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### Boundary Condition for LevelSet Reinitialization

Recently, I'm curious about the boundary condition of Levelset Reinitialization. Generally, when we try to express the interface, we use the levelset advection
$$\phi_t + (V\cdot\nabla)\phi = 0$$
But ...

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### Bits of precision matrix reconstruction

We have a real rank $r$ matrix $M\in\{0,1\}^{n\times n}$.
Suppose we have diagonalized using $LMR=D$.
I want to recover a real matrix $\widetilde{M}$ such that maximum absolute entry of ...

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### efficiently checking that a field extension is Galois

Let $K \subset L$ be an algebraic extension of fields finitely presented over a prime field or over an algebraically closed field. Is there an efficient procedure to check that $L/K$ is Galois? To ...

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### Refutation of $A \land \lnot\lnot\lnot A$ by resolution [closed]

$ A \land \lnot\lnot\lnot A $ this is a very simple example. Resolution is refutation complete. So it should be able to refute this formula. However, I don't see how would it do that without using ...

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### Weak randomness relative to finite-state machines

Is there a nice example of a sequence that looks random to any predictor whose predictions use a finite-state machine?
More precisely, consider a finite-state machine $M$ with input alphabet {0,1} ...

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### procedure-based (as opposed to definition-based) concepts

Euler's work on divergent series was guided by computational procedures, rather than any definition of the "value" of such a series. E.g., he was happy to have half a dozen procedures that indicated ...

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### System of quadratic equations with 18 unknown

So I want to solve for a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r which satisfy the following system of equations: ( I only need positive integer (or 0) solution)
a g + c h + b i + g j + i ...

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### Important open problems that have already been reduced to a finite but infeasible amount of computation

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer."
Some questions ...

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### What to do when your research runs into a computationally challenging problem?

Occasionally, but more frequently lately, I would like to perform some hard computations. As an example, yesterday the following question came up:
What is the projective dimension of the edge ...

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### Efficiently computing with pullbacks and pushouts

Often when computing in category theory, one has to show that some square is cartesian. Depending on the number of maps involved, and their arrangement, it's somewhat difficult to write down exactly ...