#How Big Data Carried Graph Theory Into New Dimensions | Explore Tumblr posts and blogs

spoonieengineer · 8 years ago

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And here I thought I’d never write an actual article of my own, and limit myself to posting pictures and reblogging other people’s stuff. But from what I’ve seen there isn’t much stuff out there for STEM students, so I guess I’ll leave here my little grain of sand.

.*DURING CLASS*.

Just the usual. Pay attention. If you have that subject’s book or powerpoint slides, print them out so you can annotate on those during class. Or if you’re like me, lacking in the attention department, disregard this tip and take your own notes. Write constantly. It helps you keep yourself engaged and not fall asleep. (Not always works. Spoonies are spoonies for a reason.)

.*TACKLING SCHOOLWORK*.

And by schoolwork I mean the practice of those more math-based subjects, since whatever involves lots of reading or essay writing, already has several guides on Tumblr and all over the Internet.

See how your homework guide is structured. If it involves lots of practice exercises from the lower level difficulty to the hardest, and specially if you’re short on time, I’d do one of the easiest first, to get familiar with the formulas, one of the middle difficulty ones, to get some thinking involved with those formulas, and then the difficult ones, because they tend to be long and use the highest amount of formulas, and incorporate important concepts that will give you a deep understanding of the subject. Plus if you know how to solve the harder ones, the rest should be easy.

If instead of following a pattern of increasing in difficulty, your exercises are splattered all over the place or are of similar difficulty, well, feel free to skip, or do them all in a row, but do as many as you can.

.*METHOD FOR SOLVING A MATH-BASED EXERCISE*.

This is useful if you’re new or got un-used to it, but most of the time you get the hang of it, and don’t need to do ALL of this so strictly:

-Read the WHOLE exercise. Sometimes important information will be at the end, or you’ll find answers in there to previous questions.

-Divide a space in two columns. In one of them, put all of the information you have. In the other one, put down all the information the exercise is asking you to find (you have to find the X? The X goes in this column. That’s what I meant.)

-FOR PHYSICS BASED SUBJECTS: if you can, make a small drawing/diagram of your situation, together with all the information you have gathered so far.

-Write down all the formulas you have to use for this part of your subject. You might not use them all for the exercise, but the act of writing them over and over again makes memorizing them easier.

-Start using those formulas, replacing the data you have in them, and all that jazz.

-IF YOU END UP WITH A BIG-ASS, LONG-ASS EQUATION: do yourself a favour. Put all the terms that have the X on them (or whatever you have to find) to the left, and all the terms that can be calculated without having to find any Xs to the right. Do it before you being calculating things to shrink the equation. This will make clearing that X so much easier, and you won’t put an X in the wrong term by accident.

.*TACKLING THE THEORY*.

For text based stuff, your usual methods for text based subjects. Pay special attention to:

-Graphs. They’re very useful visual representations of what you’re learning.

-In long demonstrations, THOSE SPECIFIC STEPS. You know them. Math demonstrations are pretty logical in nature, and easy to explain and develop out of common sense, until you reach that specific step that was pulled out of the mathematician’s ass. There’s no specific reason for it, other than adjust the dimensions of the equation, make it more neat, use a trigonometric identity they needed to put in there... The likes of “add +X sin(alpha) to both sides of the equation”. Sometimes these terms are quite long, so it’s all more important to memorize, so you don’t get lost in that specific step.

-Fall in love with mindmaps. Explain them verbally while you draw them. It helps retain information.

.*OTHER TIPS*.

-If applicable: always write down your units. If you clear your X and end up with the height of a building being 380lbs/seconds... Something went wrong.

-Keep in mind how exact you have to be in your calculations. For designing a batch of concrete, calculating everything in grams without decimals might be fine. But if you want to find out the permeability of the ground, you’ll need several decimals to get a value that actually means something.

-Use graph paper. Really.

-Have two scientific calculators if possible. One for homework, one for carrying at uni. Otherwise at some point you’ll forget your calculator for your exam.

-Fall in love with Excel.

-AutoCAD, in its official website, offers a free version for students, that is extremely complete and so far has been perfect for my engineering college career.

Well here it is. It was a bit rushed. If anyone has any more tips, or if more come to mind, I’ll add them here. Have a great study session~

#spoonieengineer #spoonie student #engineering student #studyblr #study tips #engblr #math #physics #engineering #engineer #maths #studyspo #study community #study motivation #studyspiration #studytips

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wozziebear · 4 years ago

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To illustrate the kinds of relationship that a hypergraph can tease out of a big data set — and an ordinary graph can’t — Purvine points to a simple example close to home, the world of scientific publication. Imagine two data sets, each containing papers co-authored by up to three mathematicians; for simplicity, let’s name them A, B and C. One data set contains six papers, with two papers by each of the three distinct pairs (AB, AC and BC). The other contains only two papers total, each co-authored by all three mathematicians (ABC).

A graph representation of co-authorship, taken from either data set, might look like a triangle, showing that each mathematician (three nodes) had collaborated with the other two (three links). If your only question was who had collaborated with whom, then you wouldn’t need a hypergraph, Purvine said

But if you did have a hypergraph, you could also answer questions about less obvious structures. A hypergraph of the first set (with six papers), for example, could include hyperedges showing that each mathematician contributed to four papers. A comparison of hypergraphs from the two sets would show that the papers’ authors differed in the first set but was the same in the second.

Such higher-order methods have already proved useful in applied research, such as when ecologists showed how the reintroduction of wolves to Yellowstone National Park in the 1990s triggered changes in biodiversity and in the structure of the food chain. And in one recent paper, Purvine and her colleagues analyzed a database of biological responses to viral infections, using hypergraphs to identify the most critical genes involved. They also showed how those interactions would have been missed by the usual pairwise analysis afforded by graph theory.

[...]

That’s especially clear when you try to consider a higher-dimensional version of a Markov chain, he said. A Markov chain describes a multistage process in which the next stage depends only on an element’s current position; researchers have used Markov models to describe how things like information, energy and even money flow through a system. Perhaps the best-known example of a Markov chain is a random walk, which describes a path where each step is determined randomly from the one before it. A random walk is also a specific graph: Any walk along a graph can be shown as a sequence moving from node to node along links.

But how to scale up something as simple as a walk? Researchers turn to higher-order Markov chains, which instead of depending only on current position can consider many of the previous states. This approach proved useful for modeling systems like web browsing behavior and airport traffic flows. Benson has ideas for other ways to extend it: He and his colleagues recently described a new model for stochastic, or random, processes that combines higher-order Markov chains with another tool called tensors. They tested it against a data set of taxi rides in New York City to see how well it could predict trajectories. The results were mixed: Their model predicted the movement of cabs better than a usual Markov chain, but neither model was very reliable.

How Big Data Carried Graph Theory into New Dimensions

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