I want to implement the following equation given in a paper “A Three-Layered Mutually Reinforced Model for
Personalized Citation Recommendation” (Page 4). According to the description in the paper, B should be a square matrix, whereas I am getting a vector.
I have tried the following code:
querySplit = query.split(',')
queryText = querySplit[0]
qt_tag = word_tokenize(queryText.rstrip().lower().translate(translator))
qt_vector = model.infer_vector(qt_tag)
def eq_b(query):
vecs = np.asarray(
[spatial.distance.cosine(spatial.distance.cosine(query, model.docvecs[i]), model.docvecs[i]) for i in
range(Docs_len)])
return vecs / vecs.sum()
b = eq_b(qt_vector)
print("B", b)
The formula you wrote for B is not correct. From the paper, B*Rt_p is equal to what you have, but not B itself. This means that the actual formula for the matrix is:
B=np.matmul(eq_b(qt_vector),transpose(Rt_p))/norm(Rt_p)^2
You basically add that extra stuff so that when you do the multiplication with Rt_p, all the terms involving Rt_p are cancelled and you are left with eq_b(qt_vector). The cancellation is due to the fact that
transpose(Rt_p)*Rt_p ==norm(Rt_p)^2
I am having problem with this problem.
Let A = {〈N1, N2〉 | N1 and N2 are NFAs and L(N1) ∩ L(N2) =∅}. Show that A is decidable.
Any help is appreciated.
Given an input , here is an algorithm that determines whether L(N1) ∩ L(N2) =∅:
determinize N1 and N2 into D1 and D2 using the powerset construction. slow, but effective.
intersect D1 and D2 into M using the Cartesian product machine construction.
minimize M into M' using some DFA minimization algorithm
see whether M' has an accepting state. if so, halt-reject; otherwise, halt-accept.
This is an effectively computable procedure for determining inclusion and/or exclusion from the set, so the set is decidable.
I am dealing with a problem which is a variant of a subset-sum problem, and I am hoping that the additional constraint could make it easier to solve than the classical subset-sum problem. I have searched for a problem with this constraint but I have been unable to find a good example with an appropriate algorithm either on StackOverflow or through googling elsewhere.
The problem:
Assume you have two lists of positive numbers A1,A2,A3... and B1,B2,B3... with the same number of elements N. There are two sums Sa and Sb. The problem is to find the simultaneous set Q where |sum (A{Q}) - Sa| <= epsilon and |sum (B{Q}) - Sb| <= epsilon. So, if Q is {1, 5, 7} then A1 + A5 + A7 - Sa <= epsilon and B1 + B5 + B7 - Sb <= epsilon. Epsilon is an arbitrarily small positive constant.
Now, I could solve this as two completely separate subset sum problems, but removing the simultaneity constraint results in the possibility of erroneous solutions (where Qa != Qb). I also suspect that the additional constraint should make this problem easier than the two NP complete problems. I would like to solve an instance with 18+ elements in both lists of numbers, and most subset-sum algorithms have a long run time with this number of elements. I have investigated the pseudo-polynomial run time dynamic programming algorithm, but this has the problems that a) the speed relies on a short bit-depth of the list of numbers (which does not necessarily apply to my instance) and b) it does not take into account the simultaneity constraint.
Any advice on how to use the simultaneity constraint to reduce the run time? Is there a dynamic programming approach I could use to take into account this constraint?
If I understand your description of the problem correctly (I'm confused about why you have the distance symbols around "sum (A{Q}) - Sa" and "sum (B{Q}) - Sb", it doesn't seem to fit the rest of the explanation), then it is in NP.
You can see this by making a reduction from Subset sum (SUB) to Simultaneous subset sum (SIMSUB).
If you have a SUB problem consisting of a set X = {x1,x2,...,xn} and a target called t and you have an algorithm that solves SIMSUB when given two sets A = {a1,a2,...,an} and B = {b1,b2,...,bn}, two intergers Sa and Sb and a value for epsilon then we can solve SUB like this:
Let A = X and let B be a set of length n consisting of only 0's. Set Sa = t, Sb = 0 and epsilon = 0. You can now run the SIMSUB algorithm on this problem and get the solution to your SUB problem.
This shows that SUBSIM is as least as hard as SUB and therefore in NP.
In my situation I have territory objects. Each territory knows what other territories they are connected to through an array. Here is an visualization of said territories as they would appear on a map:
If you were to map out the connections on a graph, they would look like this:
So say I have a unit stationed in territory [b] and I want to move it to territory [e], I'm looking for a method of searching through this graph and returning a final array that represents the path my unit in territory [b] must take. In this scenario, I would be looking for it to return
[b, e].
If I wanted to go from territory [a] to territory [f] then it would return:
[a, b, e, f].
I would love examples, but even just posts pointing me in the right direction are appreciated. Thanks in advance! :)
Have you heard of Breadth-First Search (BFS) before?
