#BingChat (precise) has concluded that P=NP

I asked it to write a Python script that when given a graph where there are no more than 5 edges for every vertex, it returns the length of the longest path that visits each vertex no more than once. Then lifted the edge count restriction.

In both cases it claimed polynomial time complexity to solve an NP-hard problem

#ComputerScience #complexity #PequalsNP #NPhard #NPcomplete #python #GraphTheory

@benleis If I may toot my own horn here...here's a #crochet mug cozy I made with my favorite proof of the Pythagorean theorem, and a mobius strip showing an embedding of 𝐾₆ .

#crochet #graphtheory #geometry

Anyone on here know about #Python #PyTorch #GDC #DiffusionAlgorithms #GraphTheory?

I've got this problem where I have a graph which I want to automatically layout. I have some example layouts which I want to train it with. I just don't have the first clue about how to formulate it, validate it, tweak it. Even though I've been programming for 25 years and I have a degree in Maths, I'm bewildered.

The wider context: it's a power system network, and I want to layout substations.

Where to begin?

#Stormwater ponds don’t make great #wetlands, but in #urban areas, they can be the only #aquatic #habitat around. In our latest paper, led by Waverley Birch, we investigate the effect of stromwater ponds on connectivity within the #wetlandscape using #graphtheory. We find that wetlands were more connected before #urbanization, but ponds may provide stepping stones connecting remnant wetlands in urban areas.

Read it here:

https://www.tandfonline.com/doi/abs/10.1080/07011784.2023.2224522

Can I call edge covering resulting in a disjoint union of cographs simply "cograph covering"? (Example attached)

#math #GraphTheory

Are there any good tools for analysing your Mastodon network in a #GraphTheory / #NetworkAnalysis kind of way?

I'd love to be able to:
- visualise the different groups of people that I follow: what are the connections between the people that I follow? (And that follow me?)
- see which accounts post a lot, or not at all

#Mastodon

One way to study graphs using category theory is to define a morphism between graphs to be a map on the vertices that sends edges to edges.

This allows you to define an n-colouring of the vertices as a map to the complete graph on n vertices. The rule about edges guarantees that adjacent vertices recieve different colours.

Therefore, when we have a graph with a complete subgraph, we shouldn't call it a clique; we should call it a *louring*.

#GraphTheory #CategoryTheory #Math #Maths #Mathematics

Since I have a fair amount of work from before this venture into social media, I'll share some older things I did sometimes.

My first single-author paper was about multiplayer versions of rock-paper-scissors. You can find a copy on arXiv (https://arxiv.org/abs/1903.07252) which is pretty similar to the version published in the journal Algebra Universalis.

I had the idea for this paper when I was stranded in #Yosemite national park for a month in 2017 after I finished my bachelor's degree. I wanted to explain to my non-mathy friends that I was into #UniversalAlgebra and this is what I came up with. There are a lot of connections with tournaments from #GraphTheory. You can find videos of me talking about this on YouTube too.

#math #combinatorics #algebra #AbstractAlgebra

A smörgåsbord of free books

- #DistributedSystems
- #GraphTheory
- #ComputerNetworks

https://www.distributed-systems.net/index.php/books/

#TIL about "Dijkstra Maps"

TLDR a map of the the "costs" (time/effort) associated with traversing each node/edge of a space to a specified location.

Commonly applied to video games pathfinding AI (eg Dijkstra's). Neat use cases in adding factors to influence NPC AI behavior (eg fleeing monsters).

It makes me wonder if there is an equivalent in graph theory and thus applicable to real life domains of graph theory.

https://www.roguebasin.com/index.php?title=The_Incredible_Power_of_Dijkstra_Maps

#graphtheory #pathfinding #ai #Dijkstra

@flypapers

Analyses the #Hemibrain #Drosophila #connectome with graph theory and discovers neuron communites. Then applies the same method to a light-microscopy dataset of the zebrafish larval brain where they first infer synaptic connectivity by proximity and then proceed to discover neuron communities.

Tagging as #connectomics #neuroscience #GraphAnalysis #GraphTheory

1736: In solving the “Seven Bridges of Königsberg” problem, Leonhard Euler invented graph theory. #Poetry #Science #History #GraphTheory #Mathematics #Euler (https://sharpgiving.com/thebookofscience/items/p1736a.html)

A Very Big Small Leap Forward in #GraphTheory : Quanta Mag

#Spacetime: is it real and #Physical, or just a calculational tool? : Big Think

With #Temperatures Rising, Can #Animals Survive the #Heat Stress? : Yale

Check our latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

New paper out! 😎

https://www.sciencedirect.com/science/article/pii/S0370157323001643

Everything you always wanted to know about higher-order interactions (But were afraid to ask).

#networks #graphs #hypergraphs #graphtheory #Physics #Mathematics #physic #complexsystems #science #Structure #dynamics

We are moving to Boston for my job & my significant other is #lookingforajob in the greater #boston area. He has a #PhD in #math with experience doing #graphtheory as well as #quantumcomputing #quantumcompilation. Several yrs of post phd experience doing research in govt group & he is looking to continue doing #research. Open to #postdoc #StaffScientist or other roles in #academia or #industry. Plz share & dm if you’re willing to chat with him or have a lead

jj@noboilerplate@tech.lgbt one of the great things about this video is it's discussion of how to do state machines in #Rust.StateMachinesAreAParticularLoveOfMineAndEverSinceILearnedAboutThemICan'tGetEnough.StateMachinesAreeverywhere. Did you know that they're even in the them text editor? #vim #fsm #dfa #nfa #node #edge #GraphTheory

Hi folks, I have somebody who is #lookingforajob in the greater #boston area. He’s a PhD in #math with experience doing #graphtheory as well as #quantumcomputing #quantumcompilation. Several yrs of post phd experience in govt looking to get back to #academia and is open to #postdoc or other roles in #research

I wish there was a standard file format for graph data. There is technically the .dot format for graphviz, but that's more for rendering graphs not representing graph data. I think Gephi also has it's own weird binary format.
#graphtheory #graphdb #graphdata

"DIARY OF A SERIAL PAINTER". Digital design by A.G. (c) 2023. All Rights Reserved. #historiotheque #antiquemoderne #concreterealism #networkscience #graphtheory #paintingseries

Peak #NFL off-season but this is fun due to the #graphtheory angle: https://www.reddit.com/r/nfl/comments/11ykzg9/oc_the_longest_chain_of_names_among_nfl_players/

#nflstatheads