Matrix similarity Puns

Hans Zimmer - Escaping the Ship vs Tom Tykwer & Johnny Klimek - Two and the Same

I picked up Supernatural again the other day, and suddenly found this intro scene in one of the episodes. The song, the psychologist, talk about a cat. Suddenly I got a rush of deja vu.

https://youtu.be/0Xjt3vv6Cxc

This isnt really gonna be a big text or some complicated theory, I just want to hear some people’s opinions on this. To those who havent seen the Matrix (prob very few of y’all) its very similar to what Dr. M tried to do in the 3rd semester. Agent Smith in his speech states that there was a previous version of the Matrix that actually gave everyone a happy life and was a paradise; however, it ended up failing as nobody could accept it as reality. Agent Smith states that this is due to the fact that “human beings define their reality through misery and suffering” and I was wondering do you guys think this would have happened in Dr. M’s reality? We kind of see glimpses of it and it can be assumed that Joker and Akechi two people who’s lives is defined by “misery and suffering” were the first to notice that this reality was fabricated. This same thing could be applied to the confidants as well who all had some degree of suffering in their lives, some more than others. Idk just interested to hear you guys thoughts and this will help me kill time at work so lmk what you guys think!

I realised watching Mr. Robot that every time someone called Elliot “ Mr. Alderson “ it sounded vaguely familiar to me. It sounded like something I had heard so many times before without having watched the show more than once.

It sounded similar to how the program used to called Neo “ Mr. Anderson “ and how similarly close they are to sounding and spelling.

This raises the question if the two shows have similarities ( which they do ) and how its about one man fighting for the freedom of his world from a sentient program ( the 1% ).

g_Undirected<-sample_gnp(10, .6, directed = FALSE, loops = FALSE)
g_Directed<-sample_gnp(10, .6, directed = TRUE, loops = FALSE)

similarity(g_Undirected, method = "invlogweighted")

https://preview.redd.it/r256gpdd22m51.png?width=749&format=png&auto=webp&s=2f718a23e5c438458448dbd3d7299ace31b4967d

similarity(g_Directed, method = "invlogweighted")

https://preview.redd.it/zv9ye85vv4m51.png?width=708&format=png&auto=webp&s=f6a835cba70732b2e0ca741b4acc01216e003584

Does anyone know why this is the case?

(1) Why are numbers along the diagonal for the similarity matrix for the directed graph not a constant? Furthermore, some self-similarity cells are less than similarity to other nodes, which does not make any conceptual sense.

(2) Why do directed and undirected graphs confer different similarity matrices? They should be identical, right? I understand similarity to be agnostic to direction and simply concerned with common neighbors.

Hello Everyone!

TL;DR: Title explains it all: Is there a way to run a hierarchical cluster analysis w/ a similarity matrix based on counts?

Long version

I'm playing around with some card sort data where each vector has the frequency at which it was paired with each other. For example:

------------ Card_1_____Card_2 ____Card_3

Card_1 - [ 0________ 3 ___________1]

Card_ 2 - [3_________0____________5]

Card_3 - [1__________5___________0]

So Card_3 and Card_2 were paired 5 times with each other, and Card_1 and Card_2 were paired 3 times together, etc.

Can we create a correlation matrix from this then run a hierarchical clustering analysis on it? I frankly don't know if it's possible/appropriate to transform a similarity matrix based on counts to a correlation matrix, etc.

Any information will be greatly appreciated!

Edit: Formatting

1.If you notice around 1:08:05 in the first movie(THE MATRIX). There is "Continental" graved on the black car that Cypher was going to after throwing the phone in the Garbage Can. Ummmm...... Interesting.

2. In the final movie of the trilogy, we see the building where Neo and Agent smith collided, looked a lot like the Continental from John Wick.

3. The line "Guns, Lots of GUNS!!! " ( Both Matric and John wick 3 )

4. Both are indestructible

I know some of these you already saw but just wanted to share something that I thought was interesting.

Do you have any thoughts about this ??

Write your theories below.

V

In the Matrix humanity is trapped inside a simulation, run by the machines. In AoT humanity outside the walls is dominated by Marly.

A small hold out of humans free from the machines/Marly exist inside a safe zone, Zion/Paradis.

Neo has godlike powers in the Matrix, while Eren has God like powers through the founding titan.

