Abstract: In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a ...

Abstract: We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis ...

To learn how to use this wrapper, see example subdir in the source directory. Notation for the two-particle Green's functions is adopted from the PhD thesis of Lewin Boehnke. This program is free ...

Paid media is often treated like a checklist item in a marketing plan: launch a few search ads, run a Meta campaign, maybe test YouTube if there’s budget left. But not all paid media is created equal, ...

Ahead of the November presidential election, just 19% of Americans say democracy in the United States is a good example for other countries to follow, according to a Pew Research Center survey ...

From ancient Greek soapbox soliloquies to viral TikTok videos of poetry slams, spoken word has always charged language with kinetic immediacy. Encompassing a unique blend of honesty and an engaging ...

The publics surveyed are largely skeptical that democracy in the U.S., at least in its current form, is a good example for other countries to follow. A median of four-in-ten across the 34 nations ...

Many processed foods have nutritional value and are safe to eat on a regular basis, unlike ultraprocessed foods. A dietitian shares how to tell the difference. Much of the food we eat has been ...

Imagine a frame so close that every subtle twitch becomes a narrative in itself. That’s the essence of an extreme close-up shot. In the world of filmmaking, this technique isn’t just about zooming ...

As education becomes more an experience of learning in the digital age, technologies play a pivotal role in reshaping the learning experiences of K-12 students. From interactive applications to ...