Basically, you simply put your initial territory, "a" in your example, into an otherwise empty queue Q
The second data structure you need is an array of booleans with as many elements as you have territories, in this case 9. It helps with remembering which territories we have already checked. We call it V (for "visited"). It needs to be initialized as follows: All elements equal false except the one corresponding to the initial square. That is for all territories t, we have V[t] = false, but V[a] = true because "a" is already in the queue.
The third and final data structure you need is an array to store the parent nodes (i.e. which node we are coming from). It also has as many elements as you have territories. We call it P (for "parent") and every element points to itself initially, that is for all t in P, set P[t] = t.
Then, it is quite simple:
while Q is not empty:
t = front element in the queue (remove it also from Q)
if t = f we can break from while loop //because we have found the goal
for all neighbors s of t for which V[s] = false:
add s into the back of Q //we have never explored the territory s yet as V[s] = false
set V[s] = true //we do not have to visit s again in the future
//we found s because there is a connection from t to s
//therefore, we need to remember that in s we are coming from the node t
//to do this we simply set the parent of s to t:
P[s] = t
How do you read the solution now?
Simply check the parent of f, then the parent of that and then the parent of that and so on until you find the beginning. You will know what the beginning is once you have found an element which has itself as the parent (remember that we let them point to itself initially) or you can also just compare it to a.
Basically, you just need a empty list L, add f into it and then
while f != a:
f = P[f]
add f into L
Note that this obviously fails if there exists no path because f will never equal a.
Therefore, this:
while f != P[f]:
f = P[f]
add f into L
is a bit nicer. It exploits the fact that initially all territories point to themselves in P.
If you try this on paper with you example above, then you will end up with
L = [f, e, b, a]
If you simply reverse this list, then you have what you wanted.
I don't know C#, so I didn't bother to use C# syntax. I assume that you know it is easiest to index your territories with integers and then use an array to access them.
You will realize quite quickly why this works. It's called breadth-first search because you consider only neighbors of the territory "a" first, with trivially shortest path to them (only 1 edge) and only once you processed all these, then territories that are further away will appear in the queue (only 2 edges from the start now) and so on. This is why we use a queue for this task and not something like a stack.
Also, this is linear in the number of territories and edges because you only need to look at every territory and edge (at most) once (though edges from both directions).
The algorithm I have given to you is basically the same as https://en.wikipedia.org/wiki/Breadth-first_search with only the P data structure added to keep track where you are coming from to be able to figure out the path taken.
I have a code in Gnu Mathprog for an energy model:
s.t.EBa1_RateOfFuelProduction1{r in REGION, l in TIMESLICE, f in FUEL, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR: OutputActivityRatio[r,t,f,m,y] <> 0}:
RateOfActivity[r,l,t,m,y]*OutputActivityRatio[r,t,f,m,y] = RateOfProductionByTechnologyByMode[r,l,t,m,f,y];
s.t.EBa4_RateOfFuelUse1{r in REGION, l in TIMESLICE, f in FUEL, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR: InputActivityRatio[r,t,f,m,y]<>0}:
RateOfActivity[r,l,t,m,y]*InputActivityRatio[r,t,f,m,y] = RateOfUseByTechnologyByMode[r,l,t,m,f,y];
I want to put these two constraints in one, and i am thinking to insert two conditional expressions(if).The first if, will be referred to technology(t) and fuel(f)where the OutputActivityRatio<>0 and the second one for the same technology(t) it will start checking again the f(fuels) to see if the InputActivityRatio<>0.
Like that:
s.t.RateOfProduction{r in REGION, l in TIMESLICE, f in FUEL, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR: OutputActivityRatio[r,t,f,m,y] <>0}:
RateOfActivity[r,l,t,m,y]*OutputActivityRatio[r,t,f,m,y] = RateOfProductionByTechnologyByMode[r,l,t,m,f,y]
If InputActivityRatio[r,t,ff,m,y]<>0 then
RateOfActivity[r,l,t,m,y]*InputActivityRatio[r,t,f,m,y] = RateOfUseByTechnologyByMode[r,l,t,m,f,y]
else 0
else 0 ;
My question is: is it possible to have two if in series (nested if) and between them to have an equation as well?How can I write something like that?
Thank you very much!
As described in your other Question (regarding nested if-then-else in mathprog) there are no If-Then-Else statements in mathprog. The workaround with conditional for-loops is also no solution for your problem, since you can only use them in pre- or post processing of your data (you can't use this in your constraints!).
But there are still possibilities to merge your constraints. I think something like the following would work, if your condition is that either Input or Output is 0.
s.t.RateOfProduction{r in REGION, l in TIMESLICE, f in FUEL, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR}:
(RateOfActivity[r,l,t,m,y]*OutputActivityRatio[r,t,f,m,y])
+ (RateOfActivity[r,l,t,m,y]*InputActivityRatio[r,t,f,m,y])
= RateOfProductionByTechnologyByMode[r,l,t,m,f,y];
Here in the lefthandside summation one multiplication would turn zero.
Since I don't know which parts are variables and which a parameters, this solution could also fail (for example it could be problematic if there is input and output at the same time and the rest of the model doesn't contain the right bounds for that)