All Questions
8 questions
8
votes
2
answers
270
views
Equal segmentation of a series of numbers
How can a series of real numbers be split into subsets in a way that the sum of the real numbers within each subset is as equal as possible?
Coming across from StackOverflow this is the first time, I'...
- 83
4
votes
1
answer
139
views
How to find an optimal sequence of merging operations?
Given a set of items, each characterized by a quality $q_i\in(0,1)$. We can merge two items of quality $q_i$ and $q_j$ to a single item $k$ of quality $q_k=f(q_i,q_j)$, where $f$ is increasing in $q_i$...
- 367
15
votes
2
answers
974
views
n sets, each is large, the intersection of every three is small, what is the size of the union?
Let $A_1, A_2, \ldots, A_n$ be $n$ sets such that:
(1) for each $i\in [n]$, $\frac{n}{3}\leq |A_i|\leq n$;
(2) for any $1\leq i<j<k\leq n$, $|A_i\cap A_j\cap A_k|\leq a$, where $a$ is a constant ...
- 373
3
votes
0
answers
121
views
Matrix inequality $a X \succeq arcsin(X)$ for some $a > 0$
Let $X \in S^{n}_{+}$ be a positive semi-definite matrix with $X_{ii} = 1$ for all $i \leq n$ (thus $X$ is a correlation matrix).
Since $X$ is positive semi-definite, we have $|X_{ij}| \leq 1$ for any ...
- 205
0
votes
0
answers
127
views
Maximizing a vector after a series of matrix multiplications
Problem Statement
Let's say we have a set of $n\times n$ matrices $X=\{M_1,\ldots,M_r\}$ and weights of these matrices $\{w_1,\ldots,w_r\}$ along with a set of "initial vectors" $\{v_1,\...
- 509
0
votes
1
answer
221
views
Minimize overlap penalty between paths in graph
Suppose we have a weighted undirected graph $G(V,E)$. We are given the information that $V_a \cap V_b = \emptyset$ and $V_a,V_b \subset V$.
We want to find paths from all vertices in $V_a$ to all ...
- 25
1
vote
1
answer
444
views
Looking for an efficient way of maximising 'pair scores' for subset of 30 selected from 50 to 10 000 objects
Context: I have a tiling program that uses a directed breadth first search algorithm. It is 'directed' by what I call 'pair scoring'. There are $N$ polyforms (pieces) used in the tiling. I have an $N\...
- 613
5
votes
1
answer
109
views
Improved estimates of $n$ quantities via $n$ measurements
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- 128k