The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient f...The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.展开更多
In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,...In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.展开更多
We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows.These schemes are designed to preserve mass and positivity and to be uniquely solvable.In addition,they als...We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows.These schemes are designed to preserve mass and positivity and to be uniquely solvable.In addition,they also ensure energy dissipation in many typical scenarios.Through extensive numerical experiments,we demonstrate the schemes’robustness,accuracy,and efficiency.展开更多
This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider...This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.展开更多
Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is ani...Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.展开更多
Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) sys...Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) systolic function. It results in symptoms and reduced quality of life and carries a high mortality. Whilst this form of severe AS, termed paradoxical low flow low gradient (pLFLG), is well reported, patients with this diagnosis experience inappropriate barriers to aortic valve replacement (AVR), the only efficacious treatment. We present the case of an 88-year-old female with 12 months of exertional dyspnoea on a background of hypothyroidism and hypercholesterolemia. Transthoracic echocardiogram (TTE) revealed LV hypertrophy, with a small LV cavity size and reduced stroke volume, yet normal systolic function. A heavily calcified aortic valve was identified with severe aortic stenosis, based on valve area, yet with incongruous mean transvalvular gradient of 25 mmHg (severe ≥ 50 mmHg). Following exclusion of other differential diagnoses, her symptoms were attributed to paradoxical LFLG severe AS. She was however declined definitive transcatheter aortic valve implantation (TAVI) due to her paradoxically low mean aortic gradient. Following further deterioration in her symptoms and supportive quantification of poor exercise performance, she was ultimately re-referred, accepted, and underwent TAVI. Following her AVR, the patient experiences significant improvement in both symptoms and quality of life after only one month. Paradoxical LFLG severe AS remains a well-documented yet under recognized disease. It carries high morbidity and mortality if untreated, yet is significantly less likely to be referred and accepted for intervention. With its prevalence expected to rise with an ageing population, this case serves as a timely reminder for clinicians to address the under recognition of important pathology.展开更多
Revealing the latent low-dimensional geometric structure of high-dimensional data is a crucial task in unsupervised representation learning.Traditional manifold learning,as a typical method for discovering latent geom...Revealing the latent low-dimensional geometric structure of high-dimensional data is a crucial task in unsupervised representation learning.Traditional manifold learning,as a typical method for discovering latent geometric structures,has provided important nonlinear insight for the theoretical development of unsupervised representation learning.However,due to the shallow learning mechanism of the existing methods,they can only exploit the simple geometric structure embedded in the initial data,such as the local linear structure.Traditional manifold learning methods are fairly limited in mining higher-order nonlinear geometric information,which is also crucial for the development of unsupervised representation learning.To address the abovementioned limitations,this paper proposes a novel dynamic geometric structure learning model(DGSL)to explore the true latent nonlinear geometric structure.Specifically,by mathematically analysing the reconstruction loss function of manifold learning,we first provide universal geometric relational function between the curvature and the non-Euclidean metric of the initial data.Then,we leverage geometric flow to design a deeply iterative learning model to optimize this relational function.Our method can be viewed as a general-purpose algorithm for mining latent geometric structures,which can enhance the performance of geometric representation methods.Experimentally,we perform a set of representation learning tasks on several datasets.The experimental results show that our proposed method is superior to traditional methods.展开更多
ABSTRACT： The Damintun （大民屯） depression, a small （about 800km^2 in area） subunit in the Bohai （渤海） Bay basin, hosts nearly 2×10^8 t of high-wax oils with wax contents up to 60%. The high-wax oils have...ABSTRACT： The Damintun （大民屯） depression, a small （about 800km^2 in area） subunit in the Bohai （渤海） Bay basin, hosts nearly 2×10^8 t of high-wax oils with wax contents up to 60%. The high-wax oils have high consolidation temperatures and viscosities. The high-wax oils were generated from the fourth member of the Shahejie Formation （Es4）, which is also important source rocks for oils in other subunits of the Bohai Bay basin. Yet high-wax oils have not been found in significant volumes elsewhere in the Bohai Bay basin. Geological conditions favourable for high-wax oil enrichment were studied. This study shows that the unusual concentrations of high-wax oils in the depression seem to result from at least three different factors： （1） the presence of organic-matter rich source rocks which were prone to generate wax-rich hydrocarbons; （2） the formation of early overpressures which increased the expul- sion efficiency of waxy hydrocarbons; and （3） reductions in subsidence rate and basal heat flows, which minimized the thermal cracking of high molecular-weight （waxy） hydrocarbons, and therefore prevented the high-wax oils from being transformed into less waxy equivalents.展开更多
