arXiv subjects

Qing Tang

Publications and source records attributed to Qing Tang.

17 recordsLinked to original sources

arXiv2026

Finite difference methods for a continuous-time heterogeneous agent model with recursive utility

We propose, analyze and test computational methods for solving a continuous-time heterogenous agent model with Epstein-Zin utility. Such recursive utilities allow the model to disentangle between risk aversion and intertemporal substitution. Having discretized the Hamilton-Jacobi-Bellman (HJB) equation arising in the model, we propose a Howard-Newton algorithm for the late resolution preference case, and a Howard-Tarski-Kantorovich algorithm for the early resolution preference case. We prove the convergence of the iterative algorithms. We obtain as a consequence the existence of solutions to the discretized HJB equations. In the late resolution case, we supply a priori estimates between the unique solutions of the continuous and discretized HJB equations.

math.OC↗

arXiv2026

Continuous-Time Heterogeneous Agent Models with Recursive Utility and Preference for Late Resolution

We consider continuous-time heterogeneous agent models with recursive utility (Epstein-Zin utility) cast as mean field games, in which agents prefer late resolution of uncertainty. The model leads to a system coupling a pair of Hamilton-Jacobi-Bellman equations with state constraints and Fokker-Planck-Kolmogorov equations. We investigate the existence of solutions to the mean field game system and discuss some important qualitative features of the model.

math.OC↗

arXiv2025

A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics

We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for individual optimization with a Fokker-Planck-Kolmogorov equation for the wealth distribution. We establish a comparison principle for constrained viscosity solutions of the HJB equation and propose a semi-Lagrangian (SL) scheme for its numerical solution, proving convergence via the Barles-Souganidis method. A policy iteration algorithm handles state constraints, and a dual SL scheme is used for the FPK equation. Numerical methods are presented in a fully discrete, implementable form.

math.OC↗

arXiv2025

Analytical Formulation of Autonomous Vehicle Freeway Merging Control with State-Dependent Discharge Rates

The core of the freeway merging control problem lies in dynamic queue propagation and dissipation linked to merging vehicle behavior. Traditionally, queuing is modeled through demand-supply interactions with time varying demand and fixed capacity. However, field observations show flow rates decrease during congestion at freeway merges due to the impact of intersecting traffic, a factor overlooked in fundamental diagrams. This manuscript introduces an analytical approach to characterize and control the dynamic multi-stage merging of autonomous vehicles, prioritizing traffic efficiency and safety. For the first time, the effective discharge rate at the merging point, reduced by the multi-stage dynamic merging process, is analytically derived using a closed form formulation. Leveraging this expression, performance metrics such as queue length and traffic delay are derived as the first objective. Additionally, a crash risk function is established to quantitatively assess potential collisions during the merging process, serving as the second objective. Finally, the problem is formulated as a dynamic programming model to jointly minimize delay and crash risk, with the merging location and speed as decision variables. Given the terminal state, the ramp vehicle merging task is formulated as a recursive optimization problem, employing backward induction to find the minimum cost solution. Numerical experiments using the NGSIM dataset validate the derived effective discharge rate. The results indicate that the proposed model outperforms two benchmark algorithms, leading to a more efficient and safer merging process.

cs.RO↗

arXiv2025

Organometallic-Inorganic Hybrid MXenes with Tunable Superconductivity

Ti-based two-dimensional transition-metal carbides (MXenes) have attracted attention due to their superior properties and are being explored across various applications1,2. Despite their versatile properties, superconductivity has never been demonstrated, not even predicted, for this important group of 2D materials. In this work, we have introduced an electrochemical intercalation protocol to construct versatile organometallic-inorganic hybrid MXenes and achieved tunable superconductivity in the metallocene-modified layered crystals. Through structural editing of MXene matrix at atomic scale and meticulously modulated intercalation route, Ti3C2Tx intercalated with metallocene species exhibits a superconductive transition temperature (Tc) of 10.2 K. Guest intercalation induced electron filling and strain engineering are responsible for the emerging superconductivity in this intrinsically non-superconducting material. Theoretically, simulated electron-phonon interaction effects further elucidate the nature of the changes in Tc. Furthermore, the Tc of crafted artificial superlattices beyond Ti-based MXenes have been predicted, offering a general strategy for engineering superconductivity and magnetism in layered hybrid materials.

