Shi Chen, Kenji Fukushima, Hiromichi Nishimura, Yuya Tanizaki
We discuss the deconfinement and the CP-breaking phase transitions at $θ=π$ in Yang-Mills theories. The 't Hooft anomaly matching prohibits the confined phase with CP symmetry and requires $T_{dec}(θ=π) \le T_{CP}$, where $T_{dec}(θ=π)$ and $T_{CP}$ denote the deconfinement and the CP-restoration temperatures, respectively, at $θ=π$. We analytically study these two phase transitions in softly-broken $\mathcal{N}=1$ supersymmetric Yang-Mills theories on small $\mathbb{R}^3\times S^1$ with the periodic boundary condition for gluinos. For most gauge groups except SU(2) in this model, we find that the inequality is saturated, so deconfinement and CP restoration occur simultaneously. We demonstrate special features of the SU(2) gauge theory: There is a finite window of two temperatures, $T_{dec}(π)<T_{CP}$, which indicates the existence of a novel CP-broken deconfined phase. We also discuss an implication of the novel phase for domain walls and their junctions.
Chen Shi, Marco Velli, Fulvia Pucci, Anna Tenerani, Maria Elena Innocenti
The tearing mode instability is one important mechanism that may explain the triggering of fast magnetic reconnection in astrophysical plasmas such as the solar corona and the Earth's magnetosphere. In this paper, the linear stability analysis of the tearing mode is carried out for a current sheet in the presence of a guide field, including the Hall effect. We show that the presence of a strong guide field does not modify the most unstable mode in the two-dimensional wave vector space orthogonal to the current gradient direction, which remains the fastest growing parallel mode. With the Hall effect, the inclusion of a guide field turns the non-dispersive propagation along the guide field direction to a dispersive one. The oblique modes have a wave-like structure along the normal direction of the current sheet and a strong guide field suppresses this structure while making the eigen-functions asymmetric.
Shi Chen, Qin Li, Xu Yang
The varying-mass Schrödinger equation (VMSE) has been successfully applied to model electronic properties of semiconductor hetero-structures, for example, quantum dots and quantum wells. In this paper, we consider VMSE with small random heterogeneities, and derive a radiative transfer equation as its asymptotic limit. The main tool is to systematically apply the Wigner transform in the classical regime when the rescaled Planck constant $ε\ll 1$, and expand the Wigner equation to proper orders of $ε$. As a proof of concept, we numerically compute both VMSE and its limiting radiative transfer equation, and show that their solutions agree well in the classical regime.
Shi Chen, Qin Li, Jianfeng Lu, Stephen J. Wright
We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress local solution manifolds. Our framework is applied to a semilinear elliptic equation with oscillatory media and a nonlinear radiative transfer equation; in both cases, significant improvements in efficacy are observed. This new method does not rely on detailed analytical understanding of the multiscale PDEs, such as their asymptotic limits, and thus is more versatile for general multiscale problems.
Shi Chen, Qin Li
It is a classical derivation that the Wigner equation, derived from the Schrödinger equation that contains the quantum information, converges to the Liouville equation when the rescaled Planck constant $ε\to0$. Since the latter presents the Newton's second law, the process is typically termed the (semi-)classical limit. In this paper, we study the classical limit of an inverse problem for the Schrödinger equation. More specifically, we show that using the initial condition and final state of the Schrödinger equation to reconstruct the potential term, in the classical regime with $ε\to0$, becomes using the initial and final state to reconstruct the potential term in the Liouville equation. This formally bridges an inverse problem in quantum mechanics with an inverse problem in classical mechanics.
Shi Chen, Kenji Fukushima, Yusuke Shimada
We perturbatively compute the Polyakov loop potential at high temperature with finite imaginary angular velocity. This imaginary rotation does not violate the causality and the thermodynamic limit is well defined. We analytically show that the imaginary angular velocity induces the perturbatively confined phase and serves as a new probe to confinement physics. We discuss a possible phase diagram that exhibits adiabatic continuity from the perturbative confinement to the confined phase at low temperature. We also mention subtlety in the analytical continuation from imaginary to real angular velocity by imposing a causality bound.
