arXiv subjects

Zhihui Liu

Publications and source records attributed to Zhihui Liu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Analysis of Radiation Level and Estimation of Protection Distance of γ Mobile Flaw Detection Source

Objective To analyze the radiation dose associated with gamma-ray mobile flaw detection, estimate the extent of the supervision and control areas, and assess the associated radiation risks. Methods A combination of theoretical calculations and actual measurements was used to compare and analyze the ambient equivalent dose rates of 192 Ir and 75 Se at their nominal source strengths. Measurements were conducted at distances of 1 m, 2 m, and 5 m from the radiation source. The extents of the control and supervision areas were estimated under three working scenarios: 1 without considering air attenuation, 2 considering air attenuation, and 3 after shielding by the flaw detection workpiece, using source activities of 3.7 * 10^10 Bq and 3.7 * 10^12Bq. Results Actual measurement of radiation dose of 192 Ir and 75 Se were measured under three different nominal activities. Theoretical calculation of radiation dose estimates at various distances were obtained for both nuclides, and the results showed that the theoretical values were basically consistent with the measured values. Conclusion The estimated scope of the supervision and control areas provided in this study can serve as a reference for flaw detection companies. Technicians can use these estimates to calculate appropriate distances for safety zones based on different nuclide activities. This enables flaw detection personnel to reduce the measurement scope on-site and to quickly and accurately define area boundaries.

physics.ins-det↗

arXiv2025

Numerical Unique Ergodicity of Monotone SDEs driven by Nondegenerate Multiplicative Noise

We first establish the unique ergodicity of the stochastic theta method (STM) with $θ\in [1/2, 1]$ for monotone SODEs, without growth restriction on the coefficients, driven by nondegenerate multiplicative noise. The main ingredient of the arguments lies in constructing new Lyapunov functions involving the coefficients, the stepsize, and $θ$ and deriving a minorization condition for the STM. We then generalize the arguments to the Galerkin-based full discretizations for a class of monotone SPDEs driven by infinite-dimensional nondegenerate multiplicative trace-class noise. Applying these results to the stochastic Allen--Cahn equation indicates that its Galerkin-based full discretizations are uniquely ergodic for any interface thickness. Numerical experiments verify our theoretical results.

math.NA↗

arXiv2025

Numerical Ergodicity of Stochastic Allen--Cahn Equation driven by Multiplicative White Noise

We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise. The main ingredient of our method depends on the satisfaction of a Lyapunov condition followed by a uniform moments' estimate, combined with the regularity property for the full discretization. We transform the original stochastic equation into an equivalent random equation where the discrete stochastic convolutions are uniformly controlled to derive the desired uniform moments' estimate. Applying the main result to the stochastic Allen--Cahn equation driven by multiplicative white noise indicates that this full discretization is uniquely ergodic for any interface thickness. Numerical experiments validate our theoretical results.

math.NA↗

arXiv2025

Numerical Ergodicity and Uniform Estimate of Monotone SPDEs Driven by Multiplicative Noise

We analyze the long-time behavior of numerical schemes for a class of monotone stochastic partial differential equations (SPDEs) driven by multiplicative noise. By deriving several time-independent a priori estimates for the numerical solutions, combined with the ergodic theory of Markov processes, we establish the exponential ergodicity of these schemes with a unique invariant measure, respectively. Applying these results to the stochastic Allen--Cahn equation indicates that these schemes always have at least one invariant measure, respectively, and converge strongly to the exact solution with sharp time-independent rates. We also show that these numerical invariant measures are exponentially ergodic and thus give an affirmative answer to a question proposed in (J. Cui, J. Hong, and L. Sun, Stochastic Process. Appl. (2021): 55--93), provided that the interface thickness is not too small.