cond-mat.supr-con↗

arXiv2024

Learning equilibria in Cournot mean field games of controls

We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function. Then, we prove convergence of a learning algorithm which gives existence of a solution to the mean field games system. The learning algorithm is implemented with a suitable finite difference discretization to get a numerical method to the solution. We supplement our theoretical analysis with several numerical examples and illustrate the impacts of model parameters.

math.OC↗

arXiv2023

On the quadratic convergence of Newton's method for Mean Field Games with non-separable Hamiltonian

We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation of the Mean Field Game system by Newton's method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence.

math.OC↗

arXiv2023

Deployment of Leader-Follower Automated Vehicle Systems for Smart Work Zone Applications with a Queuing-based Traffic Assignment Approach

The emerging technology of the Autonomous Truck Mounted Attenuator (ATMA), a leader-follower style vehicle system, utilizes connected and automated vehicle capabilities to enhance safety during transportation infrastructure maintenance in work zones. However, the speed difference between ATMA vehicles and general vehicles creates a moving bottleneck that reduces capacity and increases queue length, resulting in additional delays. The different routes taken by ATMA cause diverse patterns of time-varying capacity drops, which may affect the user equilibrium traffic assignment and lead to different system costs. This manuscript focuses on optimizing the routing for ATMA vehicles in a network to minimize the system cost associated with the slow-moving operation. To achieve this, a queuing-based traffic assignment approach is proposed to identify the system cost caused by the ATMA system. A queuing-based time-dependent (QBTD) travel time function, considering capacity drop, is introduced and applied in the static user equilibrium traffic assignment problem, with a result of adding dynamic characteristics. Subsequently, we formulate the queuing-based traffic assignment problem and solve it using a modified path-based algorithm. The methodology is validated using a small-size and a large-size network and compared with two benchmark models to analyze the benefit of capacity drop modeling and QBTD travel time function. Furthermore, the approach is applied to quantify the impact of different routes on the traffic system and identify an optimal route for ATMA vehicles performing maintenance work. Finally, sensitivity analysis is conducted to explore how the impact changes with variations in traffic demand and capacity reduction.

eess.SY↗

arXiv2022

Learning optimal policies in potential Mean Field Games: Smoothed Policy Iteration algorithms

We introduce two Smoothed Policy Iteration algorithms (\textbf{SPI}s) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfy the Lasry Lions monotonicity condition. Local convergence to a stable solution is proved for system which may have multiple solutions. The convergence analysis shows close connections between \textbf{SPI}s and the Fictitious Play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.

math.OC↗

arXiv2021

Policy iteration method for time-dependent Mean Field Games systems with non-separable Hamiltonians

We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in sufficiently small time intervals with Banach fixed point method. Moreover, we prove that the convergence rates are linear. We illustrate our theoretical results by numerical examples, and we discuss the performance of the proposed algorithms.

math.OC↗

arXiv2021

Interference fringes in a nonlinear Michelson interferometer based on spontaneous parametric down-conversion

Quantum nonlinear interferometers (QNIs) can measure the infrared physical quantities of a sample by detecting visible photons. A QNI with Michelson geometry based on the spontaneous parametric down-conversion in a second-order nonlinear crystal is studied systematically. A simplified theoretical model of the QNI is presented. The interference visibility, coherence length, equal-inclination interference, and equal-thickness interference for the QNI are demonstrated theoretically and experimentally. As an application example of the QNI, the refractive index and the angle between two surfaces of a BBO crystal are measured using equal-inclination interference and equal-thickness interference.

quant-ph↗

arXiv2021

Rates of convergence for the policy iteration method for Mean Field Games systems

Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm. For Mean Field Games, convergence of the policy iteration method has been recently proved in [9]. Here, we provide an estimate of its rate of convergence.

math.OC↗

arXiv2021

Modeling and Development of Operation Guidelines for Leader-Follower Autonomous Truck-Mounted Attenuator Vehicles

Mobile and slow moving operations, such as striping, sweeping, bridge flushing and pothole patching, are critical for efficient and safe operation of the highway transportation system. A successfully implemented leader follower autonomous truck mounted attenuators system will eliminate all injuries to DOT employees in follow truck provided appropriate Statutory authority. The leader follower system design imposes more requirements to the lead truck drivers in order to ensure a safe and smooth system operation. The driver is now required to make driving decisions not only from the lead truck's perspective, but also consider the potential implications of his decisions to the follow truck. This project aims to develop a set of rules and clear instructions for ATMA system operation

cs.RO↗

arXiv2020

Approximation of an optimal control problem for the time-fractional Fokker-Planck equation

