Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Majorana zero modes,unconventional real-complex transition,and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

A one-dimensional non-Hermitian quasiperiodic p-wave superconductor without PT-symmetry is studied.By analyzing the spectrum,we discovered that there still exists real-complex energy transition even if the inexistence of PT-symmetry breaking.By the inverse participation ratio,we constructed such a correspondence that pure real energies correspond to the extended states and complex energies correspond to the localized states,and this correspondence is precise and effective to detect the mobility edges.After investigating the topological properties,we arrived at a fact that the Majorana zero modes in this system are immune to the non-Hermiticity.

Invariable mobility edge in a quasiperiodic lattice

We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts:Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved.To demonstrate the validity of this mapping,we apply it to two non-Hermitian localization models:an Aubry-Andre-like model with nonreciprocal hopping and complex quasiperiodic potentials,and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping.We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models.This general mapping may catalyze further studies on mobility edges,Lyapunov exponents,and other significant quantities pertaining to localization in non-Hermitian mosaic models.

Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge

Recently, an interesting family of quasiperiodic models with exact mobility edges（MEs） has been proposed（Phys.Rev. Lett. 114 146601（2015））. It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended（localized） states in the real space to localized（extended） ones in the Fourier space. Therefore,it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively.Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.

Mobility edges generated by the non-Hermitian flatband lattice

We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We firstly identify the exact expression of quadratic mobility edges through analytical calculation, then verify the theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real–complex spectrum transition and the localization–delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.

Mobility edges in one-dimensional finite-sized models with large quasi-periodic disorders

We study the one-dimensional tight-binding model with quasi-periodic disorders,where the quasi-period is tuned to be large compared to the system size.It is found that this type of model with large quasi-periodic disorders can also support the mobility edges,which is very similar to the models with slowly varying quasi-periodic disorders.The energy-matching method is employed to determine the locations of mobility edges in both types of models.These results of mobility edges are verified by numerical calculations in various examples.We also provide qualitative arguments to support the fact that large quasi-periodic disorders will lead to the existence of mobility edges.

A Fault-Tolerant Mobility-Aware Caching Method in Edge Computing

Mobile Edge Computing(MEC)is a technology designed for the on-demand provisioning of computing and storage services,strategically positioned close to users.In the MEC environment,frequently accessed content can be deployed and cached on edge servers to optimize the efficiency of content delivery,ultimately enhancing the quality of the user experience.However,due to the typical placement of edge devices and nodes at the network’s periphery,these components may face various potential fault tolerance challenges,including network instability,device failures,and resource constraints.Considering the dynamic nature ofMEC,making high-quality content caching decisions for real-time mobile applications,especially those sensitive to latency,by effectively utilizing mobility information,continues to be a significant challenge.In response to this challenge,this paper introduces FT-MAACC,a mobility-aware caching solution grounded in multi-agent deep reinforcement learning and equipped with fault tolerance mechanisms.This approach comprehensively integrates content adaptivity algorithms to evaluate the priority of highly user-adaptive cached content.Furthermore,it relies on collaborative caching strategies based onmulti-agent deep reinforcement learningmodels and establishes a fault-tolerancemodel to ensure the system’s reliability,availability,and persistence.Empirical results unequivocally demonstrate that FTMAACC outperforms its peer methods in cache hit rates and transmission latency.

Exact mobility edges and topological phase transition in two-dimensional non-Hermitian quasicrystals

The emergence of the mobility edge(ME)has been recognized as an important characteristic of Anderson localization.The difficulty in understanding the physics of the MEs in three-dimensional(3 D)systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs.While most of the previous studies are concerned with one-dimensional(1 D)quasiperiodic systems,the analytic results that allow for an accurate understanding of two-dimensional(2 D)cases are rare.In this work,we disclose an exactly solvable 2 D quasicrystal model with parity-time(PT)symmetry displaying exact MEs.In the thermodynamic limit,we unveil that the extended-localized transition point,observed at the PT symmetry breaking point,is topologically characterized by a hidden winding number defined in the dual space.The coupling waveguide platform can be used to realize the 2 D non-Hermitian quasicrystal model,and the excitation dynamics can be used to detect the localization features.