Neo is guided by an oracle who can see the future while Eren is guided by Ymir/the Attack titan that can see future memories.

Eren is opposed by a group loyal to Marly, the warriors, while Neo is opposed by a group loyal to the machines, Agents.

At the end of each story, the last hold outs of humans, Paradis and Zion, face complete annihilation from an incoming army.

This is reaching but you could maybe compare agent Smith to Zeke. Has a connection to the protaginist, was once loyal to machines/Marly, betrays them yet also has a different devious evil plan, both try to convince the protagonist of their righteous cause.

It just leads me to think. In the Matrix Neo saves Zion and is able to free humanity from the machines. At the time Agent Smith controlled humanity so it was Neo vs all of humanity except Zion. Just like how now it's Eren vs the world. How crazy would it have been if Neo had to kill all of humanity inside the Matrix to save Zion?

Suppose that there's a large a sparse matrix where each row represents an individual. I want to look at different regions/windows the matrix and see how similar the individuals are in that region. What are some different ways to calculate how similar the rows of a matrix are?

Here's an example of what the matrix may look like for the first few rows and columns. Edit: Most of the non-zero entries are 1s but there are also some 2s.

0 0 0 0 1 0 0 0 0
0 0 1 0 1 0 1 2 0
0 0 1 0 1 0 0 2 0
0 0 1 0 1 0 0 2 0
0 0 1 0 1 0 0 1 0

I am pretty sure I am not the first or the last one to make this comparison.

Neo Noir Mystery. Supernatural. Science Fiction. All of these terms and others do not adequately describe this movie.

I welcome your thoughts.

If you haven't watched it I invite you to experience this wonderful underrated and hidden gem.

Hey /r/bioinformatics

I was wondering if anyone knows of a amino acid substitution matrix that is biochemical in nature. I know PAM and BLOSUM, but they are based on evolutionary distance. Don't get me wrong--they're better in most situations than what I am looking for. But does anyone know of a matrix that gives some similarity/dissimilarity values based on the biochemical/physical properties of the AA residues themselves? Not looking for precision or accuracy, just a rough estimate that is generally agreed not to be absurdly wrong.

Thank you kindly for your time!

The techno. The moody, dark cinematography. The leather costume design. The all-powerful superhero. The martial arts and action sequences. The end scene beginning with crushing a bunch of SWAT style police officers in a building lobby.

Not accusing the Wachowski Brothers of anything, but Blade came out first.

Edit - This is a disappointing sub. Just trying to bring up the fact that The Matrix, one of the greatest films of all time, ripped off Blade in more than one way. No one really addressed that at all and this post has downvotes when there’s no reason for them.

The similarity is massive is just that what we are doing is much worse.

Hello people, I have a question.

I have only 2x2 matrices. I know matrix A and B. how can I find matrix T given that

B = TAT^(-1)

We can assume that B, T, and A are all invertable.

For example, if I have the 2x2 matrix A =

1 1

0 2

we see that this is not symmetric. In my textbook, they just diagonalize this matrix A using the similarity transformation

D = P^(-1)AP. So they construct P from the eigenvectors of A, and they just construct P^(-1) by taking the inverse of P.

My question is why can't we use this method for a real, symmetric matrix, such as S =

4 1

1 -2 ?

So if its a real, symmetric matrix, we have to diagonalize it using the similarity transformation O^(T)SO = D? We can't use the similarity transformation P^(-1)AP = D?

The WatchTower is constantly compared to 1984 and The Borg, but to me personally it has always been The Matrix. I'm a HUGE Matrix fan and each time I watch them, I find more and more similarities. I'll share some but please feel free to share yours as well or re-interpret mine.

1. The Matrix is a prison for the mind = WT indoctrination and cult mind control

2. A small percentage of the inhabitants of The Matrix realize there is something fishy about it all and want to know the truth = those starting to have doubts or mentally wake up

3. But most are happily content where they are even when there's weird shit going down. (Glitches in the Matrix, Agents possessing people, deja vus = complains about the blood issue and kids dying, shunning, ARC, flip flops in doctrine, false prophecies, etc.)

4. There's someone out there willing to show you the Truth, but you must be ready to accept it. (Morpheus = Ray Franz, John Cedars, a friend that wanted to help wake you, this subreddit, etc.)

