We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian i...
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossible, to check. By taking advantage of several relaxations of the probl...
The pretraining-finetuning paradigm has become the prevailing trend in modern deep learning. In this work, we discover an intriguing linear phenomenon in models that are initialized from a common pretrained checkpoint and finetuned on different tasks...
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The origin of obscuration in Active Galactic Nuclei (AGN) is still a matter of contention. It is unclear whether obscured AGN are primarily due to line-of-sight effects, a transitory, dust-enshrouded phase in galaxy evolution, or a combination of bot...
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Generative AI has put many professional writers on the defensive; a major negotiation point of the recent Writers Guild of America's strike concerned use of AI. However, must AI threaten writers, their livelihoods or their creativity? And under what...
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We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in one-to-one...
Applying the Poincare-Birkhoff-Witt property and the Groebner-Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of V. Ginzburg and M. Kapranov of a pair of compatible Lie brackets. We stat...
You’ve probably seen this line on every beauty page — *“Glowing skin starts from within.”* But here’s the catch: most of us don’t really believe it. We buy new serums every month, layer o...
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