Idiomatic Python implementation for finite sets, images, and preimages of finite functions?
By : Karan Prashad
Date : March 29 2020, 07:55 AM
Hope that helps For arbitrary images from a set to another, I would use a Python dictionary. For example, f(n)=n^2 on a set of {1,2,3,4}, I can do this: code :
preimage = set([1,2,3,4])
mapping = {x: x*x for x in preimage}
image = set(mapping.values())
assert set(mapping.keys()) == preimage
function = lambda x: mapping[x] # so you can now have y = function(x)
check_image = set([function(x) for x in preimage])
assert check_image == image
preimage = set([1,2,3,4])
function = lambda x: x*x
image = set([function(x) for x in preimage])
check_preimage = set([y for x in image for y in preimage if function(y)==x])
assert check_preimage == preimage
import math
preimage = set([1,2,3,4])
function = lambda x: x*x
inv_func = lambda x: int(math.sqrt(x))
image = set([function(x) for x in preimage])
check_preimage = set([inv_func(x) for x in image])
assert check_preimage == preimage

Can anyone please explain difference between finite state machine and finite automata?
By : David
Date : March 29 2020, 07:55 AM
I hope this helps you . Both "Finite State Machine" FSM and "Finite Automata" (or Finite State Automata) FA means same, represents an abstract mathematical model of computation for the class of regular languages. The word "Finite" significance the presence of the finite amount of memory in the form of the finite number of states Q (read: Finiteness of Regular Language).

Getting a random transversal for finite family of finite sets
By : shinichi2381
Date : March 29 2020, 07:55 AM
I wish did fix the issue. As Ante observes, we're looking for a bipartite matching, but the hard part here is finding a random one. If your graph is large enough, then you probably have to settle for the rapidly mixing Markov chain of Jerrum and Sinclair. Otherwise, there's an O(2^n poly(n))time dynamic program for counting maximum matchings (as opposed to the O(n!)time algorithm for enumerating them), which you can use to sample by repeatedly counting the number of matchings after either using an edge or not to match.

optim in r :non finite finite difference error
By : Jan Danvill
Date : March 29 2020, 07:55 AM
around this issue The error you ran into is because ϕ becomes negative beyond a certain number of iterations (which indicates that the constraints are not being applied correctly by the algorithm). Also, the solution does not converge to a single value but jumps between a few small values before reaching a situation where the updated covariance matrix is nolonger positive definite. At that stage you get det(v) < 0 and log[det(v)] is undefined. The optim algorithm bails out at that stage. To see what's happening, play with the maxit and ndeps parameters in the code below.

MLE error in R: nonfinite finitedifference value/ value in 'vmmin' is not finite
By : Grant Redfearn
Date : March 29 2020, 07:55 AM
wish of those help Your Loss variable is negative. In R, raising negative values to a fractional power (i.e. set$Loss^alpha where alpha is noninteger) returns NaN values. (The only general alternative is to return a complexvalued answer, which you probably don't want.) Did you mean to code Loss as positive rather than negative? Or maybe you want abs(set$Loss^alpha) ? As a general purpose debugging tip, it helps to add