Mobility-driven user-centric AP clustering in mobile edge computing-based ultra-dense networks

ultra-Dense Network(UDN)has been envisioned as a promising technology to provide high-quality wireless connectivity in dense urban areas,in which the density of Access Points(APs)is increased up to the point where it is comparable with or surpasses the density of active mobile users.In order to mitigate inter-AP interference and improve spectrum efficiency,APs in UDNs are usually clustered into multiple groups to serve different mobile users,respectively.However,as the number of APs increases,the computational capability within an AP group has become the bottleneck of AP clustering.In this paper,we first propose a novel UDN architecture based on Mobile Edge Computing(MEC),in which each MEC server is associated with a user-centric AP cluster to act as a mobile agent.In addition,in the context of MEC-based UDN,we leverage mobility prediction techniques to achieve a dynamic AP clustering scheme,in which the cluster structure can automatically adapt to the dynamic distribution of user traffic in a specific area.Simulation results show that the proposed scheme can highly increase the average user throughput compared with the baseline algorithm using max-SINR user association and equal bandwidth allocation,while it guarantees at the same time low transmission delay.

Air-Ground Collaborative Mobile Edge Computing:Architecture,Challenges,and Opportunities

By pushing computation,cache,and network control to the edge,mobile edge computing(MEC)is expected to play a leading role in fifth generation(5G)and future sixth generation(6G).Nevertheless,facing ubiquitous fast-growing computational demands,it is impossible for a single MEC paradigm to effectively support high-quality intelligent services at end user equipments(UEs).To address this issue,we propose an air-ground collaborative MEC(AGCMEC)architecture in this article.The proposed AGCMEC integrates all potentially available MEC servers within air and ground in the envisioned 6G,by a variety of collaborative ways to provide computation services at their best for UEs.Firstly,we introduce the AGC-MEC architecture and elaborate three typical use cases.Then,we discuss four main challenges in the AGC-MEC as well as their potential solutions.Next,we conduct a case study of collaborative service placement for AGC-MEC to validate the effectiveness of the proposed collaborative service placement strategy.Finally,we highlight several potential research directions of the AGC-MEC.

UAV-assisted cooperative offloading energy efficiency system for mobile edge computing

Reliable communication and intensive computing power cannot be provided effectively by temporary hot spots in disaster areas and complex terrain ground infrastructure.Mitigating this has greatly developed the application and integration of UAV and Mobile Edge Computing(MEC)to the Internet of Things(loT).However,problems such as multi-user and huge data flow in large areas,which contradict the reality that a single UAV is constrained by limited computing power,still exist.Due to allowing UAV collaboration to accomplish complex tasks,cooperative task offloading between multiple UAVs must meet the interdependence of tasks and realize parallel processing,which reduces the computing power consumption and endurance pressure of terminals.Considering the computing requirements of the user terminal,delay constraint of a computing task,energy constraint,and safe distance of UAV,we constructed a UAV-Assisted cooperative offloading energy efficiency system for mobile edge computing to minimize user terminal energy consumption.However,the resulting optimization problem is originally nonconvex and thus,difficult to solve optimally.To tackle this problem,we developed an energy efficiency optimization algorithm using Block Coordinate Descent(BCD)that decomposes the problem into three convex subproblems.Furthermore,we jointly optimized the number of local computing tasks,number of computing offloaded tasks,trajectories of UAV,and offloading matching relationship between multi-UAVs and multiuser terminals.Simulation results show that the proposed approach is suitable for different channel conditions and significantly saves the user terminal energy consumption compared with other benchmark schemes.