Siltation gradient and siltation length are important parameters for designing gravity check dams for debris flows,which directly affect the accuracy of estimates of interception capacity.At present,siltation gradient...Siltation gradient and siltation length are important parameters for designing gravity check dams for debris flows,which directly affect the accuracy of estimates of interception capacity.At present,siltation gradient calculations are based primarily on empirical values,and range from 0.4 to 0.95 times the channel slope coefficient.The middle reaches of the Bailong River are one of the four areas in China that are most severely affected by debris flow hazards.Gravity dams are widely employed in this mountainous area.However,field studies of their capacity are lacking.In this paper,the operations of check dams were investigated.Based on field investigation results and theoretical analysis,calculations for siltation gradient,siltation length,and dam storage capacity are established.The impact of debris flow density,channel slope,and particle size weight percentages are discussed.The calculations show that the theoretical values for siltation gradient are consistent with measured values with 83.6% accuracy;and theoretical values of siltation length are consistent with measured values with 91.6% accuracy.The results of this research are an important reference for optimal height and spacing of dams,estimation of dam storage capacity,and disaster prevention.展开更多
For the high-dimensional Frenkel-Kontorova(FK)model on lattices,we study the existence of minimal foliations by depinning force.We introduce the tilted gradient flow and define the depinning force as the critical valu...For the high-dimensional Frenkel-Kontorova(FK)model on lattices,we study the existence of minimal foliations by depinning force.We introduce the tilted gradient flow and define the depinning force as the critical value of the external force under which the average velocity of the system is zero.Then,the depinning force can be used as the criterion for the existence of minimal foliations for the FK model on a Z^(d)lattice for d>1.展开更多
The classical gradient flow optimization algorithm requires a valid initial point before starting the recursive algorithm,and the existing methods can’t guarantee that the initial values fully satisfy the friction co...The classical gradient flow optimization algorithm requires a valid initial point before starting the recursive algorithm,and the existing methods can’t guarantee that the initial values fully satisfy the friction cone constraints of contact point in the optimization process of gradient flow algorithm.In order to improve safety margin and prevent the finger from slipping at contact point,we present an iterative method of safe initial values with safety margin detection and develop a gradient flow optimization algorithm based on the safe initial values.Firstly,the safety margin is defined which more intuitively reflects the margin of the grasping forces at contact point.The resulting safe initial values can be achieved by the detection of desired safety margin at each iteration.Secondly,the safe initial values are usually not optimal,even with the valid initial values,and it can’t always ensure that the finger contact force always satisfies the friction cone constraints during the optimization.It is an effective way to eliminate the unreliable initial values in the optimization and obtain a safer initial values by increasing the safety margin.By transforming the safe initial values into an initial point of the gradient flow algorithm,the final optimized values of grasping forces can be generated efficiently by gradient flow iteration.Grasp examples of the soft multi-fingered hand indicate the effectiveness of the general solution of the force optimization algorithm based on safety margin detection.The method eliminates the shortcomings of the gradient flow optimization process caused by the initial value problem and provides a more accurate and reliable force optimization result for multi-fingered dexterous manipulation.展开更多
An adaptive object tracking algorithm based on particle filtering and a modified Gradient Vector Flow (GVF) Snake is proposed for tracking moving and deforming objects. The original contours of objects are obtained by...An adaptive object tracking algorithm based on particle filtering and a modified Gradient Vector Flow (GVF) Snake is proposed for tracking moving and deforming objects. The original contours of objects are obtained by using the background differencing method,and the true contours of objects can be converged by means of the powerful searching ability of a modified GVF-Snake. Finally,an Energetic Particle Filtering (EPF) algorithm is obtained by combining particle filtering and a modified GVF-Snake,and by using K-means and the EPF algorithm,multiple objects can be tracked. The proposed tracking tactic for partially occluded objects can effectively improve its anti-occlusion ability. Experiments show that this algorithm can obtain better tracking effect even though the tracked object is occluded.展开更多