In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives. This system is derived from an optimal control problem for a time-fractional Fokker-Planck equation with time dependent drift by convex duality argument. The system is composed by a time-fractional backward Hamilton-Jacobi-Bellman and a forward Fokker-Planck equation and can be used to describe the evolution of probability density of particles trapped in anomalous diffusion regimes. We approximate Caputo derivatives in the system by means of L1 schemes and the Hamiltonian by finite differences. The scheme for the Fokker-Planck equation is constructed such that the duality structure of the PDE system is preserved on the discrete level. We prove the well posedness of the scheme and the convergence to the solution of the continuous problem.

math.NA↗

arXiv2019

Computer-aided Detection of Squamous Carcinoma of the Cervix in Whole Slide Images

Goal: Squamous cell carcinoma of cervix is one of the most prevalent cancer worldwide in females. Traditionally, the most indispensable diagnosis of cervix squamous carcinoma is histopathological assessment which is achieved under microscope by pathologist. However, human evaluation of pathology slide is highly depending on the experience of pathologist, thus big inter- and intra-observer variability exists. Digital pathology, in combination with deep learning provides an opportunity to improve the objectivity and efficiency of histopathologic slide analysis. Methods: In this study, we obtained 800 haematoxylin and eosin stained slides from 300 patients suffered from cervix squamous carcinoma. Based on information from morphological heterogeneity in the tumor and its adjacent area, we established deep learning models using popular convolution neural network architectures (inception-v3, InceptionResnet-v2 and Resnet50). Then random forest was introduced to feature extractions and slide-based classification. Results: The overall performance of our proposed models on slide-based tumor discrimination were outstanding with an AUC scores > 0.94. While, location identifications of lesions in whole slide images were mediocre (FROC scores > 0.52) duo to the extreme complexity of tumor tissues. Conclusion: For the first time, our analysis workflow highlighted a quantitative visual-based slide analysis of cervix squamous carcinoma. Significance: This study demonstrates a pathway to assist pathologist and accelerate the diagnosis of patients by utilizing new computational approaches.

cs.CV↗

arXiv2017

An Enhanced LMMSE Channel Estimation under High Speed Railway Scenarios

With the rapid deployment of the high speed railway (HSR), the wireless communication in HSR has been one of the indispensable scenarios in the fifth generation (5G) communications. In order to improve the performance of the orthogonal frequency division multiplexing (OFDM) system in the HSR scenarios, we propose an enhanced linear minimum mean square error channel estimation scheme based on multi-path Doppler frequency offset (DFO) estimation in this paper. The proposed scheme can estimate DFO of each path, and generate the frequency and time channel correlation more accurately, which can improve the accuracy of channel estimation in the HSR scenarios. Simulation results show that the proposed scheme can reduce the channel estimation error and achieve attractive gain in the HSR scenarios.

cs.IT↗

arXiv2014

Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation

Multicomponent multiphase reactive transport processes with dissolution-precipitation are widely encountered in energy and environment systems. A pore-scale two-phase multi-mixture model based on the lattice Boltzmann method (LBM) is developed for such complex transport processes, where each phase is considered as a mixture of miscible components in it. The liquid-gas fluid flow with large density ratio is simulated using the multicomponent multiphase pseudo-potential LB model; the transport of certain solute in the corresponding solvent is solved using the mass transport LB model; and the dynamic evolutions of the liquid-solid interface due to dissolution-precipitation are captured by an interface tracking scheme. The model developed can predict coupled multiple physicochemical processes including multiphase flow, multicomponent mass transport, homogeneous reactions in the bulk fluid and heterogeneous dissolution-precipitation reactions at the fluid-solid interface, and dynamic evolution of the solid matrix geometries at the pore-scale. The model is then applied to a physicochemical system encountered in shale gas/oil industry involving multiphase flow, multicomponent reactive transport and dissolution-precipitation, with several reactions whose rates can be several orders of magnitude different at a given temperature. The pore-scale phenomena and complex interaction between different sub-processes are investigated and discussed in detail.

physics.flu-dyn↗