how does your state not excel

Hey lovely followers, I have some exciting news for you! Thanks to your love and support, I finally hit 1.3k! *cheering* Now this came right on the heels of my platonic soulmate, the Sam to my Dean, my best friend, Em ( @brothersonahotelbed ) coming up with an excellent idea for a writing challenge for all of you awesome people!

We know you guys are secretly just as dirty as us. Come on. Admit it. So, this challenge is called 50 Toys in 50 Days, or: 50 States of Sex.

How Does It Work?

  • You do not have to be following me or the lovely Em (but you’re more than welcome to!)
  • Reblog this post
  • No sign up deadline - we’ll keep this open until the prompts run out!
  • Send an ask to me or Em listing a state from the US (list below - one person per state, first come, first serve).
  • We will reply to you with a specific adult toy that we have on a private list.
  • You then have 50 days (due 6 July, 2017) to write a fic involving said toy and your state.
  • It can be angst, crack, darkfic, smut, fluff - anything! (It doesn’t have to be dirty at all - some of these toys are somewhat funny!)
  • Ship, RPF, and reader insert are allowed, anyone from SPN. All ships and polyships welcome!
  • Post your finished fic on your blog with the tag #50toysin50dayschallenge , and @ me ( @justanothersaltandburn ) and/or Em @brothersonahotelbed
  • Then Em and I will read it and reblog it to our blogs with a nice comment, and at the end of the challenge, we’ll make a masterlist of everyone’s hard work!

There are no winners and losers in this challenge, it’s purely for fun! Everyone’s a winner with sex toys!

Below is the list of remaining states. We’re looking forward to reading what you write!

  • Alabama
  • Rhode Island

“Because imagery is so effective a device in poetry, and because an image gives the reader a very specific touch of detail, poets learning the craft sometimes get the idea that detail of any kind makes for good poetry. In fact, lines of plain detailed description–of an old building or a field of flowers or of a mountain range or how one picks strawberries–can be deadly to a poem and except from the hands of an excellent writer of prose almost never sounds new to us. One focused image or one sweeping suggestion will do a lot more to keep a poem your own than will detailed description. Remember that suggestion always triggers the imagination; description almost never does.”

Miller Williams, from “Writing Your Own Poems,” Making a Poem: Some Thoughts about Poetry and the People Who Write It (Louisiana State University Press, 2006)

How I Attempted To Mathematically Model the Spread of Memes on the Internet, pt 1.

This is my first ever /actual/ Tumblr post, so first of all, let’s hope I’m doing this right.

I’ll make my introduction fairly brief as to get to the mathematics ASAP. This was part of my senior project for my mathematics B.S. (which I am very close to completing!). I presented parts of this research at the Michigan MAA Section Meeting in April of 2017. And I am really excited to share what I found in a more casual setting (rather than in a formal paper for my class or a conference presentation).

So let’s get to it, eh?

For the first installment of this series, I want to touch on two main things:

  1. Why Did I Decide To Do This?
  2. Things You Need To Know Before We Can Get To The Cool Stuff (I Know, I Know, But You Need To Know These Things)

Why Did I Decide To Do This?

My senior mathematics capstone course was on the topic of Markov chains. The main purpose of this class was for each student to complete an individual research project. I struggled for quite some time to determine what I wanted to do my project on. I eventually settled on disease modeling, but found myself disinterested with the material. I credit one visit to my advisor’s office for what sparked in me the most academic drive and passion for a project I’ve ever had.

I walked in, planning on just talking about my ideas for my disease modeling project. My advisor suggested that I could use this sort of model to work with other things, and me, being the Internet-addicted smart ass that I am, asked, “Like memes?”

So here we are.

Things You Need To Know Before We Can Get To The Cool Stuff

First, I’m assuming that you are familiar with the following concepts from linear algebra:

  • Matrix algebra
  • Eigenvalues and eigenvectors
  • Diagonalizing matrices

For the sake of time and length, I leave reviewing those as an exercise to the reader. Ha, I’ve always wanted to say that.

So I’ll begin with Markov chains.

A Markov chain is a stochastic process where the probability of being in the current state is dependent solely on the previous state you were in.

What’s an example of this?

Suppose you are playing a game on a rectangular board of 7 squares. Your piece starts on the center square. For each move, you have a probability of 1/3 of moving to the left (which I’ll denote L) and a probability of 2/3 of moving to the right (which I’ll denote R). If you get all the way to the right, you win! However, if you get all the way to the left, you lose (*sadface*). Once you reach either the leftmost square or the rightmost square, you can’t move out of them. We’ll talk about this in more detail later, but these are what we call absorbing states.

See below for the starting position.

