Algorithm to check gibbs phase rule

I am looking for an algorithm to solve the following problem. I am unsure whether to post this in computational science or here, but since this is an algorithm I thought I would try here first.

I have a set of species made from a number of components.
Let’s number each component $ 0, 1, 2 … n$ .
So now each species can be described as a set of these components.

I am given a set of species, and I need to check whether any subset of these species fulfills the following condition: that the number of species in this subset is greater than or equal to the number of unique components in this subset.

For example: the set of species {[0, 1, 2], [0, 2], [1, 2]} fulfills the criterion, as the set has 3 species and 3 unique components. The set of species {[0, 1, 2], [0, 2], [1, 2], [3,4]} also fulfills the criterion, as a subset of the set fulfills the criterion. The system {[0, 1, 2], [0, 2]} does not fulfill the criterion, as there are 2 species and 3 unique components.
In case it is relevant: there can be many species (40-50) and components (10-20) but the number of components per species remains relatively small (2-5)

Can this be done with polynomial time complexity? It seems kind of similar to the set cover problem, so I don’t have much hope.

How do superior successes work in Eclipse Phase 2?

Re-reading the rules for Eclipse Phase 2, in preparation for a game that I’ll be running for a group that is entirely new to Eclipse Phase, I saw this:

If a critical is also a superior result, only the critical applies.” p. 31 EP2

Since critical results occur when a character rolls doubles (e.g. 00, 11, 22, etc.) on a test, and superior results are scored on either a 33 or 66, this means that superior results are only ever scored on a critical.

Given the above, it seems like RAW you can actually never score superior results.

Is this an accurate reading of the rules? It doesn’t seem like this is what the designers intended.

How to plot multicolor phase daigram with three parameters?

enter image description here

I am trying to plot like the diagram given above. I have two nonlinear equations that I have separated in imaginary and complex forms (u1,v1, and x1,y1). As shown in the figure in the x-axis I want ‘p0’ which varies from (0,2.5*10^3) and in the y-axis, I want ‘del0’ which varies from (0,3) and inside the plot where rectangular color region box it is ‘NL=u1^2+v1^2’which varies from (0,6*10^7). I am trying this but unable to plot this type of diagram and gives me an error: “solve was unable to solve the system with inexact coefficients. The \ the answer was obtained by solving a corresponding exact system and \ numericizing the result. >>” Should I give another command to get this type of plot or anything else? If anyone can short it out will be appreciated.

A1 = 1; B1 = 0; delta = -1.5;(*Subscript[Δ, L] ; Laser-Lower polariton \ detuning*) g0 = .315; (* Subscript[g, 0] ; vacuum optomechanical strength *) ome = 3.014; (* Ω ; Rabi splitting *) ome1 = .125; (* Subscript[Ω, m] ; mechanical \ resonator's frequency *) kexc = 0.002;  (* Subscript[κ, exc  ;  ]exciton decay rate*) kk = .2;   (* κ; cavity decay rate *) gma = 0.00001;  (* Γ ; phonon dcay rate *) ka = (kk + kexc)/2 - del0*(kk - kexc)/(2*ome); Sol = NSolve[{-delta*v1 - ka*u1/2 - (kk - kexc)*B1*g0*x1*u1/ome == 0,      delta*u1 + g0*(1 - del0/ome)*A1*x1*u1 +        p0*(1 - del0/(2*ome))/Sqrt[2] + p0*g0*B1*x1/(Sqrt[2]*ome) -        ka*v1/2 - (kk - kexc)*g0*x1*B1*v1/ome == 0,      ome1*y1 - gma*x1/2 ==       0, -ome1*x1 + g0/2*(1 - del0/ome)*A1*(u1^2 + v1^2) +        p0*g0*u1*B1/(Sqrt[2]*ome) - gma*y1/2 == 0}, {u1, v1, x1, y1},     del0]; ContourPlot[{Evaluate[(u1^2 + v1^2)] /. Sol}, {p0, 0, 5}, {del0, 0,    3}, PlotLegends -> BarLegend[{"LakeColors", {0, 6}}]]  After running this code I am getting the plot. Which is not the same as above. I don't know what the problem with it?    

Please help with Investigator Development phase and Skill Improvement the Optional Luck Point use?

I just got introduced to this game and I’d like to understand some more of the how EXP and PC improvement is done.

So far I get that the more you use a skill the more you have a chance to improve that skill/skills or even gain new ones from multiple successful attempts. Now in standard play you mark off skills successfully used during the session once no matter how often those skill are used and that at the end of specific amount of game time are allowed to attempt to improve those skills used individually.

However the Keeper uses the Optional Luck rules for his games. Now the rules for the Luck option is if you use Luck to modify skills rolls then you don’t get a chance to improve skills at Investigator Development Phase. Now I’d like some clarification on this. If you use Luck Points to modify a skill or number skill rolls to pass the check, then during the next Investigator Development Phase, you are not allowed to a chance at improving any skills successfully passed or just those modified by Luck Points?

EX: Game 3 – Investigator use Luck points to pass History, and a Drive check, but were successful with Firearms .45 Pistol, Jump and Natural World checks. After the game session is through and we’re at Investigator Development Phase do I get a 1d00 chance to try to improve Firearms .45 Pistol, Jump and Natural World and not with History, and Drive or I cant try to improve any skills cause I use Luck Points?

How could a level 5 Summoner detect a Phase Spider who is on Ethereal Plane?

One of the Same Game Test encounters for a level 5 character is the Phase Spider. The test was originally written for D&D 3.5e, but I wanted to run it for a character that I am creating for an upcoming campaign, an Unchained Master Summoner.

It’s a rather straightforward thing to fight once you know it’s there, whether it announces its presence by appearing, attacking, and then disappearing, or if you notice it via a successful Perception roll.

However, is there any way for a level 5 Unchained Master Summoner to at least locate the Spider after is uses its Ethereal Jaunt ability?

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by: thedas
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