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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 #25 : The p-value – 365 DoA

P-value joke showing a very confident man with this is what p less than .05 feels like printed on top of the image

It’s true!

Now it seems like we are getting somewhere. Last post we covered z-score and you can read that if you haven’t already, it might be good to familiarize yourself with it since today we are going to talk p-value and the difference between z-score and p-value. That said, let’s dive in and look at the value in the p-value.*

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Day #24 : The z-score – 365 DoA

Statistics cartoon

So if you recall from last post… well I’m not linking to it. It was hellishly personal and frankly I’m still attempting to recover from it. We’re going to take it light this time and we can do a deep dive into something in another post. For that reason, let’s talk about z-score and what exactly it is, I mean we used it in this post and never defined it formally, so let’s do that. Let’s talk z-score!*

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Day #23 : I was lucky… – 365 DoA

IMG_20130704_221101_377 (2)

This was home, for a while anyway.

Okay, so not every post has to be strictly academic. If my twitter feed is any indication yesterday was world suicide prevention day. So with a heavy heart I have not one, but two very personal stories regarding suicide. Obviously this is a content warning for those wanting to go further, we will be dealing with suicide, death, and suicidal ideation.

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Day #22 : Parametric vs. NonParametric Statistics – 365 DoA

How Mean Meme

Technically we could call this parametric statistics part 2. However, since we are covering nonparametric statistics and more importantly the difference between parametric and nonparametric statistics, it would seem that this title makes more sense. As usual with a continuation, you probably want to start at the beginning where we define parametric statistics. Ready to get started?*

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Day #21 : Defining Parametric Statistics – 365 DoA

normal-distribution

It’s halloween time, we are talking about normally distributed data, so this fits, and I don’t want to hear otherwise!

Well my lovely readers, we’ve made it to the three week mark, 5.7% of the way through! Okay maybe that doesn’t seem like a big deal written like that, but hey it’s progress. So last post we had our independence day, or rather defined what it meant to have independent events vs. dependent events. We also said it was an important assumption in parametric statistics that our events are independent, but then we realized we never defined what parametric statistics even is, oops. So let’s stop dragging our feet and talk parametric statistics!*

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Day #20 : Independent Events – 365 DoA

correlation

By: xkcd

 

Because we introduced the central limit theorem last post, it’s time to introduce another important concept. The idea of independent events, while this may seem intuitive, it is one of the assumptions we make in parametric statistics, another concept we will define, but for now let’s jump into independence.*

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Day #19 : The Central Limit theorem – 365 DoA

 

 

CLT

Well here we are again, if you recall from our last post, we talked Bonferroni Correction. You may also recall that when the post concluded, there was no real topic for today. Well after some ruminating, before we jump into more statistics, we should talk about the central limit theorem. So let’s do a quick dive into what that is and why you should know it!*

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Day #18 : The Bonferroni Correction – 365 DoA

Keep calm and do the Bonferroni corrrection

By now we are masters of statistics… right? Okay, not really, but we are getting there. So far we’ve covered two types of errors, type 1 which you can read about here, and type 2 which you can read about here. Armed with this new knowledge we can break into a way to correct for type 1 errors that come about from multiple comparisons. Sound confusing? Well, not for long, let’s break it down and talk Bonferroni.*

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Day #17 : Type 2 errors – 365 DoA

 

cat asleep

Last post we did a quick bit on type 1 errors. As with anything, there is more than one way to make an error. Today we are talking type 2 errors! They are related in the sense and we’ll go over what that means and compare the two right… now!*

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Day #16 : Type 1 errors – 365 DoA

tiny dog yawning

We did it, we cracked the coin conundrum! We managed the money mystery! We checked the change charade! We … well you get the idea. Last post we (finally) determined if our coin was bias or not. Don’t worry, I won’t spoil it for you if you haven’t read it yet. I actually enjoyed working through a completely made up problem, so if you haven’t read it, you really should. Today we’re going to talk dogs, you’ll see what I mean, so let’s dive in.*

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Day #15 : Significance, Part 3 – 365 DoA

Standard_deviation

Where does our observation fall on the probability density function?

It looks like we’ve arrived at part 3 of what is now officially a trilogy of posts on statistical significance. There is so much more to say I don’t want to quite call this the conclusion. Instead, let’s give a quick review of where we left off and we can get back to determining if an observed value is significant.*

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Day #14 : Significance, Part 2 – 365 DoA

Bar graph showing z score across trials

Z-score bar graph that I made just for all of you using some data I had laying around. If you’re new to statistics it may not make sense, but rest assured we will make sense of it all!

Well here we are two weeks into 365DoA, I was excited until I realized that puts us at 3.8356% of the way done. So if you remember from last post we’ve started our significance talk, as in what does it mean to have a value that is significant, what does that mean exactly, and how to do we find out? Today is the day I finally break, we’re going to have to do some math. Despite my best efforts I don’t think we can finish the significance discussion without it and still manage to make sense. With that, let’s just dive in.*

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Day #13 : Significance, Part 1 – 365 DoA

Normally distributed data shown using a histogram plot

Histogram of normally distributed data. It looks very… nomal. No it really is normally distributed, read on to find out what that means and how we can use it.

If you’ve read my last post I hinted that today we would discuss filtering. Instead I think I want to take this a different direction. That isn’t to say we won’t go over filtering, we most definitely will. Today I want to cover something else though, significance. So you’ve recorded your signal, took an ensemble average, and now how do we tell if it actually means something, or if you are looking at an artificial or arbitrary separation in your data (IE two separate conditions lead to no difference in your data). Let’s look at significance.*

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Day #12 : Signal, cutting through the noise – 365 DoA

example data

45 separate trials of very noisy data with the average of those trials (black). Believe it or not, this is actually very useful and very real data from something I am currently working on.

Noise, it can be troublesome. Whether you are studying and someone is being loud or you are trying to record something, noise is everywhere <stern look at people who talk during movies>. Interestingly enough the concept of noise in a signal recording sense isn’t all too different from dealing with talkative movie goers, so let’s talk noise!*

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Day #11 : Why even use the spectrogram? – 365 DoA

rotated spectrogram showing all three dimensions

A spectrogram plot rotated so we can see all three dimensions.

So you wanna use a spectrogram… but why? What does a spectrogram do that we can’t do using some other methods for signal processing? As it turns out, there is a lot of reasons you may want to use the spectrogram and today we are going to cover some of those reasons and number four may shock you! (okay not really, what do you think this is a clickbait website?)*

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Day #10 : Spectrogram vs. the banana of uncertainty – 365 DoA

banana

The banana of uncertainty (okay, it’s not a real banana)

Well ten days in and we’ve just introduced the idea of the spectrogram. While a lot of this information is just the broad strokes, I like to think that we’ve covered enough to give you a good idea about how to use these tools and what they are used for. However, we do need to discuss a limitation to the spectrogram, something called the banana of uncertainty, okay not quite the name, but you’ll see why I keep calling it that.*

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Day #9 : Reading a Spectrogram – 365 DoA

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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Day #7 : Small waves, or wavelets! – 365 DoA

Meyer Mother wavelet

This is the Meyer wave, a representation of a so-called mother wavelet function to use for the wavelet transform. Notice that it is finite!

Waves! We’re officially one week through 365 Days of Academia! Woo! 1 week down, 51(.142…) weeks left! Let’s wrap up this weeks theme (there wasn’t originally a theme, but it kind of ended up that way) by talking about other ways we can get to the frequency domain. Specifically, let’s stop the wave puns and let’s talk wavelets!*

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Day #6 : The fast and the Fourier – 365 DoA

Fourier_transform_time_and_frequency_domains_(small)

A good example of how the Fourier transform can approximate signals. The red signal is our input signal and the blue shows how the output of the Fourier transform.