In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the ex...In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the exchangecorrelation energy is introduced into the model for a more comprehensive description of the quantum system,utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database;(ii)both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme;(iii)a C0 tetrahedral spectral element method is adopted for the quality spatial discretization,of which a quality initial condition can be designed using low order one for effectively accelerating the simulation.A series of numerical experiments validate the effectiveness of our method,encompassing various atoms and molecules.All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number.Moreover,the efficiency of the extended framework is discussed in detail on updating schemes.展开更多
The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021...The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021)]for the numerical approximation of the ground state of the Gross–Pitaevskii equation can equally be applied for the effective approximation of excited states of Schr¨odinger’s equation.That procedure employs an adaptive interplay of a Sobolev gradient flow iteration and a novel local mesh refinement strategy,and yields a guaranteed energy decay in each step of the algorithm.The computational tests in the present work highlight that this strategy is indeed able to approximate excited states,with(almost)optimal convergence rate with respect to the number of degrees of freedom.展开更多
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure.These properties allow for accurate computations of stationary states and long...We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure.These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential.The proposed scheme is able to cope with non-smooth stationary states,different time scales including metastability,as well as concentrations and self-similar behavior induced by singular nonlocal kernels.We use the scheme to explore properties of these equations beyond their present theoretical knowledge.展开更多
In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure syste...In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.展开更多
In this paper,we start to study the gradient flow of the functional L_(β) introduced by Han-Li-Sun in[8].As a first step,we show that if the initial surface is symplectic in a Kähler surface,then the symplectic ...In this paper,we start to study the gradient flow of the functional L_(β) introduced by Han-Li-Sun in[8].As a first step,we show that if the initial surface is symplectic in a Kähler surface,then the symplectic property is preserved along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.When β=1,we derive a monotonicity formula for the flow.As applications,we show that the l-tangent cone of the flow consists of the finite flat planes.展开更多
In this paper,we propose a new gradient vector flow model with advection enhancement,called advection-enhanced gradient vector flow,for calculating the external force employed in the active-contour image segmentation....In this paper,we propose a new gradient vector flow model with advection enhancement,called advection-enhanced gradient vector flow,for calculating the external force employed in the active-contour image segmentation.The proposed model is mainly inspired by the functional derivative of an adaptive total variation regularizer whose minimizer is expected to be able to effectively preserve the desired object boundary.More specifically,by incorporating an additional advection term into the usual gradient vector flow model,the resulting external force can much better help the active contour to recover missing edges,to converge to a narrow and deep concavity,and to preserve weak edges.Numerical experiments are performed to demonstrate the high performance of the newly proposed model.展开更多
This article concerns the construction of high-order energy-decaying numerical methods for gradient flows of evolving surfaces with curvature-dependent energy functionals.The semidiscrete evolving surface finite eleme...This article concerns the construction of high-order energy-decaying numerical methods for gradient flows of evolving surfaces with curvature-dependent energy functionals.The semidiscrete evolving surface finite element method is derived based on the calculus of variation of the semidiscrete surface energy functional.This makes the semidiscrete problem naturally inherit the energy decay structure.With this property,the semidiscrete problem is furthermore formulated as a gradient flow system of ODEs.The averaged vector-field collocation method is used for time discretization of the ODEs to preserve energy decay at the fully discrete level while achieving high-order accuracy in time.Extensive numerical examples are provided to illustrate the accuracy and energy diminishing property of the proposed method,as well as the effectiveness of the method in capturing singularities in the evolution of closed surfaces.展开更多
