How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – ...

In this work, a finite volume formulation developed for two-dimensional models is extended to deal with axisymmetric models of heat conduction applications. This formulation uses a vertex centered ...

As enterprises increasingly demand fail-safes against single-vendor reliance, Sakana is proving that packaging collective intelligence into a single API endpoint is a highly viable commercial path.

AI is expected to increase productivity but human capacity remains limited. To fully leverage AI, humans need space for learning and deeper thinking.

In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

We study the problem of measuring group differences in choices when the dimensionality of the choice set is large. We show that standard approaches suffer from a severe finite-sample bias, and we ...

Abstract: For electromagnetic problems, physics-informed neural networks (PINNs) based on automatic differentiation (AD) often suffer from high computational cost and difficulty in accurately ...

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among ...

Abstract: In this paper, we present a hybrid finite difference/finite volume method and we apply it to solve an automotive electromagnetic compatibility (EMC) problem. The principles of the hybrid ...

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...

Current clear aligners have the problem of long treatment duration, and the effect of traditional molar distalization sequences is not ideal. To address these issues, this study proposes a new molar ...