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by Cuchulainn
Yesterday, 8:55 pm
Forum: Off Topic
Topic: Global Warming - What We Can Do (Mitigation)
Replies: 614
Views: 199212

Re: Global Warming - What We Can Do (Mitigation)

It's the only book I know where they sell soap. 
It's Ulysses, which I read when I was 16 ..found it to be very easy to  read. People overthink.
by Cuchulainn
Yesterday, 7:24 pm
Forum: Off Topic
Topic: Global Warming - What We Can Do (Mitigation)
Replies: 614
Views: 199212

Re: Global Warming - What We Can Do (Mitigation)

My bad. I read it in arabic. Rus and Russians are written the same. It was also about Russiya...
Russ ska ja
www.youtube.com/watch?v=rIYJCQwpk14
by Cuchulainn
Yesterday, 7:14 pm
Forum: Off Topic
Topic: Global Warming - What We Can Do (Mitigation)
Replies: 614
Views: 199212

Re: Global Warming - What We Can Do (Mitigation)

"depicted them as handsome people but filthy and barbaric." (m ?) "Good looking, filthy and crazy" (w ?) think then how good we look after the annual bath ;-) soon Christmas, time to buy soap! filthy goes hand in hand with low carbon foot print, you clean basXXX ! I recommend Sweney's sweet lemony ...
by Cuchulainn
Yesterday, 6:48 pm
Forum: Politics Forum
Topic: UK and the EU: In or out?
Replies: 2030
Views: 76491

Re: UK and the EU: In or out?

It has become so unpleasant that we could end up with Leavers boycotting Remainer businesses and vice versa. I'll boycott lawyers, journalists, academics, Prosecco and foie gras, etc. Although I'll make an exception for doctors! And Remainers can boycott plumbers, electricians, mechanics, farmers, ...
by Cuchulainn
Yesterday, 1:34 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12683

Re: Universal Approximation theorem

Indeed, I would be much more general than Cybenko theorem, thus much more general than any feed forward neural network, writing consider [$]\varphi(x,y)[$] any function, don't call it an activation function, because such functions are called kernels, and define the following space [$]\psi(x) \in Sp...
by Cuchulainn
Yesterday, 10:43 am
Forum: Politics Forum
Topic: All Things DUP (Democratic Unionist)
Replies: 23
Views: 2573

Re: All Things DUP (Democratic Unionist)

Thrown under the bus?

Image
by Cuchulainn
Yesterday, 10:34 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12683

Re: Universal Approximation theorem

f has to be continuous on a compact set.
Good point.
by Cuchulainn
Yesterday, 10:31 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12683

Re: Universal Approximation theorem

To really understand Cybenko and Hornik you really need to have a degree in pure mathematics (lots of Measure Theory and hard Real Analysis). CS or Physics won't cut  it!  Otherwise, how's it possible to visualise [$]L_1[$] functions which are slippery at the best of times? Here's a test of Cybenko...
by Cuchulainn
Yesterday, 10:30 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12683

Re: Universal Approximation theorem

As an activation function in an NN? I don't think so. Here is Cybenko decomposition in wikipedia. [$]\sum_{i=1}^{N}v_i\varphi \left(w_i^T x+b_i\right)  [$] I am not authorized to consider [$]\varphi(x) =1 [$] ? NO. This is a polynomial and see Theorem 3.1 of Pinkus!! This class of activation functi...
by Cuchulainn
October 17th, 2019, 8:22 pm
Forum: Off Topic
Topic: Great Funky Music
Replies: 13
Views: 1181

Re: Great Funky Music

But not everyone deserves one.

Not funky, but I thought you might like it:
https://www.youtube.com/watch?v=HSuYUItahrE
Spiddal Funky

I used to do my boating up here

www.youtube.com/watch?v=Ag99KDfF9Q8
by Cuchulainn
October 17th, 2019, 8:14 pm
Forum: Off Topic
Topic: Great Funky Music
Replies: 13
Views: 1181

Re: Great Funky Music

by Cuchulainn
October 17th, 2019, 7:30 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12683

Re: Universal Approximation theorem


It's enough to read the abstract of Cybenko's paper to answer your questions. Function A is nowhere continuous. B is alright.
Function B is not continuous at x = {0,1}.

Which activation function should we use to approximate function B?
by Cuchulainn
October 17th, 2019, 7:20 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12683

Re: Universal Approximation theorem

To really understand Cybenko and Hornik you really need to have a degree in pure mathematics (lots of Measure Theory and hard Real Analysis). CS or Physics won't cut  it!  Otherwise, how's it possible to visualise [$]L_1[$] functions which are slippery at the best of times? Oh please. Let's just re...
by Cuchulainn
October 17th, 2019, 7:03 pm
Forum: Politics Forum
Topic: Boris Johnson - the last 100 days
Replies: 192
Views: 10797

Re: Boris Johnson - the last 100 days

This is the same continuing story since 1801.

www.youtube.com/watch?v=djfX5je1uys
by Cuchulainn
October 17th, 2019, 6:30 pm
Forum: General Forum
Topic: You are back!
Replies: 8
Views: 189899

Re: You are back!

The original bad boys of QF.  Think the movie The Expendables.
I never knew the old forum before the war with its music, its glamour and easy charm.
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