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Any idea what $\land$ means in the below formula?

$$ \left( \sum_{i=1}^S p_i \land \sqrt{\frac{e^\epsilon p_i}{n}} \right)^2 $$

Here, $S \in \mathbb{N}$ is a natural number, $p_i \in \mathbb{R}$ are probability estimates, $\epsilon \in [0,\infty)$ is a non-negative real number, $e$ is the mathematical constant, and $n \in \mathbb{N}$ is a number of samples.

I have seen this in a paper (e.g., Equation 5), and another version of the same paper also contains it (e.g., Algorithm 1). The latter paper also contains

$$ 0 \lor \left(1 \land \sum_{i=1}^S \delta_i \right). $$

I would usually expect $\land$ to mean logical and, but that does not really seem appropriate here.

Peter
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  • $a\wedge b$ denotes the minimum between $a$ and $b$ and $a\vee b$ denotes the maximum between $a$ and $b$. – Surb Apr 03 '20 at 12:05

1 Answers1

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It's used for minimum and maximum.

$a \vee b$ = maximum of $a$ and $b$.

$a \wedge b$ = minimum of $a$ and $b$.

The notation comes from lattice theory (think of the maximum moving down from infinity until it hits one of $a$ or $b$ and likewise for the minimum moving up), but is surprisingly common in probability theory.

John Gowers
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