I have a question that concerns visualising the output of a simple matrix. For instance, take a 4 x 10 matrix in the example attached (rows are denoted by i and columns, j) with entries either 0 or 1. This gives the on/off relationship between any i and j. Let i and j denote 2-dimensional locations whose coordinates are known. The matrix gives the connections (1's) between both locations; 0's otherwise.

Can Maple output a map that visually represents the connections between nodes?

In the example here, I wish to plot location 2 (in i) connected to location 3 (in j), location 3 (in i) connected to location 1 (in j), and so on. Can I output a plot / map that presents the nodes with radiating / connecting arrows?

I'm hoping someone can help, since the matrix form is not quite appealing for a large number of entries.

Thanks for reading!
 

Download Matrix_Plot_Question.mw

I wish to write a simple procedure to evaluate the Poisson quantile function, F, for many possible parameter values, lambda.

The Maple commands to evaluate F for individual lambda values works just fine, however, I have tried to write a simple procedure to evaluate F for prescribed lambda values (imported from Excel) but to no avail. I'm missing something quite basic, I'm sure.

Can anybody offer a suggestion please? Thanks.

Inverse_Poisson_Procedure.mw

Given any threshold value, I am interested in obtaining a quantity of interest using the inverse negative binomial distribution. This requires extracting the value from the discrete CDF and I am using the Quantile(X, threshold value) function.

The parameters of the NBD are given as r and p and the routine I have written (attached) works in some cases, but I have noticed that, for small values of p, the Maple program runs for excessive times to attempt to output the Quantile solution. For instance, if p = 0.3, the solution is fast but when p = 0.003, Maple continues to evaluate the solution with no result (I have interrupted computations after 2 hours).

In the attached example, p is set to 1.965 and r is 0.5. The threshold value is 0.98 and the associated solution, Q, for this value is determined to be Q=7.

Does anybody know how to help with this? I would be grateful for any help along the way. 

I'm hoping somebody can help with this problem.

The Poisson Loss Function is defined by the series:

L := sum((n-s)*lambda^n*exp(-lambda)/factorial(n), n = s .. infinity)

Where lambda is the mean value that is prescribed and s is the variable in question.

Now, if the value of L is given, can anyone tell me how to solve for  s?

Poisson Distribution Loss Function Tables are available and give values for s for a given lambda, so I's like to see if Maple can handle this.

Thanks for reading!

I wish to extract a minimum route in a network given both start and end positions.

Also, I wish to avoid a spur in the circuit and obtain one continuous orthogonal  path. 

As an example, take the 7-node case having 14 arcs (see worksheet) using Dijkstra's algorithm (I assume this is fit for purpose in this particular case).

Starting with node 1, the algorithm suggests the paths:

1>2>3>4>5>6>7.>8>9 and 1>2>3>4>5>10>11>12>13>14 (here, there is a spur at node 5 where the paths separate)

Is it possible obtain one minimum path?

The source node is prescribed in the routine - can anyone explain how to prescribe the end node?

Thanks for reading!

Shortest_Circuit.mw