Say your first four moves are R, L, R, R. 

Your probability of moving to the right is still 2/3 and your probability of moving to the left is still 1/3. Much like the honey badger, the probabilities don’t care that you moved R, L, R, R already; they are still the same as before. Examining this as a Markov chain is nice because it allows us to answer two important and interesting questions: 

  1. What is the probability of winning after a certain number of moves?
  2. What is the average number of moves it takes until I win? 

I’ll attempt to answer question 1, and I’ll leave question 2 as an exercise.

In order to find the probability, we must first create a transition matrix. The transition matrix, $T$, is a matrix where $T_{i,j}$ is the probability of getting to the $i^{th}$ state from the $j^{th}$ state. In this example, each state is a square on our board. Our transition matrix looks something like this:

Let’s discuss!

We note that every column sums to 1. This makes sense! We have to move every turn, so the sum of the different probabilities of leaving each state should equate to exactly 1. We also note that $T_{1,1}$ and $T_{7,7}$ are both equal to 1. These are our absorbing states! Absorbing states are those states where the probability of returning to itself is exactly 1. So, you’re essentially trapped (mwa-ha-ha) in these absorbing states. 

How does this help us find the probability of winning?

Excellent question! If we want to find the probability of being in the $i^{th}$ state after starting in the $j^{th}$ state after n moves, we simply find $T^n_{i,j}$. This can be done using your favorite computing software (I personally opt for SageMath), or if you’re feeling particularly ambitious, you can do it by hand (but I don’t recommend this, for the sake of your health). 

So if I want to find the probability of winning the game in at most, say, 10 moves, I would look at $T^{10}_{7,4}$, as this entry shows the probability of ending in the 7th state (win!) from the 4th state. Additionally, I could also find the probability of losing after at most 10 moves by looking at $T^{10}_{1,4}$. 

Here’s $T^{10}$ as outputted by SageMath:

Our $T_{7,4}$ entry is $\approx$ 0.7133, giving us a nice 71.33% chance of winning the game in at most 10 moves!

We can continue to raise $T$ to higher and higher powers and see if we can find the values that the probabilities approach, but there’s an easier way! We can find the steady state distribution of our transition matrix. 

The steady state distribution is the vector that when we multiply $T$ by this vector, we just obtain the same vector. In other words, it’s a vector $v$ of probabilities such that $vT = v$. Also, this vector $v$ is actually the eigenvector associated with the eigenvalue of 1!

For the sake of time, and since I’m assuming you’re comfortable with matrix algebra, I’ll leave the solution to you.

After finding the steady state distribution, we can determine that the overall probability of winning is 8/9 and the overall probability of losing is 1/9. Good odds! 

How does this fit into my research? / Preview for the next post!

I’ll talk more in the next post about how I viewed the spread of memes as a Markov chain, but in general, I worked sort of backwards from how I solved this example. In my research, I don’t know my probabilities, and my goal is to try to find them! So I use these ideas to create some ~pretty dope~ equations involving these unknown probabilities and try to match these equations to data sets I obtain from Google Trends. Of course, this will make more sense with my future posts!

Hope you enjoyed! Any questions/comments/concerns, feel free to send me an ask. 

Best wishes and stay positive!

(I promise that wasn’t a math pun)

(Okay, maybe it was)

Update: Here’s Part 2 of this series. 

anonymous asked:

hi! do u know some classic drarry fics? i'm pretty new in drarry fandom and want to read something rly good. Thanks!

Yes I do !!!!! Welcome to the drarry squad <3 I have a lil starter pack in my fic rec that I’m going to copy paste here because I feel Very strongly about this starter pack of great fics. I don’t think its what a lot of people consider the #classics but they’re my gold standard for what I think ideal drarry fic is based on like writing quality, relationship development, characterization and charm.

At Your Service - faithwood - 95k - this fic does it right !!! Summary doesn’t begin to cover how truly excellent this fic it. It’s a great crash course for everything drarry fic should be.
Summary: Hogwarts students are in danger; Harry is determined to save them all. There’s only one thing he knows for certain: Draco Malfoy is somehow involved.

The Stately Homes of Wiltshire - waspabi - 57k - The tags on this are ‘pining’ ‘mystery’ and ‘humor’ and honestly if that’s not enough to get you to read this Shining Gold Star of a fic we r not on the same level as people.
Summary: Malfoy Manor has mould, dry rot, and an infestation of usually historical poltergeists. Harry Potter is on the case.

The Way Down - 70k - lettered - this fic is one of my absolute favorites. It just AFFECTED ME MAN.
Summary: Malfoy’s all, “Come out of there,” the way you say to a cat who is badly behaved. And Harry’s all like, “No, what, I’m a hermit! And I have a chest-monster! And I am crazy magically powerful!” and Malfoy’s all, “We all have problems, bub.” (thoughtfully) “You are crazy though. I’ll give you that.”

