arXiv subjects

Kai Yang

Publications and source records attributed to Kai Yang.

At least 199 records · Page 11Linked to original sources

arXiv2022

Arbitrarily high-order conservative schemes for the generalized Korteweg-de Vries equation

This paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg-de Vries (KdV) equation. This approach is based on the scalar auxiliary variable (SAV) method. The equation is reformulated into an equivalent system by introducing a scalar auxiliary variable, and the energy is reformulated into a sum of two quadratic terms. Therefore, the quadratic preserving Runge-Kutta method will preserve all the three invariants (momentum, mass and the reformulated energy) in the discrete time flow (assuming the spatial variable is continuous). With the Fourier pseudo-spectral spatial discretization, the scheme conserves the first and third invariant quantities (momentum and energy) exactly in the space-time full discrete sense. The discrete mass possesses the precision of the spectral accuracy. Our numerical experiment shows the great efficiency of this scheme in simulating the breathers for the mKdV equation.

math.NA↗

arXiv2022

Heterogeneous Ultra-Dense Networks with Traffic Hotspots: A Unified Handover Analysis

With the ever-growing communication demands and the unceasing miniaturization of mobile devices, the Internet of Things is expanding the amount of mobile terminals to an enormous level. To deal with such numbers of communication data, plenty of base stations (BSs) need to be deployed. However, denser deployments of heterogeneous networks (HetNets) lead to more frequent handovers, which could increase network burden and degrade the users experience, especially in traffic hotspot areas. In this paper, we develop a unified framework to investigate the handover performance of wireless networks with traffic hotspots. Using the stochastic geometry, we derive the theoretical expressions of average distances and handover metrics in HetNets, where the correlations between users and BSs in hotspots are captured. Specifically, the distributions of macro cells are modeled as independent Poisson point processes (PPPs), and the two tiers of small cells outside and inside the hotspots are modeled as PPP and Poisson cluster process (PCP) separately. A modified random waypoint (MRWP) model is also proposed to eliminate the density wave phenomenon in traditional models and to increase the accuracy of handover decision. By combining the PCP and MRWP model, the distributions of distances from a typical terminal to the BSs in different tiers are derived. Afterwards, we derive the expressions of average distances from a typical terminal to different BSs, and reveal that the handover rate, handover failure rate, and ping-pong rate are deduced as the functions of BS density, scattering variance of clustered small cell, user velocity, and threshold of triggered time. Simulation results verify the accuracy of the proposed analytical model and closed-form theoretical expressions.

eess.SP↗

arXiv2022

FedGBF: An efficient vertical federated learning framework via gradient boosting and bagging

Federated learning, conducive to solving data privacy and security problems, has attracted increasing attention recently. However, the existing federated boosting model sequentially builds a decision tree model with the weak base learner, resulting in redundant boosting steps and high interactive communication costs. In contrast, the federated bagging model saves time by building multi-decision trees in parallel, but it suffers from performance loss. With the aim of obtaining an outstanding performance with less time cost, we propose a novel model in a vertically federated setting termed as Federated Gradient Boosting Forest (FedGBF). FedGBF simultaneously integrates the boosting and bagging's preponderance by building the decision trees in parallel as a base learner for boosting. Subsequent to FedGBF, the problem of hyperparameters tuning is rising. Then we propose the Dynamic FedGBF, which dynamically changes each forest's parameters and thus reduces the complexity. Finally, the experiments based on the benchmark datasets demonstrate the superiority of our method.

cs.LG↗

arXiv2022

Arbitrary Handwriting Image Style Transfer

This paper proposed a method to imitate handwriting style by style transfer. We proposed an neural network model based on conditional generative adversarial networks (cGAN) for handwriting style transfer. This paper improved the loss function on the basis of the GAN. Compared with other handwriting imitation methods, the handwriting style transfer's effect and efficiency have been significantly improved. The experiments showed that the shape of the generated Chinese characters is clear and the analysis of experimental data showed the Generative adversarial networks showed excellent performance in handwriting style transfer. The generated text image is closer to the real handwriting and achieved a better performance in term of handwriting imitation.