IRS Assisted UAV Communications against Proactive Eavesdropping in Mobile Edge Computing Networks

In this paper,we consider mobile edge computing(MEC)networks against proactive eavesdropping.To maximize the transmission rate,IRS assisted UAV communications are applied.We take the joint design of the trajectory of UAV,the transmitting beamforming of users,and the phase shift matrix of IRS.The original problem is strong non-convex and difficult to solve.We first propose two basic modes of the proactive eavesdropper,and obtain the closed-form solution for the boundary conditions of the two modes.Then we transform the original problem into an equivalent one and propose an alternating optimization(AO)based method to obtain a local optimal solution.The convergence of the algorithm is illustrated by numerical results.Further,we propose a zero forcing(ZF)based method as sub-optimal solution,and the simulation section shows that the proposed two schemes could obtain better performance compared with traditional schemes.

Cost-Efficient Edge Caching for NOMA-Enabled IoT Services

Mobile edge computing(MEC)is a promising paradigm by deploying edge servers(nodes)with computation and storage capacity close to IoT devices.Content Providers can cache data in edge servers and provide services for IoT devices,which effectively reduces the delay for acquiring data.With the increasing number of IoT devices requesting for services,the spectrum resources are generally limited.In order to effectively meet the challenge of limited spectrum resources,the Non-Orthogonal Multiple Access(NOMA)is proposed to improve the transmission efficiency.In this paper,we consider the caching scenario in a NOMA-enabled MEC system.All the devices compete for the limited resources and tend to minimize their own cost.We formulate the caching problem,and the goal is to minimize the delay cost for each individual device subject to resource constraints.We reformulate the optimization as a non-cooperative game model.We prove the existence of Nash equilibrium(NE)solution in the game model.Then,we design the Game-based Cost-Efficient Edge Caching Algorithm(GCECA)to solve the problem.The effectiveness of our GCECA algorithm is validated by both parameter analysis and comparison experiments.

Secure Computation Efficiency Resource Allocation for Massive MIMO-Enabled Mobile Edge Computing Networks

In this article,the secure computation efficiency(SCE)problem is studied in a massive multipleinput multiple-output(mMIMO)-assisted mobile edge computing(MEC)network.We first derive the secure transmission rate based on the mMIMO under imperfect channel state information.Based on this,the SCE maximization problem is formulated by jointly optimizing the local computation frequency,the offloading time,the downloading time,the users and the base station transmit power.Due to its difficulty to directly solve the formulated problem,we first transform the fractional objective function into the subtractive form one via the dinkelbach method.Next,the original problem is transformed into a convex one by applying the successive convex approximation technique,and an iteration algorithm is proposed to obtain the solutions.Finally,the stimulations are conducted to show that the performance of the proposed schemes is superior to that of the other schemes.

Proactive Caching at the Wireless Edge:A Novel Predictive User Popularity-Aware Approach

Mobile Edge Computing(MEC)is a promising technology that provides on-demand computing and efficient storage services as close to end users as possible.In an MEC environment,servers are deployed closer to mobile terminals to exploit storage infrastructure,improve content delivery efficiency,and enhance user experience.However,due to the limited capacity of edge servers,it remains a significant challenge to meet the changing,time-varying,and customized needs for highly diversified content of users.Recently,techniques for caching content at the edge are becoming popular for addressing the above challenges.It is capable of filling the communication gap between the users and content providers while relieving pressure on remote cloud servers.However,existing static caching strategies are still inefficient in handling the dynamics of the time-varying popularity of content and meeting users’demands for highly diversified entity data.To address this challenge,we introduce a novel method for content caching over MEC,i.e.,PRIME.It synthesizes a content popularity prediction model,which takes users’stay time and their request traces as inputs,and a deep reinforcement learning model for yielding dynamic caching schedules.Experimental results demonstrate that PRIME,when tested upon the MovieLens 1M dataset for user request patterns and the Shanghai Telecom dataset for user mobility,outperforms its peers in terms of cache hit rates,transmission latency,and system cost.

Achieving dynamic privacy measurement and protection based on reinforcement learning for mobile edge crowdsensing of IoT

With the maturity and development of 5G field,Mobile Edge CrowdSensing(MECS),as an intelligent data collection paradigm,provides a broad prospect for various applications in IoT.However,sensing users as data uploaders lack a balance between data benefits and privacy threats,leading to conservative data uploads and low revenue or excessive uploads and privacy breaches.To solve this problem,a Dynamic Privacy Measurement and Protection(DPMP)framework is proposed based on differential privacy and reinforcement learning.Firstly,a DPM model is designed to quantify the amount of data privacy,and a calculation method for personalized privacy threshold of different users is also designed.Furthermore,a Dynamic Private sensing data Selection(DPS)algorithm is proposed to help sensing users maximize data benefits within their privacy thresholds.Finally,theoretical analysis and ample experiment results show that DPMP framework is effective and efficient to achieve a balance between data benefits and sensing user privacy protection,in particular,the proposed DPMP framework has 63%and 23%higher training efficiency and data benefits,respectively,compared to the Monte Carlo algorithm.

GCAGA: A Gini Coefficient-Based Optimization Strategy for Computation Offloading in Multi-User-Multi-Edge MEC System

To support the explosive growth of Information and Communications Technology(ICT),Mobile Edge Comput-ing(MEC)provides users with low latency and high bandwidth service by offloading computational tasks to the network’s edge.However,resource-constrained mobile devices still suffer from a capacity mismatch when faced with latency-sensitive and compute-intensive emerging applications.To address the difficulty of running computationally intensive applications on resource-constrained clients,a model of the computation offloading problem in a network consisting of multiple mobile users and edge cloud servers is studied in this paper.Then a user benefit function EoU(Experience of Users)is proposed jointly considering energy consumption and time delay.The EoU maximization problem is decomposed into two steps,i.e.,resource allocation and offloading decision.The offloading decision is usually given by heuristic algorithms which are often faced with the challenge of slow convergence and poor stability.Thus,a combined offloading algorithm,i.e.,a Gini coefficient-based adaptive genetic algorithm(GCAGA),is proposed to alleviate the dilemma.The proposed algorithm optimizes the offloading decision by maximizing EoU and accelerates the convergence with the Gini coefficient.The simulation compares the proposed algorithm with the genetic algorithm(GA)and adaptive genetic algorithm(AGA).Experiment results show that the Gini coefficient and the adaptive heuristic operators can accelerate the convergence speed,and the proposed algorithm performs better in terms of convergence while obtaining higher EoU.The simulation code of the proposed algorithm is available:https://github.com/Grox888/Mobile_Edge_Computing/tree/GCAGA.

Multilayer Satellite Network Collaborative Mobile Edge Caching:A GCN-Based Multi-Agent Approach

With the explosive growth of highdefinition video streaming data,a substantial increase in network traffic has ensued.The emergency of mobile edge caching(MEC)can not only alleviate the burden on core network,but also significantly improve user experience.Integrating with the MEC and satellite networks,the network is empowered popular content ubiquitously and seamlessly.Addressing the research gap between multilayer satellite networks and MEC,we study the caching placement problem in this paper.Initially,we introduce a three-layer distributed network caching management architecture designed for efficient and flexible handling of large-scale networks.Considering the constraint on satellite capacity and content propagation delay,the cache placement problem is then formulated and transformed into a markov decision process(MDP),where the content coded caching mechanism is utilized to promote the efficiency of content delivery.Furthermore,a new generic metric,content delivery cost,is proposed to elaborate the performance of caching decision in large-scale networks.Then,we introduce a graph convolutional network(GCN)-based multi-agent advantage actor-critic(A2C)algorithm to optimize the caching decision.Finally,extensive simulations are conducted to evaluate the proposed algorithm in terms of content delivery cost and transferability.