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Zhixin Liu

Publications and source records attributed to Zhixin Liu.

At least 37 records · Page 2Linked to original sources
arXiv2025

Contest for system observability as an infinitely repeated game

This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace, which is set as the value function. Utilizing tools from geometric control, we construct the best response sets considering one-step and two-step optimality respectively to maximize or minimize the value function. We establish a unified necessary-and-sufficient condition for Nash equilibrium that holds for both one-step and two-step optimizations. Our analysis further uncovers two evolutionary patterns, lock and loop modes, and shows an asymmetry between defense and attack. The defender can lock the game into equilibrium, whereas the attacker can disrupt it by sacrificing short-term utility for longer-term advantage. Six representative numerical examples corroborate the theoretical results and highlight the complexity of possible game outcomes.

math.OC↗
arXiv2025

Synchronous Clock and RF Carrier Transmission for Radio Access Network Fronthaul

We simultaneously achieve clock synchronisation, clock-synchronised data transmission and ultra-low noise RF carrier generation by combining clock phase caching and frequency comb transmission in radio access networks (RAN). We demonstrate <100fs jitter for 25GHz RF carrier and 2.5GHz clock, and 16-hour 6.6ps RMS wander.

eess.SY↗
arXiv2025

Spacing and Wavelength Tunable Frequency Comb

Optical frequency combs are increasingly used in applications such as optical communications, radio signal processing, and dual-comb spectroscopy. Many of these applications require a broad, flat spectrum with tunable center wavelength and tone spacing, while maintaining a consistent spectral profile. However, most existing OFC generators either lack tunability or cannot preserve their spectral shape during tuning. In this paper, we demonstrate a cavity-less OFC system based on an electro-optic comb combined with parametric spectral broadening, achieving tone spacing tunability from 25 to 32 GHz and wavelength tunability from 1548 to 1568 nm. Our OFC features high output power (greater than 2 W), broad bandwidth (greater than 90 nm), high optical signal-to-noise ratio (OSNR greater than 25 dB), and, critically, a preserved spectral profile. We show that this consistent spectral shape can be maintained by primarily adjusting the RF drive power and the gain of the optical amplifiers. We also provide a quantitative analysis of the spectral profile variations during tuning.

physics.optics↗
arXiv2025

Pattern formation using an intrinsic optimal control approach

This paper investigates a pattern formation control problem for a multi-agent system modeled with given interaction topology, in which $m$ of the $n$ agents are chosen as leaders and consequently a control signal is added to each of the leaders. These agents interact with each other by Laplacian dynamics on a graph. The pattern formation control problem is formulated as an intrinsic infinite time-horizon linear quadratic optimal control problem, namely, no error information is incorporated in the objective function. Under mild conditions, we show the existence of the optimal control strategy and the convergence to the desired pattern formation. Based on the optimal control strategy, we propose a distributed control strategy to achieve the given pattern. Finally, numerical simulation is given to illustrate theoretical results.

eess.SY↗
arXiv2025

Partial-Wetting Phenomena in Active Matter

Abundant interfacial phenomena in nature, such as water droplets on lotus leaves and water transport in plant vessels, originate from partial-wetting phenomena, which can be well described by Young's equation. It remains an intriguing question whether similar behaviors exist in active matter. In this letter, we present a clear demonstration of the partial-wetting phenomenon in a ternary laning system, which is a typical active system. A phase diagram is constructed in which the relative drift velocities of different components govern the transitions among drying, partial wetting, and complete wetting states. The mechanical balance on the contact lines of the partial-wetting phase described by Young's equation is verified. A theoretical picture is proposed to explain the analogy of partial wetting in the laning system to that in the equilibrium system.

cond-mat.soft↗
arXiv2025

Learning a Class of Mixed Linear Regressions: Global Convergence under General Data Conditions

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable efforts have been devoted to the learning problem of such systems, i.e., estimating data labels and identifying model parameters, most existing investigations employ the offline algorithm, impose the strict independent and identically distributed (i.i.d.) or persistent excitation (PE) conditions on the regressor data, and provide local convergence results only. In this paper, we investigate the recursive estimation and data clustering problems for a class of stochastic MLRs with two components. To address this inherently nonconvex optimization problem, we propose a novel two-step recursive identification algorithm to estimate the true parameters, where the direction vector and the scaling coefficient of the unknown parameters are estimated by the least squares and the expectation-maximization (EM) principles, respectively. Under a general data condition, which is much weaker than the traditional i.i.d. and PE conditions, we establish the global convergence and the convergence rate of the proposed identification algorithm for the first time. Furthermore, we prove that, without any excitation condition on the regressor data, the data clustering performance including the cumulative mis-classification error and the within-cluster error can be optimal asymptotically. Finally, we provide a numerical example to illustrate the performance of the proposed learning algorithm.