cs.CV↗

arXiv2022

Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation

We present a numerical study of solutions to the $2d$ cubic and quintic focusing nonlinear Schrödinger equation in the exterior of a smooth, compact and strictly convex obstacle (a disk) with Dirichlet boundary condition. We first investigate the effect of the obstacle on the behavior of solutions traveling toward the obstacle at different angles and with different velocities directions. We introduce a new concept of weak and strong interactions of the solutions with the obstacle. Next, we study the existence of blow-up solutions depending on the type of the interaction and show how the presence of the obstacle changes the overall behavior of solutions (e.g., from blow-up to global existence), especially in the strong interaction case, as well as how it affects the shape of solutions compared to their initial data, (e.g., splitting into transmitted and reflected parts). We also investigate the influence of the size of the obstacle on the eventual existence of blow-up solutions in the strong interaction case in terms of the transmitted and the reflected parts of the mass. Moreover, we show that the sharp threshold for global existence vs. finite time blow-up solutions in the mass critical case in the presence of the obstacle is the same as the one given by Weinstein for {\rm{NLS}} in the whole Euclidean space $\R^d$. Finally, we construct new Wall-type initial data that blows up in finite time after a strong interaction with an obstacle and having a very distinct dynamics compared with all other blow-up scenarios and dynamics for the {\rm{NLS}} in the whole Euclidean space $\R^d$.

math.AP↗

arXiv2022

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers of nonlinearity, an example of which is the Schamel equation. We first prove the local well-posedness of both equations in a weighted subspace of $H^1$ that includes functions with polynomial decay, extending the result of Linares et al [39] to fractional weights. We then investigate solutions numerically, confirming the well-posedness and extending it to a wider class of functions that includes exponential decay. We include a comparison of solutions to both types of equations, in particular, we investigate soliton resolution for the positive and negative data with different decay rates. Finally, we study the interaction of various solitary waves in both models, showing the formation of solitons, dispersive radiation and even breathers, all of which are easier to track in nonlinearities with lower power.

math.AP↗

arXiv2021

Fed-EINI: An Efficient and Interpretable Inference Framework for Decision Tree Ensembles in Federated Learning

The increasing concerns about data privacy and security drive an emerging field of studying privacy-preserving machine learning from isolated data sources, i.e., federated learning. A class of federated learning, vertical federated learning, where different parties hold different features for common users, has a great potential of driving a great variety of business cooperation among enterprises in many fields. In machine learning, decision tree ensembles such as gradient boosting decision trees (GBDT) and random forest are widely applied powerful models with high interpretability and modeling efficiency. However, stateof-art vertical federated learning frameworks adapt anonymous features to avoid possible data breaches, makes the interpretability of the model compromised. To address this issue in the inference process, in this paper, we firstly make a problem analysis about the necessity of disclosure meanings of feature to Guest Party in vertical federated learning. Then we find the prediction result of a tree could be expressed as the intersection of results of sub-models of the tree held by all parties. With this key observation, we protect data privacy and allow the disclosure of feature meaning by concealing decision paths and adapt a communication-efficient secure computation method for inference outputs. The advantages of Fed-EINI will be demonstrated through both theoretical analysis and extensive numerical results. We improve the interpretability of the model by disclosing the meaning of features while ensuring efficiency and accuracy.