math.NA↗

arXiv2024

A Bayesian joint model for mediation analysis with matrix-valued mediators

Unscheduled treatment interruptions may lead to reduced quality of care in radiation therapy (RT). Identifying the RT prescription dose effects on the outcome of treatment interruptions, mediated through doses distributed into different organs-at-risk (OARs), can inform future treatment planning. The radiation exposure to OARs can be summarized by a matrix of dose-volume histograms (DVH) for each patient. Although various methods for high-dimensional mediation analysis have been proposed recently, few studies investigated how matrix-valued data can be treated as mediators. In this paper, we propose a novel Bayesian joint mediation model for high-dimensional matrix-valued mediators. In this joint model, latent features are extracted from the matrix-valued data through an adaptation of probabilistic multilinear principal components analysis (MPCA), retaining the inherent matrix structure. We derive and implement a Gibbs sampling algorithm to jointly estimate all model parameters, and introduce a Varimax rotation method to identify active indicators of mediation among the matrix-valued data. Our simulation study finds that the proposed joint model has higher efficiency in estimating causal decomposition effects compared to an alternative two-step method, and demonstrates that the mediation effects can be identified and visualized in the matrix form. We apply the method to study the effect of prescription dose on treatment interruptions in anal canal cancer patients.

stat.ME↗

arXiv2024

Strong Approximation of Stochastic Semiclassical Schroedinger Equation with Multiplicative Noise

We consider the stochastic nonlinear Schroedinger equation driven by a multiplicative noise in a semiclassical regime, where the Plank constant is small. In this regime, the solution of the equation exhibits high-frequency oscillations. We design an efficient numerical method combining the spectral Galerkin approximation and the midpoint scheme. This accurately approximates the solution, or at least of the associated physical observables. Furthermore, the strong convergence rate for the proposed scheme is derived, which explicitly depends on the Planck constant. This conclusion implies the semiclassical regime's admissible meshing strategies for obtaining "correct" physical observables.

math.NA↗

arXiv2024

A marginal structural model for normal tissue complication probability

The goal of radiation therapy for cancer is to deliver prescribed radiation dose to the tumor while minimizing dose to the surrounding healthy tissues. To evaluate treatment plans, the dose distribution to healthy organs is commonly summarized as dose-volume histograms (DVHs). Normal tissue complication probability (NTCP) modelling has centered around making patient-level risk predictions with features extracted from the DVHs, but few have considered adapting a causal framework to evaluate the safety of alternative treatment plans. We propose causal estimands for NTCP based on deterministic and stochastic interventions, as well as propose estimators based on marginal structural models that impose bivariable monotonicity between dose, volume, and toxicity risk. The properties of these estimators are studied through simulations, and their use is illustrated in the context of radiotherapy treatment of anal canal cancer patients.

stat.ME↗

arXiv2024

Photonic RF Channelization Based on Microcombs

In recent decades, microwave photonic channelization techniques have developed significantly. Characterized by low loss, high versatility, large instantaneous bandwidth, and immunity to electromagnetic interference, microwave photonic channelization addresses the requirements of modern radar and electronic warfare for receivers. Microresonator-based optical frequency combs are promising devices for photonic channelized receivers, enabling full advantage of multicarriers, large bandwidths, and accelerating the integration process of microwave photonic channelized receivers. In this paper, we review the research progress and trends in microwave photonic channelization, focusing on schemes that utilize integrated microcombs. We discuss the potential of microcomb-based RF channelization, as well as their challenges and limitations, and provide perspectives for their future development in the context of on-chip silicon-based photonics.

physics.optics↗

arXiv2022

Electromagnetic Environment Analysis of High-Power Wireless Charging Device

Objective Aiming at the problems of many interference factors in the electromagnetic radiation simulation of electric vehicles, a field measurement scheme for charging devices is designed. Through the monitoring of wireless charging equipment, the radiation level and distribution of the electric field value and magnetic field value around the charging equipment is explored, to analyze the influence law of the electromagnetic environment. Method This paper introduces the principle and development status of electric vehicle charging, and analyzes the classification and methods of wireless charging. In this paper, the electric field and magnetic field of cars and minibuses are monitored, at positions such as: around the body, attenuation section, inside the car and inside the minibus. Result The range of electric field strength is 0.9 V/m to 48.1 V/m for cars, and 0.8 V/m to 74.7 V/m for minibuses. The electric field strength decays rapidly with the increase of the distance from the vehicle body, and the law is obvious. The range of magnetic induction intensity is 0.12μT-12.70μT for cars, and 0.15μT-27.06μT for minibuses. The magnetic induction intensity decays rapidly with the increase of the distance from the vehicle body, and the law is obvious. Conclusion This paper explores the radiation level and distribution of the electromagnetic field around this type of charging equipment. It is recommended that manufacturers of wireless charging devices for electric vehicles strengthen research on electromagnetic radiation shielding and take corresponding measures to control the level of electromagnetic radiation in areas accessible to the public.

