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I'm following this paper and came across some notation that I don't know; I've tried a number of queries such as "power to the plus", "plus exponent" etc but can't seem to find anything:

From page 4:

$\text{sign}(\beta_j)(|\beta_j| - \gamma)^+$

The "$+$" exponent is what I'm confused about.

Git Gud
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tmakino
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  • Did you try looking up the paper by Donoho and Johnstone? They seem to get similar results in a different context based on what the authors suggested. Maybe what $^+$ means will be more clear there. – Cameron Williams Jul 29 '13 at 19:48
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    Great question. A good example of why authors should take steps to define all but the most standard notation... – user7530 Jul 29 '13 at 19:48
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    I think the definition is $a^{+}:=max{0,a}$. – OR. Jul 29 '13 at 20:16
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    I love it. "The solutions... are easily shown to be [insert domain-specific or sparsely-defined notation here]." – Emily Jul 29 '13 at 20:22

1 Answers1

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The notations $f^+$ and $f^-$ for (real valued) functions and constants denote what RGB hints at the positive and negative part, respectively.

In detail $f^+ = \max \{0, f\}$ and $f^- = - \min \{0, f \}$, so that $f = f^+ - f^-$.

See the wikipedia page Positive and negative parts.

GEdgar
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quid
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