arXiv subjects

Chao Liang

Publications and source records attributed to Chao Liang.

68 records · Page 4Linked to original sources

arXiv2022

Valley Piezoelectric Mechanism for Interpreting and Optimizing Piezoelectricity in Quantum Materials via Anomalous Hall Effect

Quantum materials have exhibited attractive electro-mechanical responses, but their piezoelectric coefficients are far from satisfactory due to the lack of fundamental mechanisms to benefit from the quantum effects. We discovered the valley piezoelectric mechanism that is absent in traditional piezoelectric theory yet promising to overcome this challenge. A theoretical model was developed to elucidate the valley piezoelectricity as the Valley Hall effect driven by pseudoelectric field, which can be significant in quantum systems with broken time reversal symmetry. Consistent tight-binding and density-functional-theory (DFT) calculations validate the model and unveil the crucial dependence of valley piezoelectricity on valley splitting, hybridization energy, bandgap, and Poisson ratio. Doping, passivation, and external stress are proposed as rational strategies to optimize piezoelectricity, with a more than 130% increase of piezoelectricity demonstrated by DFT simulations. The general valley piezoelectric model bridges the gap between electro-mechanical response and quantum effects, which opens an opportunity to achieve outstanding piezoelectricity in quantum materials via optimizing spin-valley and spin-orbit couplings.

physics.comp-ph↗

arXiv2021

One More Check: Making "Fake Background" Be Tracked Again

The one-shot multi-object tracking, which integrates object detection and ID embedding extraction into a unified network, has achieved groundbreaking results in recent years. However, current one-shot trackers solely rely on single-frame detections to predict candidate bounding boxes, which may be unreliable when facing disastrous visual degradation, e.g., motion blur, occlusions. Once a target bounding box is mistakenly classified as background by the detector, the temporal consistency of its corresponding tracklet will be no longer maintained. In this paper, we set out to restore the bounding boxes misclassified as ``fake background'' by proposing a re-check network. The re-check network innovatively expands the role of ID embedding from data association to motion forecasting by effectively propagating previous tracklets to the current frame with a small overhead. Note that the propagation results are yielded by an independent and efficient embedding search, preventing the model from over-relying on detection results. Eventually, it helps to reload the ``fake background'' and repair the broken tracklets. Building on a strong baseline CSTrack, we construct a new one-shot tracker and achieve favorable gains by 70.7 $\rightarrow$ 76.4, 70.6 $\rightarrow$ 76.3 MOTA on MOT16 and MOT17, respectively. It also reaches a new state-of-the-art MOTA and IDF1 performance. Code is released at https://github.com/JudasDie/SOTS.

cs.CV↗

arXiv2020

Feature Robust Optimal Transport for High-dimensional Data

Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for high-dimensional data, which solves high-dimensional OT problems using feature selection to avoid the curse of dimensionality. Specifically, we find a transport plan with discriminative features. To this end, we formulate the FROT problem as a min--max optimization problem. We then propose a convex formulation of the FROT problem and solve it using a Frank--Wolfe-based optimization algorithm, whereby the subproblem can be efficiently solved using the Sinkhorn algorithm. Since FROT finds the transport plan from selected features, it is robust to noise features. To show the effectiveness of FROT, we propose using the FROT algorithm for the layer selection problem in deep neural networks for semantic correspondence. By conducting synthetic and benchmark experiments, we demonstrate that the proposed method can find a strong correspondence by determining important layers. We show that the FROT algorithm achieves state-of-the-art performance in real-world semantic correspondence datasets.

stat.ML↗

arXiv2018

$C^1$-openness of non-uniform hyperbolic diffeomorphisms with bounded $C^2$ norm

We study the $C^1$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^2$ partially hyperbolic symplectic systems which have bounded $C^2$ distance to the identity. In this set, we prove the stability of non-uniform hyperbolicity as a function of the diffeomorphism and the measure, and the existence of an open and dense subset of continuity points for the center Lyapunov exponents. These results are generalized to the volume-preserving context.

math.DS↗

arXiv2018

Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle

We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps are $C^r$ open and there exists a $C^r$ open and dense subset of continuity points for the center Lyapunov exponents. We also generalize these results to volume-preserving systems.

math.DS↗

arXiv2017

Smarr formula for BTZ black holes in general three-dimensional gravity models

Recent studies have presented the interpretation of thermodynamic enthalpy for the mass of BTZ black holes and the corresponding Smarr formula. All these are made in the background of three-dimensional (3D) general relativity. In this paper, we extend such interpretation into general 3D gravity models. It is found that the direct extension is unfeasible and some extra conditions are required to preserve both the Smarr formula and the first law of black hole thermodynamics. Thus, BTZ black hole thermodynamics enforces some constraints for general 3D gravity models, and these constraints are consistent with all previous discussions.