Shi Chen, Qi Zhao
Visual attention has shown usefulness in image captioning, with the goal of enabling a caption model to selectively focus on regions of interest. Existing models typically rely on top-down language information and learn attention implicitly by optimizing the captioning objectives. While somewhat effective, the learned top-down attention can fail to focus on correct regions of interest without direct supervision of attention. Inspired by the human visual system which is driven by not only the task-specific top-down signals but also the visual stimuli, we in this work propose to use both types of attention for image captioning. In particular, we highlight the complementary nature of the two types of attention and develop a model (Boosted Attention) to integrate them for image captioning. We validate the proposed approach with state-of-the-art performance across various evaluation metrics.
Shi Chen, Yuya Tanizaki
Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover this phenomenon in a concrete quantum field theory, the $4$d $\mathbb{C}P^1$ model. This model has two kinds of solitonic excitations, vortices and hopfions, which would follow two $U(1)$ solitonic symmetries according to homotopy groups. Nevertheless, we demonstrate the nonexistence of the hopfion $U(1)$ symmetry by evaluating the hopfion charge of vortex operators. We clarify that what conserves hopfion numbers is a non-invertible symmetry generated by 3d spin topological quantum field theories (TQFTs). Its invertible part is just $\mathbb{Z}_2$, which we recognize as a spin bordism invariant. Compared with the 3d $\mathbb{C}P^1$ model, our work suggests a unified description of solitonic symmetries and couplings to topological phases.
Shi Chen, Yuya Tanizaki
Originating from the topology of the path-integral target space $Y$, solitonic symmetry describes the conservation law of topological solitons and the selection rule of defect operators. As Ref.~\cite{Chen:2022cyw} exemplifies, the conventional treatment of solitonic symmetry as an invertible symmetry based on homotopy groups is inappropriate. In this paper, we develop a systematic framework to treat solitonic symmetries as non-invertible generalized symmetries. We propose that the non-invertible solitonic symmetries are generated by the partition functions of auxiliary topological quantum field theories (TQFTs) coupled with the target space $Y$. We then understand solitonic symmetries as non-invertible cohomology theories on $Y$ with TQFT coefficients. This perspective enables us to identify the invertible solitonic subsymmetries and also clarifies the topological origin of the non-invertibility in solitonic symmetry. We finally discuss how solitonic symmetry relies on and goes beyond the conventional wisdom of homotopy groups. This paper is aimed at a tentative general framework for solitonic symmetry, serving as a starting point for future developments.
Shi Chen, JiaKun Dan, ZiYu Chen, JianFeng Li
The possibility of spontaneous magnetization due to the "asymmetry in mass" of charge carriers in a system is investigated. Analysis shows that when the masses of positive and negative charge carriers are identical, no magnetization is predicted. However, if the masses of two species are different, spontaneous magnetic field would appear, either due to the equipartition of magnetic energy or due to fluctuations together with a feedback mechanism. The conditions for magnetization to occur are also obtained, in the form of n-T phase diagram. The theory proposed here, if confirmed by future observations and/or experiments, would provide a new insight on the origin of magnetic fields in the universe.
Chen Shi, Fang Yuan
Apr 28, 2009·q-bio.PE·PDF Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this paper we present a dynamic programming implemented method to compute 2x2 non-cooperative finite resource allocation game's payoff matrix. We assume in one population there exists two types of individuals, aggressive and non-aggressive and each individual has equal and finite resource. The strength of individual could be described by a function of resource consumption in discrete development stages. Each individual undergoes logistic growth hence we divide the development into three stages: initialization, quasilinear growth and termination. We first discuss the theoretical frame of how to dynamic programming to calculate payoff matrix then give three numerical examples representing three different types of aggressive individuals and calculate the payoff matrix for each of them respectively. Based on the numerical payoff matrix we further investigate the evolutionary stable strategies (ESS) of the games.
