arXiv subjects

Zhou Zhou

Publications and source records attributed to Zhou Zhou.

At least 91 records · Page 5Linked to original sources

arXiv2021

Harnessing Tensor Structures -- Multi-Mode Reservoir Computing and Its Application in Massive MIMO

In this paper, we introduce a new neural network (NN) structure, multi-mode reservoir computing (Multi-Mode RC). It inherits the dynamic mechanism of RC and processes the forward path and loss optimization of the NN using tensor as the underlying data format. Multi-Mode RC exhibits less complexity compared with conventional RC structures (e.g. single-mode RC) with comparable generalization performance. Furthermore, we introduce an alternating least square-based learning algorithm for Multi-Mode RC as well as conduct the associated theoretical analysis. The result can be utilized to guide the configuration of NN parameters to sufficiently circumvent over-fitting issues. As a key application, we consider the symbol detection task in multiple-input-multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems with massive MIMO employed at the base stations (BSs). Thanks to the tensor structure of massive MIMO-OFDM signals, our online learning-based symbol detection method generalizes well in terms of bit error rate even using a limited online training set. Evaluation results suggest that the Multi-Mode RC-based learning framework can efficiently and effectively combat practical constraints of wireless systems (i.e. channel state information (CSI) errors and hardware non-linearity) to enable robust and adaptive learning-based communications over the air.

cs.LG↗

arXiv2020

Theoretical and numerical analysis for angular acceleration being determinant of brain strain in mTBI

Mild traumatic brain injury (mTBI, also known as concussion) caused by the head impact is a crucial global public health problem, but the physics of mTBI is still unclear. During the impact, the rapid movement of the head injures the brain, so researchers have been endeavoring to investigate the relationship between head kinematic parameters (e.g., linear acceleration, angular velocity, angular acceleration) and brain strain, which is associated with the injury of the brain tissue. Although previous studies have shown that linear acceleration had a limited contribution to brain strain, whether angular velocity or angular acceleration causes brain strain is still unclear because of their interdependency (acceleration being the velocity time-derivative). By reframing the problem through the lens of inertial forces, we propose to use the skull frame of reference instead of the ground frame of reference to describe brain deformation during head impact. Based on the rigid-body rotation of the brain, we present a theoretical framework of mechanical analysis about how the inertial forces cause brain strain. In this way, we theoretically show that angular acceleration determines brain strain, and we validate this by numerical simulations using a finite element head model. We also provide an explanation of why previous studies based on peak values found the opposite: that angular velocity determined brain strain in certain situations. Furthermore, we use the same framework to show that linear acceleration causes brain strain in a different mechanism from angular acceleration. However, because of the brain's different resistances to compressing and shearing, the brain strain caused by linear acceleration is small compared with angular acceleration.

physics.bio-ph↗

arXiv2020

Learning with Knowledge of Structure: A Neural Network-Based Approach for MIMO-OFDM Detection

In this paper, we explore neural network-based strategies for performing symbol detection in a MIMO-OFDM system. Building on a reservoir computing (RC)-based approach towards symbol detection, we introduce a symmetric and decomposed binary decision neural network to take advantage of the structure knowledge inherent in the MIMO-OFDM system. To be specific, the binary decision neural network is added in the frequency domain utilizing the knowledge of the constellation. We show that the introduced symmetric neural network can decompose the original $M$-ary detection problem into a series of binary classification tasks, thus significantly reducing the neural network detector complexity while offering good generalization performance with limited training overhead. Numerical evaluations demonstrate that the introduced hybrid RC-binary decision detection framework performs close to maximum likelihood model-based symbol detection methods in terms of symbol error rate in the low SNR regime with imperfect channel state information (CSI).

eess.SP↗

arXiv2020

Pareto Deterministic Policy Gradients and Its Application in 5G Massive MIMO Networks

