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Ting Zhou

Publications and source records attributed to Ting Zhou.

At least 37 records · Page 2Linked to original sources
arXiv2024

Oxygen vacancies modulated VO2 for neurons and Spiking Neural Network construction

Artificial neuronal devices are the basic building blocks for neuromorphic computing systems, which have been motivated by realistic brain emulation. Aiming for these applications, various device concepts have been proposed to mimic the neuronal dynamics and functions. While till now, the artificial neuron devices with high efficiency, high stability and low power consumption are still far from practical application. Due to the special insulator-metal phase transition, Vanadium Dioxide (VO2) has been considered as an idea candidate for neuronal device fabrication. However, its intrinsic insulating state requires the VO2 neuronal device to be driven under large bias voltage, resulting in high power consumption and low frequency. Thus in the current study, we have addressed this challenge by preparing oxygen vacancies modulated VO2 film(VO2-x) and fabricating the VO2-x neuronal devices for Spiking Neural Networks (SNNs) construction. Results indicate the neuron devices can be operated under lower voltage with improved processing speed. The proposed VO2-x based back-propagation SNNs (BP-SNNs) system, trained with the MNIST dataset, demonstrates excellent accuracy in image recognition. Our study not only demonstrates the VO2-x based neurons and SNN system for practical application, but also offers an effective way to optimize the future neuromorphic computing systems by defect engineering strategy.

cs.NE↗
arXiv2023

Partial Data Inverse Problems for the Nonlinear Schrödinger Equation

In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient $β(t, x)$ in the Schrödinger equation $(i\partial_t + Δ+ q(t, x))u + βu^2 = 0$, from the boundary Dirichlet-to-Neumann (DN) map. In particular, we are interested in the partial data problem, in which the DN-map is measured on a proper subset of the boundary. We show two results: a local uniqueness of the coefficient at the points where certain type of geometric optics (GO) solutions can reach; and a stability estimate based on the unique continuation property for the linear equation.

math.AP↗
arXiv2023

The spectrality of Cantor-Moran measure and Fuglede's Conjecture

Let $\{(p_n, \mathcal{D}_n, L_n)\}$ be a sequence of Hadamard triples on $\mathbb{R}$. Suppose that the associated Cantor-Moran measure $$ μ_{\{p_n,\mathcal{D}_n\}}=δ_{p_1^{-1}\mathcal{D}_1}\astδ_{(p_2p_1)^{-1}\mathcal{D}_2}\ast\cdots, $$ where $\sup_n\{|p_n^{-1}d|:d\in \mathcal{D}_n\}<\infty$ and $\sup\#\mathcal{D}_n<\infty$. It has been observed that the spectrality of $μ_{\{p_n,D_n\}}$ is determined by equi-positivity. A significant problem is what kind of Moran measures can satisfy this property. In this paper, we introduce the conception of \textit{Double Points Condition Set} (\textit{DPCS}) to characterize the equi-positivity equivalently. As applications of our characterization, we show that all singularly continuous Cantor-Moran measures are spectral. For the absolutely continuous case, we study Fuglede's Conjecture on Cantor-Moran set. We show that the equi-positivity of $μ_{\{p_n,D_n\}}$ implies the tiling of its support, and the reverse direction holds under certain conditions.

math.FA↗
arXiv2022

Integrating Satellites and Mobile Edge Computing for 6G Wide-Area Edge Intelligence: Minimal Structures and Systematic Thinking

The sixth-generation (6G) network will shift its focus to supporting everything including various machine-type devices (MTDs) in an everyone-centric manner. To ubiquitously cover the MTDs working in rural and disastrous areas, satellite communications become indispensable, while mobile edge computing (MEC) also plays an increasingly crucial role. Their sophisticated integration enables wide-area edge intelligence which promises to facilitate globally-distributed customized services. In this article, we present typical use cases of integrated satellite-MEC networks and discuss the main challenges therein. Inspired by the protein structure and the systematic engineering methodology, we propose three minimal integrating structures, based on which a complex integrated satellite-MEC network can be treated as their extension and combination. We discuss the unique characteristics and key problems of each minimal structure. Accordingly, we establish an on-demand network orchestration framework to enrich the hierarchy of network management, which further leads to a process-oriented network optimization method. On that basis, a case study is utilized to showcase the benefits of on-demand network orchestration and process-oriented network optimization. Finally, we outline potential research issues to envision a more intelligent, more secure, and greener integrated network.

