arXiv subjects
Publications and source records attributed to Wang Cong.
In this paper, we provide examples to show that for $1 \leq k \leq n/2$, solutions to $k$-Hessian equations $S_k(D^2u)=1$ in the exterior of a strictly convex domain need not be quasiconvex, when prescribing quadratic growth at infinity. Additionally, we give a new proof for the quasiconvexity of harmonic functions in such exterior domains that decay to zero at infinity.
In this paper, we propose SmartFreeze, a framework that effectively reduces the memory footprint by conducting the training in a progressive manner. Instead of updating the full model in each training round, SmartFreeze divides the shared model into blocks consisting of a specified number of layers. It first trains the front block with a well-designed output module, safely freezes it after convergence, and then triggers the training of the next one. This process iterates until the whole model has been successfully trained. In this way, the backward computation of the frozen blocks and the corresponding memory space for storing the intermediate outputs and gradients are effectively saved. Except for the progressive training framework, SmartFreeze consists of the following two core components: a pace controller and a participant selector. The pace controller is designed to effectively monitor the training progress of each block at runtime and safely freezes them after convergence while the participant selector selects the right devices to participate in the training for each block by jointly considering the memory capacity, the statistical and system heterogeneity. Extensive experiments are conducted to evaluate the effectiveness of SmartFreeze on both simulation and hardware testbeds. The results demonstrate that SmartFreeze effectively reduces average memory usage by up to 82%. Moreover, it simultaneously improves the model accuracy by up to 83.1% and accelerates the training process up to 2.02X.
Mismatched lattice-constants at a van-der-Waals epitaxy interface often introduce in-plane strains to the lattice of the epitaxial layer, termed epitaxy-strain, where the strains do not follow the intra-layer Poisson's relation. Here, we presented the magnetic phase diagrams of the CrSe2 and CrTe2 mono- and bi-layers under epitaxy-strain up to 8 %, as predicted using density-functional-theory calculations. They show that the in-plane epitaxy-strain manipulates either the intra- or inter-layer magnetism of them. The in-plane strain varies the interlayer distance, defined using an inter-layer Poisson's ratio, which governs the inter-layer magnetism in two opposite ways depending on the in-plane magnetism. The tunability of the intra-layer magnetism is a result of competing intra-layer Cr-Cr super-exchange interactions. A graphene substrate was introduced to examine the validity of our diagrams in practice. Our work also gives a tentative explanation on the controversially reported magnetizations in CrSe2 and CrTe2 epitaxial mono- or bi-layers under epitaxy-strains.
In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincaré's one \cite{Po}, the Furta's one, part of Chen's ones, and the Shi's one. The key point in the proof of our main results is that functionally independence of generalized rational functions implies the functionally independence of their lowest order rational homogeneous terms.