Okay, if you’ve been keeping up with these posts, we know about Welch’s method, Thomson’s method, the things that make them different, and the things that make them similar. The thing that both of these transforms rely on is the Fourier transform. What is the Fourier transform? Well, something I probably should have covered first, but whatever this is my blog we do it in whatever order we feel like, so let’s dive in!*

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Day #5 : Whose window function is it anyway? – 365 DoA

Window function - funny

This is not how we use a window function on the computer…

One day someone looked at the windowed fourier transform and said, “Don’t be such a square!” and thus window functions were invented. If you believe that, then I have an island for sale, real cheap. But seriously, let’s do a dive into what a window function is and why the heck there are so many of them, because there ARE a LOT! So let’s get started!*

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Day #4 : Spectral leakage… embarrassing – 365 DoA

Day 4 - Leakage - arrows

Look at that leakage!

Leakage, it’s never a good thing. For today’s post we’re going to cover a very important topic. Spectral leakage, it’s a big reason why spectral density estimation is well, an estimation. The other reason it is an estimation is because the fourier transform is an approximation of the original signal, but the Fourier transform is a whole other post on its own. So let’s talk leakage!*

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Day #3 : Power Spectral Density Overview – 365 DoA

In our last post we introduced the two main characters in this story of spectrogram. On one end we have Welch’s method (pwelch) on the other end we have the Thomson multitaper method (pmtm). As promised here is a awful basic breakdown of why is more than one way to compute power spectral density (in fact there are several, far more than the two I’m talking about). So, let’s just dig right in!*

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Day #2 : Power Spectral Density (pmtm) – 365 Days of Academia

Day 2 - EKG

A example EKG signal

This is a (somewhat) continuation on what we were discussing in the previous post. We covered the pwelch MATLAB function, this time we will cover the PMTM function, this function uses the Thomson multitaper method to calculate power spectral density. We can do a deep dive into the differences between the two next time, but for now let’s talk about the command itself.*

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Day #1 : Power Spectral Density (pwelch) – 365 Days of Academia

EEG

Some EEG data that I’ve aligned, processed, and made look nice and pretty.

Signal processing, it’s complex, there are a million ways to go about processing a signal, and like life, there is no best way to go about doing it. Trust me, it is as frustrating as it sounds. Today’s scratch pad note is on power spectral density or PSD for short. So let’s dive in.*

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Back again with 365 Days of Academia

It’s been an awful time. dusts off the cobwebs around the blog Things have been rough, but I figure it’s time to try and blog regularly again.

So what’s new?

Robo legs - no trash2

Humanoid bipedal robot for balance testing, 100% designed and built by me!

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The power of indifference an open letter to the scientific community

indifference

Suddenly your absent-minded thoughts are shattered by a loud noise. Quickly you look around, to the left of you, you see it, and a child has been shot, you see them bleeding heavily. People are standing around with their phones, some calling emergency services, some filming, but most looking confused and scared. No one is actively trying to help; you hear that they are afraid that the person, or persons, who shot the child is still around. What do you do next, do you choose indifference, or do you help?

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Trumped: Why the election is a symptom of a bigger problem

Donald trump hands

Right now you are probably thinking that I am going to unleash some poorly thought out diatribe about president elect Trump. No, that is not going to happen. It is not going to happen because he is not the problem, you are the problem, I am the problem, and we are the problem. That goes for those of you who are atheists, Catholics, Muslims, conservatives and liberals, or anything in-between.

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The science behind real life zombies

zombies ahead

In the spirit of Halloween we bring you the science fact and fiction behind the undead. Zombies, those brain loving little guys, (and girls) are everywhere. Sure, we are all familiar with the classic  zombie, but did you know that we aren’t the only zombie lovers out there? It turns out that nature has its own special types of zombies, but this isn’t a science fiction movie, this is science fact! Sometimes fact can be scarier than fiction, so let’s dive in.

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Study uncovers brain changes in offending pedophiles

pedophiles

New research reveals that certain alterations in the brain may be present in pedophiles, with differences between hands-on offenders and those who have not sexually offended against children.

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Your BMI might affect your brain function

brain wieght

There are plenty of reasons it’s important to maintain a healthy weight, and now you can add one more to the list: It may be good for your brain. Researchers have found that having a higher body mass index, or BMI, can negatively impact cognitive functioning in older adults.

