ManifoldsBase.jl 0.14.10 introduces an interface to implement `Weigarten(M, p, X, V)` maps (https://juliamanifolds.github.io/ManifoldsBase.jl/dev/functions/#ManifoldsBase.Weingarten-Tuple{AbstractManifold,%20Any,%20Any,%20Any}).
Together with the new ManifoldDiff.jl 0.3.6 this allows for a generic implementation of a conversion from Euclidean to Riemannian Hessians for embedded submanifolds, see https://juliamanifolds.github.io/ManifoldDiff.jl/dev/library/#ManifoldDiff.riemannian_Hessian-Tuple{AbstractManifold,%20Any,%20Any,%20Any,%20Any}. #Manifolds #Julia

Neural Implicit Manifold Learning for Topology-Aware Density Estimation

https://openreview.net/forum?id=lTOku838Zv

#generative #manifolds #manifold

Wrapped $\beta$-Gaussians with compact support for exact probabilistic modeling on manifolds

https://openreview.net/forum?id=KrequDpWzt

#embedding #manifolds #hypersphere

New #preprint by @AitorMoraGre on #neural #manifolds in #V1 changing with top-down signals from #V4 targeting the foveal region

🌎 https://www.biorxiv.org/content/10.1101/2023.06.14.544966v1.article-info
#Twitter thread: https://twitter.com/AitorMoraGre/status/1669375717149220864 (including a cool animation 💫)

#computationalneuroscience #compneuro

'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

'Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metrics', by Mu Niu, Zhenwen Dai, Pokman Cheung, Yizhu Wang.

http://jmlr.org/papers/v24/22-0627.html

#gaussian #manifolds #manifold

'Online Optimization over Riemannian Manifolds', by Xi Wang, Zhipeng Tu, Yiguang Hong, Yingyi Wu, Guodong Shi.

http://jmlr.org/papers/v24/21-1308.html

#manifolds #optimization #manifold

'Density estimation on low-dimensional manifolds: an inflation-deflation approach', by Christian Horvat, Jean-Pascal Pfister.

http://jmlr.org/papers/v24/21-0235.html

#manifolds #manifold #densities

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.

Learning Identity-Preserving Transformations on Data Manifolds

Marissa Catherine Connor, Kion Fallah, Christopher John Rozell

https://openreview.net/forum?id=gyhiZYrk5y

#transformations #manifolds #manifold

Manifold Density Estimation via Generalized Dequantization

https://openreview.net/forum?id=MnnoMhFeFb

#manifolds #manifold #densities

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

next step is welding the manifold mounts and pushing the manifold through the wool.

I'll put details on the manifold separately.

#propane #manifolds #assembly #ribbonforge

@julesh I'd never heard of locales before your post, but also, how many people actually use *just* topological spaces with no additional structure?
In the area of maths where I live, it's Hausdorff spaces, #manifolds (top or smooth, sometimes non-Hausdorff), CW complexes...
Otherwise, history is a powerful force, and if you want to teach students differential or algebraic #topology, starting from point-set topology is easy and feels very natural.

I see a lot of fellow neuroscientists are now moving to the neuromatch instance. I see how this movement to a topic-based instance make total sense, as you now get the hottest takes on #manifolds or #bayesian statistics fresh in your neighborhood.

#SignRelationalManifolds • Discussion 1

• https://inquiryintoinquiry.com/2022/11/07/sign-relational-manifolds-discussion-1-2/

Torkild Thellefsen asks on #Facebook, “What's at the End of a Chain of Interpretants?”

It is a #RecurringQuestion — I answered as I often do.

#SemioticManifolds, like physical & mathematical manifolds, may be finite & bounded or infinite & unbounded but they may also be finite & unbounded, having no boundary in the topological sense. Thus #UnboundedSemiosis does not imply #InfiniteSemiosis.

#Peirce #Semiotics #Manifolds

#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

I just migrated to bayes.club, so here is another (and hopefully the last for a while) introduction

I'm a #MachineLearning engineer with a focus on probabilistic programming at @unituebingen where I help scientists use ML for their research. In the office and out, one of my main passions is #FOSS, and I work on a number of #OpenSource packages, mostly in #JuliaLang :julia: with a focus on #ProbProg, #manifolds, and #AutoDiff.

#introduction

#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