eess.SY↗

arXiv2022

Optimal Hölder Continuity and Hitting Probabilities for SPDEs with Rough Fractional Noises

We investigate the optimal Hölder continuity and hitting probabilities for systems of stochastic heat equations and stochastic wave equations driven by an additive fractional Brownian sheet with temporal index $1/2$ and spatial index $H\le1/2$. Using stochastic calculus for fractional Brownian motion, we prove that these systems are well-posed and the solutions are Hölder continuous. Furthermore, the optimal Hölder exponents are obtained, which is the first result, as far as we knew, on the optimal Hölder continuity of SHEs and SWEs driven by fractional Brownian sheet that is rough in space. Based on this sharp regularity, we obtain lower and upper bounds of hitting probabilities of the solutions in terms of Bessel--Riesz capacity and Hausdorff measure, respectively.

math.PR↗

arXiv2022

Strong Approximation of Monotone Stochastic Partial Differential Equations Driven by Multiplicative Noise

We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener process. The equation is spatially discretized by Galerkin methods and temporally discretized by drift-implicit Euler and Milstein schemes. By the monotone and Lyapunov assumptions, we use both the variational and semigroup approaches to derive a spatial Sobolev regularity under the $L_ω^p L_t^\infty \dot H^{1+γ}$-norm and a temporal Hölder regularity under the $L_ω^p L_x^2$-norm for the solution of the proposed equation with an $\dot H^{1+γ}$-valued initial datum for $γ\in [0,1]$. Then we make full use of the monotonicity of the equation and tools from stochastic calculus to derive the sharp strong convergence rates $O(h^{1+γ}+τ^{1/2})$ and $O(h^{1+γ}+τ^{(1+γ)/2})$ for the Galerkin-based Euler and Milstein schemes, respectively.

math.NA↗

arXiv2021

Instrumental variable estimation of early treatment effect in randomized screening trials

The primary analysis of randomized screening trials for cancer typically adheres to the intention-to-screen principle, measuring cancer-specific mortality reductions between screening and control arms. These mortality reductions result from a combination of the screening regimen, screening technology and the effect of the early, screening-induced, treatment. This motivates addressing these different aspects separately. Here we are interested in the causal effect of early versus delayed treatments on cancer mortality among the screening-detectable subgroup, which under certain assumptions is estimable from conventional randomized screening trial using instrumental variable type methods. To define the causal effect of interest, we formulate a simplified structural multi-state model for screening trials, based on a hypothetical intervention trial where screening detected individuals would be randomized into early versus delayed treatments. The cancer-specific mortality reductions after screening detection are quantified by a cause-specific hazard ratio. For this, we propose two estimators, based on an estimating equation and a likelihood expression. The methods extend existing instrumental variable methods for time-to-event and competing risks outcomes to time-dependent intermediate variables. Using the multi-state model as the basis of a data generating mechanism, we investigate the performance of the new estimators through simulation studies. In addition, we illustrate the proposed method in the context of CT screening for lung cancer using the US National Lung Screening Trial (NLST) data.

