arXiv subjects

Xiaofeng Yang

Publications and source records attributed to Xiaofeng Yang.

At least 199 records · Page 11Linked to original sources

arXiv2019

Machine-learning-based Classification of Lower-grade gliomas and High-grade gliomas using Radiomic Features in Multi-parametric MRI

Objectives: Glioblastomas are the most aggressive brain and central nervous system (CNS) tumors with poor prognosis in adults. The purpose of this study is to develop a machine-learning based classification method using radio-mic features of multi-parametric MRI to classify high-grade gliomas (HGG) and low-grade gliomas (LGG). Methods: Multi-parametric MRI of 80 patients, 40 HGG and 40 LGG, with gliomas from the MICCAI BRATs 2015 training database were used in this study. Each patient's T1, contrast-enhanced T1, T2, and Fluid Attenuated Inversion Recovery (FLAIR) MRIs as well as the tumor contours were provided in the database. Using the given contours, radiomic features from all four multi-parametric MRIs were extracted. Of these features, a feature selection process using two-sample T-test and least absolute shrinkage, selection operator (LASSO), and a feature correlation threshold was applied to various combinations of T1, contrast-enhanced T1, T2, and FLAIR MRIs separately. These selected features were then used to train, test, and cross-validate a random forest to differentiate HGG and LGG. Finally, the classification accuracy and area under the curve (AUC) were used to evaluate the classification method. Results: Optimized parameters showed that on average, the overall accuracy of our classification method was 0.913 or 73 out of 80 correct classifications, 36/40 for HGG and 37/40 for LGG, with an AUC of 0.956 based on the combination with FLAIR, T1, T1c and T2 MRIs. Conclusion: This study shows that radio-mic features derived from multi-parametric MRI could be used to accurately classify high and lower grade gliomas. The radio-mic features from multi-parametric MRI in combination with even more advanced machine learning methods may further elucidate the underlying tumor biology and response to therapy.

physics.med-ph↗

arXiv2019

A preliminary study on a multi-resolution-level inverse planning algorithm for Gamma Knife radiosurgery

Manual forward planning for GK radiosurgery is complicated and time-consuming, particularly for cases with large or irregularly shaped targets. Inverse planning eases GK planning by solving an optimization problem. However, due to the vast search space, most inverse planning algorithms have to decouple the planning process to isocenter preselection and sector duration optimization. This sequential scheme does not necessarily lead to optimal isocenter locations and hence optimal plans. In this study, we attempt to optimize the isocenter positions, beam shapes and durations simultaneously by proposing a multi-resolution-level (MRL) strategy to handle the large-scale GK optimization problem. In our approach, several rounds of optimizations were performed with a progressively increased spatial resolution for isocenter candidate selection. The isocenters selected from last round and their neighbors on a finer resolution were used as new isocenter candidates for next round of optimization. After plan optimization, shot sequencing was performed to group the optimized sectors to deliverable shots supported by GK treatment units. We have tested our algorithm on 6 GK cases previously treated in our institution (2 meningioma cases, 3 cases with single metastasis and 1 case with 6 metastases). Compared with manual planning, achieving same coverage and similar selectivity, our algorithm improved the gradient index averagely from 3.1 to 2.9 and reduced the maximum dose of brainstem from 8.0Gy to 5.6Gy. The average beam-on time was also reduced by from 103.8 mins to 87.4 mins. Our method was also compared with the inverse planning algorithm provided in Leksell GammaPlan planning system, and outperformed it with better plan quality for all the 6 cases.This preliminary study has demonstrated the effectiveness and feasibility of our MRL inverse planning approach for GK radiosurgery.

physics.med-ph↗

arXiv2019

Efficient Second Order Unconditionally Stable Schemes for a Phase-field Moving Contact Line Model Using Invariant Energy Quadratization Approach