Shi Chen, Lefei Zhang, Liangpei Zhang
Hyperspectral image super-resolution has attained widespread prominence to enhance the spatial resolution of hyperspectral images. However, convolution-based methods have encountered challenges in harnessing the global spatial-spectral information. The prevailing transformer-based methods have not adequately captured the long-range dependencies in both spectral and spatial dimensions. To alleviate this issue, we propose a novel cross-scope spatial-spectral Transformer (CST) to efficiently investigate long-range spatial and spectral similarities for single hyperspectral image super-resolution. Specifically, we devise cross-attention mechanisms in spatial and spectral dimensions to comprehensively model the long-range spatial-spectral characteristics. By integrating global information into the rectangle-window self-attention, we first design a cross-scope spatial self-attention to facilitate long-range spatial interactions. Then, by leveraging appropriately characteristic spatial-spectral features, we construct a cross-scope spectral self-attention to effectively capture the intrinsic correlations among global spectral bands. Finally, we elaborate a concise feed-forward neural network to enhance the feature representation capacity in the Transformer structure. Extensive experiments over three hyperspectral datasets demonstrate that the proposed CST is superior to other state-of-the-art methods both quantitatively and visually. The code is available at \url{https://github.com/Tomchenshi/CST.git}.
Shi Chen, Ming Jiang, Qi Zhao
In recent years, deep saliency models have made significant progress in predicting human visual attention. However, the mechanisms behind their success remain largely unexplained due to the opaque nature of deep neural networks. In this paper, we present a novel analytic framework that sheds light on the implicit features learned by saliency models and provides principled interpretation and quantification of their contributions to saliency prediction. Our approach decomposes these implicit features into interpretable bases that are explicitly aligned with semantic attributes and reformulates saliency prediction as a weighted combination of probability maps connecting the bases and saliency. By applying our framework, we conduct extensive analyses from various perspectives, including the positive and negative weights of semantics, the impact of training data and architectural designs, the progressive influences of fine-tuning, and common failure patterns of state-of-the-art deep saliency models. Additionally, we demonstrate the effectiveness of our framework by exploring visual attention characteristics in various application scenarios, such as the atypical attention of people with autism spectrum disorder, attention to emotion-eliciting stimuli, and attention evolution over time. Our code is publicly available at \url{https://github.com/szzexpoi/saliency_analysis}.
Chen Shi, Marco Velli, Anna Tenerani
Magnetohydrodynamic simulations have shown that a non-unique critical Lundquist number $S_c$ exists, hovering around $S_c \sim 10^4$, above which threshold Sweet-Parker type stationary reconnecting configurations become unstable to a fast tearing mode dominated by plasmoid generation. It is known that the flow along the sheet plays a stabilizing role, though a satisfactory explanation of the non-universality and variable critical Lundquist numbers observed is still lacking. Here we discuss this question using 2D linear MHD simulations and linear stability analyses of Sweet-Parker type current sheets in the presence of background stationary inflows and outflows at low Lundquist numbers ($S\le 10^4$). Simulations show that the inhomogeneous outflow stabilizes the current sheet by stretching the growing magnetic islands and at the same time evacuating the magnetic islands out of the current sheet. This limits the time during which fluctuations which begin at any given wave-length can remain unstable, rendering the instability non-exponential. We find that the linear theory based on the expanding-wavelength assumption works well for $S$ larger than $\sim 1000$. However we also find that the inflow and location of the initial perturbation also affect the stability threshold.
Chen Shi, Nikos Sioulas, Zesen Huang, Marco Velli, Anna Tenerani, Victor Réville
Aug 23, 2023·astro-ph.SR·PDF We conduct 3D magnetohydrodynamic (MHD) simulations of decaying turbulence in the solar wind context. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counter-propagating Alfvén waves and exhibits an isotropic power spectrum. Our findings reveal the consistent generation of negative residual energy whenever nonlinear interactions are present, independent of the normalized cross helicity $σ_c$ and compressibility. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with $[S_2(\mathbf{b})-S_2(\mathbf{u})] \propto l_\perp$ or equivalently $-E_r \propto k_\perp^{-2}$. Here $S_2(\mathbf{b})$ and $S_2(\mathbf{u})$ are second-order structure functions of magnetic field and velocity respectively. In most runs, $S_2(\mathbf{b})$ develops a scaling relation $S_2(\mathbf{b}) \propto l_\perp^{1/2}$ ($E_b \propto k_\perp^{-3/2}$). In contrast, $S_2(\mathbf{u})$ is consistently shallower than $S_2(\mathbf{b})$, which aligns with in-situ observations of the solar wind. We observe that the higher-order statistics of the turbulence, which act as a proxy for intermittency, depend on the initial $σ_c$ and are strongly affected by the expansion effect. Generally, the intermittency is more pronounced when the expansion effect is present. Finally, we find that in our simulations although the negative residual energy and intermittency grow simultaneously as the turbulence evolves, the causal relation between them seems to be weak, possibly because they are generated on different scales.