Running on Air - 74k - eleventy7 - This fic is like receiving such a gentle and beautiful gift its like being tucked into bed or handed a cup of hot cocoa at the exact perfect temperature it is The drarry fic honestly. (its a lil less emo than the summary imo but just as beautiful as it sounds)
Summary: Draco Malfoy has been missing for three years. Harry is assigned the cold case and finds himself slowly falling in love with the memories he collects.

I’d say these are great places to start ! I have a more lengthy fic rec if u make it through those and u want to read more. There’s also a ton of stuff out there and I’d definitely advise you to explore rec blogs like @capiturecs @dragontamerdrarry and @mxlfoydraco for more niche stuff beyond the classic fics. I think starting out its really easy to stick to the big authors (lumosed_quill, faithwood, sara’s girl, lettered) and they are great !! But I definitely think that there are so many non-classic fics that should be getting just as much love.

10 fanfics that stayed with me

I was tagged by a-compass-for-his-ship and stylesinaflowercrown

haha i am very excited about doing this because i love fanfic so much. here are the first 10 i thought of: 

  1. TIF by mdasch and everydayslike - I know everyone always talks about it, but it’s really a great fic.  plus, when 100percentsassy and i first got into the fandom we had this weird idea that we only wanted to read canon fics (lol forever at us, it seems so absurd now)  anyway this was one of the first AUs I read and holy shit. i used to get overwhelmed at strange times just thinking of it.
  2. Thought The Song was Sung by 100percentsassy - haha speaking of Lexy! I love all of Lexy’s writing, but this story especially wonderful because it’s a super great fanfic premise, famous!harry and regular!louis meet on an online dating website, but it also has such an emotional pull to it.  The characters feel immediately real and you care about them a lot!! Lexy is very good at that. (ok also we came up with the idea of the fic at a shopko in green bay together AND she used excerpts from my embarrassing high school fanfics about me and orlando bloom in it, so haha really this is about me!!)
  3. you are my favorite place by soleilouis - i love the tone of this fic and the louis characterization. I’ve reread it a ton of times. the first phone call between harry and louis is fanfic GOLD!!!!!!!! 
  4. ain’t had none like you in a while by istajmaal - this is a lot of smut and it’s great smut. but what i really love about it is the way the author gives just the right amount of information about Harry and Louis’s relationship in the present and also about their future selves.  it’s the kind of thing where a single sentence will reveal a little info tidbit and in my mind i’m like “TELL ME EVERYTHING!!!! PLEASE! MORE!!!” but really i want to fill in the blanks myself as a reader. the author balances it so well and i’m so impressed by it. it makes me want read the story again and again.
  5. Pull Me Under by zarah5 - I read this as a wip and loved reading it as one.  Lexy and I would send each other tons of emails discussing what we thought was going to happen while waiting for the next installment.  I like it how zarah’s long fics like this tend to become fandom events of a sort in that way.  it makes me love the internet so much. it’s great when the dark period of a fanfic has a perfectly executed resolution and your brain and heart feel healed. ahaha that sounds pretty ridiculous but i’m being serious. 
  6. The Bachelor by mylifeslibrary - this fic was taken down from ao3 and it makes me so sad. this was another one of the first AUs i read, probably early 2013. and  i just remember reading lines in it about the state of harry’s heart and realizing like HARRY’S HEART IS SO IMPORTANT TO ME! ahaha and it still is. anyway, the author did an excellent job with the characterizations. harry’s heart felt real. 
  7. The Dreams That You Wish by Keep_Calm_And_Read_Fic - I like the romantic comedy tone of this and how the angst still hits really hard. but especially i loved how the character druscilla was developed in it. yay original lady characters!!
  8. But If You Close Your Eyes Does it Almost Feel by pukeandcry - this is a marcel fic. i love marcel SO MUCH and i love this fic. suddenly veronica is there too and it’s the greatest. having this fic exist is basically a fanfic dream come true for me. I reread it a lot. 
  9. We’re All Stars Now by galaxy_soup - there is just something about famous!harry and regular!louis that gets me!!!  Sometimes Lexy and I just start talking about how much Harry wanted Louis in this fic and then i have to go reread practically the whole thing.
  10. Butterfly Gun by Eravain -  this is still a wip. but god, it’s soooo emotional and so great and i think about it a lot. the setting and atmosphere are so well done. it’s the good kind of heartache!!!!!!!!!!!!

i’m tagging 100percentsassy and 1diamondinthesun