Reducedness of twisted loop groups
We give an elementary proof of the reducedness of twisted loop groups along the lines of the Kneser-Tits problem.
math.RT↗
arXiv subjects
Zhiyuan Ding
Publications and source records attributed to Zhiyuan Ding.
Detective Quantum Efficiency of the Timepix4 Hybrid Pixel Detector and its Application to Parallel-Beam Diffraction
The detective quantum efficiency (DQE) and normalised noise power spectrum (NNPS) of the Timepix4 hybrid pixel detector in event-driven mode in TEM have been measured at 100 kV and 200 kV. In a raw data readout mode, the zero-frequency DQE exceeds 0.9 at both 100 kV and 200 kV. At the Nyquist frequency, the DQE remains above 0.2 at 100 kV but drops close to zero at 200 kV. Initial parallel-beam diffraction data from a polycrystalline gold nanoparticle sample is reported which shows that at 200 kV Timepix4 can detect weak diffracted information beyond a 75 mrad half-angle.
physics.ins-det↗
Knowledge Condensation Distillation
Knowledge Distillation (KD) transfers the knowledge from a high-capacity teacher network to strengthen a smaller student. Existing methods focus on excavating the knowledge hints and transferring the whole knowledge to the student. However, the knowledge redundancy arises since the knowledge shows different values to the student at different learning stages. In this paper, we propose Knowledge Condensation Distillation (KCD). Specifically, the knowledge value on each sample is dynamically estimated, based on which an Expectation-Maximization (EM) framework is forged to iteratively condense a compact knowledge set from the teacher to guide the student learning. Our approach is easy to build on top of the off-the-shelf KD methods, with no extra training parameters and negligible computation overhead. Thus, it presents one new perspective for KD, in which the student that actively identifies teacher's knowledge in line with its aptitude can learn to learn more effectively and efficiently. Experiments on standard benchmarks manifest that the proposed KCD can well boost the performance of student model with even higher distillation efficiency. Code is available at https://github.com/dzy3/KCD.
cs.CV↗
A toy model of shtukas
Motivated by the question of constructing certain rational functions (modular units) on the moduli stack of Drinfeld shtukas, we introduce the notion of toy shtukas. We prove basic properties of the moduli scheme of toy shtukas. Analogously to horospherical divisors on the moduli stack of Drinfeld shtukas, there are toy horospherical divisors on the moduli scheme of toy shtukas. We describe the space of principal toy horospherical divisors. There is a canonical morphism from the moduli stack of Drinfeld shtukas to the moduli scheme of toy shtukas. Our main result is a description of the space of principal horospherical divisors obtained from the pullback.
math.AG↗
Construction of certain rational functions on the moduli stack of Drinfeld shtukas
We construct certain rational functions (modular units) on the moduli stack of Drinfeld shtukas. The divisors of these rational functions are supported on horospherical divisors of the moduli stack. The key to our construction is a vanishing theorem for shtukas with zeros and poles satisfying certain conditions. Using deformation theory, we calculate the divisors of these rational functions.
math.AG↗