Prismix
arXiv — Machine Learning · · 2 min read

The Planar Case of Thomas Positive Circuits Conjecture

#paper #developer-tool

Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.

Like Read original ↗

Mathematics > Dynamical Systems

arXiv:2607.14143 (math)
[Submitted on 13 Jul 2026]

Title:The Planar Case of Thomas Positive Circuits Conjecture

Authors:Natan Katz
View a PDF of the paper titled The Planar Case of Thomas Positive Circuits Conjecture, by Natan Katz
View PDF HTML (experimental)
Abstract:The notion of circuit refers to a cyclic oriented influence between the elements of a dynamical system. There are two classes of circuit: positive and negative. R. Thomas conjectured that a necessary condition of multi stationarity is the existence of positive circuits. In this paper we use dynamical system tools and planar analysis to find conditions for which the conjecture holds for planar systems.
Subjects: Dynamical Systems (math.DS); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
Cite as: arXiv:2607.14143 [math.DS]
  (or arXiv:2607.14143v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2607.14143
arXiv-issued DOI via DataCite

Submission history

From: Natan Katz [view email]
[v1] Mon, 13 Jul 2026 16:27:59 UTC (8 KB)
Full-text links:

Access Paper:

Current browse context:

math.DS
< prev   |   next >
Change to browse by:

References & Citations

Loading...

BibTeX formatted citation

loading...
Data provided by:

Bookmark

BibSonomy Reddit
Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos

Demos

Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers

Recommenders and Search Tools

Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Discussion (0)

Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.

Sign in →

No comments yet. Sign in and be the first to say something.

More from arXiv — Machine Learning