A new slip velocity model based on molecular potential theory and macro-force analysis,which is applied in Couette flow with pressure gradient,is built up.The model is validated by later being introduced in hydrodynam...A new slip velocity model based on molecular potential theory and macro-force analysis,which is applied in Couette flow with pressure gradient,is built up.The model is validated by later being introduced in hydrodynamic system to predict film distribution,which shows a good agreement with experimental data obtained from multi-beam intensity-based tests with Fe and Cu ball materials under accurate controlled temperature,load and different wall velocities.Results show that the slip length for Fe case is ignorable so it seems like no slip,but for Cu case,the slip length is large to make 20%discrepancy with no slip simulation and also behaves shear-dependently.Moreover,during the experimental cases when both Fe and Cu ball velocities rise from-133 mm/s to 1330 mm/s,the slip velocity changes its direction with entrainment velocity and thus contributes to first enhance and then diminish the hydrodynamic film,but due to slip length on Cu case varying largely than that on Fe case,the film from Cu case and from Fe case has a clear cross-point between uh=80 mm/s and uh=220 m m/s(ub is the ball speed).The results above support strongly that Cu surface will lead to stronger slip than Fe case because of its smaller solid-liquid interaction,and obviously slip will influence hydrodynamic characteristics prominently.展开更多
基金supported by the National Key Research and Development Program of China(2020YFA0714300)the National Natural Science Foundation of China(62003084,62203108,62073079)+3 种基金the Natural Science Foundation of Jiangsu Province of China(BK20200355)the General Joint Fund of the Equipment Advance Research Program of Ministry of Education(8091B022114)Jiangsu Province Excellent Postdoctoral Program(2022ZB131)China Postdoctoral Science Foundation(2022M720720,2023T160105).
文摘The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.
基金supported by National Natural Science Foundation of China(Grant No.12371409)supported by National Natural Science Foundation of China(Grant No.12271240)+1 种基金National Natural Science Foundation of China/Hong Kong Research Grants Council Joint Research Scheme(Grant No.11961160718)the Shenzhen Natural Science Fund(Grant No.RCJC20210609103819018)。
文摘In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.
文摘We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows.These schemes are designed to preserve mass and positivity and to be uniquely solvable.In addition,they also ensure energy dissipation in many typical scenarios.Through extensive numerical experiments,we demonstrate the schemes’robustness,accuracy,and efficiency.
基金Project supported by the National Natural Science foundation of China(No.51079095)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51021004)
文摘This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.
基金Supported by the National Natural Science Foundation of China(60805004)the State Key Lab of Space Medicine Fundamen-tals and Application(SMFA09A16)
文摘Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.
文摘Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) systolic function. It results in symptoms and reduced quality of life and carries a high mortality. Whilst this form of severe AS, termed paradoxical low flow low gradient (pLFLG), is well reported, patients with this diagnosis experience inappropriate barriers to aortic valve replacement (AVR), the only efficacious treatment. We present the case of an 88-year-old female with 12 months of exertional dyspnoea on a background of hypothyroidism and hypercholesterolemia. Transthoracic echocardiogram (TTE) revealed LV hypertrophy, with a small LV cavity size and reduced stroke volume, yet normal systolic function. A heavily calcified aortic valve was identified with severe aortic stenosis, based on valve area, yet with incongruous mean transvalvular gradient of 25 mmHg (severe ≥ 50 mmHg). Following exclusion of other differential diagnoses, her symptoms were attributed to paradoxical LFLG severe AS. She was however declined definitive transcatheter aortic valve implantation (TAVI) due to her paradoxically low mean aortic gradient. Following further deterioration in her symptoms and supportive quantification of poor exercise performance, she was ultimately re-referred, accepted, and underwent TAVI. Following her AVR, the patient experiences significant improvement in both symptoms and quality of life after only one month. Paradoxical LFLG severe AS remains a well-documented yet under recognized disease. It carries high morbidity and mortality if untreated, yet is significantly less likely to be referred and accepted for intervention. With its prevalence expected to rise with an ageing population, this case serves as a timely reminder for clinicians to address the under recognition of important pathology.
基金supported in part by the Young Elite Scientists Sponsorship Program by China Association for Science and Technology(2022QNRC001)the National Natural Science Foundation of China(62406315)+2 种基金China Postdoctoral Science Foundation(2025M771504)GuangDong Basic and Applied Basic Research Foundation(2024A1515110108)Shaanxi Provincial Key Research and Development Program(2025SF-YBXM-023).
