Graph Theory – Confused About Ball Bay's Algorithm – Helps to Achieve Conditional Independence Relationships

I'm trying to determine ALL conditional independence relationships of the form $ C perp X | Y $ for the following four graphs:
enter the description of the image here

The problem is that I get exactly the same answer for the four graphs, which probably can not be correct. The answer I get is that

  • $ C perp A | B $
  • $ C perp A | {B, D } $
  • $ C perp emptyset | emptyset $

And I can not find others. Here is my reasoning for each graph:

(i) The directed graph follows the Bayes Ball algorithm. There is no active way to $ A $ does not matter when $ B $ is included in the packaging set.

(ii) The directed graph follows the Bayes Ball algorithm. Since $ C $ is the root node, we can always reach $ B $ and $ D $. Again, there is no active path for $ A $ does not matter when $ B $ is included in the packaging set.

(iii) The undirected graph so that conditional independence requires the separability of the graph. There is nothing to separate $ C $ form $ B $ or $ C $ of $ D $ But $ C $ can be separated from $ A $ does not matter when $ B $ is included in the packaging set.

(iv) The factor graph so that conditional independence requires the separability of the graph. Same reasons as above.

I'm sure I'm missing something really important here?

Confused, how to transpose lists

I have two lists and I want to find the MAC value using the formula belowformula. But the problem is transpose to the list is not admissible in Mathematica?. If I'm just transposing, the MAC value is 1. Which is wrong. I expect a MAC value between 0.9 and 0.95. And the other question, does the Transpose function apply only to matrices?

Subscript(ϕ, 
  a) = {0., 0.00758684, 0.0151222, 0.0225548, 0.0298332, 0.036906, 
   0.0437221, 0.0502304, 0.0563798, 0.0621194, 0.0673986, 0.0721668, 
   0.0763735, 0.0799688, 0.0829025, 0.085125, 0.0865867, 0.0872383, 
   0.0870309, 0.0859154, 0.0838435, 0.0807667, 0.076637, 0.0714063, 
   0.0650272, 0.057452, 0.0486335, 0.0385245, 0.027078, 
   0.0142472, -0.0000147872, -0.0207673, -0.043783, -0.0688821, 
-0.095885, -0.124613, -0.154887, -0.18653, -0.219366, -0.25322, 
-0.287917, -0.323288, -0.359162, -0.395372, -0.431753, -0.468145, 
-0.504389, -0.540329, -0.575814, -0.610698, -0.644836, -0.67809, 
-0.710325, -0.741414, -0.771232, -0.799661, -0.826587, -0.851904, 
-0.875511, -0.897313, -0.917222, -0.935156, -0.95104, -0.964807, 
-0.976394, -0.985748, -0.992822, -0.997576, -0.999977, -1., 
-0.997627, -0.992848, -0.98566, -0.976065, -0.964077, -0.949712, 
-0.932996, -0.913962, -0.892648, -0.869101, -0.843373, -0.815522, 
-0.785615, -0.75372, -0.719916, -0.684284, -0.646911, -0.607891, 
-0.567319, -0.525299, -0.481935, -0.437337, -0.391619, -0.344896, 
-0.297288, -0.248917, -0.199906, -0.150381, -0.100469, -0.0502993, 0.};
Subscript(ϕ, x) = {8.61215*10^-6, 0.00907824, 0.0180589, 
  0.0268619, 0.0353983, 0.0435798, 0.0513177, 0.0585241, 0.0651109, 
  0.0709904, 0.0760754, 0.0802789, 0.0835142, 0.0856953, 0.0867361, 
  0.0865515, 0.0850563, 0.0821661, 0.0777966, 0.0718642, 0.0642853, 
  0.054977, 0.0438563, 0.0308408, 
  0.015848, -0.00120439, -0.02042, -0.0415716, -0.0645701, 
-0.0892686, -0.11552, -0.143179, -0.1721, -0.202138, -0.23315, 
-0.264993, -0.297527, -0.330612, -0.36411, -0.397886, -0.431805, 
-0.465736, -0.49955, -0.53312, -0.566323, -0.599037, -0.631146, 
-0.662535, -0.693093, -0.722713, -0.751293, -0.778732, -0.804937, 
-0.829815, -0.853282, -0.875254, -0.895657, -0.914417, -0.931468, 
-0.946747, -0.960198, -0.971769, -0.981414, -0.989092, -0.994769, 
-0.998413, -1., -0.999512, -0.996936, -0.992263, -0.985491, 
-0.976624, -0.965671, -0.952645, -0.937566, -0.920459, -0.901355, 
-0.880288, -0.857298, -0.832431, -0.805737, -0.777269, -0.747088, 
-0.715256, -0.68184, -0.646913, -0.610549, -0.572828, -0.533831, 
-0.493644, -0.452356, -0.410057, -0.366842, -0.322806, -0.278048, 
-0.232667, -0.186765, -0.140444, -0.0938079, -0.0469617, 
-0.0000101546}
mac = (Abs(
 Subscript(ϕ, a).Subscript(ϕ, x)))^2/((Subscript(ϕ, 
    a).Subscript(ϕ, x)) (Subscript(ϕ, x).Subscript(ϕ, 
    a)))

remains – Confused as to how APIs are called

I am new to APIs. Conceptually, I understand what is an API, but I am confused about some technical details.