In this paper, we consider jointly optimizing cell load balance and network throughput via a reinforcement learning (RL) approach, where inter-cell handover (i.e., user association assignment) and massive MIMO antenna tilting are configured as the RL policy to learn. Our rationale behind using RL is to circumvent the challenges of analytically modeling user mobility and network dynamics. To accomplish this joint optimization, we integrate vector rewards into the RL value network and conduct RL action via a separate policy network. We name this method as Pareto deterministic policy gradients (PDPG). It is an actor-critic, model-free and deterministic policy algorithm which can handle the coupling objectives with the following two merits: 1) It solves the optimization via leveraging the degree of freedom of vector reward as opposed to choosing handcrafted scalar-reward; 2) Cross-validation over multiple policies can be significantly reduced. Accordingly, the RL enabled network behaves in a self-organized way: It learns out the underlying user mobility through measurement history to proactively operate handover and antenna tilt without environment assumptions. Our numerical evaluation demonstrates that the introduced RL method outperforms scalar-reward based approaches. Meanwhile, to be self-contained, an ideal static optimization based brute-force search solver is included as a benchmark. The comparison shows that the RL approach performs as well as this ideal strategy, though the former one is constrained with limited environment observations and lower action frequency, whereas the latter ones have full access to the user mobility. The convergence of our introduced approach is also tested under different user mobility environment based on our measurement data from a real scenario.

cs.LG↗

arXiv2020

Multiscale Linear-Quadratic Stochastic Optimal Control With Multiplicative Noise

We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated differential Riccati equation and reformulating it as a classical and deterministic singular perturbation problem. Asymptotic properties of this deterministic problem can be gathered from the well-known Tikhonov Theorem. Consequently, we are able to propose two approximation methods to the value function of the stochastic optimal control problem. The first is by constructing an approximately optimal control process whilst the second is by finding the direct limit to the value function. Both approximation methods rely on the existence of a solution to a coupled differential-algebraic Riccati equation with certain stability properties - this is the main difficulty of the paper.

math.OC↗

arXiv2020

Singular Perturbation of Zero-Sum Linear-Quadratic Stochastic Differential Games

We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by multiscale state equations. The multiscale nature of the problem can be leveraged to reformulate the associated generalised Riccati equation as a deterministic singular perturbation problem. In doing so, we show that, for small enough $ε$, the existence of solution to the associated generalised Riccati equation is guaranteed by the existence of a solution to a decoupled pair of differential and algebraic Riccati equations with a reduced order of dimensionality. Furthermore, we are able to formulate a pair of asymptotic estimates to the value function of the game problem by constructing an approximate feedback strategy and observing the limiting value function.

math.OC↗

arXiv2020

Learning for Integer-Constrained Optimization through Neural Networks with Limited Training

In this paper, we investigate a neural network-based learning approach towards solving an integer-constrained programming problem using very limited training. To be specific, we introduce a symmetric and decomposed neural network structure, which is fully interpretable in terms of the functionality of its constituent components. By taking advantage of the underlying pattern of the integer constraint, as well as of the affine nature of the objective function, the introduced neural network offers superior generalization performance with limited training, as compared to other generic neural network structures that do not exploit the inherent structure of the integer constraint. In addition, we show that the introduced decomposed approach can be further extended to semi-decomposed frameworks. The introduced learning approach is evaluated via the classification/symbol detection task in the context of wireless communication systems where available training sets are usually limited. Evaluation results demonstrate that the introduced learning strategy is able to effectively perform the classification/symbol detection task in a wide variety of wireless channel environments specified by the 3GPP community.

cs.LG↗

arXiv2020

A novel control mode of bionic morphing tail based on deep reinforcement learning

In the field of fixed wing aircraft, many morphing technologies have been applied to the wing, such as adaptive airfoil, variable span aircraft, variable swept angle aircraft, etc., but few are aimed at the tail. The traditional fixed wing tail includes horizontal and vertical tail. Inspired by the bird tail, this paper will introduce a new bionic tail. The tail has a novel control mode, which has multiple control variables. Compared with the traditional fixed wing tail, it adds the area control and rotation control around the longitudinal symmetry axis, so it can control the pitch and yaw of the aircraft at the same time. When the area of the tail changes, the maneuverability and stability of the aircraft can be changed, and the aerodynamic efficiency of the aircraft can also be improved. The aircraft with morphing ability is often difficult to establish accurate mathematical model, because the model has a strong nonlinear, model-based control method is difficult to deal with the strong nonlinear aircraft. In recent years, with the rapid development of artificial intelligence technology, learning based control methods are also brilliant, in which the deep reinforcement learning algorithm can be a good solution to the control object which is difficult to establish model. In this paper, the model-free control algorithm PPO is used to control the tail, and the traditional PID is used to control the aileron and throttle. After training in simulation, the tail shows excellent attitude control ability.