stat.ML↗
arXiv2024

Stability analysis of distributed Kalman filtering algorithm for stochastic regression model

In this paper, a distributed Kalman filtering (DKF) algorithm is proposed based on a diffusion strategy, which is used to track an unknown signal process in sensor networks cooperatively. Unlike the centralized algorithms, no fusion center is need here, which implies that the DKF algorithm is more robust and scalable. Moreover, the stability of the DKF algorithm is established under non-independent and non-stationary signal conditions. The cooperative information condition used in the paper shows that even if any sensor cannot track the unknown signal individually, the DKF algorithm can be utilized to fulfill the estimation task in a cooperative way. Finally, we illustrate the cooperative property of the DKF algorithm by using a simulation example.

eess.SY↗
arXiv2024

Convergence Analysis of Weighted-Median Opinion Dynamics with Prejudice

The Friedkin-Johnsen (FJ) model introduces prejudice into the opinion evolution and has been successfully validated in many practical scenarios; however, due to its weighted average mechanism, only one prejudiced agent can always guide all unprejudiced agents synchronizing to its prejudice under the connected influence network, which may not be in line with some social realities. To fundamentally address the limitation of the weighted average mechanism, a weighted-median opinion dynamics has been recently proposed; however, its theoretical analysis is challenging due to its nonlinear nature. This paper studies the weighted-median opinion dynamics with prejudice, and obtains the convergence and convergence rate when all agents have prejudice, and a necessary and sufficient condition for asymptotic consensus when a portion of agents have prejudice. These results are the first time to analyze the discrete-time and synchronous opinion dynamics with the weighted median mechanism, and address the phenomenon of the FJ model that connectivity leads to consensus when a few agents with the same prejudice join in an unprejudiced group.

eess.SY↗
arXiv2024

How do financial variables impact public debt growth in China? An empirical study based on Markov regime-switching model

The deep financial turmoil in China caused by the COVID-19 pandemic has exacerbated fiscal shocks and soaring public debt levels, which raises concerns about the stability and sustainability of China's public debt growth in the future. This paper employs the Markov regime-switching model with time-varying transition probability (TVTP-MS) to investigate the growth pattern of China's public debt and the impact of financial variables such as credit, house prices and stock prices on the growth of public debt. We identify two distinct regimes of China's public debt, i.e., the surge regime with high growth rate and high volatility and the steady regime with low growth rate and low volatility. The main results are twofold. On the one hand, an increase in the growth rate of the financial variables helps to moderate the growth rate of public debt, whereas the effects differ between the two regimes. More specifically, the impacts of credit and house prices are significant in the surge regime, whereas stock prices affect public debt growth significantly in the steady regime. On the other hand, a higher growth rate of financial variables also increases the probability of public debt either staying in or switching to the steady regime. These findings highlight the necessity of aligning financial adjustments with the prevailing public debt regime when developing sustainable fiscal policies.

econ.EM↗
arXiv2024

Characterizing Public Debt Cycles: Don't Ignore the Impact of Financial Cycles

Based on the quarterly data from 26 advanced economies (AEs) and 18 emerging market economies (EMs) over the past two decades, this paper estimates the short- and medium-term impacts of financial cycles on the duration and amplitude of public debt cycles. The results indicate that public debt expansions are larger than their contractions in duration and amplitude, aligning with the "deficit bias hypothesis" and being more pronounced in EMs than in AEs. The impacts of various financial cycles are different. Specifically, credit cycles in EMs significantly impact the duration and amplitude of public debt cycles. Notably, short- and medium-term credit booms in EMs shorten the duration of public debt contractions and reduce the amplitude. Fast credit growth in AEs prolongs the duration of public debt expansions and increases the amplitude. However, credit cycles in AEs show no significant impact. For house price cycles, the overall impact is stronger in EMs than in AEs, differing between short- and medium-term cycles. Finally, the impact of equity price cycles is significant in the short term, but not in the medium term. Equity price busts are more likely to prolong the expansion of public debt in EMs while increasing the amplitude of public debt contractions in AEs. Uncovering the impacts of multiple financial cycles on public debt cycles provides implications for better debt policies under different financial conditions.