cs.LG↗

arXiv2021

Efficient Batch Homomorphic Encryption for Vertically Federated XGBoost

More and more orgainizations and institutions make efforts on using external data to improve the performance of AI services. To address the data privacy and security concerns, federated learning has attracted increasing attention from both academia and industry to securely construct AI models across multiple isolated data providers. In this paper, we studied the efficiency problem of adapting widely used XGBoost model in real-world applications to vertical federated learning setting. State-of-the-art vertical federated XGBoost frameworks requires large number of encryption operations and ciphertext transmissions, which makes the model training much less efficient than training XGBoost models locally. To bridge this gap, we proposed a novel batch homomorphic encryption method to cut the cost of encryption-related computation and transmission in nearly half. This is achieved by encoding the first-order derivative and the second-order derivative into a single number for encryption, ciphertext transmission, and homomorphic addition operations. The sum of multiple first-order derivatives and second-order derivatives can be simultaneously decoded from the sum of encoded values. We are motivated by the batch idea in the work of BatchCrypt for horizontal federated learning, and design a novel batch method to address the limitations of allowing quite few number of negative numbers. The encode procedure of the proposed batch method consists of four steps, including shifting, truncating, quantizing and batching, while the decoding procedure consists of de-quantization and shifting back. The advantages of our method are demonstrated through theoretical analysis and extensive numerical experiments.

cs.CR↗

arXiv2021

High order conservative schemes for the generalized Benjamin-Ono equation in the unbounded domain

This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by the pseudo-spectral method with the rational basis functions, which can be implemented by the Fast Fourier transform (FFT) with the computational cost $\mathcal{O}( N\log(N))$. By reformulating the spatial discretized system into the different equivalent forms, either the spatial semi-discretized mass or energy can be preserved exactly under the continuous time flow. Combined with the symplectic Runge-Kutta, with or without the scalar auxiliary variable reformulation, the fully discrete energy or mass conservative scheme can be constructed with arbitrarily high-order temporal accuracy, respectively. Our numerical results show the conservation of the proposed schemes, and also the superior accuracy and stability to the non-conservative (Leap-frog) scheme.

math.NA↗

arXiv2021

SiamCorners: Siamese Corner Networks for Visual Tracking

The current Siamese network based on region proposal network (RPN) has attracted great attention in visual tracking due to its excellent accuracy and high efficiency. However, the design of the RPN involves the selection of the number, scale, and aspect ratios of anchor boxes, which will affect the applicability and convenience of the model. Furthermore, these anchor boxes require complicated calculations, such as calculating their intersection-over-union (IoU) with ground truth bounding boxes.Due to the problems related to anchor boxes, we propose a simple yet effective anchor-free tracker (named Siamese corner networks, SiamCorners), which is end-to-end trained offline on large-scale image pairs. Specifically, we introduce a modified corner pooling layer to convert the bounding box estimate of the target into a pair of corner predictions (the bottom-right and the top-left corners). By tracking a target as a pair of corners, we avoid the need to design the anchor boxes. This will make the entire tracking algorithm more flexible and simple than anchorbased trackers. In our network design, we further introduce a layer-wise feature aggregation strategy that enables the corner pooling module to predict multiple corners for a tracking target in deep networks. We then introduce a new penalty term that is used to select an optimal tracking box in these candidate corners. Finally, SiamCorners achieves experimental results that are comparable to the state-of-art tracker while maintaining a high running speed. In particular, SiamCorners achieves a 53.7% AUC on NFS30 and a 61.4% AUC on UAV123, while still running at 42 frames per second (FPS).

cs.CV↗

arXiv2021

A High-fidelity, Machine-learning Enhanced Queueing Network Simulation Model for Hospital Ultrasound Operations

We collaborate with a large teaching hospital in Shenzhen, China and build a high-fidelity simulation model for its ultrasound center to predict key performance metrics, including the distributions of queue length, waiting time and sojourn time, with high accuracy. The key challenge to build an accurate simulation model is to understanding the complicated patient routing at the ultrasound center. To address the issue, we propose a novel two-level routing component to the queueing network model. We apply machine learning tools to calibrate the key components of the queueing model from data with enhanced accuracy.

