applied-math

‘Well, regular math, or applied math, is what I suppose you could call practical math,’ he said. ‘It’s used to solve problems, to provide solutions, whether it’s in the realm of economics, or engineering, or accounting, or what have you. But pure math doesn’t exist to provide immediate, or necessarily obvious, practical applications. It’s purely an expression of form, if you will – the only thing it proves is the almost infinite elasticity of mathematics itself, within the accepted set of assumptions by which we define it, of course.’
—  Hanya Yanagihara, A Little Life
Stable Transmission Trees on Moving Sinks of Wireless Sensor Networks

This talk was given by Yoshihiro Kaneko at SEICCGTC 2017. He’s been working on this with a bunch of students, whose names I didn’t get a chance to write down. We had a long conversation afterwards because I wanted to clarify some things that came up in the talk, but we also ended up talking about some differences between applied math and engineering ;)

——

I think the name wireless sensor network is pretty self-explanatory: we have a bunch of sensors that are all collecting data, and we want to bring it all together to one place. So we allow them to communicate with each other by sending all of the data packets to a single CPU. The CPU will generally be pretty far away from most of the sensors, so it can’t connect with them directly. But it is pretty computationally expensive to set up communication channels, so we want to do it somewhat efficiently.

However, there is a fairly serious practical issue with this model, which is that the sensors closest to the CPU are then responsible for handling every data packet sent by every single sensor. If the network is large, this can lead to a backlog, or an excess of energy usage. (The latter might be a really big problem if you’re running on a charge!)

Fortunately, people have proposed many fixes for this problem, which have their own strengths and weaknesses. The one that Kaneko chooses is called the moving sink model, in which the responsibility for doing the computations moves between multiple CPUs. Note that this is not parallel processing: at any given time, only one of the CPUs is considered “active” (or the sink) and receives all the packets.

One big problem with the moving sink model is that every time the sink moves, we need to figure out how we’re re-routing the data from each sensor to get there. Remember that it’s expensive to set up communication channels, so we don’t want to have to keep re-establishing them: we’d like our network to change as little as possible.

Moving into the world of abstract graph theory, the problem looks like this: the network is a graph with a collection of distinguished vertices (corresponding to CPUs). We “move the sink” by creating a (finite) sequence $(v_1, v_2,\dots, v_k)$ of distinguished vertices (repeats are allowed), and for each $v_i$ we want to create a spanning tree $T_i$.

In this language, the goal is to construct the $T_i$ in such a way that “no two adjacent $T_i$ are too different from one another”. In other words, for some fixed distance function $d$ on the set of spanning trees and minimize the total distance between consecutive $T_i$:

$$ D = d(T_1, T_2) + d(T_2, T_3) + d(T_3, T_4) + \cdots + d(T_{k-1}, T_k). $$

Hmmm… distance function…… on the space of trees…… hmmm………….

But sadly to all the geometry fans out there, we went with something a little more mundane: to get the distance between two spanning trees you count the number of edges that are in one tree and not the other.

He spent the last bit of the talk describing the algorithm they created for creating the $T_i$ in a particular setting (the network is a grid graph, the $v_i$ are the boundary vertices ordered counterclockwise). His students claim to have a proof that their algorithm generates spanning trees which minimizes $D$, but apparently the proof involves a lot of casework and he wasn’t quite willing to confirm it yet.

——

I actually asked him when we were talking if they had considered the BHV metric (which is the professional way of saying “You should consider this” to someone). They had not, but he said that it wouldn’t be likely to be useful: we want $D$ to represent the cost it takes to set up a communication channel. Since we expect this to be a fixed-cost operation, the edge-counting distance makes sense for this particular application. Conversely, the operation of “shrinking the tree to zero”, which is fairly common in BHV-geodesics, is pretty meaningless.

