arXiv subjects

Qi Zhou

Publications and source records attributed to Qi Zhou.

At least 145 records · Page 8Linked to original sources

arXiv2023

Rural Access Index: A global study

The Rural Access Index (RAI), one of the UN Sustainable Development Goal indicators (SDG 9.1.1), represents the proportion of the rural population residing within 2 km of all-season roads. It reflects the accessibility of rural residents to transportation services and could provide guidance for the improvement of road infrastructure. The primary deficiencies in assessing the RAI include the limited studying area, its incomplete meaning and the absence of correlation analysis with other influencing factors. To address these issues, this study proposes the "Not-served Rural Population (NSRP)" as a complementary indicator to RAI. Utilizing multi-source open data, we analysed the spatial patterns of RAI and NSRP indicators for 203 countries and then explored the correlation between these 2 indicators and other 10 relevant factors. The main findings are as follows: 1) North America, Europe, and Oceania exhibit relatively high RAI values (>80%) and low NSRP values (<1 million). In contrast, African regions have relatively low RAI values (<40%) and high NSRP values (>5 million). There is a negative correlation between RAI and NSRP. 2) There is spatial autocorrelation and significant imbalances in the distribution of these two indicators. 3) The RAI exhibit a positive correlation with the factors showing levels of the development of countries such as GDP, education, indicating that improving the road infrastructure could reduce the poverty rates and enhance access to education. And in contrast with RAI, NSRP exhibit the completely negative correlations with these factors.

cs.CY↗

arXiv2023

Exact new mobility edges between critical and localized states

The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This work may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.

cond-mat.dis-nn↗

arXiv2023

Multiplicative Jensen's formula and quantitative global theory of one-frequency Schrödinger operators

We introduce the concept of dual Lyapunov exponents, leading to a multiplicative version of the classical Jensen's formula for one-frequency analytic Schrödinger cocycles. This formula, in particular, gives a new proof and a quantitative version of the fundamentals of Avila's global theory \cite{avila}, fully explaining the behavior of complexified Lyapunov exponent through the dynamics of the dual cocycle. In particular, concepts of (sub/super) critical regimes and acceleration are all explained (in a quantitative way) through the duality approach. This leads to a number of powerful spectral and physics applications

math.DS↗

arXiv2023

Holographic energy loss near critical temperature in an anisotropic background

We study the energy loss of a quark moving in a strongly coupled QGP under the influence of anisotropy. The heavy quark drag force, diffusion coefficient, and jet quenching parameter are calculated using the Einstein-Maxwell-dilaton model, where the anisotropic background is characterized by an arbitrary dynamical parameter $A$.Our findings indicate that as the anisotropic factor $A$ increases, the drag force and jet quenching parameter both increase, while the diffusion coefficient decreases. Additionally, we observe that the energy loss becomes more significant when the quark moves perpendicular to the anisotropy direction in the transverse plane.The enhancement of the rescaled jet quenching parameters near critical temperature $T_c$, as well as drag forces for a fast-moving heavy quark is observed, which presents one of the typical features of QCD phase transition.

hep-ph↗

arXiv2023

Exact mobility edges for almost-periodic CMV matrices via gauge symmetries

We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant fashion by passing to the class of generalized extended CMV matrices via explicit diagonal unitaries in the spirit of Cantero-Grünbaum-Moral-Velázquez. As an application of these ideas, we construct an explicit family of almost-periodic CMV matrices, which we call the mosaic unitary almost-Mathieu operator, and prove the occurrence of exact mobility edges. That is, we show the existence of energies that separate spectral regions with absolutely continuous and pure point spectrum and exactly calculate them.

math.SP↗

arXiv2023

Non-Self-Adjoint Quasi-periodic Operators with complex spectrum

We give a precise and complete description on the spectrum for a class of non-self-adjoint quasi-periodic operators acting on $\ell^2(\mathbb{Z}^d)$ which contains the Sarnak's model as a special case. As a consequence, one can see various interesting spectral phenomena including $\mathscr{P}\mathscr{T}$ symmetric breaking, the non-simply-connected two-dimensional spectrum in this class of operators. Particularly, we provide new examples of non-self-adjoint operator in $\mathscr{l}^{2}(\mathbb{Z})$ whose spectra (actually a two-dimensional subset of $\mathbb{C}$) can not be approximated by the spectra of its finite-interval truncations.

math.SP↗

arXiv2023

Absolute continuity of the integrated density of states in the localized regime

We establish the absolute continuity of the integrated density of states (IDS) for quasi-periodic Schrödinger operators with a large trigonometric potential and Diophantine frequency. This partially solves Eliasson's open problem in 2002. Furthermore, this result can be extended to a class of quasi-periodic long-range operators on $\ell^2(\Z^d)$. Our proof is based on stratified quantitative almost reducibility results of dual cocycles. Specifically, we prove that a generic analytic one-parameter family of cocycles, sufficiently close to constant coefficients, is reducible except for a zero Hausdorff dimension set of parameters. This result affirms Eliasson's conjecture in 2017.

math.SP↗

arXiv2023

Winding number, density of states and acceleration

Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schrödinger operators, which reflect the asymptotic distribution of zeros of the characteristic determinants of the truncated operators under Dirichlet boundary condition, with respect to complexified phase and the energy respectively. We will prove that the winding number is in fact Avila's acceleration and it is also closely related to the density of states by a generalized Thouless formula for non-self-adjoint Schrödinger operators and Avila's global theory.

math-ph↗

arXiv2023

On the abominable properties of the almost Mathieu operator with well approximated frequencies

We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators. For the class of critical coupling, we show that the Hausdorff measure of the spectrum may vanish (for appropriately chosen frequencies) whenever the gauge function tends to zero faster than logarithmically. For arbitrary coupling, we show that modulus of continuity of the integrated density of states can be arbitrary close to logarithmic; we also prove a similar result for the Lyapunov exponent as a function of the spectral parameter. Finally, we show that (for any coupling) there exist frequencies for which the spectrum is not homogeneous in the sense of Carleson, and, moreover, fails the Parreau-Widom condition. The frequencies for which these properties hold are explicitly described in terms of the growth of the denominators of the convergents.

math-ph↗

arXiv2023

Building Krylov complexity from circuit complexity

Krylov complexity has emerged as a new probe of operator growth in a wide range of non-equilibrium quantum dynamics. However, a fundamental issue remains in such studies: the definition of the distance between basis states in Krylov space is ambiguous. Here, we show that Krylov complexity can be rigorously established from circuit complexity when dynamical symmetries exist. Whereas circuit complexity characterizes the geodesic distance in a multi-dimensional operator space, Krylov complexity measures the height of the final operator in a particular direction. The geometric representation of circuit complexity thus unambiguously designates the distance between basis states in Krylov space. This geometric approach also applies to time-dependent Liouvillian superoperators, where a single Krylov complexity is no longer sufficient. Multiple Krylov complexity may be exploited jointly to fully describe operator dynamics.

quant-ph↗

arXiv2023

Study of $X(6900)$ with unitarized coupled channel scattering amplitudes

In this paper, we study the resonant state $X(6900)$. The scattering amplitudes of coupled channels, $J/ψJ/ψ$-$J/ψψ(2S)$-$J/ψψ(3770)$, are constructed with the interaction of four vector mesons described by effective Lagrangians. The amplitudes are calculated up to one loop, decomposed by partial wave projection, and unitarized by Pad$\acute{e}$ approximation. These amplitudes are fitted to the latest experimental data sets of di-$J/ψ$ and $J/ψψ(2S)$ invariant mass spectra of LHCb, CMS, and ATLAS. High-quality solutions are obtained. With these partial wave amplitudes, we extract the pole parameters of the $X(6900)$. Its quantum number is likely to be $0^{++}$. According to the pole counting rule as well as analysis of the phase shifts of the partial waves, it supports our previous conclusion that the $X(6900)$ prefers to be a compact tetra-quark.