5. A choice has to be made to either know the entire truth (choosing the red pill) or stay "blissfully ignorant" inside the walls of the Watchtower/Matrix (choosing the blue pill)

6. The Agents are the Elders, out there making sure everyone conforms and plays by the rules and to eliminate the Red Pill/apostate threat.

7. There is a Resistance (Ex-jw activists) who want to fight the control of the Matrix and aim to help as much people as possible wake up.

8. Just like Cypher in the first film who wanted to be plugged back in, there are always those that still want to go back to the Safety Net of the WT even after knowing TTATT no matter the cost.

Those are just a few from the top of my head. Have a great day you guys!

The Matrix has you ...

How do I characterize a matrix by the amount of (dis)similarity between the rows? For example [[1,0,0],[0,1,0],[0,0,1]] has more dissimilar rows than [[1,0,0],[1,0,0],[0,1,0]] -- the elements are either 0 or 1. Any measures that are useful here? I understand the different measures of similarity, but they all seem to be for comparing two objects. (I just need a starting point or the key phrase to search in google if there are no common measures or many).

Hello all,

This is my first post on the group. I'm hoping that the group can help me better understand something.

I'm designing a feedback controller with LQR in Matlab. My LTI model (A,B,C,D) is very stiff and the LQR numerics struggle with it (complaining about an ill-conditioned system). So, I chose to balance the system using Matlab's BALREAL. This resolved the numerical challenge (atleast LQR stopped complaining).

BALREAL returns the similarity transformation matrices to convert between the original state vector 'x' and the newly balanced state vector 'x_b'. That relation is,

x_b = Tx, and x = Tix_b

LQR produces an optimal state-feedback gain matrix that minimizes,

J = Integral {x'Qx + u'Ru + 2*x'Nu} dt

or, if used with the new system it would be,

J = Integral {x_b'Q_bx_b + u'Ru + 2*x_b'Nu} dt

(NOTE: I'm not specifying an N matrix...)

where 'u' are the inputs into the system.

Now to my question. The state-space for the original LTI system has physical meaning, where the state-space for the newly balanced system does not. When designing my controllers with LQR I know how to construct my Q & R matrices because of the physical meaning in the state vector 'x'. However, I lose that intuition when trying to apply LQR to the new balanced system. Meaning, what is the relationship between Q_b and Q?

If we subsitute the definition of 'x_b' into the cost function for the original system we get,

J = Integral {x_b'Ti'QTix_b + u'Ru + 2*x'Nu} dt

To me this means that,

Q_b = Ti'QTi

Now for the problem... let's assume that I have a fully actuated 2 degree-of-freedom mass-spring-damper with a state vector of,

x = [z1; z2; zdot1; zdot2]

where z1 and z2 are the positions of the masses and zdot1 and zdot2 are their respective rates.

My experience with an LQR based controller design process has been that if I want to control z1 more than z2 and I don't really care about zdot1 and zdot 2 then a good set of Q & R matrices would be,

Q = [a 0 0 0 0 b 0 0 0 0 0 0 0 0 0 0] R = [1 0 0 1]

chosing the ratio between 'a' and 'b' in defining 'Q' determines how well z1 performs relative to z2. Meaning, if I make 'a' a lot bigger than 'b' then the feedback control law from LQR will allocate more control authority to z1 and assuming the dynamices between the two DOFs are similar then then response time of z1 will be superior to z2. Correct?

I can construct my Q matrix this way because of

One of my favorite scenes in the Matrix is when Cypher meets with Agent Smith in the restaurant. Cypher knows the Matrix is fake, but wants still wants to be placed into the Matrix and have his memory wiped. "Ignorance is bliss".

That scene reminded me a lot of Mack and his decision to stay in the framework. He can be ignorant to the fact that his world isn't real and still be happy because he has with his daughter. I understand why Daisy, Simmons, etc wanted Mack to leave, but it would have been best to never bring him on the mission, never tell him about the real world, and allow him to stay in the framework.

Hello! I was able to finish both helpers.py and index.html without much issue, but I am very confused as to how to use Jinja in matrix.html. I read the documentation and figure that I should be using a for loop, but I am having trouble using the Jinja and HTML together to create a table.

Additionally, I have having trouble testing different things using flask, because I'm receiving a 400 error which states that I am "missing strings."

Can someone help with either of these things?