[ In the same vein: his distance was slightly different than the usual standard, because the standard method makes the trees directed and counts reversing an edge as distance 1, but he counted it as distance 0. This is because for wireless communication networks, it would be rather unusual for the communication channels to be set up one-directionally. For security and error-correcting reasons, it’s better for the receiver to acknowledge the sender and to explicitly permit an opening channel. So while this exchange is happening, you might as well set it up bidirectionally. ]

4

D. R. Brillinger and M. Rosenblatt, Computation and Interpretation of kth-order Spectra

The highlight of Futurama math for sure is this thing that’s now known as the ‘Futurama Theorem.’ I’m descending into hyper-nerdspace now. The writer of this episode was Ken Keeler, who I mentioned earlier, who has a PhD in applied math. … And he was writing this episode where the idea was the characters are all going to switch brains, with this brain-switching machine—sort of a standard sci-fi and cartoon idea. … And we came up with this complication: If the machine switches two people’s brains, it cannot switch those same two people’s brains back. … And we were just trying to make the plot more complicated, but we realized that we had accidentally created this math problem. … Ken comes in the next morning with a stack of paper and he said, ‘I’ve got the proof,’ and he had proven that no matter how mixed up people’s brains are, if you bring in two new people who have not had their brains switched, then everybody can always get their original brain back, including those two new people. So I was very excited about this, because you rarely get to see science, let alone math, be the hero of a comedy episode of TV.
Applying To Medical School Series- Part One: Are You Sure?

It starts early.

You’re 14 years old and your teacher tells you that you’re going to be starting the GCSE syllabus now. You still have to ask permission to go to the toilet but your future begins now. You have to start paying attention, even when everyone else is talking. You have to do your homework even if the rest of the class makes a pact not to do it and tell the teacher they forgot to assign any. You have to ask questions and study hard and do loads of practice questions to perfect your exam technique so that by the time exams roll around a year or two later, you can smash them.

August comes. You get your results.

Your results need to be great. Now this is relative, it really is. If the average GCSE grade across your year is a D and you got mostly Bs, a few As and maybe somehow scraped an A* or two, this can actually better than if everyone at your school averaged 11 A*s and you got 9 A*s and 2 As. Don’t worry whatever the case, all hope is not lost here.

Sixth Form begins. A lot of people will choose an “easy A” subject. Subjects they don’t really need to work very hard in and which aren’t particularly useful to them in the future.

You, on the other hand, need to have Chemistry. You also choose Biology and Maths. For your 4th subject, you decide on Spanish because you’d quite like to go to UCL and you’ve heard they prefer a non-scientific 4th subject. But crap. You were also thinking that with GCSEs like the ones you worked your butt off to get, maybe you’d consider Cambridge if your AS Results turn out well. And don’t Cambridge love you to have 4 sciences? Well whatever. What’s done is done. Biology, Chemistry, Maths and Spanish it’ll have to be.

Oh but this isn’t all. 

You’re volunteering in a care home, tutoring younger students, acting as a mentor, working with autistic children at a weekly club, captaining the basketball and hockey teams, raising money for the school in Senegal that your own school is affiliated with and of course, you’re going to South Korea over the summer to teach English to children.

You’re also reading New Scientist and books by Atul Gawande and other popular medical books. You don’t read The Man Who Mistook His Wife For A Hat because medicslacks on tumblr told you that everyone and their hat has read that book and seriously if you put it on your personal statement you are just wasting characters.

And of course. Work experience. You emailed every GP in the area and they all told you they can’t take you because it might compromise patient confidentiality. So you ask that girl in class who you kind of know but don’t really talk to if she could ask her dad, the GP, if you can shadow him for a day or two. She looks confused but says sure, she’ll ask.

Success.

You shadow the GP and realise this is only primary care. One of the patients really gets to you, a patient with Multiple Sclerosis and this intrigues you. You go home and read up about the condition. You then decide to email all the neurologists about your interest at your local hospital on the off-chance one of them will let you shadow them.

A miracle! A week later, one of them replies! Oh, but there’s a lengthy official process. That takes a month or so and then FINALLY you get some hospital work experience- just one afternoon, but you get to meet patients and ask the doctors more about MS and you decide it’s all worth it.