eess.SY↗
arXiv2022

Deep Unsupervised Learning for Joint Antenna Selection and Hybrid Beamforming

In this paper, we propose a novel deep unsupervised learning-based approach that jointly optimizes antenna selection and hybrid beamforming to improve the hardware and spectral efficiencies of massive multiple-input-multiple-output (MIMO) downlink systems. By employing ResNet to extract features from the channel matrices, two neural networks, i.e., the antenna selection network (ASNet) and the hybrid beamforming network (BFNet), are respectively proposed for dynamic antenna selection and hybrid beamformer design. Furthermore, a deep probabilistic subsampling trick and a specially designed quantization function are respectively developed for ASNet and BFNet to preserve the differentiability while embedding discrete constraints into the network structures. With the aid of a flexibly designed loss function, ASNet and BFNet are jointly trained in a phased unsupervised way, which avoids the prohibitive computational cost of acquiring training labels in supervised learning. Simulation results demonstrate the advantage of the proposed approach over conventional optimization-based algorithms in terms of both the achieved rate and the computational complexity.

eess.SP↗
arXiv2021

Federated Dynamic Neural Network for Deep MIMO Detection

In this paper, we develop a dynamic detection network (DDNet) based detector for multiple-input multiple-output (MIMO) systems. By constructing an improved DetNet (IDetNet) detector and the OAMPNet detector as two independent network branches, the DDNet detector performs sample-wise dynamic routing to adaptively select a better one between the IDetNet and the OAMPNet detectors for every samples under different system conditions. To avoid the prohibitive transmission overhead of dataset collection in centralized learning (CL), we propose the federated averaging (FedAve)-DDNet detector, where all raw data are kept at local clients and only locally trained model parameters are transmitted to the central server for aggregation. To further reduce the transmission overhead, we develop the federated gradient sparsification (FedGS)-DDNet detector by randomly sampling gradients with elaborately calculated probability when uploading gradients to the central server. Based on simulation results, the proposed DDNet detector consistently outperforms other detectors under all system conditions thanks to the sample-wise dynamic routing. Moreover, the federated DDNet detectors, especially the FedGS-DDNet detector, can reduce the transmission overhead by at least 25.7\% while maintaining satisfactory detection accuracy.

eess.SP↗
arXiv2021

The general Albertson irregularity index of graphs

We introduce the general Albertson irregularity index of a connected graph $G$ and define it as $A_{p}(G) =(\sum_{uv\in E(G)}|d(u)-d(v)|^p)^{\frac{1}{p}}$, where $p$ is a positive real number and $d(v)$ is the degree of the vertex $v$ in $G$. The new index is not only generalization of the well-known Albertson irregularity index and $σ$-index, but also it is the Minkowski norm of the degree of vertex. We present lower and upper bounds on the general Albertson irregularity index. In addition, we study the extremal value on the general Albertson irregularity index for trees of given order. Finally, we give the calculation formula of the general Albertson index of generalized Bethe trees and Kragujevac trees.

math.CO↗
arXiv2021

Inverse transport and diffusion problems in photoacoustic imaging with nonlinear absorption

Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with internal data that are functionals of the coefficients and the solutions to the equations. Based on the techniques of first- and second-order linearization, we derive uniqueness and stability results for the inverse problems. For uncertainty quantification purpose, we also establish the stability of the reconstruction of the absorption coefficients with respect to the change in the scattering coefficient.

math.AP↗
arXiv2021

Joint Channel Estimation and Mixed-ADCs Allocation for Massive MIMO via Deep Learning

Millimeter wave (mmWave) multi-user massive multi-input multi-output (MIMO) is a promising technique for the next generation communication systems. However, the hardware cost and power consumption grow significantly as the number of radio frequency (RF) components increases, which hampers the deployment of practical massive MIMO systems. To address this issue and further facilitate the commercialization of massive MIMO, mixed analog-to-digital converters (ADCs) architecture has been considered, where parts of conventionally assumed full-resolution ADCs are replaced by one-bit ADCs. In this paper, we first propose a deep learning-based (DL) joint pilot design and channel estimation method for mixed-ADCs mmWave massive MIMO. Specifically, we devise a pilot design neural network whose weights directly represent the optimized pilots, and develop a Runge-Kutta model-driven densely connected network as the channel estimator. Instead of randomly assigning the mixed-ADCs, we then design a novel antenna selection network for mixed-ADCs allocation to further improve the channel estimation accuracy. Moreover, we adopt an autoencoder-inspired end-to-end architecture to jointly optimize the pilot design, channel estimation and mixed-ADCs allocation networks. Simulation results show that the proposed DL-based methods have advantages over the traditional channel estimators as well as the state-of-the-art networks.

eess.SP↗
arXiv2021

On the first Banhatti-Sombor index

Let $d_v$ be the degree of the vertex $v$ in a connected graph $G$. The first Banhatti-Sombor index of $G$ is defined as $BSO(G) =\sum_{uv\in E(G)}\sqrt{\frac{1}{d^2_u}+\frac{1}{d^2_v}}$, which is a new vertex-degree-based topological index introduced by Kulli. In this paper, the mathematical relations between the first Banhatti-Sombor index and some other well-known vertex-degree-based topological indices are established. In addition, the trees extremal with respect to the first Banhatti-Sombor index on trees and chemical trees are characterized, respectively.

