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For uniform samples at rate , the frequency is the Nyquist frequency. A real baseband signal confined below this boundary can avoid spectral overlap when an appropriate anti-aliasing filter is used.
Start with an inflationary patch of physical radius in units . After e-folds and subsequent expansion, its present radius is . Requiring it to cover the present Hubble radius gives the displayed inequality. With instantaneous conversion to radiation, fixed relativistic degrees of freedom and a fixed ratio , energy conservation gives , whereas adiabatic subsequent expansion gives . Thus the required increases approximately as . Holding fixed while varying the end energy independently is a different comparison and reverses that simple temperature-only trend. The inflationary energy history and post-inflationary entropy history must be specified.[ref]
The Jukes-Cantor model is a symmetric four-state continuous-time Markov chain for DNA evolution. Each change to a specified different base has rate , so the total rate of actual changes is . Its same-base probability is and its probability for one specified different base is . The probability of any mismatch is three times the latter, tending to at long times. Distinguish the exponent parameter from the actual per-site mutation rate when fitting this model.
Mapping DNA fragments protected during controlled micrococcal-nuclease digestion. Digestion titration and fragment validation help distinguish nucleosome occupancy from sequence bias and other protected complexes.
DNA connecting adjacent nucleosome cores. Its length and accessibility affect nucleosome-array organization.
Transient local unwrapping and rewrapping of nucleosomal DNA. This changes the accessibility of DNA and histone surfaces without requiring complete and irreversible loss of the histone octamer.
Resistance of a histone–DNA particle to loss or rearrangement of its components under specified conditions. Competitor-induced histone transfer can reveal destabilization even while a DNA-binding protein remains attached.
Movement of histones from one DNA substrate or complex to another. In competition experiments, loss of histones from a labelled complex need not release free DNA if another DNA-binding protein remains attached.
Nucleosome reconstitution assembles histones with DNA outside the cell to produce defined nucleosome substrates. It permits controlled comparison of DNA sequence, histone composition and associated factors. For example, comparing the same DNA with and without a nucleosome tests how packaging changes access by a DNA-binding protein. A simplified preparation isolates mechanisms but omits cellular processes such as ongoing transcription, histone turnover and chromosome-scale constraints. [ref]
Molecular Biology of the Cell, 4th edition by Bruce Alberts and others. Chapter 4, Chromosomal DNA and Its Packaging in the Chromatin Fiber: nucleosome structure and assembly
A Meisenheimer complex is a sigma-bonded anionic addition species associated with suitable nucleophilic aromatic substitution reactions. Delocalization into ortho or para nitro groups can stabilize its negative charge.
Vicarious nucleophilic substitution replaces aromatic hydrogen using a nucleophile that carries its own leaving group. In nitroarenes, reversible carbanion addition gives a sigma-H adduct; base-induced elimination of the hydrogen and the nucleophile-borne leaving group, followed by protonation, gives substitution without expelling hydride.
An intramolecular nucleophilic aromatic substitution that transfers an aryl group between sites in one molecule.
Breaking an ester linkage can proceed by different bonds and mechanisms. Acyl–oxygen and alkyl–oxygen cleavage should be distinguished when explaining protecting-group selectivity.
Formation of a lactone by intramolecular esterification or acyl substitution. Favourable ring sizes can help trap an intermediate, but do not make the product universally unreactive.
Base-promoted bimolecular acyl substitution: nucleophile addition gives a tetrahedral intermediate, then a leaving group departs from the acyl carbon.
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