You grit your teeth as the kids with doctor parents talk about how they just follow their mum or dad around whenever they want.

And all this while you HAVE to keep working hard at school. You pay attention in class. You go home and do your homework, you flag things you don’t quite understand to ask at school. You start making notes early and you revise so hard in the run up to exams because secretly you’re still hoping to go to Cambridge and you’ve heard you need a minimum of 90% UMS in all your papers to have a chance. It’s okay if you don’t though- you know a family friend who got ABBC and still got an offer from Manchester.

But you’re hoping.

Results day rolls round aaaaand… YOU’VE DONE IT!

Congratulations.

Now the nightmare that is application season begins.

UKCAT booked. Okay. You’ll worry about that later.

Everyone else has until January but YOU need to get everything done by October. You panic and sit down to draft your personal statement aaaaannnndddddd…

You draw a blank.

What.

The hell.

Do you write?

It’s okay because I AM HERE TO HELP. Personal Statement Help Post Coming Soon!

But for now, let’s just assume you somehow get through it. You draft it and you take it to your careers advisor who looks at it and then asks where you’re thinking of applying. “Cambridge, Imperial, Leicester and Hull York.” you say. You like the variety.

Your careers advisor looks baffled. “You can’t apply to those 4.” She tells you. “Your personal statement will never tick all the boxes for them all, they’re far too different and are looking for completely different things. They all teach medicine in completely different ways. On the spectrum of Traditional to PBL, you’ve really run the whole gamut.”

So you go away and you look into the courses and you decide that you’re not particularly bothered about research and you want to see patients as early as possible. You don’t really care about the city you’re in or the prestige of the university.

“Ahh that’s better.” Your careers advisor smiles as she sees you’ve scrawled across the top of your page: “Leeds, Hull York, East Anglia and Sheffield. You know, with GCSEs like yours, you should really consider Birmingham.”

You decide to see how your UKCAT goes.

Your school also registers you for the BMAT since Leeds requires it. But you’ve got the whole summer to worry about that.

Over the summer you prep for next year by reading ahead in the text books a little and making some notes. You carry on with all of the extracurriculars and volunteering you were doing. On top of this, you start doing practice questions for the UKCAT and BMAT.

After your first day of these questions, you break down. This is impossible. How does ANYBODY do this?

The next day you take a deep breath and try again.

They’re a little easier.  

A week later and you’re finally starting to get the hang of it. You’re starting to know what to look for. You’re starting to notice patterns and learn the rules. You’re starting to think the right way.

You can do this!

You sit the UKCAT in the same seat where you did your driving theory exam. You get a 750. Excellent.

School starts again.

You refine your personal statement, you fill out the rest of your UCAS form. You see your reference.

You hold your breath as your Head Teacher clicks Send on your form.

Then you wait.

You don’t have time to stop. On top of school you’re now having to go over GCSE science again for the BMAT. And practicing writing as tiny as possible so you can fit an entire essay onto a page. As well as still struggling with all those logic questions. You’ve already applied to Leeds so now you HAVE to do it. You get a 2.5 in Section 2 of one of the past papers. You wonder if you might as well just give up on Leeds now.

You sit the BMAT and are fairly sure you failed every section. Whatever.

OMG.

OMG.OMG.OMG.

You’ve got an interview. AAARGGGHHHHH.

Mock interview. You NEED a mock interview. You beg your careers advisor who sorts out for a local doctor to come in and interview you. They ask you about your personal statement, your work experience, they ask you about a few ethical dilemmas and some odd questions that seem to have no purpose. They also discuss some topical issues in the NHS with you. You make a joke about Jeremy Hunt.

They laugh.

A few days later, you get your BMAT results. You did SO much better than you thought. Excellent.

OOOOOOMG.

Another interview.

You’re on cloud nine when… UCAS Track updates again.

Your first rejection.

It feels as though someone just snapped a rubber band around your heart. Why would they reject you? What was it they didn’t like? Were you not good enough? Did you not seem dedicated enough? Why?

