Abstract: We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting using a recent result by Cardin and Teixeira. The existence of invariant manifolds is subject to hyperbolicity conditions, which we test algorithmically using Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-the-shelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations.
(with Niclas Kruff, Ovidiu Radulescu, Thomas Sturm and Sebastian Walcher)
The paper has been submitted to a journal and a preprint is available on arXiv.
I posted an updated version of my paper with faster timings and better text.
Abstract: “A novel way to use SMT (Satisfiability Modulo Theories) solvers to compute the tropical prevariety (resp. equilibrium) of a polynomial system is presented. The new method is benchmarked against a naive approach that uses purely polyhedral methods. It turns out that the SMT approach is faster than the polyhedral approach for models that would otherwise take more than one minute to compute, in many cases by a factor of 60 or more, and in the worst case is only slower by a factor of two. Furthermore, the new approach is an anytime algorithm, thus offering a way to compute parts of the solution when the polyhedral approach is infeasible. ”
Paper on arXiv: https://arxiv.org/abs/2004.07058
Source code: https://gitlab.com/cxxl/smtcut
Abstract: “I am presenting a novel way to use SMT (Satisfiability Modulo Theory) to compute the tropical prevariety (resp. equilibrium) of a polynomial system. The new method is benchmarked against a naive approach that uses purely polyhedral methods. It turns out that the SMT approach is faster than the polyhedral approach for models that would otherwise take more than one minute to compute, in many cases by a factor of 25 or more. Furthermore, the new approach offers a way to compute at least parts of the solution if the polyhedral approach is infeasible.”
The paper is available on arXiv: https://arxiv.org/abs/2004.07058
The source code is available at https://gitlab.com/cxxl/smtcut.
I have a Cygwin installation on my Windows box and now I downloaded the lastest Git version (for Windows). Git has a small Cygwin included as well and I thought the two would interact nicely—but they don’t.
The problem is that they use a different layout of mapped drives (i.e., mapped from Windows to the Posix world of Cygwin). My regular Cygwin has its root under C:\cygwin64 and from there, for example, the SSH key directory is under /home/chris/.ssh, whereas Git has its root directory somewhere in the Git installation and the home directory is where the Windows user directory is, i.e., C:\Users\chris and there lies the .ssh directory as well.
I thought some symbolic links would do the trick, so I linked the Git .ssh directory to my (real) .ssh directory in Cygwin.
Nice, but not enough. Now, SSH will not find the keys, since it still wants to load its keys from /c/Users/chris/.ssh, so I added another symbolic link to add the /home directory to Git and map it to the /home of Cygwin and add a symbolic link to /etc/ssh_config and add an IdentityFile /home/chris/.ssh/id_rsa.
Not bad, but still not good enough. This time, Git’s ssh-agent is not able to connect to the already loaded (regular Cygwin) ssh-agent. The reason is that both Cygwin’s have different /tmp directories. When I added the Git version to my regular Cygwin (that is, have /tmp map to the user’s TEMP directory, usually under C:\Users\chris\AppData\Local\Temp) by changing the /etc/fstab file, nothing changed. Calling mount to check if the changes worked showed no changes.
The trick here is: you have to close all programs that use Cygwin: ssh-agent, bash, sshd, mintty, everything. Then reload and Voilà! Now the proper /tmp is there and it’s the same on both Cygwin’s, ssh-agent can be accessed from both installations and due to the symbolic links both SSH’s use the same config and key files.
Victory at last!
I have just released PtCut 3.5.0. You can download it here. Full PtCut page here. I know, I tend to gossip. Sorry.
Wir fahren 20.000 km pro Jahr und vergleichen in dem unten genannten Artikel die Kosten für die Anschaffung eines Neuwagens, Unterhalt und Verkauf nach 10 Jahren von einem Golf, einem BMW 318d und einem Tesla Model 3. Es zeigt sich, dass das Model 3 (wenn es mit Öko-Strom betankt wird) 5-mal geringere CO2-Emissionen hat als die Verbrenner hat. Es kostet ähnlich viel wie der Golf und ist wesentlich günstiger als der BMW. Um einen eigenen Eindruck zu bekommen, stellen wir auch ein Worksheet mit den Berechnungen zur Verfügung.
Hier mein Artikel zu dem Thema und hier das Worksheet.
I use cFosSpeed to keep my Ping time low and be able to use VoIP, terminal sessions, remote desktop, IRC sessions and online games on the one hand and up/downloads on the other hand at the same time. cFosSpeed keeps the “pressure” of the file transfers on the line low, so urgent data can still pass quickly.
Since I’m one of the developers of cFosSpeed it’s probably no wonder I like it and endorse its use.
So, if you’re interested, click here to get to the cFosSpeed site:
Here are the slides of my talk on CASC 2019 conference (computer algebra in scientific computing) in Moscow, held on 27th August 2019. This is joint work with Hassan Errami, Matthias Neidhardt, Satya S. Samal and Andreas Weber.
The database can be freely accessed as odebase.cs.uni-bonn.de.
I have worked around problems that prevented PtCut from being run under Pythin 2.x and hence under SageMath. Furthermore, I have tested and fixed it to run under Linux.
Plus, computation of connected components works again and can be called on a solution file as well.
Download PtCut v3.3.3 here.
Jonas Weinz has finally managed to compiled a version of PPLpy (together with gmpy2) that works under Windows and can be installed without compiling the whole lot. Many thanks again! 🙂 This version works for Python 3.7 only.
His compiled binaries can be found on his Github page, together with his recipe how to compile it yourself.
I mirror the files here as well: