#manifolds — Public Fediverse posts

@LMPrida shares an inspiring perspective in @thetransmitter on how #neuron subtypes may control large-scale #NeuralPopulation activity, from #manifolds to #ripples:

🌍 https://www.thetransmitter.org/brain-inspired/liset-de-la-prida-explains-how-neuron-subtypes-may-control-the-activity-of-large-neural-populations-from-manifolds-to-ripples/

#CompNeuro #Neuroscience

@LMPrida shares an inspiring perspective in @thetransmitter on how #neuron subtypes may control large-scale #NeuralPopulation activity, from #manifolds to #ripples:

🌍 https://www.thetransmitter.org/brain-inspired/liset-de-la-prida-explains-how-neuron-subtypes-may-control-the-activity-of-large-neural-populations-from-manifolds-to-ripples/

#CompNeuro #Neuroscience

@LMPrida shares an inspiring perspective in @thetransmitter on how #neuron subtypes may control large-scale #NeuralPopulation activity, from #manifolds to #ripples:

🌍 https://www.thetransmitter.org/brain-inspired/liset-de-la-prida-explains-how-neuron-subtypes-may-control-the-activity-of-large-neural-populations-from-manifolds-to-ripples/

#CompNeuro #Neuroscience

@LMPrida shares an inspiring perspective in @thetransmitter on how #neuron subtypes may control large-scale #NeuralPopulation activity, from #manifolds to #ripples:

🌍 https://www.thetransmitter.org/brain-inspired/liset-de-la-prida-explains-how-neuron-subtypes-may-control-the-activity-of-large-neural-populations-from-manifolds-to-ripples/

#CompNeuro #Neuroscience

🧠 New paper by Pezon, Schmutz & Gerstner: Linking #NeuralManifolds to circuit structure in recurrent networks.

The study connects two common views of neural activity: low-dimensional #PopulationDynamics (“neural manifolds”) and single-neuron selectivity. Using recurrent network models, the authors show how circuit connectivity constrains both the geometry of neural #manifolds and the tuning of individual neurons.

📄 https://doi.org/10.1016/j.neuron.2025.12.047

#Neuroscience #NeuralDynamics #CompNeuro #RNN

🧠 New paper by Pezon, Schmutz & Gerstner: Linking #NeuralManifolds to circuit structure in recurrent networks.

The study connects two common views of neural activity: low-dimensional #PopulationDynamics (“neural manifolds”) and single-neuron selectivity. Using recurrent network models, the authors show how circuit connectivity constrains both the geometry of neural #manifolds and the tuning of individual neurons.

📄 https://doi.org/10.1016/j.neuron.2025.12.047

#Neuroscience #NeuralDynamics #CompNeuro #RNN

🧠 New paper by Pezon, Schmutz & Gerstner: Linking #NeuralManifolds to circuit structure in recurrent networks.

The study connects two common views of neural activity: low-dimensional #PopulationDynamics (“neural manifolds”) and single-neuron selectivity. Using recurrent network models, the authors show how circuit connectivity constrains both the geometry of neural #manifolds and the tuning of individual neurons.

📄 https://doi.org/10.1016/j.neuron.2025.12.047

#Neuroscience #NeuralDynamics #CompNeuro #RNN

🧠 New paper by Pezon, Schmutz & Gerstner: Linking #NeuralManifolds to circuit structure in recurrent networks.

The study connects two common views of neural activity: low-dimensional #PopulationDynamics (“neural manifolds”) and single-neuron selectivity. Using recurrent network models, the authors show how circuit connectivity constrains both the geometry of neural #manifolds and the tuning of individual neurons.

📄 https://doi.org/10.1016/j.neuron.2025.12.047

#Neuroscience #NeuralDynamics #CompNeuro #RNN

🧠 New paper by Pezon, Schmutz & Gerstner: Linking #NeuralManifolds to circuit structure in recurrent networks.

The study connects two common views of neural activity: low-dimensional #PopulationDynamics (“neural manifolds”) and single-neuron selectivity. Using recurrent network models, the authors show how circuit connectivity constrains both the geometry of neural #manifolds and the tuning of individual neurons.

📄 https://doi.org/10.1016/j.neuron.2025.12.047

#Neuroscience #NeuralDynamics #CompNeuro #RNN

🧠 New preprint by Guardamagna et al.: Using large-scale recordings in #rat pups, the authors show that toroidal #manifolds in #MEC emerge by P10, before eye and ear opening, upright gait, and active exploration. Ring-like manifolds appear even earlier, by P9. External spatial experience seems to align these preconfigured internal maps only later, as pups begin to navigate.

📄 https://doi.org/10.64898/2026.03.10.710908

#Neuroscience #GridCells #NeuralDynamics

🧠 New preprint by Guardamagna et al.: Using large-scale recordings in #rat pups, the authors show that toroidal #manifolds in #MEC emerge by P10, before eye and ear opening, upright gait, and active exploration. Ring-like manifolds appear even earlier, by P9. External spatial experience seems to align these preconfigured internal maps only later, as pups begin to navigate.

📄 https://doi.org/10.64898/2026.03.10.710908

#Neuroscience #GridCells #NeuralDynamics

🧠 New preprint by Guardamagna et al.: Using large-scale recordings in #rat pups, the authors show that toroidal #manifolds in #MEC emerge by P10, before eye and ear opening, upright gait, and active exploration. Ring-like manifolds appear even earlier, by P9. External spatial experience seems to align these preconfigured internal maps only later, as pups begin to navigate.

📄 https://doi.org/10.64898/2026.03.10.710908

#Neuroscience #GridCells #NeuralDynamics

🧠 New preprint by Guardamagna et al.: Using large-scale recordings in #rat pups, the authors show that toroidal #manifolds in #MEC emerge by P10, before eye and ear opening, upright gait, and active exploration. Ring-like manifolds appear even earlier, by P9. External spatial experience seems to align these preconfigured internal maps only later, as pups begin to navigate.

📄 https://doi.org/10.64898/2026.03.10.710908

#Neuroscience #GridCells #NeuralDynamics

🧠 New preprint by Guardamagna et al.: Using large-scale recordings in #rat pups, the authors show that toroidal #manifolds in #MEC emerge by P10, before eye and ear opening, upright gait, and active exploration. Ring-like manifolds appear even earlier, by P9. External spatial experience seems to align these preconfigured internal maps only later, as pups begin to navigate.

📄 https://doi.org/10.64898/2026.03.10.710908

#Neuroscience #GridCells #NeuralDynamics

🧠 New work by Codol et al. who show that #MotorCortex dynamics are remarkably conserved across #mice, #monkeys, and #humans. Despite very different #behaviors, #NeuralPopulation activity follows similar dynamical rules on low-dimensional #manifolds. Species differences arise mainly from the geometry of trajectories within this shared #DynamicalSystem.

📄 https://doi.org/10.64898/2026.03.06.709637

#Neuroscience #CompNeuro #NeuralDynamics

[ Lumo Kaŭstikaĵo ]

Matematika diferenciala geometrio priskribanta la ebenan koverton de kurboj spuritaj de radioj disvastiĝantaj tra manifoldo. 🤓 #nerd

~briletanta~

\eZ

#miksang #dailypic #aphotoaday
#Esperanto #photography #photo
#physics #optics #mathematics #maths
#caustics #differentialgeometry
#manifold #manifolds
#shimmering

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

"In the mid-19th century, Bernhard #Riemann conceived of a new way to think about #mathematical spaces, providing the foundation for modern #geometry and #physics."

Cool article on #manifolds on wired.com:

🌍 https://www.wired.com/story/behold-the-manifold-the-concept-that-changed-how-mathematicians-view-space/

#manifolds

There is a new episode on the #TheoreticalNeurosciencePodcast on low-dimensional #manifolds in #MotorCortex with Sara Solla ✌️, one of the pioneers of the manifold modelling approach in #Neuroscience.

🌍 http://theoreticalneuroscience.no/thn36

#CompNeuro #ComputationalNeuroscience

🧠 New #preprint by Komi et al. (2025): Neural #manifolds that orchestrate walking and stopping. Using #Neuropixels recordings from the lumbar spinal cord of freely walking rats, they show that #locomotion arises from rotational #PopulationDynamics within a low-dimensional limit-cycle #manifold. When walking stops, the dynamics collapse into a postural manifold of stable fixed points, each encoding a distinct pose.

🌍 https://doi.org/10.1101/2025.11.08.687367

#CompNeuro #NeuralDynamics #Attractor #Neuroscience

@axoaxonic @adredish Fully agree 👍 Horner's framework really begs for a formal dynamical model: defining trajectories, #attractors, and #manifolds within that 3D space. Something that could turn his conceptual #StateSpace into a genuine #computational theory of #memory dynamics.

