which will reduce the time complexity?

Find number of ways to create sequence $A$ of length $n$ satisfying $m$ conditions

Find number of ways to create sequence $ A$ of length $ n$ satisfying $ m$ conditions. This sequence $ A$ should consist of only non negative numbers. Each condition is described by three integers $ i,j,k$ signifying $ max$ ($ A_{i}$ ,$ A_{j}$ )=$ k$ .
It is guaranteed that each index of the sequence will be there in at least one condition i.e. there will be finite number of such sequences.
The maximum value of $ n$ will not exceed $ 18$ and maximum value of $ k$ will not exceed $ 10^6$ .
I tried it using dynamic programming but the time complexity came out to be exponential. Can you suggest me any better approach which will reduce the time complexity?

Calculate the total on events with two time conditions

I have a table in BigQuery that looks something like this:

    schema = [         bigquery.SchemaField('timestamp', 'TIMESTAMP', mode='REQUIRED', description='Data point timestamp'),         bigquery.SchemaField('event_id', 'STRING', description='EventID'),         [...]     ] 

The table has a fairly large dataset, and I’m trying to find write an efficient query that returns the number of events that happened in the last 24 hours but also within the last N days. That is, two different records with different conditions but the same event_id. I don’t care so much about the actual event_id, but rather the distribution.

Ideally, the query would return something like this:

7_days: 20 30_days: 15 60_days: 7 

If it’s impossible to do this in pure SQL, I also have Pandas available at my disposal.

Does Hallow remove the listed conditions when cast?

The spell Hallow has this effect when cast:

First, celestials, elementals, fey, fiends, and undead can’t enter the area, nor can such creatures charm, frighten, or possess creatures within it. Any creature charmed, frightened, or possessed by such a creature is no longer charmed, frightened, or possessed upon entering the area. You can exclude one or more of those types of creatures from this effect.

If a creature within the target area is charmed, frightened, or possessed by a listed creature type when the spell is cast, is that condition ended, suspended, or unchanged when the spell is cast?

In other words, is casting this spell on the area such a creature is in enough to end one of these effects, or must the caster get them to go in and out of the spell’s area too to achieve this?

Can a Solarian’s ability to enter a Stellar Mode take into consideration conditions affecting her?

I know there is GM discretion allowed as to the situations affecting a Solarian’s ability to enter a Stellar Mode, but I would like other GMs opinions on this situation.

RAW seem to generally require that the Solarian be "in combat" and facing a significant threat. In fact, the description specifically says that:

you must be facing a significant enemy (see page 242).

Description of Significant Enemy:

…a creature with a CR less than or equal to your character level – 4 is not a significant enemy

So… nowhere does it give consideration as to the Solarian’s personal situation.

In a hypothetical situation even a lowly CR-1 creature would present a dire threat to a Paralyzed 6th level Solarian, but she would not be permitted to enter Stellar Mode and become attuned, to use her Corona Revelation as a defense because of the low CR rating of the enemy.

In our example situation, the party encountered a group of Ghoul Soldiers who managed to paralyze the Solarian via bite. Combat moved into the next room, leaving the Solarian alone and still paralyzed (for 2 more rounds). I presumed the Solarian’s Stellar Mode ended because there was no current threat to her, and stated such. She argued that the state of paralyzation itself constituted a threat and/or the fact that I still had her in "melee round" mode meant she was still "in combat" (she wanted to become fully attuned so she could jump back in the fight if/when released from paralyzation). I ruled that it must be a threat from an enemy and that her Stellar Mode ended, but she was still in "melee mode" so I could track the rounds of her paralyzation; she was unhappy with this decision.

Issues with no flux boundary conditions in NDSolve

enter image description hereThe no flux boundary conditions are making trouble. How to handle them? The problem I’m trying to solve is as follows: PDE: 0.036*D[C[x,y],x]==2.4*10^-10*(D[C[x,y],{x,2}]+D[C[x,y],{y,2}]) Boundary conditions: 1. C[0,y]==Piecewise[{{1,H/21)==0 3. (D[C[x,y],y]/.y->0)==0 4. (D[C[x,y],y]/.y->0.005)==0

I wrote the following: sol2=NDSolve[{0.036*D[C[x,y],x]==2.4*10^-10*(D[C[x,y],{x,2}]+D[C[x,y],{y,2}]),C[0,y]==Piecewise[{{1,H/21)==0,(D[C[x,y],y]/.y->0)==0,(D[C[x,y],y]/.y->0.005)==0},C,{x,0,1},{y,0,0.005}]

The error message shows-The dependent variable in the boundary condition Dirichlet condition need to be linear. But I noticed that a similar no flux boundary condition works just fine (for a different problem though). sol3=NDSolve[{D[u[t, x], t] == D[u[t, x], x, x],u[0, x] == 0,u[t, 0] == Sin[t],(D[u[t, x], x] /. x -> 0)== 0},u, {t, 0, 10}, {x, 0, 5}]

What is the issue in the previous case and how to resolve it?

Replacement rules which for elements of a vector which meet conditions

I’m trying to create a function which will replace elements of a list with their values modulo 1, i.e. Mod[x,1], but only if Abs[x]>1. So, for example, the function would yield:

f[{-1.5,-1,0,1}]={.5,-1,0,1}].

I’m trying to do this in an elegant way. For example, I have a function for a related purpose:

C1[v_] := v /. _?Negative -> 0;.

This replaces negative elements of a list with 0, and it’s very clean.

I’d like to do something similar. My efforts so far have included breaking it into two functions:

CLim[x_] := Mod[x, 1] /; Abs[x] > 1;

C2[v_] := CQubitLim /@ v; But then, when I apply C2 to a list, it only seems to apply on some elements, for example

C2[{1,0,1.5}]={Clim[1],CLim[0],0.5}

My other idea was to use a conditional rule

v:>Mod[v,1]/;Abs[v]>1

But this doesn’t seem to evaluate when I put a vector through it.

Any ideas much appreciated.

Plotting with conditions

I am trying to plot a function with condition that x>zeta. my input is

If[x > ζ, Plot[polarizedgpd[x, -3, Λ, 0.2], {x, ζ, 1}]] 

But my output is

If[x > 0.2,Plot[polarizedgpd[x, -3, Λ, 0.2], {x, ζ, 1}]] 

However, I am defining $ \zeta=0.2$ , but still not getting anything.