文摘Revealing the latent low-dimensional geometric structure of high-dimensional data is a crucial task in unsupervised representation learning.Traditional manifold learning,as a typical method for discovering latent geometric structures,has provided important nonlinear insight for the theoretical development of unsupervised representation learning.However,due to the shallow learning mechanism of the existing methods,they can only exploit the simple geometric structure embedded in the initial data,such as the local linear structure.Traditional manifold learning methods are fairly limited in mining higher-order nonlinear geometric information,which is also crucial for the development of unsupervised representation learning.To address the abovementioned limitations,this paper proposes a novel dynamic geometric structure learning model(DGSL)to explore the true latent nonlinear geometric structure.Specifically,by mathematically analysing the reconstruction loss function of manifold learning,we first provide universal geometric relational function between the curvature and the non-Euclidean metric of the initial data.Then,we leverage geometric flow to design a deeply iterative learning model to optimize this relational function.Our method can be viewed as a general-purpose algorithm for mining latent geometric structures,which can enhance the performance of geometric representation methods.Experimentally,we perform a set of representation learning tasks on several datasets.The experimental results show that our proposed method is superior to traditional methods.
基金supported by the National Natural Science Foundation of China (No. 40772089)
文摘ABSTRACT： The Damintun （大民屯） depression, a small （about 800km^2 in area） subunit in the Bohai （渤海） Bay basin, hosts nearly 2×10^8 t of high-wax oils with wax contents up to 60%. The high-wax oils have high consolidation temperatures and viscosities. The high-wax oils were generated from the fourth member of the Shahejie Formation （Es4）, which is also important source rocks for oils in other subunits of the Bohai Bay basin. Yet high-wax oils have not been found in significant volumes elsewhere in the Bohai Bay basin. Geological conditions favourable for high-wax oil enrichment were studied. This study shows that the unusual concentrations of high-wax oils in the depression seem to result from at least three different factors： （1） the presence of organic-matter rich source rocks which were prone to generate wax-rich hydrocarbons; （2） the formation of early overpressures which increased the expul- sion efficiency of waxy hydrocarbons; and （3） reductions in subsidence rate and basal heat flows, which minimized the thermal cracking of high molecular-weight （waxy） hydrocarbons, and therefore prevented the high-wax oils from being transformed into less waxy equivalents.
基金sponsored by the National Science and Technology Support Program (2014BAL05B01)STS Project of the Chinese Academy of Science (KFJ-EW-STS-094)Scientific Project of Department of land and resources of Sichuan Province (KJ-2015-18)
文摘Siltation gradient and siltation length are important parameters for designing gravity check dams for debris flows,which directly affect the accuracy of estimates of interception capacity.At present,siltation gradient calculations are based primarily on empirical values,and range from 0.4 to 0.95 times the channel slope coefficient.The middle reaches of the Bailong River are one of the four areas in China that are most severely affected by debris flow hazards.Gravity dams are widely employed in this mountainous area.However,field studies of their capacity are lacking.In this paper,the operations of check dams were investigated.Based on field investigation results and theoretical analysis,calculations for siltation gradient,siltation length,and dam storage capacity are established.The impact of debris flow density,channel slope,and particle size weight percentages are discussed.The calculations show that the theoretical values for siltation gradient are consistent with measured values with 83.6% accuracy;and theoretical values of siltation length are consistent with measured values with 91.6% accuracy.The results of this research are an important reference for optimal height and spacing of dams,estimation of dam storage capacity,and disaster prevention.
基金supported by the National Natural Science Foundation of China(11701298)。
文摘For the high-dimensional Frenkel-Kontorova(FK)model on lattices,we study the existence of minimal foliations by depinning force.We introduce the tilted gradient flow and define the depinning force as the critical value of the external force under which the average velocity of the system is zero.Then,the depinning force can be used as the criterion for the existence of minimal foliations for the FK model on a Z^(d)lattice for d>1.