cs.LG↗

arXiv2021

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

We consider a higher-dimensional version of the Benjamin-Ono (HBO) equation in the 2D setting: $u_t- \mathcal{R}_1 Δu + \frac{1}{2}(u^2)_x=0, (x,y) \in \mathbb{R}^2$, which is $L^2$-critical, and investigate properties of solutions both analytically and numerically. For a generalized equation (fractional 2D gKdV) after deriving the Pohozaev identities, we obtain non-existence conditions for solitary wave solutions, then prove uniform bounds in the energy space or conditional global existence, and investigate the radiation region, a specific wedge in the negative $x$-direction. We then introduce our numerical approach in a general context, and apply it to obtain the ground state solution in the 2D critical HBO equation, then show that its mass is a threshold for global vs. finite time existing solutions, which is typical in the focusing (mass-)critical dispersive equations. We also observe that globally existing solutions tend to disperse completely into the radiation in this nonlocal equation. The blow-up solutions travel in the positive $x$-direction with the rescaled ground state profile while also radiating dispersive oscillations into the radiative wedge. We conclude with examples of different interactions of two solitary wave solutions, including weak and strong interactions.

math.AP↗

arXiv2020

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

We consider the generalized Benjamin-Ono (gBO) equation on the real line, $ u_t + \partial_x (-\mathcal H u_{x} + \tfrac1{m} u^m) = 0, x \in \mathbb R, m = 2,3,4,5$, and perform numerical study of its solutions. We first compute the ground state solution to $-Q -\mathcal H Q^\prime +\frac1{m} Q^m = 0$ via Petviashvili's iteration method. We then investigate the behavior of solutions in the Benjamin-Ono ($m=2$) equation for initial data with different decay rates and show decoupling of the solution into a soliton and radiation, thus, providing confirmation to the soliton resolution conjecture in that equation. In the mBO equation ($m=3$), which is $L^2$-critical, we investigate solutions close to the ground state mass, and, in particular, we observe the formation of stable blow-up above it. Finally, we focus on the $L^2$-supercritical gBO equation with $m=4,5$. In that case we investigate the global vs finite time existence of solutions, and give numerical confirmation for the dichotomy conjecture, in particular, exhibiting blow-up phenomena in the supercritical setting.

math.AP↗

arXiv2020

Waveform Optimization with Multiple Performance Metrics for Broadband Joint Communication and Radar Sensing

Joint communication and radar sensing (JCAS) integrates communication and radar/radio sensing into one system, sharing one transmitted signal. In this paper, we investigate JCAS waveform optimization underlying communication signals, where a base station detects radar targets and communicates with mobile users simultaneously. We first develop individual novel waveform optimization problems for communications and sensing, respectively. For communications, we propose a novel lower bound of sum rate by integrating multi-user interference and effective channel gain into one metric that simplifies the optimization of the sum rate. For radar sensing, we consider optimizing one of two metrics, the mutual information or the Cramer-Rao bound. Then, we formulate the JCAS problem by optimizing the communication metric under different constraints of the radar metric, and we obtain both closed-form solutions and iterative solutions to the non-convex JCAS optimization problem. Numerical results are provided and verify the proposed optimization solutions.

eess.SP↗

arXiv2020

Uplink Sensing in Perceptive Mobile Networks with Asynchronous Transceivers

Perceptive mobile network (PMN) is a recently proposed next-generation network that integrates radar sensing into communication. One major challenge for realizing sensing in PMNs is how to deal with spatially-separated asynchronous transceivers. The asynchrony between sensing receiver and transmitter will cause both timing offsets (TOs) and carrier frequency offsets (CFOs) and lead to degraded sensing accuracy in both ranging and velocity measurements. In this paper, we propose an uplink sensing scheme for PMNs with asynchronous transceivers, targeting at resolving the sensing ambiguity and improving the sensing accuracy. We first adopt a cross-antenna cross-correlation (CACC) operation to remove the sensing ambiguity associated with both TOs and CFOs. Without sensing ambiguity, both actual propagation delay and actual Doppler frequency of multiple targets can be obtained using CACC outputs. To exploit the redundancy of the CACC outputs and reduce the complexity, we then propose a novel mirrored-MUSIC algorithm, which halves the number of unknown parameters to be estimated, for obtaining actual values of delays and Doppler frequencies. Finally, we propose a high-resolution angles-of-arrival (AoAs) estimation algorithm, which jointly processes all measurements from spatial, temporal, and frequency domains. The proposed AoAs estimation algorithm can achieve significantly higher estimation accuracy than that of using samples from the spatial domain only. We also derive the theoretical mean-square-error of the proposed algorithms. Numerical results are provided and validate the effectiveness of the proposed scheme.

