question about big cat and thier “standard attack” animal companion

IM playing pathfinder with my friends and IM playing a hunter (ranged build) and I have an animal companion a Big Cat we are currently level 5, and we started at level 4 and IM going to ask something that is troublesome.

How does a "standard attack works?"

Let’s say I move 10 yards and then i want to attack an enemy:

Can I attack with bite and claws?

Only bite?

Only claws?

Do I need to do full round attack to get all 3 attacks?

is there a way to get all attacks in a round?

Any good insight about this and any future tips for big cats?

thanks alot guys!

What is an algorithm for minimizing the standard deviation of m sums summed from n summands? [with attempt]

I have m bins (sums) and n summands. Each summand goes into a bin. In order to minimize the standard deviation, I have a greedy algorithm that appears to accomplish this. I am not sure of the name, but would like to know more. All m bins must have a sum greater than zero at the end of the algorithm.

It seems simple:

sort the summands from highest to lowest.

for each summand in the summands: find the first available bin with minimum sum and place it in the bin

I haven’t proved anything about it, but I’ve come up with a few test data sets and it appears to work.

Is a Rusting Grasp touch attack a standard action and do you have to hold the charge for the duration of the spell?

The druid spell Rusting Grasp (PH 273) says

You may employ rusting grasp in combat with a successful melee touch attack.

and

The spell lasts for 1 round per level, and you can make one melee touch attack per round.

Most touch spells have one "charge", you cast them and then discharge them with a successful touch attack. There are also some spells which grant more than one charge (like Chill Touch (PH 209) which can be used "up to one time per level").

A touch spell that lasts for a fixed duration limiting the number of attacks to one per round seems to be very unusual.

My two questions are:

  • Can you make just a single melee touch attack per round – as a standard action? Or can you make more than one attack (if, for instance, the druid uses Wild Shape and has a couple of natural attacks) but only one of your attacks can deliver the spell?
  • Do you have to hold the charge* for the duration of the spell (and lose the spell if you cast another one) or does the spell simply last for one round/level giving you a "new charge" every round until it expires?

*Touch Spells and Holding the Charge: In most cases, if you don’t discharge a touch spell on the round you cast it, you can hold the charge (postpone the discharge of the spell) indefinitely. You can make touch attacks round after round. If you cast another spell, the touch spell dissipates.

Is there a standard hierarchy when two supplemental books contradict each other?

The spell, Energy Vortex, is found in:

  • Complete Divine (p.164) as a 4th level Cleric/Druid spell (published May 2004)
  • Spell Compendium (p.81) as a 3rd level Cleric/Druid spell (published Dec 2005)

In both books, the spell does the exact same effect/range/damage (choice of acid/fire/electricity/cold), aside from CD allowing Sonic as a 5th choice for damage type.

Since these books were published more than a year apart, I assumed this was more a correction than a typo. Is it standard to use the most recent book as a general hierarchy, or is there another, more preferred method?

Show that if $\mathcal{H}$ is PAC learnable in the standard one-oracle model, then $\mathcal{H}$ is PAC learnable in the two-oracle model

This is a question $ 9.1$ from Understanding Machine Learning Chapter 3. It goes like this:

Consider a variant of the PAC model in which there are two example oracles: one that generates positive examples and one that generates negative examples, both according to the underlying distribution $ \mathcal{D}$ on $ \mathcal{X}$ . Formally, given a target function $ f : \mathcal{X} \to {0,1}$ , let $ \mathcal{D}^+$ be the distribution over $ \mathcal{X}^+ = \{x \in \mathcal{X}: f(x) = 1\}$ defined by $ \mathcal{D}^+(A) = \frac{\mathcal{D}(A)}{\mathcal{D}(X^+)}$ , for every $ A \subset \mathcal{X}$ . Similary $ \mathcal{D}^-$ is the distribution over $ \mathcal{X}^{-}$ induced by $ \mathcal{D}$ .