基金National Natural Science Foundation of China(51305180)International Science&Technology Cooperation Program of China(2014DFR10620)Shandong Provincial Natural Science Foundation(ZR2013FM026,ZR2014YL009)
文摘The classical gradient flow optimization algorithm requires a valid initial point before starting the recursive algorithm,and the existing methods can’t guarantee that the initial values fully satisfy the friction cone constraints of contact point in the optimization process of gradient flow algorithm.In order to improve safety margin and prevent the finger from slipping at contact point,we present an iterative method of safe initial values with safety margin detection and develop a gradient flow optimization algorithm based on the safe initial values.Firstly,the safety margin is defined which more intuitively reflects the margin of the grasping forces at contact point.The resulting safe initial values can be achieved by the detection of desired safety margin at each iteration.Secondly,the safe initial values are usually not optimal,even with the valid initial values,and it can’t always ensure that the finger contact force always satisfies the friction cone constraints during the optimization.It is an effective way to eliminate the unreliable initial values in the optimization and obtain a safer initial values by increasing the safety margin.By transforming the safe initial values into an initial point of the gradient flow algorithm,the final optimized values of grasping forces can be generated efficiently by gradient flow iteration.Grasp examples of the soft multi-fingered hand indicate the effectiveness of the general solution of the force optimization algorithm based on safety margin detection.The method eliminates the shortcomings of the gradient flow optimization process caused by the initial value problem and provides a more accurate and reliable force optimization result for multi-fingered dexterous manipulation.
基金Supported by the Significant Term of Science and Technology Research in Ministry of Education (No. 205060)Open Research Fund of National Mobile Communications Research Laboratory,Southeast University (N200911)+2 种基金Significant Basic Research of Jiangsu Province Colleges and Universities Natural Science Projects (07 KJA51006)Research Fund of Nanjing College of Traffic Vocational Technology (JY0903)Huawei Science and Technology Fund
文摘An adaptive object tracking algorithm based on particle filtering and a modified Gradient Vector Flow (GVF) Snake is proposed for tracking moving and deforming objects. The original contours of objects are obtained by using the background differencing method,and the true contours of objects can be converged by means of the powerful searching ability of a modified GVF-Snake. Finally,an Energetic Particle Filtering (EPF) algorithm is obtained by combining particle filtering and a modified GVF-Snake,and by using K-means and the EPF algorithm,multiple objects can be tracked. The proposed tracking tactic for partially occluded objects can effectively improve its anti-occlusion ability. Experiments show that this algorithm can obtain better tracking effect even though the tracked object is occluded.
基金the Boya postdoctoral fellowship from Peking University and the support fromthe China Postdoctoral Science Foundation(No.2023M740107)the Natural Science Starting Project of SWPU(No.2024QHZ030)+2 种基金the support from The Science and Technology Development Fund,Macao SAR(No.0068/2024/RIA1)National Natural Science Foundation of China(No.11922120)MYRG of University of Macao(No.MYRG-CRG2024-00042-FST).
文摘In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the exchangecorrelation energy is introduced into the model for a more comprehensive description of the quantum system,utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database;(ii)both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme;(iii)a C0 tetrahedral spectral element method is adopted for the quality spatial discretization,of which a quality initial condition can be designed using low order one for effectively accelerating the simulation.A series of numerical experiments validate the effectiveness of our method,encompassing various atoms and molecules.All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number.Moreover,the efficiency of the extended framework is discussed in detail on updating schemes.
基金the financial support of the Swiss National Science Foundation(SNSF),Project No.P2BEP2_191760.
文摘The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021)]for the numerical approximation of the ground state of the Gross–Pitaevskii equation can equally be applied for the effective approximation of excited states of Schr¨odinger’s equation.That procedure employs an adaptive interplay of a Sobolev gradient flow iteration and a novel local mesh refinement strategy,and yields a guaranteed energy decay in each step of the algorithm.The computational tests in the present work highlight that this strategy is indeed able to approximate excited states,with(almost)optimal convergence rate with respect to the number of degrees of freedom.
基金JAC acknowledges support from projects MTM2011-27739-C04-02,2009-SGR-345 from Agencia de Gestio d’Ajuts Universitaris i de Recerca-Generalitat de Catalunya,and the Royal Society through a Wolfson Research Merit AwardJAC and YH were supported by Engineering and Physical Sciences Research Council(UK)grant number EP/K008404/1+1 种基金The work of AC was supported in part by the NSF Grant DMS-1115682The authors also acknowledge the support by NSF RNMS grant DMS-1107444.
