Vens L.

« Les mathématiques, c’est d’abord agir, pas apprendre. »
A. Connes

[Vens L. @de_toute_facon]

@fermatslibrary Another attempt to visualize « power ladder »:

[Vens L. @de_toute_facon]

@BensOscarMath @Cshearer41 Instead of vector dot product, my usual approach is complex number arithmetic.

[Gabriel Peyré @gabrielpeyre]

Oldies but goldies: Prim, R. C, Shortest connection networks And some generalizations, 1957. Computes the minimum spanning tree in n*log(n) operations. https://t.co/UueYoQwSZE

[Keenan Crane @keenanisalive]

A discrete Markov chain is basically a random walk on a graph, where each outgoing edge has a fixed probability.

Cool fact: any initial distribution on a sufficiently nice* Markov chain converges to its stationary distribution after many steps—because it's a contraction mapping.

[らんまる👀✨ @Sg3Lu]

正十二角形の面積の求め方を
視覚的に表現した映像！

[Yann Le Gall @Yann_LeGall]

newton fractal, smoothly interpolating between 0 to 8 iterations

[Gabriel Peyré @gabrielpeyre]

Optimal transport flows define particle evolutions which are classical gradient flows over the positions of the particles. Pairwise interaction potentials are ubiquitous in physics, biology, and chemistry. Corresponds to non-local PDEs over the densities.

[Cliff Pickover @pickover]

Mathematics, physics, programming.

The choices of our lives. The paths untaken. The breathing of reality.

By @FabriceNEYRET, https://t.co/a3PQDl9PEe, Used with permission.

[Gabriel Peyré @gabrielpeyre]

Encoding points as roots of polynomials and interpolating their coefficients.
Great way to interpolate between point sets. Inspired by Jens Bossaert.
https://t.co/XUGpin8fg9

[Gabriel Peyré @gabrielpeyre]

Oldies but goldies: J. Hammersley, The zeros of a random polynomial, 1956. Zeros of random polynomials define point processes. For iid coefficients, zeros cluster along the unit circle as the degree increases. https://t.co/pa6w0Xgl2H

[Vens L. @de_toute_facon]

@abakcus Somehow, magically, this unrelated problem has the same answer.
[cf. 2003, HMMT Guts Round #12]

[Sander Huisman @SGHuisman]

Flow around a Joukowsky airfoil. Notice that the lines of same color don't meet at the rear. Falsifying the 'equal transit' explanation of lift generated by an airfoil. Particles split at the front, simply don't have to join at the rear at the same time…

[Gabriel Peyré @gabrielpeyre]

The geometric, arithmetic, and arithmetic-geometric means can be extended to complex numbers. https://t.co/SkeXmdZKyW

[Vignette @vi_ne_te]

Making an interactive Möbius transformation visualizer!

You can try it out live here:

https://t.co/qe41LKmWMX

Feedback appreciated. Still a work in progress, feel free to suggest new features.

[prof-g @prof_g]

18/ if you’d like to contemplate the artwork, i’ve built an online gallery (thanks to friends at @oncyber). you can walk around and see the original works for yourself.
(these are 1/1 originals, archived)
https://t.co/m926KuXFly

[Keenan Crane @keenanisalive]

Basic boolean logical operations can be constructed by combinations of just unions and set complements (via "De Morgan's laws").

In probability & measure theory these rules serve to generate a "σ-algebra", i.e., the collection of sets which can be assigned a size or probability.

[Dugan @DuganHammock]

4D Hypertorus passing through 3D Flatland

[Keenan Crane @keenanisalive]

Tired of making the same kind of diagrams over and over by hand (e.g., in PowerPoint)?

The @UsePenrose team has been working away on Penrose 3.0, an automated notation-to-diagram tool, finally released today!

Check it out here: https://t.co/dJNMEzrPZR

[prof-g @prof_g]

the 1st video of my series w/ on
Foundations of Topological Data Analysis
is up on YouTube.
it's about combinatorial simplices & simplicial complexes.
(link below)

[Michael Breakspear @DrBreaky]

One hundred years of wave equations of physical systems from Schrödinger's model of the atom to neural field theory of the brain

Both formulations predict that the system's expressed energy is constrained into natural modes - "eigenstates - determined by the system's geometry

[Gabriel Peyré @gabrielpeyre]

Eigenvalues of random matrices with iid entries converge to the Wigner circle law. This is universal (does not depend on the law of the entries), as proved by Tao and Vu in 2010. For Gaussian matrices, this defines a determinental point process. https://t.co/QDaQO93HYG