We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary condition. A crucial and challenging issue for solving this model numerically is the time marching problem, due to the high order, nonlinear, and coupled properties of the system. We solve this issue by developing two linear, second order accurate, and energy stable schemes based on the projection method for the Navier--Stokes equations, the invariant energy quadratization for the nonlinear gradient terms in the bulk and boundary, and a subtle implicit-explicit treatment for the stress and convective terms. The well-posedness of the semidiscretized system and the unconditional energy stabilities are proved. Various numerical results based on a spectral-Galerkin spatial discretization are presented to verify the accuracy and efficiency of the proposed schemes.

math.NA↗

arXiv2018

Efficient linear, Stabilized, second-order time marching schemes for an anisotropic phase field dendritic crystal growth model

We consider numerical approximations for a phase field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation together. We propose two efficient, linear, second-order time marching schemes. The first one is based on the linear stabilization approach where all nonlinear terms are treated explicitly and one only needs to solve two linear and decoupled second-order equations. Two linear stabilizers are added to enhance the energy stability, therefore the scheme is quite efficient and stable that allows for large time steps in computations. The second one combines the recently developed Invariant Energy Quadratization approach with the linear stabilization approach. Two linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficients numerically, are added as well. We further show the obtained linear system is well-posed and prove its unconditional energy stability rigorously. For both schemes, various 2D and 3D numerical simulations are implemented to demonstrate the stability and accuracy.

math.NA↗

arXiv2018

Numerical approximations for the binary Fluid-Surfactant Phase Field Model with fluid flow: Second-order, Linear, Energy stable schemes

In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two Cahn-Hilliard type equations. We develop two, linear and second order time marching schemes for solving this system, by combining the "Invariant Energy Quadratization" approach for the nonlinear potentials, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective terms. We prove the well-posedness of the linear system and its unconditional energy stability rigorously. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

math.NA↗

arXiv2018

Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs

Many problems in areas as diverse as recommendation systems, social network analysis, semantic search, and distributed root cause analysis can be modeled as pattern search on labeled graphs (also called "heterogeneous information networks" or HINs). Given a large graph and a query pattern with node and edge label constraints, a fundamental challenge is to nd the top-k matches ac- cording to a ranking function over edge and node weights. For users, it is di cult to select value k . We therefore propose the novel notion of an any-k ranking algorithm: for a given time budget, re- turn as many of the top-ranked results as possible. Then, given additional time, produce the next lower-ranked results quickly as well. It can be stopped anytime, but may have to continues until all results are returned. This paper focuses on acyclic patterns over arbitrary labeled graphs. We are interested in practical algorithms that effectively exploit (1) properties of heterogeneous networks, in particular selective constraints on labels, and (2) that the users often explore only a fraction of the top-ranked results. Our solution, KARPET, carefully integrates aggressive pruning that leverages the acyclic nature of the query, and incremental guided search. It enables us to prove strong non-trivial time and space guarantees, which is generally considered very hard for this type of graph search problem. Through experimental studies we show that KARPET achieves running times in the order of milliseconds for tree patterns on large networks with millions of nodes and edges.

cs.SI↗

arXiv2018

Efficient schemes with unconditionally energy stability for the anisotropic Cahn-Hilliard Equation using the stabilized-Scalar Augmented Variable (S-SAV) approach

In this paper, we consider numerical approximations for the anisotropic Cahn-Hilliard equation. The main challenge of constructing numerical schemes with unconditional energy stabilities for this model is how to design proper temporal discretizations for the nonlinear terms with the strong anisotropy. We propose two, second order time marching schemes by combining the recently developed SAV approach with the linear stabilization approach, where three linear stabilization terms are added. These terms are shown to be crucial to remove the oscillations caused by the anisotropic coefficients, numerically. The novelty of the proposed schemes is that all nonlinear terms can be treated semi-explicitly, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. We further prove the unconditional energy stabilities rigorously, and present various 2D and 3D numerical simulations to demonstrate the stability and accuracy.

math.NA↗

arXiv2017

Linear, Second order and Unconditionally Energy stable schemes for The Viscous Cahn-Hilliard Equation with hyperbolic relaxation using the invariant energy quadratization method

