DeepStruct

Math,AI,Vibe Coding,Science,Physics

[DeepStruct @appleyami3]

Coupled spring oscillators exhibit the classic beat phenomenon. Energy rhythmically transfers back and forth between the two masses, creating a continuous and mesmerizing periodic exchange. ⚛️

[DeepStruct @appleyami3]

nice

[Kimi.ai @Kimi_Moonshot]

🌘 Kimi-K2.7-Code, our latest coding model, is now released and open-sourced!

🔷 Improved coding & agent performance over K2.6: +21.8% on Kimi Code Bench v2, +11.0% on Program Bench, and +31.5% on MLS Bench Lite.
🔷 Reasoning efficiency: Less overthinking, with 30% lower reasoning-token usage compared to K2.6.
🔷 Long-horizon coding: Improved instruction following, higher end-to-end coding task success rates.

⚡️ 6x High-Speed Mode coming soon!
🔌 Available today via Kimi API and Kimi Code.

🔗 Kimi Code: https://t.co/uvoSJKyGCY
🔗 API: https://t.co/EOZkbOwCN4

[DeepStruct @appleyami3]

Van der Pol oscillator limit cycle

[DeepStruct @appleyami3]

Lorenz Attractor in Chaos and Nonlinear Dynamics

[DeepStruct @appleyami3]

Simplified Simulation of Supernova Explosion.

[DeepStruct @appleyami3]

I was supposed to simulate galaxy evolution, but what on earth did I end up simulating?

[DeepStruct @appleyami3]

I’ve always thought free math books are absolutely amazing. Math cultivates rational thinking and wisdom, and scientific decision-making often lies rooted in mathematics. Thanks for sharing.

[Antonio Lupetti @antoniolupetti]

"Introduction to Applied Linear Algebra" from Stanford University is one of the best free introductions to applied linear algebra I have come across.

This resource develops vectors, matrices, and least squares from first principles, connecting them to data fitting, machine learning, optimisation, image processing and control systems.

It is a resource I would recommend to students, engineers, and anyone interested in understanding the mathematical foundations of modern data science.

https://t.co/EiQPHvQn7p

[DeepStruct @appleyami3]

Metal Recrystallization Grain Growth

[DeepStruct @appleyami3]

Cellular Automaton Physics Simulation — Forest Fire Model

[DeepStruct @appleyami3]

Three-body gravitational perturbation

[DeepStruct @appleyami3]

2D wave physics simulation in pure Python 🎯
Solves the 2D wave equation using finite differences (leap-frog method) with sponge layer boundary absorption.
#Python #Physics #Simulation #WaveEquation #ComputationalPhysics

[DeepStruct @appleyami3]

Physics in motion! 🎬
I simulated a vibrating string fixed at both ends. See how waves travel, invert when reflecting off boundaries, and perfectly reconstruct the original pulse every 2 seconds.
Energy oscillation between kinetic and potential forms + first 5 harmonic modes.

[DeepStruct @appleyami3]

Ever wondered what water flowing through a Klein bottle would look like? This 30-second simulation shows high-speed particles cascading down the impossible surface, complete with dynamic trails, splash effects, and gradient coloring.
#MathArt #3DSimulation #Topology

[Yi Ma @YiMaTweets]

Our new open-source book on the Principles and Practice of Deep Representation Learning (A Mathematical Theory of Memory) is now posted on the arXiv: https://t.co/EGURnwZr6H I will offer a new graduate course this fall at the University of Hong Kong. Everything will be open sourced!

[Mathematica @mathemetica]

Pascal's Rule reveals how combinations are built:
the ways to choose k from n+1 objects equals the ways to choose k from n plus the ways to choose k-1 from n.

(n + 1 choose k) = (n choose k) + (n choose k - 1)
Its algebraic proof manipulates factorials directly, while the combinatorial proof considers two mutually exclusive cases for object selection.

This rule is applied in probability theory, computer algorithms, and statistical analysis.

[Mathematica @mathemetica]

From perceptrons and feed-forward networks to LSTMs, GRUs, GANs, convolutional nets, residual connections, capsule networks, and attention mechanisms, this chart maps major neural network architectures with standardized diagrams and a clear legend for cell types and connections.

These designs power image recognition in medical diagnostics, language translation in virtual assistants, recommendation engines on streaming platforms, and autonomous systems in robotics and self-driving vehicles.

[Mathematica @mathemetica]

Planes in 3D geometry can be fully described using a point and a normal vector.

This diagram illustrates the vector equation of a plane: n · (r − r₀) = 0 or n · r = n · r₀, where n is the normal vector, r is the position vector to point P(x, y, z), and r₀ to known point P₀(x₀, y₀, z₀).
It also shows the scalar form a(x − x₀) + b(y − y₀) + c(z − z₀) = 0, with all vectors and points clearly labeled.

These equations are used in computer graphics for surface rendering, engineering for structural design, and data science for support vector machines.

[Mathematica @mathemetica]

Quadric surfaces shape everything from planetary models to architectural marvels.

These diagrams depict the six classic forms - the ellipsoid, elliptical paraboloid, elliptical cone, hyperboloids of one and two sheets, and hyperbolic paraboloid - complete with their cross-sections and defining equations, including x²/a² + y²/b² + z²/c² = 1 for the ellipsoid and y²/b² − x²/a² = z/c (c > 0) for the hyperbolic paraboloid.

Quadric surfaces have practical uses in real life, including hyperboloid cooling towers in power plants, parabolic reflectors in satellite dishes and telescopes, and hyperbolic paraboloid structures in contemporary architecture.

[Massimo @Rainmaker1973]

Rubiks cube and graph theory.

[🎞️ jagarikin]

[Urs Schreiber @UrsSchreiber]

Cover draft of the upcoming GOC monograph:
https://t.co/PKJo0tGY7s