Timeline for Is there an "adjacency matrix" for weighted directed graphs that captures the weights?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Nov 23, 2014 at 1:45 | comment | added | Allen Knutson | It is unfortunate that the "low-temperature" limit, which is very reasonable terminology, is also called the "tropical" limit (outside Japan, where the convention is reversed). | |
| Mar 28, 2010 at 23:41 | comment | added | Theo Johnson-Freyd | The bad TeX should read "$\mathbb R \cup \{-\infty\}$". I wish there were either "edit" or "preview" for comments. | |
| Mar 28, 2010 at 23:41 | comment | added | Theo Johnson-Freyd | Indeed, note that "plus-over-max" is precisely the low-temperature limit of "times-over-plus". Indeed, for $t>0$, define the "temperature-$t$" arithmetic on $\mathbb R \cup \\{-\infty\\}$ by $x \oplus_t y = t^{-1}\log( \exp(tx) + \exp(ty))$ and $x \odot_t y = t^{-1}\log( \exp(tx) + \exp(ty)) = x + y$. Then as $t\to 0$, we have $\lim (x\oplus_t y) = \max(x,y)$. | |
| Mar 28, 2010 at 21:20 | comment | added | Steve Huntsman | You might write $\beta$ instead of $t$. | |
| Mar 28, 2010 at 20:09 | comment | added | user4977 | Thanks! I had actually dismissed the product of the weights as being information that was "useless", stupidly ignoring the obvious (and perfectly usual) case where the weights are probabilities. This is what I get for looking at one particular application of digraphs for too long. I attempted to vote up your answer, but alas, I was reputationally (not a word) denied. | |
| Mar 28, 2010 at 20:02 | vote | accept | user4977 | ||
| Mar 28, 2010 at 19:33 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |