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How would I go about creating the below transfer function?
It would take two parameters:
position of bulge in range (-1.0, +1.0)
sharpness of bump
That picture only demonstrates movement in the first parameter.
I can think of a few possible approaches:
figure out a formula
Bezier curves?
start with a few points and do some kind of chain-links type physics dynamical simulation, where each link exerts a force of its neighbours, and the end links are held low, a particular link is held high
something like the above but starting out with a crude shape and filtering out high frequencies
However I can't see any simple way to set out on any of the above approaches.
Can anyone see a clean way to crack it?
Looks like a normal distribution with variable skew to me. I would look for something like that before I'd go for Bezier curves.
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I wonder if the training set should have the same resolution as the test set. I would like to make a CNN for object recognition. My dataset is much clearer than the data I found on web. The problem is that I found only 30 objects in my dataset which I could label. The data from web has labeled over 200 pictures but the resolution is worse. Here is a sample of my data and the data from web: https://imgur.com/a/pxSFU1x.
My two cents: it would definitely help if you had images with the same resolution.
When you load an image you get a matrix with a bunch of numbers for each pixel. Your neural network will try to identify patterns common to the labelled images and then look for those patterns in the test.
As the images differ thou, those patterns won't really be the same in the test dataset and this will definitely negatively affect the outcome.
A silly example would be if you are trying to identify antennas on the roof instead of the solar panels. In your image antennas have some kind of shape while in the web image they are just one pixel. This would make the testing dataset completely useless.
However, the solar panels in the two images have quite clear characteristics (shape, color, contrast, contour) and I believe you should still give it a try as the different resolution might not be extremely problematic in this case.
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So I have a lot of points, kind of like this:
animalid1;A;time
animalid1;B;time
animalid1;C;time
animalid2;A;time
animalid2;B;time
animalid2;A;time
animalid2;B;time
animalid2;C;time
animalid3;A;time
animalid3;B;time
animalid3;C;time
animalid3;B;time
animalid3;A;time
What I want to do is to first of all make R understand that the points A,B,C are connected. Then I want to get comparisons of movement from A to C and how long time it takes, how many steps were used, etc. So maybe I have a movement sequence like ABC on 20 animals and then ABABC on 10 animals and then ABCBA on 5 animals. I want to get some sort of statistical test done to see if the total time is different between these groups, and so on.
I bet this has been done before. But my Google skills are not good enough to find it.
Look at the msm package (msm stands for Multi State Model). Given observations of states at different times it will estimate probabilities of transitions and average time in the different states.
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This is a borderline question for Stackoverflow, I know, but I am looking for a package. If I can't get an answer here I will transfer to https://stats.stackexchange.com/. I am looking for a R package or a method to create a phase diagram. This means I have e.g. two variables, like air pressure and temperature, and a binary variable (to make it easier) indicating if the substance is liquid or frozen. Below you find a typical example of a phase diagram. I need to estimate the transition borders or something however just in a case with two groups. Every hint is appreciated.
I think about the closet you will get is function diagram in package CHNOSZ. There's a lot to read about in this package and it has some nice vignettes. But, it seems to calculate phase diagrams from first principles or theory. Perhaps if you look at the code for diagram you can figure out a fairly easy way to use your empirical data.
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i'd like to know how to solve a definite integral in Mathematica.
I do know all variables except b, and need to solve for F(b)=0.
How can i solve it in Mathematica?
Here is my try:
NSolve[Integrate[1/(8*(1 - ff) (2 Pi)^0.5) E^(-0.5*((x - 1.1)/(1 - ff)/8)^2), {x, 0, 9999}] == -0.44531779637243296, ff]
These integrals can be trivially expressed in terms of an error function: Wiki, Mathworld. Hence what you need here is a library to (i) calculate error functions, (ii) numerically solve non-linear equations. Virtually any language has this, so pick anything you're familiar with. In Mathematica, look up Erf and NSolve.
I'd start by plugging it into Wolfram Alpha and see what it gives you.
Mathematica should be able to do it. I think of statistics first when R comes up; I don't know about its calculus capabilities. Excel is not the first choice.
If I were you, I'd be less worried about the software and more worried about the solution itself. A function of this form might be well known. Plot each one and visually check to see what the functions look like and how easy they might be to integrate.
Like this:
http://www.wolframalpha.com/input/?i=graph+exp%28-%28%28x%2B5%29%2F1.5%29%5E2%29
You should be wondering why it's three similar looking integrals. Those singularities in the plot tell you why.
If there's no closed form solutions, you'll have to go with a numerical one. You'll have to choose an algorithm (simple Euler or Runga Kutta or something else), interval sizes, etc. You'll want to know about singular points and how best to tackle them.
Choosing a package is just the start.
You might find http://r.789695.n4.nabble.com/calculus-using-R-td1676727.html helpful.
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Suppose I have an Arabic character hand-drawn in Thuluth font, as in:
http://arabicletters.info/wp-content/uploads/1.jpg
I was thinking of a way I can recreate the same shape but at a much greater height, whilst leaving the other characteristics intact (stroke width, thickness, the relation of where the curving starts to happen to the height) which then got me curious about a way of finding its mathematical representation and play with it until I can get what I want or any other shape for that matter. Is there a math sub-specialty that can help with this? and for this particular problem, can it be solved using programs like Adobe Illustrator or AutoCAD?
Forgive the noobness.
I don't think deduce is the right word.
You can get what you want if you add sufficient points and do Bezier spline fits to match the letters.
There might be a way to automate the process of adding points, but the "sufficient" criterion is tricky. And then you'd have to tell how to connect points with splines.
Sounds like you're trying to reproduce optical character recognition in Arabic.