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Can a character hold a magic two-handed weapon in one hand just to leverage the weapon’s boons?

Let’s say that there’s a magic greatsword that provides some sort of a useful boon: say, it gives you advantages on all of your saving throws vs. spells.

Should I allow a character to simply hold that weapon in one of their free hands just for the sake of leveraging that boon. This character has no intention whatsoever of ever using the magic greatsword as a weapon, and in fact almost never has any intention of making a melee weapon attack since they are a spellcaster.

That the character does not even have proficiency with greatswords is another interesting, if completely tangential, fact.

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Is it possible to just use one policy in a self-play setting?

I would like to ask is it possible to train an agent under self-playing setting but with just one policy to be trained? What are the foreseeable problems with such an implementation? My concern is as such: suppose agent A starts off as in role 1, and later goes role 2 (which is role 1’s opponent) after a few iteration. When A switches to role 2, it might use the information gained when A was in role 1 to its current role’s advantage. And after another few iterations when A switches back to role 1, A might use the information gained when A was in role 2 to its current role’s advantage. This is because we assume there is just one policy for agent A, so the weights are updated and kept when A switches its role. The information gained can be things such as new strategies learnt, new information gained (when the agent’s knowledge of the environment is incomplete), etc. So a more sensible way of training I think would be using two agents A and B with two separate policies to train – more like in a generative adversarial network setting in some sense. But then by definition this is not considered as self-play isn’t it?

Add-on: So relating to the case of Alphazero playing chess, if the agent is really just playing with itself, despite chess belongs to the so-called perfect information game, but the opponent’s thoughts/strategy/decision making process should be still unknown to the player. But if my assumption of how self-playing is true, then the agent A will have the thoughts/strategy/decision making process of role 2 when it is in role 1. Isn’t that cheating (because in reality those knowledge are not attainable; rather one can only guess what are those information from its opponents)? (I haven’t read through the Alphazero paper yet because I am not proficient enough to understand those technical details, so I would really appreciate it if anyone could explain the relevant part to me)

Does Wish just give another spell slot?

The description of the wish spell reads:

The basic use of this spell is to duplicate any other spell of 8th level or lower. You don’t need to meet any requirements in that spell, including costly Components. The spell simply takes effect.

(There are other specific uses listed as well, but they aren’t relative to my question.)

So if I’m reading this right, the basic use of wish is to give you another spell slot of level 1–8? That isn’t as powerful as I expected. Or does it maybe have extra benefits when using it to duplicate one of these spells (e.g. the effects of the spell are permanent for certain spells, such as darkvision or enlarge/reduce)?

Prove that the language $\{a^ib^i | i\geq 0\}$ is not regular? (Do we just consider $a^nb^n$, where $n$ is the pumping length?

I think to prove that $ \{a^ib^i | i\geq 0\}$ is not regular, we just have to consider the string $ a^nb^n$ (which is in the language) and apply the pumping lemma. But I’m not sure how to proceed using the pumping lemma (even though I know it applies with our choice of string, since the string is at least $ n$ long).

Why can I not adjust the point color? It just goes black

Here is my code here.

Please help me correct this.

How to make these 2 points Blue and Orange respectively?

Manipulate[  pp = ParametricPlot[{{r1 Cos[Min[w1 x, 2 Pi]],       r1 Sin[Min[w1 x, 2 Pi]]},     {r1 Cos[w1 x] + r2 Cos[w2 x], r1 Sin[w1 x] + r2 Sin[w2 x]}},    {x, 0, t}, PlotRange -> 10 {{-1, 1}, {-1, 1}},     AxesLabel -> {"Time"},    PlotStyle -> {Automatic, Red}, BaseStyle -> Thick];  Legended[   Show[pp, Epilog -> {Black, AbsolutePointSize[5],       Point@Graphics`Mesh`FindIntersections[pp[[1]]],      PointSize[Large], {Blue, Orange},       Point[{{r1 Cos[w1 t],          r1 Sin[w1 t]}, {r1 Cos[w1 t] + r2 Cos[w2 t],          r1 Sin[w1 t] + r2 Sin[w2 t]}}]}],   LineLegend[{ColorData[97]@1, Red, Blue, Orange},    {"Earth Trajectory", "Moon Trajectory", "Earth", "Moon"},    Joined -> {True, True, False, False},     LegendMarkers -> {None, None, "Point", "Point"}]],  {pp, None},  {{t, 1, "Time"}, 0.01, 10 Pi, 0.01},  {{w1, 1, "Angular Velocity"}, 0.2, 5, 0.01},  {{r1, 2, "Radius"}, 0.2, 10, 0.01},  {{w2, 1, "Moon Angular Velocity"}, 0.2, 5, 0.01},  {{r2, 2, " Moon Radius"}, 0.2, 10, 0.01},  TrackedSymbols :> {t, w1, r1, w2, r2}] 

enter image description here

Conjure (Minor) Elemental into a Hallow spell, does it just fail?

Hallow states “Celestials, Elementals, fey, Fiends, and Undead can’t enter the area…” but it doesn’t say what would happen if someone tried to summon some into the area. Would the spell fail? Would the elementals appear but then be forced to leave?

Would the ruling be the same for both Conjure Minor Elementals and Conjure Elemental? The latter uses a source of the element (e.g. a fire, what if the fire is in the Hallow area?) while the former just makes some minor elementals appear from an unspecified source.

I need just to protect my website against DDoS. Is Cloudflare for me?

My website hosts 2,000,000+ webpages, and I need to protect it against frequent DDoS I suffer.

I’m considering using Cloudflare. But I’ve read that Clodflare creates some problems with the TTFB and waiting times, and I don’t want Google to penalize my website. As far as I understand, the increase of TTFB leads to an increase of the “Time Spent Downloading a page” of Search Console, leading to a penalization of the Crawl Budget and the SEO ranking.

As mentioned, I just need to protect my website agains DDoS, not extra features. Are there other services similar to Cloudflare, which just protect websites against DDoS?

Thank you very much.

Why is $O(|V| + |E|)$ the bound on DFS and BFS instead of just $O(|E|)$?

In one sense I understand why the bound on BFS and DFS is $ O(|V| + |E|)$ . Every vertex gets considered, hence the $ O(|V|)$ , and over the course of considering all adjacent vertices, we end up considering $ 2|E| = O(|E|)$ vertices total because $ \sum_{v \in V} d_v = 2|E|$ . What I don’t understand is why we even bother specifying $ O(|V| + |E|)$ in the first place because it seems to me that the tightest bound you can really have in any situation is $ O(|E|)$ . I.e., it seems to me that the $ O(|V|)$ doesn’t help you at all. To see why, consider two cases:

  • The graph is connected. Then of course $ |E| \ge |V – 1|$ .
  • The graph isn’t connected. Then you are “stuck” in the connected component you start in. Once again, inside the connected component $ A$ you start in you have $ |E_A| \ge |V_A – 1|$ . Maybe there are more edges and vertices elsewhere. But once again the $ O(|V|)$ seems redundant.

Another way I think about it: Adding a vertex alone doesn’t create any more work since the vertex will just be floating in space. Adding edges can create extra work.

So why/when is the $ O(|V|)$ useful?