Uzu Lim

GitHub - gdisarra/topology-degree: Demo and tutorial for the computation of the topology degree Demo and tutorial for the computation of the topology degree - gdisarra/topology-degree

🚀 Just released a new tool for the neuroscience and Topological Data Analysis communities!
🔗 github.com/gdisarra/top...

The topology-degree repository provides code and methods to quantify the topology in high-dimensional data using persistent homology.
🔗 doi.org/10.1371/jour...

@jeffgian.bsky.social Do you ever need to use spinors when doing Lattice QCD? To consider quarks, and not just gluons?

Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories Motivated by recent literature on the possible existence of a second higher-temperature phase transition in Quantum Chromodynamics, we revisit the proposal that colour confinement is related to the dy...

Xavier Crean, @jeffgian.bsky.social and Biagio Lucini worked on analysing the topological data arising from lattice gauge theory, like Lattice QCD. See : arxiv.org/abs/2501.19320

I think this is one of the super meaningful applications of TDA, because the data is intrinsically topological (SU(3)).

If you apply the path integral approach to a discretised computer simulation of QCD, you get Lattice QCD. When doing Lattice QCD, I think you assign SU(3) elements to each edge of a 4D cubical grid. That now gives you ... some topological data. Tada..!

The QCD Lagrangian has a Dirac operator which makes quarks and gluons interact. With this Lagrangian, you can either write down scattering amplitudes or Feynman path integrals. My understanding is that the path integral approach still keeps the differential geometry intact.

I forgot what a spinor is.. a Spin group is a subset of a Clifford algebra. You need this stuff to define fermions, which are electrons and quarks (and other stuff like neutrino). To define quantum chromodynamics (QCD), you get the spin bundle and also a SU(3)-bundle and define a Lagrangian.

A connection 1-form is also called a gauge field. This formalises, for example, gluon fields. For a full formal account of the standard model, you still need a lot more abstract machinery. Next up is spinors.

A connection 1-form omega is a g-valued 1-form on P, satisfying some well-behavedness wrt G. Ehremsann connection and connection 1-form are equivalent notions, and the horizontal subspace specified in Ehresmann connection is exactly the kernel of the projection map specified by a connection 1-form.

An Ehresmann connection H is a sub-bundle of the tangent bundle of a principal G-bundle P->M (double bundle??) The rank of H is equal to the dimension of the base manifold M. H is chosen so that it's "horizontal" and well-behaved wrt G-action.

Learning gauge theory nowadays, another attempt to learn more mathematical physics

happy mother's day

"Excuse me, I'll tell you when you've finished"

A computation that took us over 8 hours now only takes 15 seconds with tropical geometry! Very excited that Oskar Henriksson will join the algebra in data analysis (AIDA) group @mpicbg.bsky.social @tudresden.bsky.social

Cover Learning for Large-Scale Topology Representation Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold lear...

My paper with Luis Scoccola and @haharrington.bsky.social were accepted to present in ICML 2025 🥳🥳
We use gradient descent to solve a fundamental problem in computational topology: Compute a topologically good cover of a dataset. It improves Mapper and persistent homology!

arxiv.org/abs/2503.09767

Hi, this is my new professional account :)
I'm a mathematician working on geometry and topology of data. Recently I'm focused on Bobrowski-Skraba's universal statistical law of persistent homology, and also neuroscience applications - toroidal grid cell topology.

helo

would u accept "shittification"
also theres a math word called "sheafification"

me soon

더불어 저 본인도 upper middle class으로 세상을 다분히 비뚤어지게 봤는데, 여러 이유로 이제는 좌파로 정체화하게 됐어요. 더 정직하고 바르게 살 수 있게 됐어요.

카투사로 일할때 미국 유학간 애들이 다 그런 느낌이었어서 여러모로 인상이 안좋게 박힌 기억이 나네요.

he seemed viral in south korea, what's big about him?

For #WorldCamelDay 🐪🐫:
4 figurines of Bactrian #Camels
Yotkan, Xinjiang, China, 1st–6th c. CE
Clay, H 7.6, 6.0, 3.8, 3.3 cm
British Museum collection MAS.24, MAS.8, 1902,1220.375, MAS.25:
www.britishmuseum.org/collection/o...

🌱Lark Ascending.
A stunning performance this season. Only more good things to come.

reminds me of the "The Boring Side" that the ingredient lists get written as for the "hip" companies like Oatley and Aussie

나미비아 고등법원, 식민시대 제정된 동성애 금지법 "위헌" 나미비아 대법원이 동성애를 범죄화한 식민지 시대의 법률 두 개를 위헌이라고 결정했다.21일(현지시각) 로이토통신에 따르면 나미비아 대법원은 영국 인권단체의 지원을 받은 시민사회단체 HDT(Human Dignity Trust) 활동가 프리데 다우사브가 제기한 헌법소원에서 위헌결정을 내렸

나미비아 대법원이 동성애를 범죄화한 식민지 시대의 법률 두 개를 위헌이라고 결정했다.
www.womennews.co.kr/news/article...

smel flowa every day........ lov is everywhere

@nyuvyu.bsky.social bee kind

hi angel wow...

“인간이 가끔 엉망일지라도···차별에 맞선 싸움은 계속된다” [플랫] 어떤 차별은 공기처럼 존재한다. 어느새 소수자를 에워싼다. 소수자는 차별의 시선을 스스로 내면화하기에 이른다. 모욕에 가까운 차별을 당해도 피해망상은 아닐까 자기검열하는 식이...

어떤 차별은 공기처럼 존재한다. 어느새 소수자를 에워싼다. 소수자는 차별의 시선을 스스로 내면화하기에 이른다. 모욕에 가까운 차별을 당해도 피해망상은 아닐까 자기검열하는 식이다. 섣불리 부당하다고 말했다가는 혐오의 표적이 될 수도 있다. 결코 사소할 수 없는 소수자의 감정을 캐시 박 홍 UC버클리대 교수는 ‘마이너 필링스(minor feelings·소수적 감정)’라고 이름 붙였다.
m.khan.co.kr/culture/cult...