hep-ph↗

arXiv2023

Robust Representation Learning by Clustering with Bisimulation Metrics for Visual Reinforcement Learning with Distractions

Recent work has shown that representation learning plays a critical role in sample-efficient reinforcement learning (RL) from pixels. Unfortunately, in real-world scenarios, representation learning is usually fragile to task-irrelevant distractions such as variations in background or viewpoint. To tackle this problem, we propose a novel clustering-based approach, namely Clustering with Bisimulation Metrics (CBM), which learns robust representations by grouping visual observations in the latent space. Specifically, CBM alternates between two steps: (1) grouping observations by measuring their bisimulation distances to the learned prototypes; (2) learning a set of prototypes according to the current cluster assignments. Computing cluster assignments with bisimulation metrics enables CBM to capture task-relevant information, as bisimulation metrics quantify the behavioral similarity between observations. Moreover, CBM encourages the consistency of representations within each group, which facilitates filtering out task-irrelevant information and thus induces robust representations against distractions. An appealing feature is that CBM can achieve sample-efficient representation learning even if multiple distractions exist simultaneously.Experiments demonstrate that CBM significantly improves the sample efficiency of popular visual RL algorithms and achieves state-of-the-art performance on both multiple and single distraction settings. The code is available at https://github.com/MIRALab-USTC/RL-CBM.

cs.LG↗

arXiv2023

Robust fabrication of ultra-soft tunable PDMS microcapsules as a biomimetic model for red blood cells

Microcapsules with liquid cores encapsulated by thin membranes have many applications in science, medicine and industry. In this paper, we design a suspension of microcapsules which flow and deform like red blood cells (RBCs), as a valuable tool to investigate microhaemodynamics. A reconfigurable and easy-to-assemble 3D nested glass capillary device is used to robustly fabricate water-oil-water double emulsions which are then converted into spherical microcapsules with hyperelastic membranes by cross-linking the polydimethylsiloxane (PDMS) layer coating the droplets. The resulting capsules are monodisperse to within 1% and can be made in a wide range of size and membrane thickness. We use osmosis to deflate by 36% initially spherical capsules of diameter 350 μm and a membrane thickness of 4% of their radius, in order to match the reduced volume of biconcave RBCs. We compare the propagation of initially spherical and deflated capsules under constant volumetric flow in cylindrical capillaries of different confinements. We find that only deflated capsules deform broadly similarly to RBCs over a similar range of capillary numbers (Ca) -- the ratio of viscous to elastic forces. Similarly to the RBCs, the microcapsules transition from a symmetric 'parachute' to an asymmetric 'slipper'-like shape as Ca increases within the physiological range, demonstrating intriguing confinement-dependent dynamics. In addition to biomimetic RBC properties, high-throughput fabrication of tunable ultra-soft microcapsules could be further functionalized and find applications in other areas of science and engineering

cond-mat.soft↗

arXiv2023

Generalization in Visual Reinforcement Learning with the Reward Sequence Distribution

Generalization in partially observed markov decision processes (POMDPs) is critical for successful applications of visual reinforcement learning (VRL) in real scenarios. A widely used idea is to learn task-relevant representations that encode task-relevant information of common features in POMDPs, i.e., rewards and transition dynamics. As transition dynamics in the latent state space -- which are task-relevant and invariant to visual distractions -- are unknown to the agents, existing methods alternatively use transition dynamics in the observation space to extract task-relevant information in transition dynamics. However, such transition dynamics in the observation space involve task-irrelevant visual distractions, degrading the generalization performance of VRL methods. To tackle this problem, we propose the reward sequence distribution conditioned on the starting observation and the predefined subsequent action sequence (RSD-OA). The appealing features of RSD-OA include that: (1) RSD-OA is invariant to visual distractions, as it is conditioned on the predefined subsequent action sequence without task-irrelevant information from transition dynamics, and (2) the reward sequence captures long-term task-relevant information in both rewards and transition dynamics. Experiments demonstrate that our representation learning approach based on RSD-OA significantly improves the generalization performance on unseen environments, outperforming several state-of-the-arts on DeepMind Control tasks with visual distractions.