math.CO↗
arXiv2021

An Inverse Problem for Non-linear Fractional Magnetic Schrodinger Equation

In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum principle for the linearized equation and apply it to show that the problem is well-posed under suitable assumptions on the exterior data. Moreover, we explore uniqueness of recovery of both magnetic and electric potentials.

math.AP↗
arXiv2021

The Sombor index of trees and unicyclic graphs with given maximum degree

Let $d_G(v)$ be the degree of the vertex $v$ in a graph $G$. The Sombor index of $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, which is a new degree-based topological index introduced by Gutman. Let $\mathscr{T}_{n,Δ}$ and $\mathscr{U}_{n,Δ}$ be the set of trees and unicyclic graphs with $n$ vertices and maximum degree $Δ$, respectively. In this paper, the tree and the unicyclic graph with minimum Sombor index among $\mathscr{T}_{n,Δ}$ and $\mathscr{U}_{n,Δ}$ are characterized.

math.CO↗
arXiv2021

The Sombor index of trees and unicyclic graphs with given matching number

In 2021, the Sombor index was introduced by Gutman, which is a new degree-based topological molecular descriptors. The Sombor index of a graph $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, where $d_G(v)$ is the degree of the vertex $v$ in $G$. Let $\mathscr{T}_{n,m}$ and $\mathscr{U}_{n,m}$ be the set of trees and unicyclic graphs on $n$ vertices with fixed matching number $m$, respectively. In this paper, the tree and the unicyclic graph with the maximum Sombor index are determined among $\mathscr{T}_{n,m}$ and $\mathscr{U}_{n,m}$, respectively.

math.CO↗
arXiv2021

Deep Learning based Antenna Selection and CSI Extrapolation in Massive MIMO Systems

A critical bottleneck of massive multiple-input multiple-output (MIMO) system is the huge training overhead caused by downlink transmission, like channel estimation, downlink beamforming and covariance observation. In this paper, we propose to use the channel state information (CSI) of a small number of antennas to extrapolate the CSI of the other antennas and reduce the training overhead. Specifically, we design a deep neural network that we call an antenna domain extrapolation network (ADEN) that can exploit the correlation function among antennas. We then propose a deep learning (DL) based antenna selection network (ASN) that can select a limited antennas for optimizing the extrapolation, which is conventionally a type of combinatorial optimization and is difficult to solve. We trickly designed a constrained degradation algorithm to generate a differentiable approximation of the discrete antenna selection vector such that the back-propagation of the neural network can be guaranteed. Numerical results show that the proposed ADEN outperforms the traditional fully connected one, and the antenna selection scheme learned by ASN is much better than the trivially used uniform selection.

eess.SP↗
arXiv2020

Inverse problems for nonlinear Maxwell's equations with second harmonic generation

In the current paper we consider an inverse boundary value problem of electromagnetism with nonlinear Second Harmonic Generation (SHG) process. We show the unique determination of the electromagnetic material parameters and the SHG susceptibility parameter of the medium by making electromagnetic measurements on the boundary. We are interested in the case when a frequency is fixed.

math.AP↗
arXiv2020

Partial Data Inverse Problems for Nonlinear Magnetic Schrödinger Equations

We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $\mathbb{R}^n, n\geq2$, can uniquely determine, in a nonlinear magnetic Schrödinger equation, the vector-valued magnetic potential and the scalar electric potential, both being nonlinear in the solution.

math.AP↗
arXiv2020

Digital resolution enhancement in low transverse sampling optical coherence tomography angiography using deep learning

Optical coherence tomography angiography (OCTA) requires high transverse sampling density for visualizing retinal and choroidal capillaries. Low transverse sampling causes resolution degradation, such as the angiograms in wide-field OCTA. In this paper, we propose to address this problem using deep learning. We conducted extensive experiments on converting the centrally cropped 3 x 3 mm2 field of view (FOV) of the 8 x 8 mm2 foveal OCTA images (a sampling density of 22.9 $μ$m) to the native 3 x 3 mm2 en face OCTA images (a sampling density of 12.2 $μ$m). We employed a cycle-consistent adversarial network architecture in this conversion. The quantitative analysis using the perceptual similarity measures shows the generated OCTA images are closer to the native 3 x 3 mm2 scans. Besides, the results show the proposed method could also enhance signal-to-noise ratio. We further applied our method to enhance diseased cases and calculate vascular biomarkers, which demonstrates its generalization performance and clinical perspective.

eess.IV↗