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Red meat and organs may pose a significant health hazard

cooked steak

Neu5Gc, a non-human sialic acid sugar molecule common in red meat that increases the risk of tumor formation in humans, is also prevalent in pig organs, with concentrations increasing as the organs are cooked, a study has found. The research suggests that Neu5Gc may pose a significant health hazard among those who regularly consume organ meats from pigs.

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A new view of the immune system

t cells

Pathogen epitopes are fragments of bacterial or viral proteins. Attached to the surface structure of cells, they prompt the body’s immune system to mount a response against foreign substances. Researchers have determined that nearly a third of all existing human epitopes consist of two different fragments. Known as ‘spliced epitopes’, these types of epitopes have long been regarded as rare. The fact that they are so highly prevalent might, among other things, explain why the immune system is so highly flexible.

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Oligodendrocyte selectively myelinates a particular set of axons in the white matter

axon

There are three kinds of glial cells in the brain, oligodendrocyte, astrocyte and microglia. Oligodendrocytes myelinate neuronal axons to increase conduction velocity of neuronal impulses. A Japanese research team found a characteristic feature of oligodendrocytes that selectively myelinate a particular set of neuronal axons.

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Cold medicine could stop cancer spread

cold medicine

Bladder cancer is the seventh most common cancer in males worldwide. Every year, about 20,000 people in Japan are diagnosed with bladder cancer, of whom around 8,000–mostly men–succumb to the disease. Bladder cancers can be grouped into two types: non-muscle-invasive cancers, which have a five-year survival rate of 90 percent, and muscle-invasive cancers, which have poor prognoses.

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Female brains change in sync with hormones

brain

Although it has already been known for some time that the brain does not remain rigid in its structure even in adulthood, scientists have recently made a surprising discovery. The brain is not only able to adapt to changing conditions in long-term processes, but it can do this every month.

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Untangling a cause of memory loss in neurodegenerative diseases

memory loss

Tauopathies are a group of neurodegenerative disorders, including Alzheimer’s disease that are characterized by the deposition of aggregates of the tau protein inside brain cells. A new study reveals that the cutting of tau by an enzyme called caspase-2 may play a critical role in the disordered brain circuit function that occurs in these diseases.

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High cholesterol triggers mitochondrial oxidative stress leading to osteoarthritis

knee problems

High cholesterol might harm more than our cardiovascular systems. New research using animal models suggests that high cholesterol levels trigger mitochondrial oxidative stress on cartilage cells, causing them to die, and ultimately leading to the development of osteoarthritis.

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Vitamins A and C help erase cell memory

epigenetics

Vitamins A and C aren’t just good for your health, they affect your DNA too. Researchers have discovered how vitamins A and C act to modify the epigenetic ‘memory’ held by cells; insight which is significant for regenerative medicine and our ability to reprogramme cells from one identity to another.

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Doc versus machine

webMD cancer scare

Increasingly powerful computers using ever-more sophisticated programs are challenging human supremacy in areas as diverse as playing chess and making emotionally compelling music. But can digital diagnosticians match, or even outperform, human physicians? The answer, according to a new study, is “not quite.”

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New sensor material could enable more sensitive readings of biological signals

transhuman

High-tech prosthetics, computers that are controlled by thought, the ability to walk or even move again, these are just a few of the promises of technology. Unfortunately, while the tech is — mostly — up to the challenge, getting the biology side of things to cooperate has been difficult at best, but that could change. Now, scientists have created a material that could make reading biological signals, from heartbeats to brainwaves, much more sensitive.

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Concentrating on the social billions

social media

Using online social media does not lead to long-term problems with our ability to concentrate, according to new research. We are social animals, so it is really no surprise that billions of us now use online tools to communicate, educate and inform each other. The advent of social media and social networking has nevertheless been phenomenally rapid.

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First demonstration of brain-inspired device to power artificial systems

memristor

New research has demonstrated that a nanoscale device, called a memristor, could be used to power artificial systems that can mimic the human brain. Artificial neural networks (ANNs) exhibit learning abilities and can perform tasks which are difficult for conventional computing systems, such as pattern recognition, on-line learning and classification.

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