graphon convolution

[[concept]]

Graphon convolution

Given a graphon signal $(W,\mathcal{X})$, we write the graphon convolution as the map

T_{H}&: L_{2}([0,1]) \to L_{2}([0,1]) \\ T_{H}&: {\cal X} \mapsto {\cal Y} \end{align}$$ with $${\cal Y} = T_{H}{\cal X} = \sum_{k=0}^{K-1} h_{k} T_{W}^{(k)} {\cal X}$$ and $$T_{W}^{(k)} {\cal X} = \begin{cases} \int _{0}^1 W(u, \cdot) (T_{W}^{(k-1)} {\cal X})(u) \, du &k ≥1 \\ I &k=0 \end{cases}$$

Mentions

Mentions

TABLE file.mday as "Last Modified"
FROM [[]]
 
FLATTEN choice(contains(artist, this.file.link), 1, "") + choice(contains(author, this.file.link), 1, "") + choice(contains(director, this.file.link), 1, "") + choice(contains(source, this.file.link), 1, "") as direct_source
 
WHERE !direct_source
SORT file.mday ASC
SORT file.name ASC

const { dateTime } = await cJS()
 
return function View() {
	const file = dc.useCurrentFile();
	return <p class="dv-modified">Created {dateTime.getCreated(file)}     ֍     Last Modified {dateTime.getLastMod(file)}</p>
}