In application to general relativity, we use the space model corresponding to the special four-dimensional space which is Euclidean with respect to space coordinates and Riemannian with respect to the ...

Artificial Intelligence - two words that spark equal parts excitement and existential dread. But what exactly is AI? Is it the unseen force behind your eerily well-timed online ads? The chatbot ...

This limitation hinders the representation learning capability of the models. To address this issue, this paper focuses on how to better extend the representation learning from a single space to ...

With iPhones and many other devices now featuring USB-C, it's clear that the interface is here to stay. Here's why that's a good thing—even if not every USB-C port is created equal. I’m the ...

This paper tackles the Fourier Transform (FT) PR problem for sparse signals. We recast the FT PR as a novel optimization problem on the Riemannian manifold by leveraging the sparsity and structural ...

Imposter syndrome is when you doubt your own skills and successes. You feel you're not as talented or worthy as others believe, and you're scared that one day, people will realize that. Although ...

Before it was associated with the song "Clutterfunk" from Geometry Dash, the image of the cat, which appears to be a Photoshop or AI-generated image mixing a cat with a human, first popped up online ...

Telegram may be among the most popular messaging services in the world, yet many still don’t know what it’s all about. The app is often name-dropped in discussions regarding online privacy and ...

RTX Mega Geometry was revealed at CES 2025 with a range of compelling demos, but now we have our first example of the technology in a shipping game: Alan Wake 2. There are quality, efficiency and ...

Differential geometry I: Riemannian manifolds, geodesics, Levi-Civita-connection, Lemma of Gauß, Theorem of Hopf-Rinow, curvature tensor, first and second variation formula, Lemma of Synge, Theorem of ...

Capogna’s research is in analysis and partial differential equations. He is also interested in analytic aspects of quasiconformal mappings, sub-Riemannian geometry and geometric flows. More recently, ...