cs.LG↗

arXiv2022

Multitask kernel-learning parameter prediction method for solving time-dependent linear systems

Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well developed. In this paper, we present a multitask kernel-learning parameter prediction method to automatically obtain relatively optimal splitting parameters, which contains simultaneous multiple parameters prediction and a data-driven kernel learning. For solving time-dependent linear systems, including linear differential systems and linear matrix systems, we give a new matrix splitting Kronecker product method, as well as its convergence analysis and preconditioning strategy. Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. Moreover, our iteration method as a preconditioner can effectively accelerate GMRES. As the dimension of systems increases, all the advantages of our approaches becomes significantly. Especially, for solving the differential Sylvester matrix equation, the speedup ratio can reach tens to hundreds of times when the scale of the system is larger than one hundred thousand.

math.NA↗

arXiv2022

Efficient Exploration in Resource-Restricted Reinforcement Learning

In many real-world applications of reinforcement learning (RL), performing actions requires consuming certain types of resources that are non-replenishable in each episode. Typical applications include robotic control with limited energy and video games with consumable items. In tasks with non-replenishable resources, we observe that popular RL methods such as soft actor critic suffer from poor sample efficiency. The major reason is that, they tend to exhaust resources fast and thus the subsequent exploration is severely restricted due to the absence of resources. To address this challenge, we first formalize the aforementioned problem as a resource-restricted reinforcement learning, and then propose a novel resource-aware exploration bonus (RAEB) to make reasonable usage of resources. An appealing feature of RAEB is that, it can significantly reduce unnecessary resource-consuming trials while effectively encouraging the agent to explore unvisited states. Experiments demonstrate that the proposed RAEB significantly outperforms state-of-the-art exploration strategies in resource-restricted reinforcement learning environments, improving the sample efficiency by up to an order of magnitude.

cs.LG↗

arXiv2022

Nature of the $X(6900)$ in partial wave decomposition of $J/ψJ/ψ$ scattering

In this letter, we perform partial wave decomposition on coupled-channel scattering amplitudes, $J/ψJ/ψ$-$J/ψψ(2S)$-$J/ψψ(3770)$, to study the resonance appears in these processes. Effective Lagrangians are used to describe the interactions of four charmed vector mesons, and the scattering amplitudes are calculated up to the next-to-leading order. Partial wave projections are performed, and unitarization is implemented by Padé approximation. Then we fit the amplitudes to the $J/ψJ/ψ$ invariant mass spectra measured by LHCb and determine the unknown couplings. The pole parameters of the $X(6900)$ are extracted as $M=6861.0^{+6.3}_{-8.8}$~MeV and $Γ=129.0^{+5.6}_{-3.4}$~MeV. Our analysis implies that its quantum number prefers to be $0^{++}$. The pole counting rule and phase shifts show that it is a normal Breit-Wigner resonance and, hence, should be a compact tetraquark.

hep-ph↗

arXiv2022

Stability of Spectral Types of Quasi-Periodic Schrödinger Operators With Respect to Perturbations by Decaying Potentials

We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the (almost) reducibility regime we prove that for perturbations with finite first moment, the essential spectrum remains purely absolutely continuous and the newly created discrete spectrum must be finite in each gap of the unperturbed spectrum. We also prove that for fixed phase, Anderson localization occurring for almost all frequencies in the regime of positive Lyapunov exponents is preserved under exponentially decaying perturbations.

math.SP↗