physics.flu-dyn↗

arXiv2020

Equilibrium concepts for time-inconsistent stopping problems in continuous time

A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium} respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.

q-fin.MF↗

arXiv2020

Spectral Inference under Complex Temporal Dynamics

We develop unified theory and methodology for the inference of evolutionary Fourier power spectra for a general class of locally stationary and possibly nonlinear processes. In particular, simultaneous confidence regions (SCR) with asymptotically correct coverage rates are constructed for the evolutionary spectral densities on a nearly optimally dense grid of the joint time-frequency domain. A simulation based bootstrap method is proposed to implement the SCR. The SCR enables researchers and practitioners to visually evaluate the magnitude and pattern of the evolutionary power spectra with asymptotically accurate statistical guarantee. The SCR also serves as a unified tool for a wide range of statistical inference problems in time-frequency analysis ranging from tests for white noise, stationarity and time-frequency separability to the validation for non-stationary linear models.

math.ST↗

arXiv2020

Transport plans with domain constraints

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Several applications are provided: martingale measures with volatility uncertainty, optimal transport with capacity constraints, and Skorokhod embedding with bounded times. Next, we extend this result to multi-marginal constraints. Finally, we consider an optimal transport problem with constraints and obtain its Kantorovich duality. A corollary of this result is a monotonicity principle which gives a geometric way of identifying the optimizer.

math.PR↗

arXiv2020

RCNet: Incorporating Structural Information into Deep RNN for MIMO-OFDM Symbol Detection with Limited Training

In this paper, we investigate learning-based MIMO-OFDM symbol detection strategies focusing on a special recurrent neural network (RNN) -- reservoir computing (RC). We first introduce the Time-Frequency RC to take advantage of the structural information inherent in OFDM signals. Using the time domain RC and the time-frequency RC as the building blocks, we provide two extensions of the shallow RC to RCNet: 1) Stacking multiple time domain RCs; 2) Stacking multiple time-frequency RCs into a deep structure. The combination of RNN dynamics, the time-frequency structure of MIMO-OFDM signals, and the deep network enables RCNet to handle the interference and nonlinear distortion of MIMO-OFDM signals to outperform existing methods. Unlike most existing NN-based detection strategies, RCNet is also shown to provide a good generalization performance even with a limited training set (i.e, similar amount of reference signals/training as standard model-based approaches). Numerical experiments demonstrate that the introduced RCNet can offer a faster learning convergence and as much as 20% gain in bit error rate over a shallow RC structure by compensating for the nonlinear distortion of the MIMO-OFDM signal, such as due to power amplifier compression in the transmitter or due to finite quantization resolution in the receiver.

eess.SP↗

arXiv2020

Statistical Inference for High Dimensional Panel Functional Time Series

In this paper we develop statistical inference tools for high dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high dimensional functional time series. These results have numerous important statistical consequences. Exemplarily, we consider the development of joint simultaneous confidence bands for the mean functions and the construction of tests for the hypotheses that the mean functions in the spatial dimension are parallel. The results are illustrated by means of a small simulation study and in the analysis of Canadian temperature data.

math.ST↗

arXiv2020

Estimation and Inference of Time-Varying Auto-Covariance under Complex Trend: A Difference-based Approach

We propose a difference-based nonparametric methodology for the estimation and inference of the time-varying auto-covariance functions of a locally stationary time series when it is contaminated by a complex trend with both abrupt and smooth changes. Simultaneous confidence bands (SCB) with asymptotically correct coverage probabilities are constructed for the auto-covariance functions under complex trend. A simulation-assisted bootstrapping method is proposed for the practical construction of the SCB. Detailed simulation and a real data example round out our presentation.

