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Ebooks Worm Their Way into the Reference Market
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Sidebar: SafariU: Build Your Own Ebooks
Teachers looking to build custom course material for technical and computer books can use SafariU, a new service built on top of Safari, a joint venture of O'Reilly and Parsons Technologies. According to CJ Rayhill, CIO at O'Reilly Media, SafariU provides a way for teachers to search the Safari database, then build a custom text made up of material from a variety of sources. "SafariU allows instructors to mix and match content into custom books and also upload their own materials," Rayhill says.

What's more, teachers can build their course quickly and easily and share the content with other instructors in a learning exchange if they wish. Rayhill tells a story of a customer who needed to build a course on security over a weekend. "He created an online syllabus out of six or seven books on security. He went into class on Monday and said, 'here is where you can get all of your content,'" Rayhill explains.

She says that the service is also well-suited to corporate training departments because of the ability to bring together a variety of sources and build course material on the fly. "Corporate clients can customize training, and smaller developer workgroups could create manuals and standard text references to train the work group about standard ways of doing things." Academic texts are not really suited to corporate training groups' timeframes, she says, so being able to piece together stuff quickly is extremely valuable, especially for small classes.

Rayhill says the service, which is free for teachers, costs only 16 cents per page (with a 10-student/100-page minimum) plus any book store mark-up. SafariU is asking for a $700 per year in revenue from each teacher, which Rayhill estimates that teachers can probably meet with a single class of 20 students.

redpajama_set_name: RedPajamaCommonCrawl


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Q: A curious way to write the eigenvectors of the Boolean hypercube It seems that one can write the eigenvectors of the hypercube $\{ \pm 1\}^n$ as the functions, $\{ \chi_S \}_{S \subseteq [n] }$. And these functions $\chi_S$ are defined on the vertices $x \in \{ \pm 1\}^n$ as $\chi_S (x) = \prod_{i \in S} x_i$. And the eigenvalue of $\chi_S$ is $\vert S \vert/n$

*

*Even on $n=2$ I am not able to check this to be true. What is the justification for this above formulation?

A: Your eigenvalue of $L$ is slightly wrong if $L:=I-\frac{1}{n}A$ where $A$ is the adjacency matrix of the hypercube graph $Q_n$. The correct eigenvalue for the given eigenvector is $2\frac{|S|}{n}$ as I show below.
First we show $\chi_S$ is an eigenvector for $A$ (with an eigenvalue $\lambda_S$ that will be pop out from the proof of this). To do this, you need to check that for every vertex $v$, the sum of all $\chi_S(x)$ over all vertices $x$ that are adjacent to $v$ is equal to $\lambda_S\chi_S(v)$.
Well, the vertices adjacent to $v$ are those in which $v$ and $x$ differ in one position, say $i$. When $i\not\in S$, we have $\chi_S(v)=\chi_S(x)$. If $i\in S$, then $\chi_S(x)=-\chi_S(v)$. Hence, $$\sum_{x\sim v}\chi_S(x) = (n-|S|)\chi_S(v)+|S|(-\chi_S(v))=(n-2|S|)\chi_S(v).$$
So $\chi_S$ is an eigenvector for $A$ with eigenvalue $n-2|S|$. It follows that $$1-\frac{1}{n}(n-2|S|) = \frac{2|S|}{n}$$ is an eigenvalue of $L$ with eigenvector $\chi_S$.

redpajama_set_name: RedPajamaStackExchange


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northern college pures
> Uncategorized > northern college pures
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Audit Finds Inconsistencies With Medical Marijuana Program
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