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Is there a unitary $U_{AB}$ such that, for any density operator $\rho$, we have $${\rm {Tr}}_A \left[U_{AB} \left(\frac{I_A}{2} \otimes \rho_B\right)U_{AB}^{\dagger}\right]= \frac{\rho_B}{2}+\frac{I_B}... 1 vote 0 answers 27 views ### How to identify the most different short sequence from a corpus that does not occur? I would like to generate the most unique string (20 long, primer) of a defined length that does not occur in a much larger string (6.4 billion long, human genome). Of course, there could be many ... 1 vote 1 answer 31 views ### Find best matching ranges below limit in defined set of numbers I am trying to calculate the best set of cuts for some wood cutting to reduce the waste. So: Given a set of numbers, the goal is to find the best matches below a limit (size of wood beam). Example of ... • 111 1 vote 0 answers 40 views ### Largest triangle that contains a point Given the location of n points on a 2D plane (P_1, P_2, \ldots, P_n); and the location of a special point X. Find three points P_i,P_j,P_k (i \neq j \neq k) such that point X is inside the ... 2 votes 0 answers 60 views ### Alternatives to breadth-first-search in 3D grid cluster detection? I've got a question about a good way to find the quickest algorithm for my problem: problem: I've got a 3D cubical grid containing voxels that are either 1 or 0. It is stored as a flattened array. If ... 3 votes 0 answers 332 views ### Quantifying Superiority of Golden Section vs Binary Search vs Brent on Continuous Function This concerns algorithms for searching for the minimum of a continuous unidimensional unimodal function. The simplest method is three points, and bi-sectioning. The golden-section search seems more ... • 131 3 votes 0 answers 106 views ### Are the No Free Lunch Theorems Useful for Anything? I have been thinking about the No Free Lunch (NFL) theorems lately, and I have a question which probably every one who has ever thought of the NFL theorems has also had. I am asking this question here,... 0 votes 1 answer 66 views ### Efficient search strategy in a monotonic boolean function wherein the probability of solution location is known apriori A boolean-valued monotonic function is defined in the set of positive integers, \mathcal Z.$$f(n) = \begin{cases} 0, &n_{min}\le n < n\ast\\1, &n\ast\le n\le n_{max} \end{cases} ; n \in ...
I have a random point generator which takes a distance $d$ and fills an area with points such that distance between any two points is no less that $d$: I need to control the number of points in the ...