## Do shaman minds lose their spirit abilities as they transform?

Transforming a creature causes it to lose extraordinary and supernatural abilities that depend on the shape and class characteristics that depend on the shape.

Are the animal abilities of a shaman falling within the range of abilities lost through transformation?

## Color – Transform 2D points into a regular grid or grid

I've generated a series of points in 2D by a `DimensionReduce` on a list of colors:

``````colors = RandomColor(100);
coords = DimensionReduce(colors, 2, Method -> "TSNE");
ListPlot(Thread(Style(coords, colors, PointSize -> .05)))
``````

However, I would like to arrange these points in a regular 2D grid (or other grid) while preserving the neighborhoods as much as possible to achieve the following:

(This is just a model)

Is there a function to provide this transformation? Or do I rather write something to mix the colors in a grid to minimize the distances between the neighbors? Here is my rough attempt of such a process:

``````dm = DistanceMatrix(colors, DistanceFunction -> ColorDistance);
g = System`GridGraph({10, 10}, VertexSize -> .8);
vneighbors =
GatherBy(Position(adj // Normal, 1), First)((;; , ;; , 2));
vlabels = Range(100);
Fold(SetProperty({#1, #2},
VertexStyle -> colors((vlabels((#2))))) &, g, Range(100))
``````

``````Do(
While({swapi, swapj} = RandomInteger({1, 100}, 2); swapi == swapj);
cost = Total@
dm((vlabels((swapi)), vlabels((vneighbors((swapi)))))) +
Total@dm((vlabels((swapj)), vlabels((vneighbors((swapj))))));
swapcost =
Total@dm((vlabels((swapj)), vlabels((vneighbors((swapi)))))) +
Total@dm((vlabels((swapi)), vlabels((vneighbors((swapj))))));
If(cost > swapcost, temp = vlabels((swapi));
vlabels((swapi)) = vlabels((swapj)); vlabels((swapj)) = temp),
10000);
Fold(SetProperty({#1, #2},
VertexStyle -> colors((vlabels((#2))))) &, g, Range(100))
``````

Is this the best solution to the problem? There has to be something cleverer that Mathematica can give me.

## nt.number theory – Fourier transform of \$ I_Y \$, \$ Y = { text {numbers with many prime factors} } \$

To let $$Y$$ Let be the set of integers $$N with more than $$D log log N$$ Prime factors. We can think, say, $$D = ( log log N) ^ {1- epsilon}$$,

We have pretty accurate approximations for the size of $$Y$$ (I am aware of Chapter II.6 in Tenenbaum's book and the references it contains.) I wonder what work is available there for the Fourier transform $$widehat {1_Y}$$ the characteristic function of $$Y$$,

I would expect $$widehat {1_Y}$$ To have tips on the main arches (ie bows around rations $$a / q$$ with a small denominator). That's because $$Y$$ is obviously "biased towards divisibility" and should therefore be slightly over-represented in the congruence class $$0$$ mod $$d$$ given for everyone $$d$$, relative to other congruence classes mod $$d$$,
A back-of-the-envelope calculation suggests that the value at the peak is around $$a / q$$ should be roughly proportional $$c ^ { omega (q)} / q$$, But what is known?

## Fourier analysis – Fourier transform frequency

One possibility is the `FourierParameters`

``````  FourierTransform(1, x, w, FourierParameters -> {0, -2*Pi})
``````

``````  FourierTransform(Exp(I a x), x, w, FourierParameters -> {0, -2*Pi})
``````

Compare

``````funs = {1, DiracDelta(x), Exp(I a x), Cos(a x), Sin(a x)};
result= {#, FourierTransform(#, x, w, FourierParameters -> {0, -2*Pi})}& /@ funs;
Prepend(result, {"f(x)","Fourier transform unitary, ordinary frequency"});
Grid(%, Frame -> All)
``````

With wikis second column:

## Ordinary Differential Equations – Problem with mixed initial end value data using the Laplace transform:

I am trying to solve a second-order ODE with the Laplace transform, where the initial values ​​are given at different times:

$$y & # 39; & # 39; (t) + y (t) = r (t), y (0) = 0, y (( pi) = 1$$ 

$$r (t) = t, t <1$$

$$r (t) = 0, t> 1$$

With the Laplace on both sides you get:

$$s ^ 2 mathcal {L} y -sy (0) -y & # 39; (0) + mathcal {L} y = mathcal {L} r$$
$$(s ^ 2 +1) mathcal {L} y = mathcal {L} r + y (0)$$
$$mathcal {L} y = frac { mathcal {L} r} {s ^ 2 +1} + frac {y ((0)} {s ^ 2 +1}$$

