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Paper: Solving Polynomial Systems with phcpy #461

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commented May 20, 2019

With this PR we submit a draft of our paper
Solving Polynomial Systems with phcpy

Sincerely Yours,
Jan Verschelde

janverschelde and others added some commits Apr 23, 2019

Merge pull request #1 from JazzTap/2019
Three-act structure & set up lit search
Eliminated the Belief Propagation section because the calculations in…
… that

paper are perform with HOM4PS-3, which is closed source software.
Started a section on Related Software, will add references to the
literature on those three software packages later.
renamed the section title Intensive Methods into Solving Polynomial S…
…ystems,

added a subsection on polynomial homotopy continuation
Merge pull request #2 from JazzTap/2019
Add to intro for general audience
Merge pull request #4 from loldja/2019
Initial Review submission; thanks we are working on the revision.

@JazzTap JazzTap referenced this pull request Jun 18, 2019

Merged

Revise text #5

janverschelde added some commits Jun 18, 2019

Merge pull request #5 from JazzTap/2019
Revise text,  resolved conflicts.
Update phcpy.rst
removed extra references at the end of the paper
changed 'Mission' as section header into 'A Scripting Interface for P…
…HCpack' as this is the main purpose of phcpy; some other small edits
added thesis dissertation of Xiangcheng Yu, figured out floating plac…
…ement of tables, fixed an error in the table
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commented Jun 19, 2019

@janverschelde feel free to @ us when you feel this submission is ready for re-review 😄

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commented Jun 20, 2019

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commented Jun 20, 2019

I'm currently revising the abstract, besides clarifying a couple other sentences. Be ready in an hour. Ok.

JazzTap and others added some commits Jun 20, 2019

Merge pull request #6 from JazzTap/2019
Finishing up responses

It is often useful to know all the steady states of a biological network, as represented by a nonlinear system of ordinary differential equations, with some conserved quantities. These two lists of polynomials (from rates of change of form :math:`\dot{x} = p(x)`, by letting :math:`\dot{x}=0`; and from conservation laws of form :math:`c = \sum{x_i}` by subtracting :math:`c` from both sides) have a zero set which is a steady-state variety, that can be explored numerically via polynomial homotopy continuation.

Parameter hopotopies were used by Gross et al. [GHR16]_ to perform model selection on a mammalian phosphorylation pathway, determining whether the kinase acts processively (i.e. adding more than one phosphate at once, which it does not in vitro). Their analysis validated experimental work showing processivity in vivo. In doing so, they obtained >50x speedup over non-parameter homotopies (for running times in minutes, not hours) on systems tracking 20 paths.

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deniederhut Jun 22, 2019

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I still think this was meant to read "homotopies".

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commented Jun 22, 2019

Thanks for all the edits!

@cbcunc were there any other changes you wanted to see before approving the paper?

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