In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system numerically is how to develop high order temporal discretization for the hyperbolic and nonlinear terms, allowing large time-marching step, while preserving the energy stability, i.e. the energy dissipative structure at the time-discrete level. We resolve this issue by developing two second-order time-marching schemes using the recently developed "Invariant Energy Quadratization" approach where all nonlinear terms are discretized semi-explicitly. In each time step, one only needs to solve a symmetric positive definite (SPD) linear system. All the proposed schemes are rigorously proven to be unconditionally energy stable, and the second-order convergence in time has been verified by time step refinement tests numerically. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy and efficiency of the proposed schemes.

math.NA↗

arXiv2017

Numerical approximations of the Cahn-Hilliard and Allen-Cahn Equations with general nonlinear potential using the Invariant Energy Quadratization approach

In this paper, we carry out stability and error analyses for two first-order, semi-discrete time stepping schemes, which are based on the newly developed Invariant Energy Quadratization approach, for solving the well-known Cahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potentials. Some reasonable sufficient conditions about boundedness and continuity of the nonlinear functional are given in order to obtain optimal error estimates. These conditions are naturally satisfied by two commonly used nonlinear potentials including the double-well potential and regularized logarithmic Flory-Huggins potential. The well-posedness, unconditional energy stabilities and optimal error estimates of the numerical schemes are proved rigorously.

math.NA↗

arXiv2017

Stability and convergence analysis of A linear, fully decoupled and unconditionally energy stable scheme for magneto-hydrodynamic equations

In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is about the time marching problem, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper by developing a linear, fully decoupled, first order time-stepping scheme, by combining the projection method and some subtle implicit-explicit treatments for nonlinear coupling terms. We further prove that the scheme is unconditional energy stable and derive the optimal error estimates rigorously. Various numerical experiments are implemented to demonstrate the stability and the accuracy in simulating some benchmark simulations, including the Kelvin-Helmholtz shear instability and the magnetic-frozen phenomenon in the lid-driven cavity.

math.NA↗

arXiv2017

A novel energy-based phase field model for ferrodroplet deformation and breakup in a uniform magnetic field

In this paper, we propose a novel, thermodynamically consistent phase field model to simulate the deformation and breakup of a ferrodroplet that is immersed in a viscous medium and subject to an applied uniform magnetic field. Instead of using the magnetic body force in the traditional Rosensweig model, the key idea of this model is to propose a new magnetic energy that enables direct effects of the magnetic field on the interface evolution. The model can thereby be derived from the variational principle via minimizing the free energy of the total system. This energy based modeling idea can be easily extended to include more external fields in a convenient and consistent way for more complicated applications involving multiple external fields. We validate the model by performing a series of numerical simulations, including the comparison with analytic solutions, the investigation of the effect of different types of magnetic fields, the dynamical behaviors of the ferrodroplet breakup under the strong magnetic field, magnetic/velocity/pressure field distributions, the magnetic energy density, and the inertial phenomenon, etc.

physics.flu-dyn↗

arXiv2017

Second Order, linear and unconditionally energy stable schemes for a hydrodynamic model of Smectic-A Liquid Crystals

In this paper, we consider the numerical approximations for a hydrodynamical model of smectic-A liquid crystals. The model, derived from the variational approach of the modified Oseen-Frank energy, is a highly nonlinear system that couples the incompressible Navier-Stokes equations and a constitutive equation for the layer variable. We develop two linear, second-order time-marching schemes based on the "Invariant Energy Quadratization" method for nonlinear terms in the constitutive equation, the projection method for the Navier-Stokes equations, and some subtle implicit-explicit treatments for the convective and stress terms. Moreover, we prove the well-posedness of the linear system and their unconditionally energy stabilities rigorously. Various numerical experiments are presented to demonstrate the stability and the accuracy of the numerical schemes in simulating the dynamics under shear flow and the magnetic field.

