How big/little of an opening does a boggle need to use its Dimensional Rift ability?

I’m creating a giant wasp hive in the boughs of a tree in the Feywild, and it happens to have a boggle in it.

The upper sections of the hive have smaller, narrow, rigid, doorway-type openings everywhere that the boggle can use for dimension shifts.

My concern is about the bottom two sections of the hive. The doorway-type openings throughout the bottom two sections are ten or twenty feet square on those levels (so, 15’x20′ or 20’x20′ or whatever).

I’m concerned that these openings might be too big for the Boggle’s dimensional rifts. How large/small of an opening does a boggle need to use this ability?

Arranging Colors in a Grid; Two Dimensional TSP?

I am working on an interesting problem, which I believe can be solved algorithmically. I have a 6×8 on which I am attempting to arrange 48 color swatches, such that the transition from each swatch to its neighbor is as smooth as possible.

I can compute perceptual color differences using LAB-space encoding, so it is simple to generate a matrix of color differences. If I were attempting to simply order these colors, it would essentially be the traveling salesman problem; and I could use some heuristic solutions to get a near optimal result.

However, arranging the colors into a grid introduces a new dimension. In the interest of symmetry, we can wrap the edges of the grid so that each swatch has exactly 4 neighbors.

I have a hunch that this problem reduces to the following graph problem: Given a fully connected weighted graph of 48 nodes, find a subset of this graph such that the resulting graph is fully connected, each node has exactly 4 edges, and the sum of edge weights is minimized.

Any ideas on existing algorithms that might be helpful in solving this problem? Approximate solutions and heuristic solutions are acceptable as I imagine this problem is in EXP.

How to calculate the power spectrum and cross spectrum for two dimensional data?

I have two sets of data:

G={{G_1,x_1,y_1},{{G_2,x_2,y_2}},…..,{G_{n},x_n,y_n}}

H={{H_1,x_1,y_1},{{H_2,x_2,y_2}},…..,{H_{n},x_n,y_n}}

where H_{n} and G_{n} are values of G and H in the point (x_{n},y_{n}). I want to calculate the power spectrum and the cross spectrum . Can you help me ? Thanks.

How to calculate the power spectrum and cross spectrum for two dimensional data?

I have two sets of data:

G={{G_1,x_1,y_1},{{G_2,x_2,y_2}},…..,{G_{n},x_n,y_n}}

H={{H_1,x_1,y_1},{{H_2,x_2,y_2}},…..,{H_{n},x_n,y_n}}

where H_{n} and G_{n} are values of G and H in the point (x_{n},y_{n}). I want to calculate the power spectrum and the cross spectrum . Can you help me ? Thanks.

Arcanist Dimensional Slide usage specific cases!

So here it goes.

Description says that:

The arcanist can expend 1 point from her arcane reservoir to create a dimensional crack that she can step through to reach another location. This ability is used as part of a move action or withdraw action, allowing her to move up to 10 feet per arcanist level to any location she can see. This counts as 5 feet of movement. She can only use this ability once per round. She does not provoke attacks of opportunity when moving in this way, but any other movement she attempts as part of her move action provokes as normal.

Here’s what is not specified (and what causes my GM to question my way of using this skill):

a) If I can use it anytime movement action is possible can I use it while sitting (to teleport from chair to chair for example) or when lying on the ground?

b) Can I decide whether DS is first or last part of my movement? So for example use it to escape melee combat (avoid AoO) and teleport behind my team? Or do I have to do other movement first (thus inducing AoO) and DS last?

c) Can I open the crack below me so I just fall into it?

d) Can DS be the only movement that I make?

Arcanist Dimensional Slide usage specific cases!

So here it goes.

Description says that:

The arcanist can expend 1 point from her arcane reservoir to create a dimensional crack that she can step through to reach another location. This ability is used as part of a move action or withdraw action, allowing her to move up to 10 feet per arcanist level to any location she can see. This counts as 5 feet of movement. She can only use this ability once per round. She does not provoke attacks of opportunity when moving in this way, but any other movement she attempts as part of her move action provokes as normal.

Here’s what is not specified (and what causes my GM to question my way of using this skill):

a) If I can use it anytime movement action is possible can I use it while sitting (to teleport from chair to chair for example) or when lying on the ground?

b) Can I decide whether DS is first or last part of my movement? So for example use it to escape melee combat (avoid AoO) and teleport behind my team? Or do I have to do other movement first (thus inducing AoO) and DS last?

c) Can I open the crack below me so I just fall into it?

d) Can DS be the only movement that I make?

Arcanist Dimensional Slide usage specific cases!

So here it goes.

Description says that:

The arcanist can expend 1 point from her arcane reservoir to create a dimensional crack that she can step through to reach another location. This ability is used as part of a move action or withdraw action, allowing her to move up to 10 feet per arcanist level to any location she can see. This counts as 5 feet of movement. She can only use this ability once per round. She does not provoke attacks of opportunity when moving in this way, but any other movement she attempts as part of her move action provokes as normal.

Here’s what is not specified (and what causes my GM to question my way of using this skill):

a) If I can use it anytime movement action is possible can I use it while sitting (to teleport from chair to chair for example) or when lying on the ground?

b) Can I decide whether DS is first or last part of my movement? So for example use it to escape melee combat (avoid AoO) and teleport behind my team? Or do I have to do other movement first (thus inducing AoO) and DS last?

c) Can I open the crack below me so I just fall into it?

d) Can DS be the only movement that I make?

What happens when I use Drawmij’s Instant Summons on Dimensional Shackles?

If I place an enemy or individual in a set of dimensional shackles (I’ve already placed instant summons on the shackles), and I summon the shackles to me, what happens?

As I read the description of the spell and the shackles, I notice a few things:

  • The individual can’t teleport away from the shackles.
  • The individual must go where the shackles go.
  • The shackles must answer the summon because they are in my use, not in the use of some other individual.

So, would this combo:

  • Create some sort of hiccup in time/space?
  • Rip the shackled individual’s limbs from its body?
  • Teleport the individual to my location?

Associative Qualities in Relational and Dimensional Databases

Aside from how these structures differ in application (what they do), is it accurate to state that Dimensional Models represent composite entities (collection of primary keys) embodied by a fact table interconnected with its dimensions (foreign keys) and attributes – a “star” schema of relations?

Hoping for general conversation to define the interrelated concepts.

Pure functions applied to a two dimensional list

Lets say I have a two dimensional list:

list = {{a, b, c}, {aa, bb, cc}, {x, y, z}, {xx, yy, zz}}; 

and two pure functions:

f1 = Total[#]/Length[#] &; f2 = Total[##]/Length[##] &; 

I want to learn how to apply these functions over rows and columns of a list using Map, MapThread, MapAt and Apply. Here:

f1 /@ list  

produces, as expected,

enter image description here.

But, why MapThread does not work as it supposed to work in MapThread[f1, list]?

Similarly, f1 @@ list works as expected but f1 @@@ list does not work, why?

MapAt[f1, list, 2] works fine but MapAt[f1, list, {All, 2}] does not work, why?

What is the most efficient way to apply these pure functions to columns of the list without Transpose? My goal is to learn how to apply pure functions column wise most efficiently. I would appreciate general answer.