You swallow down the disappointment. You already have TWO interviews. You’re so lucky. There are thousands of people who don’t even get that. And you have EARNED it. You’ve been working hard for years for this.

You prepare for the interview. You ask yourself questions and change the answer every time. “Why do you want to be a doctor?”

You know they’re going to ask you this but what do you say? You have an idea! You’ll talk about a patient. The patient with MS you saw at the GP who really touched your heart. You can say you liked how the science that the doctor knew would be nothing without the way he was able to console her more personal worries and concerns and this kind of application of science to help people really convinced you that you want to do this. At least by adding in a patient you saw, your answer will be more personal.

Interview day arrives and you’re sitting nervously with a few other students. A boy in an oversized suit and a girl wearing heels so high you’re worried she’ll break her ankle on her walk to the room. A student at the university smiles and calls your name. She walks you to the door. “Are you ready?” she asks. You nod but it’s not true, your stomach is full of butterflies and you feel a bit sick.

And for a second you pause.

Are you sure?

Are you ready for the path this could lead you down? The life of a doctor. Forget that. The life of a medical student! Antisocial hours, a lifetime of having to keep requalifying and doing exams, mountains of paperwork, not really saving lives so much as helping to reduce the effect of symptoms. Putting your heart and soul into delaying the inevitable.

Is making a difference to even just one life, is making life less painful or less miserable for just one person, is keeping just one person alive so their loved ones can see them for another day, or helping even one person to die in as little pain as possible… is that enough for you?

You take a deep breath and open the door.

Two weeks later. You get an offer.

A*AA.

You end up getting two more offers.

August rolls around again.

You cry when you get the email from UCAS confirming your place at your Firmed University.

A*A*A.

It was all worth it. You got into medical school.

Your parents buy you a copy of Gray’s Anatomy and this is when you realise… The work has only JUST begun. The first 18 years were nothing.

So I’ll ask you again.

Are You Sure?

anonymous asked:

"I fucking hate calculus" said Baz

Simon looks up, surprise written all over his face, “Really?” 

Baz rolls his eyes, “Yes really, don’t tell me you don’t.”

Simon looks down at the book in front of him, there are eight problems left that he doesn’t even know how to start, “I mean, yeah, I hate it too, but I hate it because I don’t know how to do it. You do.”

Baz shuts his own book, “Just because I understand it doesn’t mean I don’t find it tedious and dry and any other bad adjective you can apply to maths.”

“Then why do you always volunteer to help me with it?” Simon asks.

“Well,” Baz pauses, a very light blush struggling to form across his pale nose, “because I like you.” 

Honestly I disagree with the idea that everything is applied math because math was developed to describe physical phenomena, but it isn’t in and of itself physical.

Biology isn’t applied math because biology is another tool to describe physical phenomena, and while it uses math it isn’t math. Saying it’s applied math implies that it is, on some level, just math. And I don’t think that’s true.

Same with chemistry and even some branches of physics.

Hi! It’s me. Your local Zed-obsessed tumblr user here to do a whole lotta speculation from a whole lotta nothing. This is all very disconnected and kinda a bunch of thoughts written down as they come to me. It’s way too long, as is tradition for me. Enjoy.

(If you read anything please read the large bold bit at the end + the misc questions.)

  • I’m thinking that Zed’s ult change in the assassin update is now reflected in lore. 
  • PASSIVE - REAPER OF SHADOWS: Scoring a takedown with/while Death Mark is active permanently grants Zed non-stacking bonus attack damage (he always keeps the highest value between his current bonus and his latest takedown).”

Keep reading

Math Follow Train

Hey,

I know we math people are often not like the others - and maybe this is a crazy idea - but I think we can do a follow train just like any other community!

If your tumblr is even just partly math-related, reblog this and follow the other people on this train! It is advisable and polite to follow everyone but we’re not gonna be mad if you join the train without following others. I will follow all the people who reblog this :)

You belong on this train if any of the following apply:

* you love math
* you study math
* you want to study math
* you think that math is REALLY COOL
* you want to understand math better
* you like to talk about math
* you have a math-themed blog (even just partly)
* you are a mathematician

Yes! I want to do this experiment! Are there enough math-related tumblrs for a successful math follow train!?