math.NA↗

arXiv2017

Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model

In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model with the static contact line boundary condition that coupled with incompressible Navier-Stokes equations with Navier boundary condition. The projection method is used to deal with the Navier-Stokes equa- tions and an auxiliary function is introduced for the non-convex Ginzburg-Landau bulk potential. We show that the scheme is linear, decoupled and energy stable. Moreover, we prove that fully discrete scheme is also energy stable. An efficient finite element spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed scheme is very efficient and accurate

math.NA↗

arXiv2017

Muon momentum measurement in ICARUS-T600 LAr-TPC via multiple scattering in few-GeV range

The measurement of muon momentum by Multiple Coulomb Scattering is a crucial ingredient to the reconstruction of νμ CC events in the ICARUS-T600 liquid argon TPC in absence of magnetic field, as in the search for sterile neutrinos at Fermilab where ICARUS will be exposed to ~1 GeV Booster neutrino beam. A sample of ~1000 stopping muons produced by charged current interactions of CNGS νμ in the surrounding rock at the INFN Gran Sasso underground Laboratory provides an ideal benchmark in the few-GeV range since their momentum can be directly and independently obtained by the calorimetric measurement. Stopping muon momentum in the 0.5- 4.5 GeV/c range has been reconstructed via Multiple Coulomb Scattering with resolution ranging from 10 to 25 % depending on muon energy, track length and uniformity of the electric field in the drift volume.

physics.ins-det↗

arXiv2017

On Linear and unconditionally energy stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

In this paper, we consider the numerical approximations for the fourth order Cahn-Hilliard equation with concentration dependent mobility, and the logarithmic Flory-Huggins potential. One challenge in solving such a diffusive system numerically is how to develop proper temporal discretization for nonlinear terms in order to preserve the energy stability at the time-discrete level. We resolve this issue by developing a set of the first and second order time marching schemes based on a novel, called "Invariant Energy Quadratization" approach. Its novelty is that the proposed scheme is linear and symmetric positive definite because all nonlinear terms are treated semi-explicitly. We further prove all proposed schemes are unconditionally energy stable rigorously. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy and efficiency of the proposed schemes thereafter.

math.NA↗

arXiv2017

Numerical Approximations for the Cahn-Hilliard phase field model of the binary fluid-surfactant system

In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn-Hilliard equations. The main challenge in solving the system numerically is how to develop easy-to-implement time stepping schemes while preserving the unconditional energy stability. We solve this issue by developing two linear and decoupled, first order and a second order time-stepping schemes using the so-called "Invariant Energy Quadratization" approach for the double well potentials and a subtle explicit-implicit technique for the nonlinear coupling potential. Moreover, the resulting linear system is well-posed and the linear operator is symmetric positive definite. We rigorously prove the first order scheme is unconditionally energy stable. Various numerical simulations are presented to demonstrate the stability and the accuracy thereafter.

math.NA↗

arXiv2017

A Linear, Decoupled and Energy stable scheme for smectic-A Liquid Crystal Flows

In this paper, we consider numerical approximations for the model of smectic-A liquid crystal flows. The model equation, that is derived from the variational approach of the de Gennes free energy, is a highly nonlinear system that couples the incompressible Navier-Stokes equations, and two nonlinear coupled second-order elliptic equations. Based on some subtle explicit--implicit treatments for nonlinear terms, we develop a unconditionally energy stable, linear and decoupled time marching numerical scheme. We also rigorously prove that the proposed scheme obeys the energy dissipation law at the discrete level. Various numerical simulations are presented to demonstrate the accuracy and the stability thereafter.

math.NA↗

arXiv2017

Linear and Unconditionally Energy Stable Schemes for the binary Fluid-Surfactant Phase Field Model

In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins potential. The resulting system consists of two coupled, nonlinear Cahn-Hilliard type equations. We develop a set of first and second order time marching schemes for this system using the "Invariant Energy Quadratization" approach, in particular, the system is transformed into an equivalent one by introducing appropriate auxiliary variables and all nonlinear terms are then treated semi-explicitly. Both schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable in the discrete sense. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

math.NA↗