I didn’t know Redish's book ("Beyond the Cognitive Map") before your comment! Sounds highly relevant and I’ll definitely put it on my reading list 👌

🚀✨ Behold, a #groundbreaking revelation: #counting isn't just for toddlers anymore! This esteemed cabal of academics has boldly ventured into the complex realm of... counting #characters with #imaginary #shapes. 🤯 #Manifolds have never felt so, well, manipulated! 💁‍♂️🔍
https://transformer-circuits.pub/2025/linebreaks/index.html #revelation #academic #research #HackerNews #ngated

When models manipulate manifolds: The geometry of a counting task

https://transformer-circuits.pub/2025/linebreaks/index.html

#HackerNews #models #manifolds #geometry #counting #task #AI #research

'Estimation of Local Geometric Structure on Manifolds from Noisy Data', by Yariv Aizenbud, Barak Sober.

http://jmlr.org/papers/v26/25-0183.html

#manifold #manifolds #submanifold

'Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds', by Clément Bonet, Lucas Drumetz, Nicolas Courty.

http://jmlr.org/papers/v26/24-0359.html

#manifolds #manifold #wasserstein

'Manifold Learning by Mixture Models of VAEs for Inverse Problems', by Giovanni S. Alberti, Johannes Hertrich, Matteo Santacesaria, Silvia Sciutto.

http://jmlr.org/papers/v25/23-0396.html

#autoencoders #manifold #manifolds

Nonlinear #manifolds underlie #NeuralPopulation activity during #behaviour – new #preprint by Fortunato et al. (2023)

🌍 https://www.biorxiv.org/content/10.1101/2023.07.18.549575v2

#CompNeuro #Neuroscoence

I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

#topology #AlgebraicTopology #geometry

I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

#topology #AlgebraicTopology #geometry

I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

#topology #AlgebraicTopology #geometry

I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

#topology #AlgebraicTopology #geometry

I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

#topology #AlgebraicTopology #geometry

Looking forward to tomorrow’s 2nd workshop on #symmetry, invariance and #NeuralRepresentations at the #BernsteinConference: #GroupTheory, #manifolds, and #Euclidean vs #nonEuclidean #geometry #perception … I’m pretty excited 🤟😊
#CompNeuro #computationalneuroscience

🌏 https://bernstein-network.de/bernstein-conference/program/satellite-workshops/neural-representations/

Discussing slide 49/237 with #chatgpt

#Embedded vs #Immersed #Manifolds

https://chat.openai.com/share/6cbf3e83-a52d-469e-8ea8-c003c06a1073

and with #bard

https://g.co/bard/share/f9fd23a81646

I will be at ICML for the workshops later this week. Thanks to @emtiyaz and Thomas (https://moellenh.github.io) for inviting me to the workshop on “Duality Principles for Modern Machine Learning” (https://dp4ml.github.io); hope to also attend the TAG-ML workshop https://www.tagds.com/events/conference-workshops/tag-ml23 Friday.

#ICML #Duality #Manifolds

'Large sample spectral analysis of graph-based multi-manifold clustering', by Nicolas Garcia Trillos, Pengfei He, Chenghui Li.

http://jmlr.org/papers/v24/21-1254.html

#laplacians #manifolds #laplacian

#Hopf #Fibration Explained Better than #EricWeinstein did on #JoeRogan

https://www.youtube.com/watch?v=PYR9worLEGo&ab_channel=TheTruthw%2FCarlosFarias

#HopfFibration #Physics #Math #Maths #Mathematics #Manifold #Manifolds #Geometry #ManifoldGeometry #NonManifoldGeometry #Dimensions #Dimensionality #Coordinates #Coordinate #PositionSpace #3Sphere

What is the #Hopf #Fibration?

The #HopfFibration commonly shows up in discussions surrounding #GaugeTheory and #Fundamental #Physics, though its construction is not so mysterious.

https://www.youtube.com/watch?v=nsHcKO7HvFY&ab_channel=Poppro

#Math #Maths #Mathematics #Manifold #Manifolds #Geometry #ManifoldGeometry #NonManifoldGeometry #Dimensions #Dimensionality #Coordinates #Coordinate #PositionSpace #3Sphere

Annemarie Kehl is next: LiveDocs on ENDOR, project A01

3D structures of #protein radicals reconstructed from electron-nuclear double resonance (#ENDOR) #spectroscopy, solving the statistical inverse problem which leads from measured spectra to geometric and electronic structure.
Spin dynamics, #Bayesian statistics on #manifolds, fast Markov-Chain-Monte-Carlo algorithms, conditioning molecular dynamics on observed spectra; representative biological system: ribonucleotide reductase from E. coli.

