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Data are missing not at random when the probability of missingness still depends on an unobserved value after conditioning on the observed data.
Data are missing at random when the probability of missingness, conditional on observed data, does not depend further on the missing values.
Data are missing completely at random when the missingness indicator is independent of both observed and missing data.
Pauli-based computation performs an adaptive sequence of commuting Pauli measurements on nonstabilizer resource states. Classical outcomes determine later measurements and the final output.
Prepare an ancilla in , use it to control a Hermitian Pauli operator , apply a Hadamard gate, and measure the ancilla. Outcome applies the projector to the data register.
The matter-radiation equality scale is the comoving horizon wavenumber at equality. Modes at larger wavenumber entered during radiation domination and had their matter growth suppressed.
The infinitary language permits conjunctions and disjunctions of fewer than formulas and simultaneous quantification over fewer than variables. Ordinary first-order logic is .
The Helfrich energy of a fluid membrane combines surface tension with curvature elasticity. Without spontaneous curvature or a topological term,
A cosmological transfer function relates a late perturbation to a specified primordial perturbation mode by mode. It records the scale-dependent evolution caused by horizon entry, pressure, free streaming, and changes in the dominant cosmic component.
An adiabatic mode is a long-wavelength physical perturbation whose leading local field configuration is generated by a residual gauge transformation. Its action on shorter modes produces a cosmological soft theorem or consistency relation.
During matter domination in a spatially flat universe, pressureless matter controls the expansion, , and the growing linear density mode is proportional to .
The peculiar gravitational potential is the Newtonian potential after subtracting the potential of the homogeneous expanding background. In comoving coordinates it obeys a Poisson equation sourced by the density contrast, so its gradient accelerates matter relative to the Hubble flow.
For covariant derivatives on Euclidean four-space, one anti-self-dual Yang-Mills Lax pair isThe condition for every is equivalent to anti-self-duality of the curvature.
A spectral parameter is an auxiliary complex parameter in a linear system whose compatibility encodes a nonlinear integrable equation. Its analytic dependence organizes conserved quantities and scattering data.
An -step self-avoiding walk on a graph is a sequence of distinct graph vertices with an edge between successive graph vertices. It is a graph path with edges and graph vertices. On a transitive graph, the exponential growth rate of rooted self-avoiding walk counts is the connective constant.
Elastic-net regression minimizes squared error plus both an coefficient penalty and a squared penalty. It combines exact sparsity with strict convexity when the quadratic penalty is positive.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact