Use cases for package in other packages and papers

[dpsanders]

It would be very helpful if people were willing to list some of the use cases of this package, both within other Julia packages and for calculations published in research papers etc.

EDIT: Please just add a comment with links.

[mforets]

Use case: applications of formal verification. We use intervals (among other set representations) in JuliaReach eg. in LazySets.jl and Reachability.jl to do flowpipe approximation of dynamical systems.

[Kolaru]

Use case: Count the number of non-trivial solutions of a system of equations to determine the different phases of the system and independantly verify analytic result determining the critical region of the transition. Interval arithmetic was also used to prove that in some cases the phase transition is discontinous.

I did this for my master thesis in the context of network studies. For the final results, see figures 2.6 and 2.7 of the report.

[kalmarek]

@dpsanders we had a chat at some point about citing IntervalArithmetic (or ValidatedNumerics) has a paper about it (or even a technical report) been published since?

My application: providing certified lower bounds on the spectral gap of the group Laplace operators.
This includes:

• https://arxiv.org/abs/1703.09680, or https://www.degruyter.com/view/j/gcc.2018.10.issue-1/gcc-2018-0004/gcc-2018-0004.xml
• https://arxiv.org/abs/1712.07167 has been recently accepted, I'd be very happy to add IntervalArithmetic to References!
• https://arxiv.org/abs/1812.03456 is still pending review (and will be for forseable future ;-)

[lbenet]

Sorry for the long delay, and thanks for asking. I guess (for the time being) the best is to cite the package as:

David P. Sanders and Luis Benet
JuliaIntervals/IntervalArithmetic.jl:
Rigorous floating-point calculations using interval arithmetic in Julia (Version v0.x.x).
https://github.com/JuliaIntervals/IntervalArithmetic.jl

It is a good idea to specify the version you used.

cc @dpsanders

[kalmarek]

@lbenet the nice thing about projects is that the version will be fixed by Manifest.toml which will be distributed alongside the paper

[lbenet]

@kalmarek Sorry for the late reply; somehow your reply got lost. I agree with you, but this is something maybe unknown by a reader of the bibliography.

[gwater]

our peer-reviewed article about delay differential equations references IntervalRootFinding.jl

[lucaferranti]

there's also #471, which is pinged