文摘We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure.These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential.The proposed scheme is able to cope with non-smooth stationary states,different time scales including metastability,as well as concentrations and self-similar behavior induced by singular nonlocal kernels.We use the scheme to explore properties of these equations beyond their present theoretical knowledge.
基金The first author would like to thank the support from the UM-Funded PhD Assistantship from University of MacaoThe second author was partially supported by Macao Young Scholar Program(AM201919)+5 种基金excellent youth project of Hunan Education Department(19B543)Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(2020ZYT003)The third author would like to thank financial support from National Natural Science Foundation of China(Grant Nos.11922120,11871489)FDCT of Macao SAR(Grant No.0082/2020/A2)University of Macao(Grant No.MYRG2020-00265-FST)Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications(Grant No.2020B1212030001).
文摘In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.
基金supported by theNationalNatural Science Foundation of China,Nos.11721101,12071352,12031017。
文摘In this paper,we start to study the gradient flow of the functional L_(β) introduced by Han-Li-Sun in[8].As a first step,we show that if the initial surface is symplectic in a Kähler surface,then the symplectic property is preserved along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.When β=1,we derive a monotonicity formula for the flow.As applications,we show that the l-tangent cone of the flow consists of the finite flat planes.
基金supported by the Ministry of Science and Technology of Taiwan under grants MOST 106-2115-M-005-005-MY2(Po-Wen Hsieh),MOST 107-2811-M-008-007(Pei-Chiang Shao)MOST 106-2115-M-008-014-MY2(Suh-Yuh Yang).
文摘In this paper,we propose a new gradient vector flow model with advection enhancement,called advection-enhanced gradient vector flow,for calculating the external force employed in the active-contour image segmentation.The proposed model is mainly inspired by the functional derivative of an adaptive total variation regularizer whose minimizer is expected to be able to effectively preserve the desired object boundary.More specifically,by incorporating an additional advection term into the usual gradient vector flow model,the resulting external force can much better help the active contour to recover missing edges,to converge to a narrow and deep concavity,and to preserve weak edges.Numerical experiments are performed to demonstrate the high performance of the newly proposed model.
基金partly supported by NSFC 11871092 and NSAF U1930402,ChinaPostdoctoral Science Foundation(Project No.2020M682895)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(GRF Project No.Poly U15300920)。
文摘This article concerns the construction of high-order energy-decaying numerical methods for gradient flows of evolving surfaces with curvature-dependent energy functionals.The semidiscrete evolving surface finite element method is derived based on the calculus of variation of the semidiscrete surface energy functional.This makes the semidiscrete problem naturally inherit the energy decay structure.With this property,the semidiscrete problem is furthermore formulated as a gradient flow system of ODEs.The averaged vector-field collocation method is used for time discretization of the ODEs to preserve energy decay at the fully discrete level while achieving high-order accuracy in time.Extensive numerical examples are provided to illustrate the accuracy and energy diminishing property of the proposed method,as well as the effectiveness of the method in capturing singularities in the evolution of closed surfaces.
基金This work was supported by China Scholarship Council。
文摘A new slip velocity model based on molecular potential theory and macro-force analysis,which is applied in Couette flow with pressure gradient,is built up.The model is validated by later being introduced in hydrodynamic system to predict film distribution,which shows a good agreement with experimental data obtained from multi-beam intensity-based tests with Fe and Cu ball materials under accurate controlled temperature,load and different wall velocities.Results show that the slip length for Fe case is ignorable so it seems like no slip,but for Cu case,the slip length is large to make 20%discrepancy with no slip simulation and also behaves shear-dependently.Moreover,during the experimental cases when both Fe and Cu ball velocities rise from-133 mm/s to 1330 mm/s,the slip velocity changes its direction with entrainment velocity and thus contributes to first enhance and then diminish the hydrodynamic film,but due to slip length on Cu case varying largely than that on Fe case,the film from Cu case and from Fe case has a clear cross-point between uh=80 mm/s and uh=220 m m/s(ub is the ball speed).The results above support strongly that Cu surface will lead to stronger slip than Fe case because of its smaller solid-liquid interaction,and obviously slip will influence hydrodynamic characteristics prominently.