stat.ME↗

arXiv2021

Approximate Nearest Neighbors in the Space of Persistence Diagrams

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a set of other persistence diagrams is linear in the number of diagrams or do not offer performance guarantees. In this paper, we apply concepts from locality-sensitive hashing to support approximate nearest neighbor search in the space of persistence diagrams. Given a set $Γ$ of $n$ $(M,m)$-bounded persistence diagrams, each with at most $m$ points, we snap-round the points of each diagram to points on a cubical lattice and produce a key for each possible snap-rounding. Specifically, we fix a grid over each diagram at several resolutions and consider the snap-roundings of each diagram to the four nearest lattice points. Then, we propose a data structure with $τ$ levels $\mathbb{D}_τ$ that stores all snap-roundings of each persistence diagram in $Γ$ at each resolution. This data structure has size $O(n5^mτ)$ to account for varying lattice resolutions as well as snap-roundings and the deletion of points with low persistence. To search for a persistence diagram, we compute a key for a query diagram by snapping each point to a lattice and deleting points of low persistence. Furthermore, as the lattice parameter decreases, searching our data structure yields a six-approximation of the nearest diagram in $Γ$ in $O((m\log{n}+m^2)\logτ)$ time and a constant factor approximation of the $k$th nearest diagram in $O((m\log{n}+m^2+k)\logτ)$ time.

cs.CG↗

arXiv2021

$L^p$-Convergence Rate of Backward Euler Schemes for Monotone SDEs

We give a unified method to derive the strong convergence rate of the backward Euler scheme for monotone SDEs in $L^p(Ω)$-norm, with general $p \ge 4$. The results are applied to the backward Euler scheme of SODEs with polynomial growth coefficients. We also generalize the argument to the Galerkin-based backward Euler scheme of SPDEs with polynomial growth coefficients driven by multiplicative trace-class noise.

math.NA↗

arXiv2020

Asymptotic Log-Harnack Inequality for Monotone SPDE with Multiplicative Noise

We derive an asymptotic log-Harnack inequality for nonlinear monotone SPDE driven by possibly degenerate multiplicative noise. Our main tool is the asymptotic coupling by the change of measure. As an application, we show that, under certain monotone and coercive conditions on the coefficients, the corresponding Markov semigroup is asymptotically strong Feller, asymptotic irreducibility, and possesses a unique and thus ergodic invariant measure. The results are applied to highly degenerate finite-dimensional or infinite-dimensional diffusion processes.

math.PR↗

arXiv2020

Well-posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises

The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is approximated through the spectral projection of the covariance operator, which is not required to be commutative with the Laplacian operator. Through the convergence analysis of SPDEs with the noise terms replaced by the projected noises, the well-posedness of the SPDE is established under certain covariance operator-dependent conditions. These SPDEs with projected noises are then numerically approximated with the finite element method. A general error estimate framework is established for the finite element approximations. Based on this framework, optimal error estimates of finite element approximations for elliptic SPDEs driven by power-law noises are obtained. It is shown that with the proposed approach, convergence order of white noise driven SPDEs is improved by half for one-dimensional problems, and by an infinitesimal factor for higher-dimensional problems.

math.NA↗

arXiv2020

Strong Approximation of Stochastic Allen-Cahn Equation with White Noise

We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an additive space-time white noise. Our first step is to transform the original stochastic equation into an equivalent random equation whose solution possesses more regularity than the original one. Then we use the backward Euler in time and spectral Galerkin in space to fully discretize this random equation. By the monotone assumption, in combination with the factorization method and stochastic calculus in martingale-type 2 Banach spaces, we derive a uniform maximum norm estimation and a Hölder-type regularity for both stochastic and random equations. Finally, the strong convergence rate of the proposed fully discrete scheme under the $l_t^\infty L^2_ωL^2_x \cap l_t^q L^q_ωL^q_x$-norm is obtained. Several numerical experiments are carried out to verify the theoretical result.

math.NA↗

arXiv2019

Strong convergence of numerical discretizations for semilinear stochastic evolution equations driven by multiplicative white noise

For semilinear stochastic evolution equations whose coefficients are more general than the classical global Lipschitz, we present results on the strong convergence rates of numerical discretizations. The proof of them provides a new approach to strong convergence analysis of numerical discretizations for a large family of second order parabolic stochastic partial differential equations driven by space-time white noises. We apply these results to the stochastic advection-diffusion-reaction equation with a gradient term and multiplicative white noise, and show that the strong convergence rate of a fully discrete scheme constructed by spectral Galerkin approximation and explicit exponential integrator is exactly $\frac12$ in space and $\frac14$ in time. Compared with the optimal regularity of the mild solution, it indicates that the spetral Galerkin approximation is superconvergent and the convergence rate of the exponential integrator is optimal. Numerical experiments support our theoretical analysis.

math.NA↗