Zobrazeno 1 - 10
of 330
pro vyhledávání: '"Shen, Alexander"'
Autor:
Xu, Zongzhe, Gupta, Ritvik, Cheng, Wenduo, Shen, Alexander, Shen, Junhong, Talwalkar, Ameet, Khodak, Mikhail
Following its success for vision and text, the "foundation model" (FM) paradigm -- pretraining large models on massive data, then fine-tuning on target tasks -- has rapidly expanded to domains in the sciences, engineering, healthcare, and beyond. Has
Externí odkaz:
http://arxiv.org/abs/2411.02796
Autor:
Shen, Alexander
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow) surprising exampl
Externí odkaz:
http://arxiv.org/abs/2405.09304
Autor:
Shen, Alexander
The exposition in Euclid's Elements contains an obvious gap (seemingly unnoticed by most commentators): he often compares not just angles, but *groups* of angles, and at the same time he avoids summing angles (and considering angles greater than $\pi
Externí odkaz:
http://arxiv.org/abs/2404.02272
Autor:
Shen, Alexander
The notion of a normal bit sequence was introduced by Borel in 1909; it was the first definition of an individual random object. Normality is a weak notion of randomness requiring only that all $2^n$ factors (substrings) of arbitrary length~$n$ appea
Externí odkaz:
http://arxiv.org/abs/2403.01534
Autor:
Dorigo, Tommaso, Aehle, Max, Donini, Julien, Doro, Michele, Gauger, Nicolas R., Izbicki, Rafael, Lee, Ann, Masserano, Luca, Nardi, Federico, S, Sidharth S, Shen, Alexander
In this document we describe a model of an array of water Cherenkov detectors proposed to study ultra-high-energy gamma rays in the southern hemisphere, and a continuous model of secondary particles produced on the ground from gamma and proton shower
Externí odkaz:
http://arxiv.org/abs/2310.01857
Autor:
Shen, Alexander
I was lucky to meet (and even cooperate at some extent) with Israel M. Gelfand, and tried to write down (mainly in 2003-2013) my recollections about his work style and lessons I learned from him about teaching and writing mathematics (though the view
Externí odkaz:
http://arxiv.org/abs/2308.12128
Autor:
Shen, Alexander
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the effective
Externí odkaz:
http://arxiv.org/abs/2306.12769
Autor:
Shen, Alexander
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical) counterpart: a stu
Externí odkaz:
http://arxiv.org/abs/2305.19882
Autor:
Shen, Alexander
This note provides a simplified exposition of the proof of hierarchical Kraft lemma proven by Barmpalias and Lewis-Pye and its consequences for the oracle use in the Ku\v{c}era--G\'acs theorem (saying that every sequence is Turing reducible to a rand
Externí odkaz:
http://arxiv.org/abs/2304.04852