econ.GN↗
arXiv2023

Global Convergence of Online Identification for Mixed Linear Regression

Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results focus on offline algorithms, rely on independent and identically distributed (i.i.d) data assumptions, and provide local convergence results only. This paper investigates the online identification and data clustering problems for two basic classes of MLRs, by introducing two corresponding new online identification algorithms based on the expectation-maximization (EM) principle. It is shown that both algorithms will converge globally without resorting to the traditional i.i.d data assumptions. The main challenge in our investigation lies in the fact that the gradient of the maximum likelihood function does not have a unique zero, and a key step in our analysis is to establish the stability of the corresponding differential equation in order to apply the celebrated Ljung's ODE method. It is also shown that the within-cluster error and the probability that the new data is categorized into the correct cluster are asymptotically the same as those in the case of known parameters. Finally, numerical simulations are provided to verify the effectiveness of our online algorithms.

stat.ML↗
arXiv2023

Controllability of networked multiagent systems based on linearized Turing's model

Turing's model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the dynamic evolution behavior of Turing's model since it is described by nonlinear partial differential equations. We focus on controllability of Turing's model by linearization and spatial discretization. This linearized model is a networked system whose agents are second order linear systems and these agents interact with each other by Laplacian dynamics on a graph. A control signal can be added to agents of choice. Under mild conditions on the parameters of the linearized Turing's model, we prove the equivalence between controllability of the linearized Turing's model and controllability of a Laplace dynamic system with agents of first order dynamics. When the graph is a grid graph or a cylinder grid graph, we then give precisely the minimal number of control nodes and a corresponding control node set such that the Laplace dynamic systems on these graphs with agents of first order dynamics are controllable.

eess.SY↗
arXiv2023

Stability of FFLS-based diffusion adaptive filter under a cooperative excitation condition

In this paper, we consider the distributed filtering problem over sensor networks such that all sensors cooperatively track unknown time-varying parameters by using local information. A distributed forgetting factor least squares (FFLS) algorithm is proposed by minimizing a local cost function formulated as a linear combination of accumulative estimation error. Stability analysis of the algorithm is provided under a cooperative excitation condition which contains spatial union information to reflect the cooperative effect of all sensors. Furthermore, we generalize theoretical results to the case of Markovian switching directed graphs. The main difficulties of theoretical analysis lie in how to analyze properties of the product of non-independent and non-stationary random matrices. Some techniques such as stability theory, algebraic graph theory and Markov chain theory are employed to deal with the above issue. Our theoretical results are obtained without relying on the independency or stationarity assumptions of regression vectors which are commonly used in existing literature.

eess.SY↗
arXiv2023

Distributed Least Squares Algorithm for Continuous-time Stochastic Systems Under Cooperative Excitation Condition

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS) algorithm based on diffusion strategy is proposed such that the sensors can cooperatively estimate the unknown time-invariant parameter vector from continuous-time noisy signals. By using the martingal estimation theory and Ito formula, we provide upper bounds for the estimation error of the proposed distributed LS algorithm, and further obtain the convergence results under a cooperative excitation condition. Compared with the existing results, our results are established without using the boundedness or persistent excitation (PE) conditions of regression signals. We provide simulation examples to show that multiple sensors can cooperatively accomplish the estimation task even if any individual can not.

eess.SY↗
arXiv2022

Steady state behavior of the free recall dynamics of working memory

This paper studies a dynamical system that models the free recall dynamics of working memory. This model is a modular neural network with n modules, named hypercolumns, and each module consists of m minicolumns. Under mild conditions on the connection weights between minicolumns, we investigate the long-term evolution behavior of the model, namely the existence and stability of equilibriums and limit cycles. We also give a critical value in which Hopf bifurcation happens. Finally, we give a sufficient condition under which this model has a globally asymptotically stable equilibrium with synchronized minicolumn states in each hypercolumn, which implies that in this case recalling is impossible. Numerical simulations are provided to illustrate our theoretical results. A numerical example we give suggests that patterns can be stored in not only equilibriums and limit cycles, but also strange attractors (or chaos).

eess.SY↗
arXiv2022

Distributed Sparse Identification for Stochastic Dynamic Systems under Cooperative Non-Persistent Excitation Condition

This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information from neighbors. A distributed sparse least squares algorithm is proposed by minimizing a local information criterion formulated as a linear combination of accumulative local estimation error and L_1-regularization term. The upper bounds of the estimation error and the regret of the adaptive predictor of the proposed algorithm are presented. Furthermore, by designing a suitable adaptive weighting coefficient based on the local observation data, the set convergence of zero elements with a finite number of observations is obtained under a cooperative non-persistent excitation condition. It is shown that the proposed distributed algorithm can work well in a cooperative way even though none of the individual sensors can fulfill the estimation task. Our theoretical results are obtained without relying on the independency assumptions of regression signals that have been commonly used in the existing literature. Thus, our results are expected to be applied to stochastic feedback systems. Finally, the numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

eess.SY↗