Sixu Li, Shi Chen, Qin Li
Score-based Generative Models (SGMs) is one leading method in generative modeling, renowned for their ability to generate high-quality samples from complex, high-dimensional data distributions. The method enjoys empirical success and is supported by rigorous theoretical convergence properties. In particular, it has been shown that SGMs can generate samples from a distribution that is close to the ground-truth if the underlying score function is learned well, suggesting the success of SGM as a generative model. We provide a counter-example in this paper. Through the sample complexity argument, we provide one specific setting where the score function is learned well. Yet, SGMs in this setting can only output samples that are Gaussian blurring of training data points, mimicking the effects of kernel density estimation. The finding resonates a series of recent finding that reveal that SGMs can demonstrate strong memorization effect and fail to generate.
Shi Chen, Erik Sandström, Sandro Lombardi, Siyuan Li, Martin R. Oswald
Achieving truly practical dynamic 3D reconstruction requires online operation, global pose and map consistency, detailed appearance modeling, and the flexibility to handle both RGB and RGB-D inputs. However, existing SLAM methods typically merely remove the dynamic parts or require RGB-D input, while offline methods are not scalable to long video sequences, and current transformer-based feedforward methods lack global consistency and appearance details. To this end, we achieve online dynamic scene reconstruction by disentangling the static and dynamic parts within a SLAM system. The poses are tracked robustly with a novel motion masking strategy, and dynamic parts are reconstructed leveraging a progressive adaptation of a Motion Scaffolds graph. Our method yields novel view renderings competitive to offline methods and achieves on-par tracking with state-of-the-art dynamic SLAM methods.
Yuejie Zhang, Jinjun Ding, Tao Liu, Xiaofei Yang, Taoyuan Ouyang, Shi Chen, Yongqing Peng
We report that due to the orbital Hall effect, orbital pumping effects can occur in materials with weak spin-orbit coupling. Moreover, there is a positive correlation between the strength of the orbital Hall effect and the size of spin-pumping. During the spin-pumping, with the enhancement of the orbital Hall effect, the resonant absorption of orbital current and the damping of the ferromagnetic layer also increase. Especially, when the thickness of Ti reaches 60 nm, the orbital -mixing conductance of Ti/Co is an order of magnitude higher than spin-mixing conductance of heavy metal/Co, reaching 474.1 3 ^18 m^(-2). The results indicate that the orbital current is more easily transmitted across the interface
Shi Chen, Zhiyan Ding, Qin Li
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy a large number of interactive samples, and the communication between these samples is crucial in speeding up the convergence. To justify the validity of these sampling strategies, the concept of interacting particles naturally calls for the mean-field theory. The theory establishes a correspondence between particle interactions encoded in a set of coupled ODEs/SDEs and a PDE that characterizes the evolution of the underlying distribution. This bridges numerical algorithms with the PDE theory used to show convergence in time. Many mathematical machineries are developed to provide the mean-field analysis, and we showcase two such examples: The coupling method and the compactness argument built upon the martingale strategy. The former has been deployed to show the convergence of ensemble Kalman sampler and ensemble Kalman inversion, and the latter will be shown to be immensely powerful in proving the validity of the Vlasov-Boltzmann simulator.
Chen Shi, Zhao Chen, Christina Dan Wang
Identifying individual mediators is a central goal of high-dimensional mediation analysis, yet pervasive dependence among mediators can invalidate standard debiased inference and lead to substantial false discovery rate (FDR) inflation. We propose a Factor-Adjusted Debiased Mediation Testing (FADMT) framework that enables large-scale inference for individual mediation effects with FDR control under complex dependence structures. Our approach posits an approximate factor structure on the unobserved errors of the mediator model, extracts common latent factors, and constructs decorrelated pseudo-mediators for the subsequent inferential procedure. We establish the asymptotic normality of the debiased estimator and develop a multiple testing procedure with theoretical FDR control under mild high-dimensional conditions. By adjusting for latent factor induced dependence, FADMT also improves robustness to spurious associations driven by shared latent variation in observational studies. Extensive simulations demonstrate the superior finite-sample performance across a wide range of correlation structures. Applications to TCGA-BRCA multi-omics data and to China's stock connect study further illustrate the practical utility of the proposed method.