Although I only understand a tiny percentage of this conversation, I'm tweaked by the argument made here:
Chemical Transformation Motifs - Modelling Pathways as Integer Hyperflows https://ieeexplore.ieee.org/document/8171738 <blockquote> Note that breadth-first marking of hypergraphs, and variations thereof, has in the literature also been referred to as finding scopes of molecules [33]. Breadth-first marking has in those studies been used alone to analyse metabolic networks, and define set-theoretical notions of pathways and later of autocatalysis [34]. The methods thus do not have focus on the underlying mechanism of the pathways, which is our aim in this contribution. ... The LP relaxation of an ILP yields an integer solution only under special conditions. The best known sufficient condition is that the matrix of constraint coefficients is totally unimodular (TU), i.e., when all its square submatrices have determinants −1, 0, or +1, and thus all entries of the matrix are also −1, 0, or +1. This is the case for example for integer flows in graphs [14], [32]. As the simple examples in Fig. 8 shows, this not true in general for stoichiometric matrices and hence for hyperflows. </blockquote> We recently discovered the cause of a discretization artifact in one of our simulations, which was the (overly simplistic) chunking of object counts into (massive) integer values. It was maddening trying to find the cause. (I even resorted to ensemble EMD hoping to score a free lunch! No such luck.) But a simple switch to double types smoothed it out (pun intended). Although it makes face validation easier, I'm thinking it's a mistake to keep that code change because the smoothness is the artifact ... making the result *less* mechanistic. The discretization artifact is fundamentally because we can't/don't simulate *that many* molecules ... on the order of ~2e-16 fewer, in fact. 8^D On October 14, 2021 1:52:25 AM PDT, David Eric Smith <desm...@santafe.edu> wrote: >Yes. Needing to do graph canonicalization deep in a loop that must run many >times was a core problem for these guys: >https://cheminf.imada.sdu.dk/mod/ <https://cheminf.imada.sdu.dk/mod/> >They are very Very concerned to use the most efficient algorithm known at any >time for graph isomorphism and canonicalization. There are a pair of Dagstuhl >Seminars (sponsored by the German Computer Science Society) where the state of >the art on these things was one of the themes covered: >https://www.dagstuhl.de/en/program/calendar/semhp/?semnr=17452 ><https://www.dagstuhl.de/en/program/calendar/semhp/?semnr=17452> >https://www.dagstuhl.de/en/program/calendar/semhp/?semnr=14452 ><https://www.dagstuhl.de/en/program/calendar/semhp/?semnr=14452> >The seminars are required to publish a sort of white-paper at the end of each >week with topics covered. Although not suited to learning any given thing >from, they may give helpful pointers to which methods are studied in >association with each other in various problem domains. > >I had mentioned MØD before in a thread that veered near these topics; >apologies for repetition, but things gain salience at different times. .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