The definition of PAC learnability in the two-oracle model is the same as the standard definition of PAC learnability except that here the learner has access to $ m^{+}_{\mathcal{H}}(\epsilon, \delta)$ i.i.d. examples from $ \mathcal{D}^+$ and $ m^{-}_{\mathcal{H}}(\epsilon, \delta)$ i.i.d. examples from $ \mathcal{D}^{-}$ . The learner’s goal is to output $ h$ s.t. with probability at least $ 1-\delta$ (over the choice of the two training sets, and possibly over the nondeterministic decisions made by the learning algorithm), both $ L_{(\mathcal{D}^+,f)}(h) \leq \epsilon$ and $ L_{(\mathcal{D}^−,f)}(h) \leq \epsilon$

I am trying to prove that if $ \mathcal{H}$ is PAC learnable in the standard one-oracle model, then $ \mathcal{H}$ is PAC learnable in the two-oracle model. My attempt so far:

Note that $ $ L_{(D,f)}(h) = \mathcal{D}(\mathcal{X}^+)L_{(\mathcal{D}^+,f)}(h) + \mathcal{D}(\mathcal{X^{-}})L_{(\mathcal{D}^-,f)}(h).$ $ Let $ d = min \{ \mathcal{D^+}, \mathcal{D^-}\}$ , then if $ m\geq m_\mathcal{H}(\epsilon d, \delta)$ , then it is clear that: $ $ \mathbb{P}[L_{(D,f)}(h)\leq \epsilon d] \geq 1-\delta \implies \mathbb{P}[L_{(D^+,f)}(h)\leq \epsilon] \geq 1-\delta$ $ And, $ $ \mathbb{P}[L_{(D,f)}(h)\leq \epsilon d] \geq 1-\delta \implies \mathbb{P}[L_{(D^-,f)}(h)\leq \epsilon] \geq 1-\delta$ $

So we know that if we have $ m\geq m_{\mathcal{H}}(\epsilon d, \delta)$ samples drawn iid from $ \mathcal{D}$ , then we can guarantee $ \mathbb{P}[L_{(D^+,f)}(h)\leq \epsilon] \geq 1-\delta$ and $ \mathbb{P}[L_{(D^-,f)}(h)\leq \epsilon] \geq 1-\delta$ .

How do I choose $ m_{\mathcal{H}}^+(\epsilon, \delta)$ and $ m_{\mathcal{H}}^-(\epsilon, \delta)$ such that if we have $ m^+ \geq m_{\mathcal{H}}^-(\epsilon, \delta)$ samples iid according to $ \mathcal{D}^+$ and $ m^- \geq m_{\mathcal{H}}^-(\epsilon, \delta)$ drawn iid according to $ \mathcal{D}^{-}$ , then we can guarantee $ \mathbb{P}[L_{(D^+,f)}(h)\leq \epsilon] \geq 1-\delta$ and $ \mathbb{P}[L_{(D^-,f)}(h)\leq \epsilon] \geq 1-\delta$ ?

When is drawing $ m^+$ samples according to $ \mathcal{D}^+$ and $ m^{-}$ samples according to $ \mathcal{D}^-$ the same as drawing $ (m^+ + m^-)$ samples according to $ \mathcal{D}$ ?

What are pros & cons of naming in game currency a standard name vs a gimmick?

We’re creating a store and going to add an in game currency. We did a poll and Tokens & Sheep were the top options selected by the players.

I personally think Sheep would be more fun like a barter system as well as it is an in game resource as you may know from the Settlers of Catan (my game https://colonist.io/)

I know that https://starve.io/ has Golden Bread and https://surviv.io/ has Potato as in game currency.

Are there any other such examples? What are the pros cons of such naming?

I don’t know any big games which do such a thing.

Thank you for the insights.

Is the Post Correspondence Problem with more than two rows harder than the standard two-row variant?

The standard Post Correspondence Problem concerns tiles with two rows of symbols, and whether a tile arrangement can be made so that the sequence of the top symbols of the tiles is equal to the bottom one.

Let $ \text{n-PCP}, \text{n} > 0$ a generalization of the Post Correspondence Problem where the tiles contain $ \text{n}$ rows, and the sequences of the symbols have to be equal for all of these rows.

Obviously $ \text{1-PCP}$ is decidable (in fact it’s trivial because the answer to the problem is always true). $ \text{2-PCP}$ is the standard PCP.

But what if $ \text{n} > 2$ ? Is it harder or can it be reduced to the standard PCP (like >3-SAT being reduced to 3-SAT)?

What is the standard way, if any, to announce via e-mail that you have a public PGP key and what it is?

I’m making an e-mail system/client. I’m trying to correctly detect incoming e-mails which can be replied to with PGP encryption. This means finding out their public PGP key. I currently do:

  • Parse the e-mail body for a PGP public key block.

I suspect that these could be done:

  • Check for attachments with some kind of standard file name?
  • Check for a special hidden header which either spells out the public PGP key directly, or links to an external resource where it can be fetched?

Thanks in advance for clarifying how one properly detects/sends PGP public keys in e-mail context for maximum support.