MATLAB: Generalization of Catalan’s conjecture

catalan's conjectureMATLAB

I would like to have a simple MATLAB code that can give the solutions for the generalization of the Catalan's conjecture for a given n.

This conjecture and the generalization can be found in the following link

https://en.wikipedia.org/wiki/Catalan%27s_conjecture

The link includes a table with the solutions I would like to get with a code.

Best Answer

You may explore File Exchange for solutions or related code from which you can build your own solution.

If you are attempting to come up with your own algorithm, have a look at 'factorIntegerPower'

https://in.mathworks.com/help/symbolic/factorintegerpower.html

You can use that to find all the perfect powers in a given sequence of numbers as follows:

a = 1:100;
b = findIntegerPower(a);
result = a(a~=b);   % +result is a row vector containing all the perfect powers in the given range.

This can be a starting point for your solution.

Hope it helps!

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MATLAB: Feedforward Network and Backpropagation

Use the default trn/val/tst ratio 0.7/0.15/0.15 or choose 0.6 <= Ntrn/N <= 0.7 with Ntst = Nval.

 [ I N ] = size( x )    % [ 16 3900 ]
 [ O N ] = size(t)      % [ 1  3900 ]
 Ntst = round(0.15*N)   % 2730
 Nval = Ntst            % 585

 Ntrn = N-Nval-Ntst      % 585

% My questions are: 1) I'm using patternnet default 'tansig' in both the hidden and output layers with 'mapminmax' and 'trainlm'. I'm interpretting the output by thresholding on y . 0>=0.5

 UGH.
 1. That doesn't make any sense since the range of tansig is (-1,1).
 2. The advice in help/doc/type patternnet all conflict
 3. Use { 'tansig' logsig } with mapstd or mapminmax(the default) inputs
 4. Use 'trainscg' for unipolar binary targets {0,1}
 5. class = 1+ round(net(x)). Can modify if have unequal priors and/or 
    unequal misclassification costs.
 6. Can use softmax for more than 2 classes. MATLAB now has the 
    derivative for softmax
 7. Use a val set with round(0.15*N) <= Nval = Ntst <= round(0.2*N) 
 8. Use MSEgoal = max( 0, 0.01*Ndof*MSE00a/Ntrneq)
      a. MSE00a = mean(var(t')) 
      b. Ntrneq = round(0.7*prodsize(t)) % ~ No. of training equations
      c. Ndof = Ntrneq-Nw  % No. of estimation degrees-of-freedom(See Wikipedia)
      d. Nw = (I+1)*H+(H+1)*O % No. of unknown weights to estimate    
 9. Stopping on any misclassification rate cannot be done unless
    a. Either the training is broken up into a loop of few epochs at a time 
       with breaks to check the classification rate
     b. Or patternnet is modified 
     c. It's not worth the time(a) or effort (b).
     d. If you disagree, please send me a copy of your code.
 10. Dividetrain is only useful if Ntrn >> Nw and the generalization error  
     is estimated using the DOF adjusted value Ntrneq*MSE/Ndof. 
     Unfortunately, MATLAB does not allow Nval = 0, Ntst > 0. The closest 
     fudge that I can think of is Nval = 1 (ratio = 1/N) , max_fail = inf.
 11. I find a good value for the number of hidden nodes, H, by using an  
     outer loop over j = Hmin:dH:Hmax and an inner loop over random weight 
     intializations i = 1:Ntrials with Ntrials ~ 10 and 
     Hmax <= Hub = -1+ceil( (Ntrneq-O)/(I+O+1))
 12. Nw > Ntrneq and Ndof < 0 when H > Hmax.

Hope this helps.

Thank you for formally accepting my answer

Greg

PS I have many examples in comp.ai.neural-nets and comp.soft-sys.matlab.

MATLAB: How to read Text from HTML file

Try something like this:

url = 'http://www.example.com/';
html = urlread(url);
% Use regular expressions to remove undesired markup.
txt = regexprep(html,'<script.*?/script>','');
txt = regexprep(txt,'<style.*?/style>','');
txt = regexprep(txt,'<.*?>','')

Once you have all the HTML, you can sift out the style and script blocks. Then remove any remaining tags and the result is reasonably clean. It won't be perfect, but it's easy to tune from here.

Best Answer

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MATLAB: How to read Text from HTML file

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