All the tutorials I've read speak about URLs and endpoints and describe them as the paths / addresses through which APIs can be accessed. This part is very clear. no confusion here.

However, what I do not understand is How The APIs are called. In other words, in a real-life scenario, users do not enter URLs in an input box to invoke APIs. So I suppose that the call is done behind the scenes, by some programs and in response to a triggering event? If my hypothesis is true, is it also true that when you use a client such as Postman to test APIs, you basically emulate the behavior of that program?

Finally, where are the APIs usually stored?

tickets – Disneyland Anaheim makes me confused

I am going to visit Disneyland, Anaheim, California. I have visited the Disneyland website. I want to buy a theme park ticket. But I am confused because there is no clear definition that is included in this post? I've also discovered Tom Sawyer Island, which is one of the most visited places after Disneyland. Does the attraction park ticket also include Tom Sawyer Island? I share a screenshot here. There are some palaces in the screen capture marked in red. I want to know that these are individual tourist sports or tickets to a Disneyland theme park?enter the description of the image here

Confused about comments.php and comments_template ()

I want to be able to style the comments section to work with the theme I'm building. I do not have any comments.php file on the website, but when I included:


I receive a full comment section under my post that can add and post comments and commentator information. I thought that when I included the statement above, she was supposed to extract information from the comments.php file containing all my html code.

Now, I do not know where to display the CSS code associated with the comment form, except for the "Inspection" section of Google for developers, so I can edit it.

I've looked in the twenty-nine year old theme and it has my code as well as a very complicated comments.php file. I can not claim to fully understand the comments.php file, but I do not understand how to get an output from a comment form and its answers without having to have a comments.php file.

What do I miss? Can someone help me solve this problem?

Confused in calculating the shortest path using Dijkstra's algorithm

enter the description of the image here

I have to find the shortest way using Dijkstra's algorithm. After performing the calculations, are the following values ​​correct?

A = 0
B = 13
C = 8
D = 20
E = 14
F = 25
G = 31
H = 38
I = 46
J = 52

Confused about the concept of object definition in python

I've read somewhere that "every python object is a value having a certain type stored in a particular memory location". The other definition of a python object is that each object has a type, an identity, and a value. According to this definition, we would consider an object as a thing containing a value (a rectangular box containing an integer value 36 for example and the whole thing will be called an object, not just the value 36), which is not true when we says 36 is itself an object and there is nothing like that contains 36. It does not sound good that int object 36 has an identity (id (36), type int and 36 a a value of 36. That is according to the 2nd definition so the two definitions are contradictory? Help me

Macbook gets confused by changing external USB keyboard

I have two different slots to use my MacBook Pro and connect an external USB keyboard to both places. They are both 104keys and have identical provisions.

When I plug in the keyboard for the first time, it often stops (not always) working properly. The modifier keys will be completely incorrect and most normal keys will also be incorrectly translated.

What I did was a little DIY with the keyboard built into a laptop for a moment (a few tens of seconds to about a minute) before the keyboard functionality d & # 39; habit returns to normal.

I have not been able to choose a model that works better than the previous ones – which is messy and rather unpredictable.

Has anyone encountered this difficulty and proposed a better solution?

Answers to comments

  • reboot has no effect: this behavior has been around for at least months
  • "identical place" do not know what it means, but both USB ports have been tried many times and do not affect the result

mysql – Confused with a specific SQL query, AvgPrice

Please let me know if this is correct, and if not, what would be the best or the best way to write the SQL query. I am a beginner, so I apologize if it seems obvious to you. I think I have to use a JOIN, but I do not know how.

THIS REQUIRES ONE QUESTION C) Get the average price of the products manufactured by each product line. Name the average price "AvgPrice".

my layout

        SELECT AVG (price) AS "Average price"
FROM product_line
GROUP BY line_product;

Confused about pumping the lemma, what am I missing?

When I apply the pumping lemma on this language:
$ {L = {010 ^ n: n ge0 }} $ on the alphabet $ { Sigma = {0,1 }} $ I understand that it is not regular whereas it is regular.

  1. let $ {n = 4} $then $ w = $ 010000
  2. $ w = xyz $ , $ { mid xy mid leq n} $ and $ { mid y mid geq 1} $
  3. $ x = $ 0 , $ y = $ 10 , $ z = 000 $
  4. let $ i = $ 2
  5. $ xy ^ 2z = $ 01010000 $ not in L $ therefore L is not regular.

so, what do I miss?