I've worked out that the injectivity radius under the Euclidean metric for the #unitary group U(n) is π and for real and special subgroups O(n), SO(n), and SU(n) is π√2.

This seems like a pretty basic property, but I can't find a single reference that gives the injectivity radii for any of these groups. Anyone know of one?

#DifferentialGeometry #LieGroups #Manifolds

#KleinBottles - #Numberphile

https://www.youtube.com/watch?v=AAsICMPwGPY&ab_channel=Numberphile

#KleinBottle #Topology #Math #Maths #Mathematics #Holes #CliffStoll #MSRI #Manifold #Manifolds

#KleinBottles - #Numberphile

https://www.youtube.com/watch?v=AAsICMPwGPY&ab_channel=Numberphile

#KleinBottle #Topology #Math #Maths #Mathematics #Holes #CliffStoll #MSRI #Manifold #Manifolds

#KleinBottles - #Numberphile

https://www.youtube.com/watch?v=AAsICMPwGPY&ab_channel=Numberphile

#KleinBottle #Topology #Math #Maths #Mathematics #Holes #CliffStoll #MSRI #Manifold #Manifolds

#KleinBottles - #Numberphile

https://www.youtube.com/watch?v=AAsICMPwGPY&ab_channel=Numberphile

#KleinBottle #Topology #Math #Maths #Mathematics #Holes #CliffStoll #MSRI #Manifold #Manifolds

#KleinBottles - #Numberphile

https://www.youtube.com/watch?v=AAsICMPwGPY&ab_channel=Numberphile

#KleinBottle #Topology #Math #Maths #Mathematics #Holes #CliffStoll #MSRI #Manifold #Manifolds

#arxivfeed

"Large sample spectral analysis of graph-based multi-manifold clustering'
https://arxiv.org/abs/2107.13610

#data #MMC #manifolds #clustering #graph #laplacian #statistics

#SignRelationalManifolds • 5

• https://inquiryintoinquiry.com/2022/11/06/sign-relational-manifolds-5-2/

Let me try to say in intuitive terms what I think is really going on here.

The problem is as old as those about #OtherMinds, #Intersubjectivity, or #Commensurability and it involves a whole slew of other old problems — #RealityVsAppearance or #RealityVsRepresentation, not to mention #TheOneAndTheMany. One way to sum up the question might be “conditions on the possibility of a #MutuallyObjectiveWorld ”.

#Peirce #Semiotics #Manifolds

#SignRelationalManifolds • 4
• http://inquiryintoinquiry.com/2022/11/05/sign-relational-manifolds-4-2/

Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general line of approach.

#RepresentationInvariantOntology

• https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#439

• https://web.archive.org/web/20141220180218/http://stderr.org/pipermail/inquiry/2003-April/000439.html

• https://web.archive.org/web/20141220180220/http://stderr.org/pipermail/inquiry/2003-April/000440.html

#Peirce #Semiotics #SignRelations
#Riemann #SergeLang #Manifolds
#DifferentialGeometry #DifferentialLogic

#SignRelationalManifolds • 3
• http://inquiryintoinquiry.com/2022/11/03/sign-relational-manifolds-3-2/

I'm not sure when it was I first noticed the relationship between #manifolds and #semiotics but I distinctly recall the passage in Serge Lang's Differential and Riemannian Manifolds (1995) which brought the triadic character of tangent vectors into high relief.

Excerpts from Lang's DARM

Chapter 2. Manifolds
2.1. #Atlases, #Charts, #Morphisms
• https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#442
2.2. #Submanifolds, #Immersions, #Submersions
• https://web.archive.org/web/20141220174800/http://stderr.org/pipermail/inquiry/2003-May/thread.html#448

#SignRelationalManifolds • 3
• http://inquiryintoinquiry.com/2022/11/03/sign-relational-manifolds-3-2/

I'm not sure when it was I first noticed the relationship between #manifolds and #semiotics but I distinctly recall the passage in Serge Lang's Differential and Riemannian Manifolds (1995) which brought the triadic character of tangent vectors into high relief.

Excerpts from Lang's DARM

Chapter 2. Manifolds
2.1. #Atlases, #Charts, #Morphisms
• https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#442
2.2. #Submanifolds, #Immersions, #Submersions
• https://web.archive.org/web/20141220174800/http://stderr.org/pipermail/inquiry/2003-May/thread.html#448