arXiv subjects

Yining Zhang

Publications and source records attributed to Yining Zhang.

41 records · Page 3Linked to original sources

arXiv2020

Hodge decomposition of string topology

Let $X$ be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ of the free loop space of $X$ preserves the Hodge decomposition of $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture proposed in our earlier work.

math.QA↗

arXiv2019

A Statistical Study of the Magnetic Imprints of X-Class Solar Flares

Magnetic imprints, the rapid and irreversible evolution of photospheric magnetic fields as a feedback from flares in the corona, have been confirmed by many previous studies. These studies showed that the horizontal field will permanently increase at the polarity inversion line (PIL) after eruptions, indicating that a more horizontal geometry of photospheric magnetic field is produced. In this study, we analyze 20 X-class flares since the launch of the Solar Dynamics Observatory (SDO) in 15 active regions (ARs) with heliographic angle no greater than 45 degrees. We observe clear magnetic imprints in 16 flares, whereas 4 flares are exceptional. The imprint regions of the horizontal field are located not only at the PIL but also at sunspot penumbra with strong vertical fields. Making use of the observed mass and speed of the corresponding coronal mass ejections (CMEs) , we find that the CMEs with larger momenta are associated with stronger magnetic imprints. Furthermore, a linear relationship, with a Kendall's Tau-b coefficient 0.54, between the CME momentum and the change of Lorentz force is revealed. Based on that, we quantify the back reaction time to be around 70 s, with a 90% confidence interval from about 50 s to 90 s.

astro-ph.SR↗

arXiv2018

Cyclic pairings and derived Poisson structures

There is a canonical derived Poisson structure on the universal enveloping algebra $\mathcal{U}\mathfrak{a}$ of a (DG) Lie algebra $\mathfrak{a}$ that is Koszul dual to a cyclic cocommutative (DG) coalgebra. Interesting special cases of this derived Poisson structure include (an analog of) the Chas-Sullivan bracket on string topology. We study how certain derived character of $\mathfrak{a}$ intertwine this derived Poisson structure with the induced Poisson structure on the representation homology of $\mathfrak{a}$. In addition, we obtain an analog of one of our main results for associative algebras.

math.QA↗

arXiv2018

Removing the Feature Correlation Effect of Multiplicative Noise

Multiplicative noise, including dropout, is widely used to regularize deep neural networks (DNNs), and is shown to be effective in a wide range of architectures and tasks. From an information perspective, we consider injecting multiplicative noise into a DNN as training the network to solve the task with noisy information pathways, which leads to the observation that multiplicative noise tends to increase the correlation between features, so as to increase the signal-to-noise ratio of information pathways. However, high feature correlation is undesirable, as it increases redundancy in representations. In this work, we propose non-correlating multiplicative noise (NCMN), which exploits batch normalization to remove the correlation effect in a simple yet effective way. We show that NCMN significantly improves the performance of standard multiplicative noise on image classification tasks, providing a better alternative to dropout for batch-normalized networks. Additionally, we present a unified view of NCMN and shake-shake regularization, which explains the performance gain of the latter.

cs.LG↗

arXiv2016

Dual Hodge decompositions and derived Poisson brackets

We study general properties of Hodge-type decompositions of cyclic and Hochschild homology of universal enveloping algebras of (DG) Lie algebras. Our construction generalizes the operadic construction of cyclic homology of Lie algebras due to Getzler and Kapranov. We give a topological interpretation of such Lie Hodge decompositions in terms of $S^1$-equivariant homology of the free loop space of a simply connected topological space. We prove that the canonical derived Poisson structure on a universal enveloping algebra arising from a cyclic pairing on the Koszul dual coalgebra preserves the Hodge filtration on cyclic homology. As an application, we show that the Chas-Sullivan Lie algebra of any simply connected closed manifold carries a natural Hodge filtration. We conjecture that the Chas-Sullivan Lie algebra is actually graded, i.e. the string topology bracket preserves the Hodge decomposition.

math.QA↗