eess.SP↗

arXiv2020

Weak Radio Frequency Signal Detection Based on Piezo-Opto-Electro-Mechanical System: Architecture Design and Sensitivity Prediction

We propose a novel radio-frequency (RF) receiving architecture based on micro-electro-mechanical system (MEMS) and optical coherent detection module. The architecture converts the received electrical signal into mechanical vibration through the piezoelectric effect and adopts an optical detection module to detect the mechanical vibration. We analyze the response function of piezoelectric film to an RF signal, the noise limited sensitivity of the optical detection module and the system transfer function in the frequency domain. Finally, we adopt simple on-off keying (OOK) modulation with bandwidth 1 kHz and carrier frequency 1 GHz, to numerically evaluate the detection sensitivity. The result shows that, considering the main noise sources in wireless channel and circuits, the signal detection sensitivity can reach around -160 dBm with a 50 $Ω$ impedance. Such sensitivity significantly outperforms that of the currently deployed Long Term Evolution (LTE) system, when normalizing the transmission bandwidth also to 1 kHz.

eess.SP↗

arXiv2020

TimeAutoML: Autonomous Representation Learning for Multivariate Irregularly Sampled Time Series

Multivariate time series (MTS) data are becoming increasingly ubiquitous in diverse domains, e.g., IoT systems, health informatics, and 5G networks. To obtain an effective representation of MTS data, it is not only essential to consider unpredictable dynamics and highly variable lengths of these data but also important to address the irregularities in the sampling rates of MTS. Existing parametric approaches rely on manual hyperparameter tuning and may cost a huge amount of labor effort. Therefore, it is desirable to learn the representation automatically and efficiently. To this end, we propose an autonomous representation learning approach for multivariate time series (TimeAutoML) with irregular sampling rates and variable lengths. As opposed to previous works, we first present a representation learning pipeline in which the configuration and hyperparameter optimization are fully automatic and can be tailored for various tasks, e.g., anomaly detection, clustering, etc. Next, a negative sample generation approach and an auxiliary classification task are developed and integrated within TimeAutoML to enhance its representation capability. Extensive empirical studies on real-world datasets demonstrate that the proposed TimeAutoML outperforms competing approaches on various tasks by a large margin. In fact, it achieves the best anomaly detection performance among all comparison algorithms on 78 out of all 85 UCR datasets, acquiring up to 20% performance improvement in terms of AUC score.

cs.LG↗

arXiv2020

Hybrid Beamforming for Terahertz Multi-Carrier Systems over Frequency Selective Fading

We propose novel hybrid beamforming schemes for the terahertz (THz) wireless system where a multi-antenna base station (BS) communicates with a multi-antenna user over frequency selective fading. Here, we assume that the BS employs sub-connected hybrid beamforming and multi-carrier modulation to deliver ultra high data rate. We consider a three-dimensional wideband THz channel by incorporating the joint effect of molecular absorption, high sparsity, and multi-path fading, and consider the carrier frequency offset in multi-carrier systems. With this model, we first propose a two-stage wideband hybrid beamforming scheme which includes a beamsteering codebook searching algorithm for analog beamforming and a regularized channel inversion method for digital beamforming. We then propose a novel wideband hybrid beamforming scheme with two digital beamformers. In this scheme, an additional digital beamformer is developed to compensate for the performance loss caused by the constant-amplitude hardware constraints and the difference of channel matrices among subcarriers. Furthermore, we consider imperfect channel state information (CSI) and propose a probabilistic robust hybrid beamforming scheme to combat channel estimation errors. Numerical results demonstrate the benefits of our proposed schemes for the sake of practical implementation, especially considering its high spectral efficiency, low complexity, and robustness against imperfect CSI.

eess.SP↗