How do you get Favors for use with Patrons presented in Tasha’s?

In Tasha’s, new Patron rules are presented and a number of the patron Perks require calling in, or using a favor. I may have missed it, but how does one gain a favor? There are a number of references to downtime activities, so is it the same as gaining a religious favor (one of the Patrons is religious organization)? Or, is this simply a DM call: A favor is gained by completing quests and the like on behalf of the Patron? That might raise a follow-on question in regards to perk and being your own Patron.

How is the food and water from Create Food and Water presented?

The spell create food and water says:

You create 45 pounds of food and 30 gallons of water on the ground or in containers within range, enough to sustain up to fifteen humanoids or five steeds for 24 hours. The food is bland but nourishing, and spoils if uneaten after 24 hours. The water is clean and doesn’t go bad.

When you cast this spell, how is the food and water presented? What I mean is, surely it doesn’t just dump food and water all over the floor (the water at least wouldn’t be of any use to anyone then), so does it come with plates and barrels (30 gallons is a lot of water, surely it would need large containers)? Do you have to put out plates and barrels first and then when you cast it the food and water fills the plates/barrels? How exactly does this work, or is that simply up to the DM to decide?

Is it bad UX for a form to be presented in different formats (either in a modal or separate page), depending on context?

I’m designing an internal tool in which a user, at certain points, will need to fill out a fairly detailed form in order to add a piece of content to our user-facing platform.

However, the challenge I’m facing is that the form is available at different points in the user’s journey, and I’m wondering if I can format the presentation of the form differently (either as a modal or a separate page) depending on where the user is and what they’re doing, to cater to separate use cases. Namely, I’d like to present it within a modal when the user is on a page where they’ll be engaged with a different, priority task, but needs to quickly fill out the form to create a piece of content, and then resume with the main task.

But elsewhere in the tool, I’d like to present the form on a separate page when the user is on the page where all those content pieces live – so that when the user clicks a “+New Content” CTA, they’ll be taken to a separate page where they’ll fill out the form.

Ultimately, I’m trying to cater to these separate use cases with these different interactions, but is the resulting inconsistency bad? Trying to understand the tradeoff here.

I hope this all makes sense, thanks for taking a look!

Are there any updates to the DMG that describe magic item activation in the format presented in magic item compendium?

Straightforward self explanatory question really as described in the title. Magic Item Compendium presents activating magic items in this manner [Action Type] (type of action) as per page 220. Is anyone aware of an update to the DMG that describes magic items presented therein in the same format?

Proper and flat morphism implies finitely presented?

I´ve been reading the Deligne-Mumford construction of the moduli of curves with a given genus and I have some questions about the article http://www.numdam.org/article/PMIHES_1969__36__75_0.pdf

1) When the authors talk about a scheme what are they referring to? In the EGA, a scheme is what we call separated scheme, so I don´t know if they are working on the category of separated schemes or just schemes (in our terminology).

2) My second question is about Definition 1.1. They say that a stable curve is a proper flat morphism of schemes $ f:X\rightarrow S$ whose geometric fibers are reduced, connected, 1-dimensional schemes such that:

  • $ X_{s}$ has only ordinary double points,

  • If $ E$ is a non-singular rational component of $ X_{s}$ then $ E$ meets the other components of $ X_{s}$ in more than 2 points;

  • $ \rm{dim}\rm{H}^{1}(\mathcal{O}_{X_{s}})=g$

In general, a relative curve is defined as a flat finitely presented morphism of schemes $ X\rightarrow S$ of relative dimension 1. My question is if proper+flat in this particular case implies finitely presented. It is the same true if $ f:X\rightarrow S$ is a proper and flat morphism whose geometric fibers are complete integral algebraic curves of arithmetic genus $ g$ ?

Thank you for your time.

List of Small Non-Abelian Symmetrically Presented Groups

Let $ F_n$ be the free group generated by $ x_1,\ldots,x_n$ and let $ S_n$ be the symmetric group on $ \{1,\cdots,n\}$ . Let $ w=x_{i_1}^{\pm1}\cdots x_{i_s}^{\pm1}$ be a word and for each $ \sigma \in S_n$ , define $ \sigma(w)=x_{\sigma(i_1)}^{\pm1}\cdots x_{\sigma(i_s)}^{\pm1}$ . We consider groups of the form

$ $ G_n(w)=\langle x_1,\ldots,x_n\mid\sigma(w), \sigma\in S_n\rangle,$ $ where $ w$ is a given word in $ F_n$ . Such groups are called symmetrically presented. For example, it can be proven that $ $ G_4(x_1x_2^2x_3x_4^{-1})=\langle x_1,x_2,x_3,x_4\mid\sigma(x_1x_2^2x_3x_4^{-1}), \sigma\in S_n\rangle$ $ is a non-Abelian group of order $ 96$ .

My question is, given $ n$ , what is the smallest non-Abelian symmetrically presented group? Any list of examples of non-Abelian symmetrically presented groups will also be much appreciated.

User interface for multi-dimensional data presented as lists

I have an application that lists all the modules loaded in a performance test in a baseline and a current testrun. Each run in turn has many iterations. A user can view the difference of what was loaded in the baseline versus current across all iterations by selecting All in the dropdown list. Current UI

However, I want to add the ability to go to another tool for the following combination of parameters (module, runtype(baseline or current) and iteration (0,1,2,..)) etc. For example: I will open up a call stack for Module0.dll in baseline testrun for iteration 1.

However, iterations don’t show up in this UI as the values in baseline and current columns are aggregates across all iterations.

My idea was to make the cell values in baseline and current as hyperlinks where a user can right-click -> see a menu of iterations and click on a particular iteration to go to the new tool. I am not sure that it is the best user experience/UI though.

Any suggestion on improving this workflow will be highly appreciated.

Best way to handle when typology used by tech is different than typology presented to users?

This question is a follow-up to this one on Meta.SE about the flag dialog used on SE sites. In the dialog, the first two (“spam” and “rude/abusive”) are considered the same type of flag, and the second two (“should be closed” and “duplicate”) are considered to be the same type of flag and different from the first. Thus, if someone raises one kind of flag, the UI will tell the user that s/he has already raised in both, like so:

The five options seem to me to set up an expectation that there are five types of flags and they are listed here. That is not an accurate reflection of the underlying technology or the meaning of the word “type” in this interface, though.

The SE mod response is that “It’s not really a matter of what the user expects to happen” but then what is primary in UI design decisions?

Is this good design? Specifically why or why not? What would you change about it?

Are there general guidelines for UI design in cases where a technical typology differs significantly from the typology presented to users?