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dynamical machine learning volumetric reconstruction of objects’ interiors from limited angular views

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Light(Science & Applications) 2021年第5期10卷 824-844页

作者： Iksung Kang Alexandre Goy George Barbastathis Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology77 Massachusetts AveCambridgeMAUSA Department of Mechanical Engineering Massachusetts Institute of TechnologyCambridgeMA 02139USA Singapore-MIT Alliance for Research and Technology(SMART)Centre 1 Create WaySingapore 117543Singapore Omnisens SA Morges 1110Switzerland

Limited-angle tomography of an interior volume is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al. Proc. Natl. Acad. Sci. 116, 19848–19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in the angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as a better fit to regularize the reconstructions. We devised a Recurrent Neural Network (RNN) architecture with a novel Separable-Convolution Gated Recurrent Unit (SC-GRU) as the fundamental building block. Through a comprehensive comparison of several quantitative metrics, we show that the dynamic method is suitable for a generic interior-volumetric reconstruction under a limited-angle scheme. We show that this approach accurately reconstructs volume interiors under two conditions: weak scattering, when the Radon transform approximation is applicable and the forward operator well defined;and strong scattering, which is nonlinear with respect to the 3D refractive index distribution and includes uncertainty in the forward operator.

关键词： interior dynamical angular

dynamical Convergence Trajectory in Networks

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Chinese Physics Letters 2005年第9期22卷 2447-2450页

作者：谭宁张云俊欧阳颀耿直 Department of Physics and Center for Theoretical Biology Peking University Beijing 100871 School of Mathematical Sciences Peking University Beijing 100871 不详

It is well known that topology and dynamics are two major aspects to determine the function of a network. We study one of the dynamic properties of a network： trajectory convergence, i.e. how a system converges to its steady state. Using numerical and analytical methods, we show that in a logical-like dynamical model, the occurrence of convergent trajectory in a network depends mainly on the type of the fixed point and the ratio between activation and inhibition links. We analytically proof that this property is induced by the competition between two types of state transition structures in phase space： tree-like transition structure and star-like transition structure. We show that the biological networks, such as the cell cycle network in budding yeast, prefers the tree-like transition structures and suggest that this type of convergence trajectories may be universal.

关键词： dynamical Convergence Trajectory

dynamical classification of topological quantum phases

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Science Bulletin 2018年第21期63卷 1385-1391页

作者： Lin Zhang Long Zhang Sen Niu Xiong-Jun Liu International Center for Quantum Materials School of PhysicsPeking UniversityBeijing 100871China Collaborative Innovation Center of Quantum Matter Beijing 100871China Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and TechnologyShenzhen 518055China

Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete with ongoing challenges in both theory and experiment. Here we propose to establish a universal non-equilibrium characterization of the equilibrium topological quantum phases classified by integers, and further propose the high-precision dynamical schemes to detect such states. The framework of the dynamical classification theory consists of basic theorems. First, we uncover that classifying a d-dimensional(dD) gapped topological phase of generic multibands can reduce to a(d-1)D invariant defined on so-called band inversion surfaces(BISs), rendering a bulk-surface duality which simplifies the topological characterization. Further, we show in quenching across phase boundary the(pseudo) spin dynamics to exhibit unique topological patterns on BISs, which are attributed to the post-quench bulk topology and manifest a dynamical bulk-surface correspondence. For this the topological phase is classified by a dynamical topological invariant measured from an emergent dynamical spintexture field on the BISs. Applications to quenching experiments on feasible models are proposed and studied, demonstrating the new experimental strategies to detect topological phases with high feasibility. This work opens a broad new direction to classify and detect topological phases by non-equilibrium quantum dynamics.

关键词： Quench dynamics Topological quantum phase Band inversion surface Bulk-surface duality dynamical topological invariant Ultracold atoms Synthetic gauge field

dynamical Temperature of a One- Dimensional Many-Body Systerm in the Lennard-Jones Model

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Chinese Physics Letters 2001年第9期18卷 1170-1172页

作者：刘觉平袁保仑 Department of Physics Wuhan UniversityWuhan 430072

A new way to derive the formula of the dynamical temperature by using the invariance of the Liouville measure and the ergodicity hypothesis is presented, based on the invariance of the functional under the transformation of the measure. The obtained dynamical temperature is intrinsic to the underlying dynamics of the system. A molecular dynamical simulation of a one-dimensional many-body system in the Lennard-Jones model has been performed. The temperature calculated from the Hamiltonian for the stationary state of the system coincides with that determined with the thermodynamical method.

关键词： method measure dynamical

dynamical Influence of Nodes Revisited: A Markov Chain Analysis of Epidemic Process on Networks

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Chinese Physics Letters 2012年第4期29卷 248-251页

作者：李平张捷许小可 SMALL Michael Center for Networked Systems School of Computer ScienceSouthwest Petroleum UniversityChengdu 610500 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum UniversityChengdu 610500 Center for Computational Systems Biology Fudan UniversityShanghai 200433 Hong Kong Polytechnic University Hung HomKowloonHong Kong School of Communication and Electronic Engineering Qingdao Technological UniversityQingdao 2665206 School of Mathematics and Statistics University of Western AustraliaCrawleyWA 6009Australia

We provide a theoretical analysis of node importance from the perspective of dynamical processes on *** particular,using Markov chain analysis of the susceptible-infected-susceptible (SIS) epidemic model on networks,we derive the node importance in terms of dynamical behaviors on network in a theoretical *** is found that this quantity happens to be the eigenvector centrality under some conditions,which bridges the topological centrality measure of the nodes with the dynamical influence of the nodes for the dynamical *** furthermore discuss the condition under which the eigenvector centrality is valid for dynamical phenomena on networks.

关键词： process dynamical eigenvector

dynamical Behaviour of a Modulated Torsion Pendulum in Test of Weak Equivalence Principle

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Chinese Physics Letters 2005年第8期22卷 1837-1840页

作者：岳英范淑华刘琳霞罗俊 DepartmentofPhysics HuazhongUniversityofScienceandTechnologyWuhan430074

The dynamic behaviour of a modulated torsion pendulum used to test the weak equivalence principle (WEP) is studied in detail. Theoretical analysis shows that the pendulum will be driven by a force with double-frequency of the rotating turntable no matter whether the WEP is valid or not. This double-frequency effect should be considered for improving the sensitivity of the modulated pendulum in test of the WEP.

关键词： WEP dynamical Principle

dynamical Evolution of Highway Traffic Flow:from Microscopic to Macroscopic

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Chinese Physics Letters 1997年第3期14卷 202-205页

作者：汪秉宏许伯铭顾国庆 Department of Modern Physics and The Center of Nonlinear Science University of Science and Technology of ChinaHefei 230026 Department of Physics The Chinese University of Hong KongShatinNTHong Kong Department of System Engineering Shanghai University of Science and TechnologyShanghai 200093

In this paper,a derivation of the macroscopic mean field theory of the cellular automaton(CA)model of highway traffic flow starting from the microscopic dynamical point of view is *** from an equation describing the time evolution of the Boolean state variable at each site of the basic CA model,and using a two-site approximation for the multi-site correlation functions,a dynamical mapping between the macroscopic average speeds v(t+1)and v(t)at different time can be *** field results consistent with the simulation data are obtained by considering the attractors of the mapping and their corresponding basins.

关键词： dynamical macroscopic starting

dynamical Analysis and Exact Solutions of a New(2+1)-Dimensional Generalized Boussinesq Model Equation for Nonlinear Rossby Waves

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Communications in Theoretical Physics 2019年第9期71卷 1054-1062页

作者：刘全生张再云张瑞岗黄创霞 School of Mathematical Sciences Inner Mongolia UniversityHohhot010021China School of Aeronautics Science and Engineering Beihang UniversityBeijing100191China School of Mathematics Hunan Institute of Science and TechnologyYueyang414006China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Scienceand Technology Changsha410014China School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha410014China

In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta *** methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.

关键词： generalized Boussinesq model equation nonlinear Rossby waves dynamical analysis traveling wave solutions nonlinear perturbation expansions bifurcation theory of planar dynamical systems

dynamical Symmetries of Two-Dimensional Dirac Equation with Screened Coulomb and Isotropic Harmonic Oscillator Potentials

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Communications in Theoretical Physics 2014年第11期61卷 663-666页

作者：王青侯玉龙隆正文荆坚 College of Physics Science and Technology Xinjiang University Department of Physics and Electronic School of Science Beijing University of Chemical Technology Laboratory for Photoelectric Technology and Application Department of Physics Guizhou University

In this paper, we study symmetrical properties of two-dimensional(2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude(SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly,the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed.

关键词： dynamical symmetry Dirac oscillator isotropic Hydrogen oscillator