math.ST↗

arXiv2019

Globally Optimal And Adaptive Short-Term Forecast of Locally Stationary Time Series And A Test for Its Stability

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent non-stationary and nonlinear time series can be well approximated globally by an auto-regressive process of slowly diverging order. When linear prediction with ${\cal L}^2$ loss is concerned, the latter result facilitates a unified globally-optimal short-term forecasting theory for a wide class of locally stationary time series asymptotically. A nonparametric sieve method is proposed to globally and adaptively estimate the optimal forecasting coefficient functions and the associated mean squared error of forecast. An adaptive stability test is proposed to check whether the optimal forecasting coefficients are time-varying, a frequently-encountered question for practitioners and researchers of time series. Furthermore, partial auto-correlation functions (PACF) of general non-stationary time series are studied and used as a visual tool to explore the linear dependence structure of such series. We use extensive numerical simulations and two real data examples to illustrate the usefulness of our results.

math.ST↗

arXiv2019

Holographic Astigmatic Particle Tracking Velocimetry

The formation of twin images in digital inline holography (DIH) prevents the placement of the focal plane in the center of a sample volume for DIH-based particle tracking velocimetry (DIH-PTV) with a single camera. As a result, it is challenging to apply DIH-PTV for flow measurements in large-scale laboratory facilities or many field applications where it would otherwise be desirable due to the low cost and compact setup. Here we introduce holographic astigmatic PTV (HAPTV) by inserting a cylindrical lens in the optical setup of DIH-PTV, generating distorted holograms. Such distortion is subsequently utilized in a customized reconstruction algorithm to distinguish tracers positioned on different sides of the focal plane which can in turn be placed in the middle of a sample volume. Our HAPTV approach is calibrated under high (1 um/pixel) and low (10 um/pixel) magnifications with an error standard deviation of 4.2 um (one particle diameter) and 120.7 um (~5 times the particle diameter), respectively. We compare the velocity field of a laminar jet flow obtained using HAPTV and conventional PIV to illustrate the accuracy of the technique when applied to practical flow measurement applications. The work demonstrates that HAPTV improves upon the depth of field of conventional astigmatic PTV and enables the implementation of DIH-based PTV for in situ applications.

physics.flu-dyn↗

arXiv2019

Learning for Detection: MIMO-OFDM Symbol Detection through Downlink Pilots

Reservoir computing (RC) is a special recurrent neural network which consists of a fixed high dimensional feature mapping and trained readout weights. In this paper, we introduce a new RC structure for multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) symbol detection, namely windowed echo state network (WESN). The theoretical analysis shows that adding buffers in input layers can bring an enhanced short-term memory (STM) to the underlying neural network. Furthermore, a unified training framework is developed for the WESN MIMO-OFDM symbol detector using both comb and scattered pilot patterns that are compatible with the structure adopted in 3GPP LTE/LTE-Advanced systems. Complexity analysis suggests the advantages of WESN based symbol detector over state-of-the-art symbol detectors such as the linear minimum mean square error (LMMSE) detection and the sphere decoder, when the system is employed with a large number of OFDM sub-carriers. Numerical evaluations illustrate the advantage of the introduced WESN-based symbol detector and demonstrate that the improvement of STM can significantly improve symbol detection performance as well as effectively mitigate model mismatch effects compared to existing methods.

eess.SP↗

arXiv2019

CogRF: A New Frontier for Machine Learning and Artificial Intelligence for 6G RF Systems

The concept of CogRF, a novel tunable radio frequency (RF) frontend that uses artificial intelligence (AI) to meet mission requirements for beyond 5G and 6G systems, is introduced. CogRF utilizes AI as the core to control and operate RF system components with the objective of optimizing the overall system performance. An overview of the vital elements that make up CogRF as well as the overall hierarchy of the envisioned CogRF system is provided, and potential RF components and control parameters are discussed. AI-powered flexible RF front ends, provide new opportunities to identify to enhance security, speed up optimization of device configurations, further refine radio design, improve existing spectrum sharing operations, and develop device health analytics. Top research challenges for CogRF systems have also been described and potential research directions are provided.

eess.SP↗