Because I squared, I multiplied the second derivative of y with respect I multiplied it times itself.

If pixels are negative, we just ignore the negative sign and map back to the absolute value.

No? Nonlinear equations?

How about our Gaussian kernel that we discussed in class of size 5 by 5?

First is our gradient kernel here minus 1, 1.

These are the x values, these are y values.

Now the second thing we have to figure out is this linear or is this a non linear differential equation?

And hopefully it will recognize that that is a car.

(Laughter)

You have your order, so what is the order of my differential equation?

It's ordinary, because we only have a regular derivative, no partial derivatives here.

liter

linear

lightyears

Linear

Linear Sweep

Y linear

Linear Scale

Now, all of the sudden, I have a non linear differential equation.

We talked about the gradient magnitude kernel, which was defined over a square root of the squares of the image gradients.

This answer is not at all trivial, and I don't blame you if you get it wrong.

We have an imager of a certain size and like to calculate just the average brightness of all the individual image pixels.

If they're not, then we're dealing with a non linear function.

Obviously, it's impossible to put a line through the data points over here.

Another example of a non linear equation is if I wrote y times the second derivative of y with respect to x is equal to sine of x.

There clearly is a data fit that is not linear that might be better, like this one over here.

Once again, we have a case where we can play Occam's razor.

Linear

Linger after solving

Linear motion

To sum up, whatever we see on the screen is in this nonlinear gamma space.

Addition is linear.

And why a linear function? Well, sometimes we'll want to fit more complicated, perhaps non linear functions as well.

I capture the essence of the data.

So this activation function in the neuronetro terminology, this is just another term for that function for that non linearity g of z, equals 1 over 1 plus e to the negative z.

And then of course it drops of quickly. But that obvious, obviously a function that's not linear.

They tell us, the scientists do, that the Earth's climate is a nonlinear system.

Reset curve to linear

In fact, let me write that down.

And if I plug the data, 6 goes to 7, just about here, 2 to 3, 1 to 2, and 1 to 0, not surprisingly this data is in fact, linear.

I'll, I'll show you in a scatter plot in a moment.

And I'll quickly review the linear algebra you need in order to implement and use the more powerful versions of linear regression.

And it turns out that those are correlated with super massive black holes as well.

La Scie

In the new industrial revolution extractive must be replaced by renewable