## Can multiple types of armor be stacked?

A character in my ongoing Exalted 2e game has an artifact chain shirt. Artifact chain shirts are described as being able to be worn under ordinary clothing (it has no mobility penalty or fatigue value). He’s also recently acquired a (non-artifact) reinforced breastplate. He’d like to wear them both. I don’t see any rules describing whether this can be done, what net protective effect it would have, or what effect it would have on mobility and fatigue.

Can multiple types of armor be stacked? How would I adjudicate this?

The character in question is pretty fragile so I’m not entirely opposed to his getting some kind of benefit, but I worry about setting a precedent that will bite me later.

So the Human Variant in 5E D&D gets two different ability points, proficiency in one skill and a feat.

Let’s say that human is a cleric with acolyte background. He takes a double dose of religion (Am I wrong in presuming you can do this?), then the proficiency in religion and then the “Skilled Feat” with one of the three skill as religion, can they stack and how?

## What is the percentage of possibly hitting something that has stacked Blur, Blink, Mirror Image, and Armor of Hexes?

This question is mostly for hypothetical fun because setting all of these up isn’t super practical (unless it’s a 1-on-1 campaign perhaps?)

But with all of these stacking, how likely are you to be hit by an enemy? (let’s assume they have Hexblade’s Curse on them for Armor to work)

This probably depends on AC and to-hit from the enemy too, so let’s just take a look at a decent 13 AC, with the enemy having a +7 to-hit. It’s up to you if you add to hit or AC too to really look at how hard it is to hit something with absurd AC + all these defensive buffs, or how much high to-hit really helps.

## Value flow (and economics) in stacked reinforcement learning systems: agent as reinforcement environment for other agents?

There is evolving notion of stacked reinforcement learning systems, e.g. https://www.ijcai.org/proceedings/2018/0103.pdf – where one RL systems executes actions of the second RL system and it itself executes action of the thrid and the reward and value flows back.

So, one can consider the RL system RLn with:

• S – space of states;
• A={Ai, Ainner, Ao} – space of actions which can be divided into 3 subspaces:
• Ai – actions that RLn exposes to other RL systems (like RLn-1, RLn-2, etc.) and for whome the RLn provides reward to those other systems;
• Ainner – actions that RLn executes internally under its own will and life;
• Ao – actions that RLn imports from other RL systems (like RLn+1, RLn+2, etc.) and that RLn executes on the other systems and form which RLn gets some rewards, that can be used for providing rewards for Ai actions.

So, one can consider the network (possibly hierarchical) of RL systems . My questions are:

• is there some literature that consider such stacks/networks of reinforcement learning systems/environments?
• is there economic research about value flow, about accumulation of wealth, about starvation and survival proceses and evolution in such stacks/networks of RL systems/environments

Essentially – my question is about RL environments that can function in the role of agents for some other environments and about agents that can function in the role of environemnts for some other agents. How computer science/machine learning/artificial intelligence name such systems, what methods are used for research and how the concepts of economics/governance/preference/utility are used in the research of evolution of such systems?

## Is a “stacked”, “local” version of 3-SAT NP-hard?

In this previous question, I learned that if each variable in a string $$C \in 3\text{-SAT}$$ appears only “locally”, then finding a satisfying assignment is no longer NP-hard. My question below builds on this to ask whether NP-hardness is recovered when, loosely speaking, there are multiple “layers” of variables leading up to the formula of interest. (This elaboration emerges naturally from a study of spatial Bayesian networks.)

Question

Consider a graph with nodes arranged in rows. The number of nodes doubles in each subsequent row; the graph has one node in the first row, two in the second, four in the third, and so on, for $$m$$ rows. (There are $$n = 2^m – 1$$ nodes total in the graph.) Each node takes a state of either 0 or 1 and has up to three “parent” nodes in the subsequent row (when there is such a row). Each parent is “$$k$$-local”: there are fewer than $$k$$ nodes between the first and last nodes for which it is a parent. ($$k$$ is a fixed natural number that does not change with $$n$$.)

For each node $$v$$, there is a table $$T_v$$ that lists all possible combinations of states of the parents of $$v$$ and, for each combination, assigns a state of 0 or 1 to $$v$$ in a fashion consistent with $$v$$ being a disjunctive clause of literals of its parents.

Let $$(3,k)\text{-SATSTACK}$$ denote the decision problem of determining whether there is an assignment of states to the nodes of the graph that assigns state 1 to the first node and is consistent with all $$T_v$$.

Are there $$k$$ for which $$(3,k)\text{-SATSTACK}$$ is NP-hard?

Notes

(1) It appears that $$(3,k)\text{-SATSTACK}$$ is in NP, since we can choose an assignment for each node in the last row, then work backward through the rows, computing the assignment for the rest of the graph in linear time and accepting it if and only if it assigns state 1 to the first node.

(2) It also seems plausible that $$(3,k)\text{-SATSTACK}$$ is NP-hard, at least for $$k$$ large enough, since it seems difficult to do better than a procedure in which we work forward from the first row, applying the polynomial-time algorithm noted above to each row and keeping inventory of all satisfying assignments out to that row (which may be an exponentially growing collection).

(3) Nevertheless, it appears challenging to find a polynomial-time reduction showing that $$(3,k)\text{-SATSTACK}$$ is NP-hard because many of the subsets of $$3\text{-SAT}$$ (and related problems) that map naturally into $$(3,k)\text{-SATSTACK}$$ are not NP-complete (see again). So how should we proceed?

## Separating stacked time series in excel file into python upload

I have downloaded time series price data, but the data has 4 effective columns (not exactly, but all thats pertinent for this question):

date, contract, open price, close price.

The issue is how do I slice each open and close price by contract, and separate them into their own columns so that ‘contract1_open_price”, etc is its own column, with one date column for all series.

Otherwise, I could rearrange the series in the source csv file, but that would be less preferable.

Thanks, I hope that is clear.