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We're a little crazy, about science!

Posts tagged “mathematics

Day #32 : The Laplace p.d.f. – 365 DoA

laplace plot

The laplace p.d.f with a θ = 0.

Well here we are again… maybe unless you’re new, in which case welcome. If you are just joining us we are talking p.d.f. no not the file format, the probability density function version. If you’re new, you may want to start back here(ish) If not, then let’s talk the strangely similar laplace distribution.*

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Day #31 : The Exponential p.d.f. – 365 DoA

Exponential_probability_density

Today we are talking this guy! The exponential p.d.f and its C.D.F.

Well, it has been a week, don’t even get me started. But if you’re here you don’t want to hear me complain about my week, that isn’t why we come together! Well today let’s do a bit of a dive into the exponential p.d.f. I hope you’ve brushed up, because this is going to get interesting.*

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Day #30 : Confidence Interval – 365 DoA

Confidence intervals

Yep, we’re talking confidence!

Day 30 already! Where does the time go? It feels like we just started this whole project and it probably wouldn’t be a good idea to look at the remaining time to completion, so let’s not and just enjoy the nice round 30. We will get back to our p.d.f another day, but today is going to be short. That’s what I usually say before typing out 10 pages worth of information so to avoid that, let’s touch on something important, but something I can do briefly. Today we’re talking about confidence intervals*

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Day #29 : Probability density functions, Part 3 – 365 DoA

gaussian CDF vs pdf

Don’t be scared, we’re going to tackle this guy today!

Well, apparently you guys really appreciated my probability density function posts. It’s good to see people interested in something a little less well-known (at least to me). So for those of you just joining us, you’ll want to start at part 1 here. For those of you who are keeping up with the posts, let’s review and then look at specific functions. Namely let’s start by going back to our gaussian distribution function and talk about what’s going on with that whole mess. It will be fun, so let’s do it!*

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Day #28 : Cumulative Distribution Functions – 365 DoA

Exponential_distribution_cdf

An example C.D.F. of an exponential distribution

Today we were going to do another deep dive into the p.d.f and C.D.F. relationship. Specifically today we were going to talk about specific p.d.f. functions and why we use them, however… I am not doing so hot today, so instead we are going to back track just a bit and talk about what how a C.D.F. differs from our p.d.f. even though we kind of covered it, it would be nice to be clear and I can do this in a (fairly) short post for the day. So that said, let’s get started and we will pick up our p.d.f. discussion next time (maybe).*

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Day #27 : Probability density functions, Part 2 – 365 DoA

PDF_CDF

Today we are looking at our p.d.f. (yes this image has p.d.f. written as PDF, please don’t be confused!) and our C.D.F.’s let’s do this!

Oh hi didn’t see you there. Today is part 2 of the probability density functions notes (posts?), whatever we are calling these. You can read part 1 here as you should probably be familiar with the (super confusing) notation we use to describe our p.d.f. and our C.D.F. now that we’ve given that lovely disclaimer, let’s look once again at probability density functions!*

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Day #26 : Probability density functions, Part 1 – 365 DoA

statisics jokes

Dashing dreams one comic at a time, via Saturday Morning Breakfast Cereal 

We are well on our way to wrapping up week 4, what a ride it’s been! It’s been a long day for me, so today might be short. However, I really, really, really want to break into probability density functions. This topic is going to be a bit more advanced than some of the things we’ve covered (IE more writing) so it will most definitely be broken up. Let’s look at why and discover the wonderful weirdness of probability density functions!*

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Day #9 : Reading a Spectrogram – 365 DoA

rotated spectrogram showing all three dimensions
other example

Definitely not the same spectrogram as yesterday, no really look. Now for the part where I tell you how to read this thing…

Last post we introduced a new tool in our arsenal of signal processing analysis, the spectrogram. Without knowing how to read it, it just looks sort of like a colored mess. Don’t get me wrong, it is an interesting looking colored mess, but a mess nonetheless. Well today we are going to talk about how to interpret the plot and why exactly we would ever use this seeming monstrosity.*

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Day #8 : The Spectrogram Function – 365 DoA

Spectrogram

Example spectrogram from some data I had recently processed

To (somewhat) continue with our signal processing theme that we have going on at the moment, over the next few days, let’s look at something called the spectrogram. It’s three dimensions of fun!*

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Physicists retrieve ‘lost’ information from quantum measurements

quantum mechanics

quantum mechanics

Typically when scientists make a measurement, they know exactly what kind of measurement they’re making, and their purpose is to obtain a measurement outcome. But in an “unrecorded measurement,” both the type of measurement and the measurement outcome are unknown.

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The music of the mind: throwing light on human consciousness

New theory linking brain activity to brain shape could throw light on human consciousness

New theory linking brain activity to brain shape could throw light on human consciousness

UNSW Australia scientists have shown that complex human brain activity is governed by the same simple universal rule of nature that can explain other phenomena such as the beautiful sound of a finely crafted violin or the spots on a leopard. The UNSW team has identified a link between the distinctive patterns of brain function that occur at rest and the physical structure of people’s brains.

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Beam me up! Teleporting the memory of an organism

Physicists propose the first scheme to teleport the memory of an organism
Physicists propose the first scheme to teleport the memory of an organism

LLAP, Leonard Nimoy

In “Star Trek”, a transporter can teleport a person from one location to a remote location without actually making the journey along the way. Such a transporter has fascinated many people. Quantum teleportation shares several features of the transporter and is one of the most important protocols in quantum information.

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Computing with time travel

Computing with time travel

Computing with time travel

Why send a message back in time, but lock it so that no one can ever read the contents? Because it may be the key to solving currently intractable problems. It turns out that an unopened message can be exceedingly useful. This is true if the experimenter entangles the message with some other system in the laboratory before sending it.

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Anyone hear the new Taylor Shift song?

Since I’m apparently feeling a little punny…

Taylor shift


Suicide and skin color, or how being black is killing you

Racism, it takes many forms

The great racial divide, despite all the evidence showing that racism, hate and frankly plain stupidity is alive and well, there are people who cannot accept it. This probably will not change anything for those people, but for the first time a new study shows that while suicide rates in children younger than 12 have remained steady for the past 20 years, there are significantly higher suicide rates among black children.

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Black hole hunters tackle a cosmic conundrum

Henize 2-10 galaxy

Image credit goes to : NASA

While mass media was busy misquoting Stephen Hawking and arguing about black holes, astrophysicists have been hard at work trying to solve still unanswered questions about them. Now a team has not only proven that a supermassive black hole exists in a place where it isn’t supposed to be, but in doing so have opened a new door to what things were like in the early universe.

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