How many creatures can step through a Teleportation Circle before it closes?

The party has just rescued 100 slaves. How many of them can conceivably enter a teleportation circle before the spell ends? It seems absurd to think all 100 can make it.

The teleportation circle spell description states that:

A shimmering portal opens within the circle you drew and remains open until the end of your next turn. Any creature that enters the portal instantly appears within 5 feet of the destination circle or in the nearest unoccupied space if that space is occupied.

Does the duration of the invisibility from the Firbolg’s Hidden Step trait allow me to make an attack roll with advantage on the following turn?

The firbolg’s Hidden Step trait (VGtM, p. 107) is described as being active "until the start of your next turn" at most:

As a bonus action, you can magically turn invisible until the start of your next turn

I’m unclear on the exact mechanics of turn starts. For instance, if I use Hidden Step as a bonus action at the end of my turn, would the invisibility stay active for my next attack?

My initial reading was "no" as the trait would stay active from when I use it, into the next round, and drop as soon as my turn came up in the initiative order. I would then become visible, and take my action. This also gels conceptually: I can use Hidden Step to protect myself from combat for a round, or I can use it to gain advantage on an attack. But I can’t use it for both.

However, I’ve also read that advantage for invisibility is determined at the start of the round, and thus the advantage would in fact carry over to the next round’s attack, as if I was attacking from hiding or something similar.

Which is it, and what source would resolve it?

Periodical sum of rows by a certain step

I’ve been struggling with one problem. I have a classic matrix in this example 12×4 such as: matrix = Table[i, {i, 12}, {4}]

TableForm@matrix

I need to sum the rows according to the example below.

Total@matrix[[{1, 5, 9}]]

Total@matrix[[{2, 6, 10}]]

Total@matrix[[{3, 7, 11}]

I tried using MapAt, but without any real success so far. I need to make a function out of it, cause later I will be using it for matrix 1036×37. Any tips?

Can you cast Thunderwave and then Misty Step on the same turn in that order? [duplicate]

Imra the wizard is cornered! Surrounded by multiple foes, she casts Thunderwave in an attempt to push her enemies back. One of them succeeds on the saving throw!

Knowing that moving out of their range might trigger an attack of opportunity, can she cast Misty Step in the same turn?

I’m asking this because the rules under Casting a Spell states that

A spell cast with a Bonus Action is especially swift. You must use a Bonus Action on Your Turn to cast the spell, provided that you haven’t already taken a Bonus Action this turn. You can’t cast another spell during the same turn, except for a cantrip with a Casting Time of 1 action.

Does the order of spells casted matter? The wording makes it seem like you can’t cast a Bonus Action spell and then an Action spell, but you can do it the other way around.

Step size is effectively zero; singularity or stiff system suspected

\[Eta] = 0.125; rg1s = Derivative[1][u1][t] - u1[t]*u3[t] - 3*u1[t]*u4[t] + u2[t]*u3[t] + 3*u2[t]*u4[t] + 2*(1 + 2*\[Eta])*u1[t]^2 == 0; rg2s = Derivative[1][u2][t] - u2[t]*u3[t] - 3*u2[t]*u4[t] + u1[t]*u3[t] + 3*u1[t]*u4[t] + 2*(1 + 2*\[Eta])*u2[t]^2 == 0; rg3t = Derivative[1][u3][t] - 0.5*((u1[t] - u2[t])^2 + u3[t]^2 - 3*u4[t]^2 + 6*u3[t]*u4[t]) == 0; rg4t = Derivative[1][u4][t] - 0.5*((u1[t] - u2[t])^2 + u3[t]^2 + 5*u4[t]^2 - 2*u3[t]*u4[t]) == 0; sol = NDSolve[{rg1s, rg2s, rg3t, rg4t, u1[0] == -0.6*0.2, u2[0] == -0.6*0.2, u3[0] == 0.6*0.2, u4[0] == 0.2}, {u1, u2, u3, u4}, {t, 1, 10}]I am trying to solve four coupled nonlinear differential equations. But, everytime I am getting NDSolve::ndsz: At t == 2.0833315360868916`, step size is effectively zero; singularity or stiff system suspected. I have tried all the possible ways to solve such kind of problem with similar kind of problems available in stack. I want to get the value of g1,g2,g3 and g4 for large value of t i.e. 1 to 100 but I am getting only for small value of t? Could you please suggest me some way to sort out the issue?

Thank you

Fixed physics time step and input lag

Everywhere I read says I should fix the time step of my physics simulation, and interpolate the result to the actual frame rate of my graphics. This helps with simplicity, networking, reproducibility, numerical stability, etc.

But as I understand it, fixed time step guarantees between 1 and 2 Δt of input lag, because you have to calculate one step ahead in order to interpolate. If I use 90 Hz physics, it gives me an input lag of about 17 ms, on average.

Since I often see gaming enthusiasts talking about 1 ms input lag, 1 ms delay, and how that makes a difference, I wonder how fast-action games does it, and how they reduce the input lag using fixed time step.

Or they don’t, and 1 ms delay is just marketing mumbo jumbo?

Would there be a problem to incorporate Pathfinder-2e’s “Step” action in place of DND 5e’s “Disengage” action?

Pathfinder’s Step:

You carefully move 5 feet. Unlike most types of movement, Stepping doesn’t trigger reactions, such as Attacks of Opportunity, that can be triggered by move actions or upon leaving or entering a square. You can’t Step into difficult terrain, and you can’t Step using a Speed other than your land Speed.

DND 5e’s Disengage:

If you take the Disengage action, your Movement doesn’t provoke Opportunity Attacks for the rest of the turn.

My intention would be to create for DND 5e something like:

If you take the Step action, you can move 5 feet to an unoccupied space not in difficult terrain without triggering any opportunity attacks.

As Disengage applies for a creature’s full movement, I think giving the creature an extra 5 feet of movement when taking the Step action makes up for the loss. This would of course apply for NPCs and PCs, so I don’t see this giving an unfair advantage to one group over the other, except for maybe those with the ability to disengage as a bonus action, like Goblins or Rogues; switching that for the Step action about may be a slight nerf to the class/creature/race.

I find the Pathfinder Step makes more sense than the DND Disengage, as I can’t make sense of Disengage working for more than the enemies directly threatening the character: a creature that takes the disengage action could then run there full movement, potentially avoiding a dozen or more attacks.

Match types don’t apply after moving to “Create Ads” step” in Google Ads

I’m trying to set up a Google Ads campaign. On step 2 "Set up ad groups" I add keywords to Ad groups with match types:

+ipad +apps
"ipad apps"
[ipad apps]

Then I click "Save and Continue" and on Step 3 my keywords appear changed to:

ipad apps, +ipad +apps

Then I click back to Step 2 and I see the following:

ipad apps
ipad apps
+ipad +apps

For some reason, my keywords are changed to "broad match". How to prevent this behavior? What do I need to do to turn on Matching Types?