I know how to find the inverse Laplace transform of:
$$frac { mathcal {L} r} {s ^ 2 +1}$$

and I know that too

$$mathcal {L} ^ {- 1} ( frac {y ((0)} {s ^ 2 +1}) = y & # 39; (0) sin (t)$$

But I do not know how to find the constant $$y & # 39; (0)$$or if there's anything else I need to do, help would be very grateful!

## Can there be an algorithm faster than the fast Fourier transform to square a polynomial?

FFT is a fast algorithm for multiplying two polynomials, but if it is a square (ie, the polynomial multiplied by itself), can we find something better? (I have reached a paper by Jaewook Chung and M. Anwar Hussain and then something known as the Toom-Cook algorithm, but can no longer find any claims.)

## Fourier Transform – Use of FFT in the following convolution in a simulation

I have the following convolution as part of a numerical simulation.

$$T (r) = int d ^ 3r_2 p (r_2) f (r_2) alpha (r-r_2)$$

My problem is that the analytic expressions for $$f$$ and $$p$$ exist however, I have the expression for $$alpha$$ only in the Fourier domain in the form of $$alpha (k)$$, I intended to rate as follows:

1. Construct a grid with the grid of $$100 times100 times100$$ With mesh and linspace in numpy
``````ran = linspace(-1,1,N_r)
x,y,z = meshgrid(ran,ran,ran) #position space
``````
1. Construct the components xf, yf, zf in the Fourier domain from x, y, z
``````xf = fftn(x)
yf = fftn(y)
zf = fftn(z)
``````
1. Find the Fourier transform of $$f (r) times p (r)$$ With FFTn in numpy
2. Multiply it with $$alpha (k)$$
3. Take the inverse Fourier transformation with you ifftn in numpy.

I'm not sure if the above method works, and in fact I could not validate it properly. I've tried using scipy.ndimage.convolve to compare the results with the inverse Fourier transform of the product in the Fourier domain. Is it correct what I do with the code? And is there a way to check if a method works by using a simpler example?

Try to check:

I tried the following to test the theory. Seems like it would not work. I expect the result RES_1 and res_2 be equal. I also used the function real cut off the tiny imaginary part that results from that FFTn and ifftn functions.

``````x = linspace(-1,1,10)
xf = fftn(x)

def f(x):
return x**2+x**3*sin(x)

def g(k):
return k**2+k**3/(3-k**2)

g_k = g(xf)
g_x = real(ifftn(g_k))

res_1 = img_con(g_x,f(x))

res_2 = real(ifftn(g(xf)*fftn(f(x))))

print(res_1)
print(res_2)
``````

Am I doing something wrong?

## typescript – Submit the form and transform the model to match the backend

I have different models in frontend and backend. When I submit a form in the frontend, I have to transform this object to match the backend model. Is there a better way than this:

``````submit(confirmed: boolean) {
this.transformCreditCardModel(confirmed);
this.dialogRef.close({
success: confirmed,
productAdjustment: confirmed === true ? this.exposuresForm.value : null
});
}

private transformCreditCardModel(confirmed: boolean) {
const product = this.exposuresForm.value;
if (confirmed && product.hasOwnProperty(ExposuresFieldNamesEnum.creditCardProductIdentification)) {
const prefix = product.creditCardProductIdentification.accountPrefix;
const number = product.creditCardProductIdentification.accountNumber;
delete product.creditCardProductIdentification.accountNumber;
delete product.creditCardProductIdentification.accountPrefix;
product.creditCardProductIdentification.cardNumber = prefix + this.CREDIT_CARD_MASK + number;
}
}
``````

I do not like the part where I ask if the object contains a property, if so, then I create a new one and delete the old one. Is there a better way to do this?

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## The inverse Fourier transform of a given function

I would like to perform an inverse Fourier transform of the following function:

$$mathcal {F} _t ^ {- 1} ( exp left (- frac { log ^ 2 (t)} {2 sigma ^ 2} right)) (t)$$