invariant

[[concept]]

Topics

const fieldName = "theme"; // Your field with links
const oldPrefix = "Thoughts/01 Themes/";
const newPrefix = "Digital Garden/Topics/";
 
const relatedLinks = dv.current()[fieldName];
 
if (Array.isArray(relatedLinks)) {
    // Map over the links, replace the path, and output only clickable links
    dv.el("span",
        relatedLinks
            .map(link => {
                if (link && link.path) {
                    let newPath = link.path.startsWith(oldPrefix)
                        ? link.path.replace(oldPrefix, newPrefix)
                        : link.path;
                    return dv.fileLink(newPath);
                }
            })
            .filter(Boolean).join(", ") 
	// Remove any undefined/null items
    );
} else {
    dv.el(dv.current().theme);
}
 
 

Definition

Invariant

Let $G$ be a group acting on a (data) set $X$. Then $F:X\to Y$ is invariant if $F(g\circ x)=F(x)\forall g\in G\text{ and }x\in X$

Random Matrix Theory

Orthogonal Invariance

Let $x\in {\mathbb{R}}^d$ be a random vector. We say that $x$ (or its law $\text{Law}(x)$) is orthogonally invariant if for each (deterministic) orthogonal matrix $Q\in \mathcal{O}(d)$ we have $\text{Law}(Qx)=\text{Law}(x)$

NOTE

The law is the distribution of the random vector. We sometimes use “model” instead of “law” or “distribution” to remind us that our choice includes assumptions and judgements.

• We are modelling a situation we might encounter in applications

References

References

See Also

Mentions

Mentions

const modules = await cJS()
 
const COLUMNS = [  
	{ id: "Name", value: page => page.$link },  
	{ id: "Last Modified", value: page => modules.dateTime.getLastMod(page) },
];  
  
return function View() {  
	const current = dc.useCurrentFile();
// Selecting `#game` pages, for example. 
	let queryString = `@page and linksto(${current.$link})`;
	let pages = dc.useQuery(queryString);
	
	// check types
	pages = pages.filter( (p) => !modules.typeCheck.checkAll(p, current) ).sort()
	
	
	return <dc.Table columns={COLUMNS} rows={pages} paging={20}/>;  
}  

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>
}