How I Study for Tests

I have done posts like this before with more general tips for studying history and techniques, but this is going to break down exactly what I do step by step. Just so you know, this is more for history/geography/english/languages, and I don’t think very many of the tips apply to math or applied sciences. 

Step 1: Flashcards

I honestly love flashcards for studying! While they seem passive, if you are a linguistic learner like me, they are extremely useful. Because you have to read over your notes and then rewrite them, it’s basically like going over the material twice right there. And, once you’re done you can study them with a friend or parents really easily, which is another active way of studying. 

General Tips for Flashcards: 

  1. Don’t be too worried about keeping them super neat or colour coded. Just make sure they are legible! 
  2. Try to fit as much as you can onto one card. Flashcards are not very eco-friendly, unfortunately, so don’t be wasteful by writing one term on each card that could fit five or six. 
  3. If you are going to list lots of information on the back, write how many points there are on the front. For example, if you need to know 6 really important things about the Cold War, write “Cold War (6 points)” on the card so when you actually go through them you can remember. 
  4. Buy flashcards at the dollar store because places like Staples will jack the prices up so much! Also, don’t worry about getting the heavy cardstock ones if you only need them for the week coming up to a test. 
  5. When you study, remove the ones that you still need help with from the bigger stack. That way you have less and less to review each time and don’t bother studying things you already know. 
  6. If you have an exam, keep your flashcards! This way, you don’t have to rewrite the entire course worth of notes. You can also buy cute little containers for index cards at Staples! 

Step 2: Significance Tables

I made a post about these here, but I thought I would share again. When you know there are specific terms/concepts that you need to know a lot about, these are a godsend! A lot of teachers do identify and explain the significance paragraphs in English or history classes, so this is really specifically useful for that. But it can also be really good for essays and other long answer questions! 

How to Make a Significance Table

  • Go through your notes and find all the most important terms. Be selective, because this entire thing is kind of redundant if you just do everything. 
  • Make a table in Word or on paper with three columns: “Term”, “Definition”, and “Significance”. 
  • In the definition section, include all the basic details you need to know, like dates, people involved, and a brief description of what happened/what it is. This should be about 3-5 sentences. 
  • In the significance section, write why it is important to what you’re learning about. Think about things like what it lead to, what major terms or ideas from the unit it connects to, what other major events happened around the same time, etc. This should be 1-2 sentences.
  • Study from the chart in addition to studying with flashcards and other techniques! 

Step 3: Essay Outline

If there is an essay or long answer as part of the test, I always prepare sample outlines! Even if you aren’t 100% sure what the topic will be, you can prepare a few and one of them will probably be similar. Even if your guess is way off base, its good practice to write out an outline and organize your ideas! 

Step 4: Study Group

I love studying with friends! However, I recommend studying alone or with someone really, really focused for the first couple nights, then getting together with a bigger group later on in the week. You can also consider talking to the teacher if you don’t have close friends in the class. 

Tips for Study Groups

  1. Study with people you are comfortable with, so you won’t feel awkward asking questions or getting an answer wrong. 
  2. Try to find people who have the same goals as you and are equally as dedicated to the course, so you will both/all have the drive to get work done.
  3. Go to the library or another public place instead of studying at home, because you will be less likely to get distracted. 
  4. Bring a list of questions that you have and topics/ideas you don’t understand, so you can possibly get help from someone who gets it. Also, if no one there can help you, go ask the teachers afterwards. 
  5. Compare essay outlines and quiz each other. There is no point in doing a study group if you don’t actually review the material together. 
  6. Make sure everyone is putting in a fair share of work. It really bothers me when you show up to a study session with three essay outlines and a bunch of work done and then everyone else just wants to take pictures of them without offering you anything. Stand up for yourself and make sure you aren’t getting used!

my kink is solving complex circuit matrices