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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com
per introduction
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "per introduction" is correct and usable in written English.
It can be used to refer to something that is in accordance with or as stated in an introduction, often in formal or business contexts. Example: "As outlined per introduction, we will be implementing the new policy starting next month."
✓ Grammatically correct
Science
News & Media
Formal & Business
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Human-verified examples from authoritative sources
Exact Expressions
2 human-written examples
Payment only occurs if further action is taken, starting at $12.95 per introduction, though the first three are free.
News & Media
Given a population of N individuals, a type of allele that emerges by mutation with a rate μ per gene per generation is introduced into the population at a rate 2Nμ (assuming diploids, i.e., 2 genes per individual), where it faces acceptance with probability π fixations per introduction.
Science
Human-verified similar examples from authoritative sources
Similar Expressions
58 human-written examples
HomeAdvisor (acquired by IAC) had been the frontrunner in the pay-per-lead (or pay-per-introduction) model.
News & Media
This could be attributed to the relatively sparse nature of the scale-free networks and a larger variation in node degree (refer to Figs. 32, 33, 34, 35, 36, 37, 38, 39, 40) as we increase the initial number of nodes (for a fixed value of the initial number of links added per node introduction), especially for lower values of the number of new links added per node introduction.
On the other hand, for a given number of new links added per node introduction, the assortativity index for both the MNM and MAM decreases significantly as we increase the initial number of nodes from 3 to 10 and further to 20 (especially, for lower values of the number of new links added per node introduction).
The A.Index of the MAM is significantly larger than that of the MNM for scale-free networks that have a lower number of new links added per node introduction (as large as by a difference of 0.4); as we increase the number of links added per node introduction, the A.Index of MNM approaches to that of the MAM.
As a result, the initial set of nodes are bound to have a considerably larger degree than the newly introduced nodes (especially for smaller values of new links added per node introduction).
For a given initial number of nodes ((n_mathrm{init})) during the evolution of a scale-free network, we could observe that the difference in the assortative index values for the MAM and MDM gets larger with increase in the values for the number of new links (links (_mathrm{new})) added per node introduction (which leads to a decrease in the spectral radius ratio for node degree).
For a given number of new links added per node introduction, the % of node matches does not appreciably change for both the MAM and MNM as we increase the initial number of nodes from 3 to 10 and further to 20.
6: the values for the initial number of nodes ((n_mathrm{init})) are 3, 10 and 20; the values for the number of new links added per node introduction (links (_mathrm{new})) are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 15 and 20.
Though there is a tradeoff expected between A.Index and the % of node matches, the % of node matches incurred with the MAM is only about 3 9%% low compared to the % of node matches incurred with the MNM (the larger differences are observed when the number of new links added per node introduction is low).
Expert writing Tips
Best practice
When using "per introduction", ensure the introduction clearly defines the details you're referencing. This avoids ambiguity and maintains clarity for your audience.
Common error
Avoid using "per introduction" if the introduction is not readily accessible or well-remembered by your audience. Instead, restate the relevant information for better clarity and comprehension.
Source & Trust
85%
Authority and reliability
4.1/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "per introduction" functions as an adverbial phrase, modifying a verb or clause by specifying that something is happening or being done according to what was stated in the introduction. Ludwig indicates that it is mostly used as a prepositional phrase.
Frequent in
Science
33.3%
News & Media
33.3%
Formal & Business
33.3%
Less common in
Wiki
0%
Encyclopedias
0%
Social Media
0%
Ludwig's WRAP-UP
In summary, "per introduction" serves as a concise way to reference information that has already been detailed in the introductory section of a document or presentation. According to Ludwig, this prepositional phrase, while grammatically correct, is relatively rare. Its usage is most common in scientific, news, and formal business contexts. When using "per introduction", ensure the introduction is clear and easily accessible to your audience to prevent confusion. If clarity cannot be guaranteed, consider restating the information for better comprehension.
More alternative expressions(10)
Phrases that express similar concepts, ordered by semantic similarity:
at the point of introduction
Similar, but stresses the specific time of when something is first made known or launched.
as initially stated
Emphasizes that the detail or rate was set at the introduction.
in accordance with the introduction
This is more formal, indicating strict compliance with what the introduction specifies.
in the introductory phase
Specifies details or conditions related to the beginning or introductory stages of a launch.
as a starting rate
Focuses specifically on the rate that applies at the beginning or upon introduction.
according to the preamble
Refers to information that's clarified in the initial section or introduction of a document.
based on the initial offer
Highlights that a pricing or condition depends on an introductory promotional offer.
following its launch
Focuses on the period immediately after something new is introduced or released.
on first exposure
Describes the initial experience or encounter with something after its introduction.
by way of introduction
Refers to something shared as part of an introductory action or communication.
FAQs
What does "per introduction" mean?
"Per introduction" means according to what was stated or explained in the introduction. It's often used to reference details, rates, or conditions initially outlined.
When is it appropriate to use "per introduction" in writing?
It's appropriate when you want to refer back to information already provided in the introductory section of a document or presentation, especially in business or formal contexts. Make sure the introduction is clear to the audience before using "per introduction".
What are some alternatives to "per introduction"?
Alternatives include phrases like "as initially stated", "according to the preamble", or "at the point of introduction". The best choice depends on the specific context and what you want to emphasize.
How can I ensure my use of "per introduction" is clear?
To ensure clarity, make sure your introduction explicitly covers the details you're referencing. If there's any ambiguity or if the introduction isn't easily accessible, restate the information instead of relying solely on "per introduction".
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Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Source & Trust
85%
Authority and reliability
4.1/5
Expert rating
Real-world application tested