gr-qc↗

arXiv2016

Variational equalities of entropy in nonuniformly hyperbolic systems

In this paper we prove that for an ergodic hyperbolic measure $ω$ of a $C^{1+α}$ diffeomorphism $f$ on a Riemannian manifold $M$, there is an $ω$-full measured set $\widetildeΛ$ such that for every invariant probability $μ\in \mathcal{M}_{inv}(\widetildeΛ,f)$, the metric entropy of $μ$ is equal to the topological entropy of saturated set $G_μ$ consisting of generic points of $μ$: $$h_μ(f)=h_{\top}(f,G_μ).$$ Moreover, for every nonempty, compact and connected subset $K$ of $\mathcal{M}_{inv}(\widetildeΛ,f)$ with the same hyperbolic rate, we compute the topological entropy of saturated set $G_K$ of $K$ by the following equality: $$\inf\{h_μ(f)\mid μ\in K\}=h_{\top}(f,G_K).$$ In particular these results can be applied (i) to the nonuniformy hyperbolic diffeomorphisms described by Katok, (ii) to the robustly transitive partially hyperbolic diffeomorphisms described by ~Ma{ñ}{é}, (iii) to the robustly transitive non-partially hyperbolic diffeomorphisms described by Bonatti-Viana. In all these cases $\mathcal{M}_{inv}(\widetildeΛ,f)$ contains an open subset of $\mathcal{M}_{erg}(M,f)$.

math.DS↗

arXiv2015

The $C^1$ density of nonuniform hyperbolicity in $C^{ r}$ conservative diffeomorphisms

Let $\Diff^{ r}_m(M)$ be the set of $C^{ r}$ volume-preserving diffeomorphisms on a compact Riemannian manifold $M$ ($\dim M\geq 2$). In this paper, we prove that the diffeomorphisms without zero Lyapunov exponents on a set of positive volume are $C^1$ dense in $\Diff^{ r}_m(M), r\geq 1$. We also prove a weaker result for symplectic diffeomorphisms $\mathcal{S}ym^{r}_ω(M), r\geq1 $ saying that the symplectic diffeomorphisms with non-zero Lyapunov exponents on a set of positive volume are $C^1$ dense in $\mathcal{S}ym^{r}_ω(M), r\geq1 $.

math.DS↗

arXiv2015

On density of positive Lyapunov exponents for $C^1$ symplectic diffeomorphisms

Let $M$ be a 2$d-$dimensional compact connected Riemannian manifold and $ω$ be a symplectic form on $M$. In this paper, we prove that a symplectic diffeomorphism, with all Lyapunov exponent zero for almost everywhere, can be $C^1$ approximated by one with a positive Lyapunov exponent for a positive-measured subset of $M$. That is, the set \[ \left\{ f\in \mathcal{S}ym^1_ω(M)\,| \begin{array}{ll} &\mbox{The largest Lyapunov exponent }λ_1(f,\,x)>0\\ &\mbox{ for a positive measure set } \end{array} \right\} \] is dense in $\mathcal{S}ym^1_ω(M)$. \end{abstract} \end{center}

math.DS↗

arXiv2015

Some New Symplectic Multiple Timestepping Methods for Multiscale Molecular Dynamics Models

We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are obtained by eliminating the dominant terms in the error. These new methods can be viewed as a generalization of the impulse method. In the implementation of these methods, the long-range forces only need to be computed on the slow time scale, which reduces the computational cost considerably. Preliminary analysis for the energy conservation property is provided.

math.NA↗

arXiv2012

Approximation of Oseledets Splittings

We prove that the Oseledets splittings of an ergodic hyperbolic measure of a $C^{1+ r}$ diffeomorphism can be approximated by that of atomic measures on hyperbolic periodic orbits. This removes the assumption on simple spectrum in \cite{Liang} and strengthens Katok's closing lemma.

math.DS↗

arXiv2010

Some results on perturbations to Lyapunov exponents

In this paper, we study two properties of the Lyapunov exponents under small perturbations: one is when we can remove zero Lyapunov exponents and the other is when we can distinguish all the Lyapunov exponents. The first result shows that we can perturb all the zero integrated Lyapunov exponents $\int_M λ_j(x)dω(x)$ into nonzero ones, for any partially hyperbolic diffeomorphism. The second part contains an example which shows the local genericity of diffeomorphisms with non-simple spectrum and three results: one discusses the relation between simple-spectrum property and the existence of complex eigenvalues; the other two describe the difference on the spectrum between the diffeomorphisms far from homoclinic tangencies and those in the interior of the complement. Moreover, among the conservative diffeomorphisms far from tangencies, we prove that ergodic ones form a residual subset.

math.DS↗

arXiv2010

Ergodic Properties of Invariant Measures for C^{1+α} nonuniformly hyperbolic systems

For an ergodic hyperbolic measure $ω$ of a $C^{1+α}$ diffeomorphism, there is an $ω$ full-measured set $\tildeΛ$ such that every nonempty, compact and connected subset $V$ of $\mathbb{M}_{inv}(\tildeΛ)$ coincides with the accumulating set of time averages of Dirac measures supported at {\it one orbit}, where $\mathbb{M}_{inv}(\tildeΛ)$ denotes the space of invariant measures supported on $\tildeΛ$. Such state points corresponding to a fixed $V$ are dense in the support $supp(ω)$. Moreover, $\mathbb{M}_{inv}(\tildeΛ)$ can be accumulated by time averages of Dirac measures supported at {\it one orbit}, and such state points form a residual subset of $supp(ω)$. These extend results of Sigmund [9] from uniformly hyperbolic case to non-uniformly hyperbolic case. As a corollary, irregular points form a residual set of $supp(ω)$.

math.DS↗

arXiv2005

Circle bundles over 4-manifolds

Every 1-connected topological 4-manifold M admits a $S^{1}$-covering by $#_{r-1}S^{2}\times S^{3}$, where $r=$rank$H^{2}(M;\QTR{Bbb}{Z})$.

math.GT↗