Manus become a big hype, and in a few day, anus posted open-source codes replicating manus, so let me dive into manus codes to see how to build a multi0agent cool app leveraging AI! The Anus AI agent architecture combines the best aspects of OpenManus and OWL while introducing unique features that address limitations in … Continue reading How to Build a Multi-Agent Cool App Levering AI

If I measure three points in a space with three temperature, it's easy and straightforward to interpolate every point in this triangle so I have a smooth view approximately. We can use simple weighting schema depending on distance to each of the three points. It's exactly the same logic to be applied when elevate to … Continue reading Discrete Differential Geometry: Interpolation and Discretization

Here are the examples of exterior derivative computations for 0-forms, 1-forms, and 2-forms provided by deepseek: Note exterior derivative of the 1-form looks like Green's theorem. Let me try to deduce the exterior derivative of 1-form: This is the stunning beauty of MATH!

In calculus, we learn that the derivative measures change. But in a deeper mathematical sense, differentiation acts as the opposite of taking a boundary. This idea is best understood using the language of differential forms and chains. At its core, differentiation isn't just about slopes—it's about how things flow across a space. And just as … Continue reading Derivative is the Opposite of the Boundary

To thoroughly grasp the concept of a gradient, one needs to think deeply. First, we must understand that the gradient represents the steepest slope, which can be illustrated with an analogy like standing at a position on a mountain. However, while analogies can be helpful, they are often not rigorous enough. Mathematics, on the other … Continue reading Is Gradient a Vector or 1-Form?

Differential Forms is a beauty! Multivariable calculus can be greatly simplified and generalized when applying differential forms.

I have written 4 blogs on MCP several months ago and am glad to see that it's integrated in Windsurf and Cursor now. Basically, MCP is a standardized interface so AI agents can communicate seamlessly to various servers such as servers of Github, Slack, Google map, so on and so forth and certainly could be … Continue reading MCP is Available in Windsurf and Cursor

A cylinder can be viewed as a fiber bundle: The Möbius band is a slightly more complicated example but still a fiber bundle. Here's how we can understand it:

Let's consider our familiar workflow of portfolio weighting and capping. Have you ever thought about the essence of weight capping? When we cap a position at 10% and redistribute the excess weight proportionally to the rest of the portfolio, what are we really doing? In essence, we're optimizing the portfolio weights by minimizing a weight … Continue reading A Simple Perceptron to Understand Neural Network

It's essential to understand Stokes' Theorem, why? first of all, it's a higher dimensional generalization of the fundamental theorem of calculus. to dive deep, first understand or go over basic concepts again: what is k form in R n? then what is derivative of this k form in Rn? Examples to make it more concrete: