Diffusion kurtosis imaging can be used to assess pathophysiological changes in tissue structure and to diagnose central nervous system diseases. However, its sensitivity in assessing hippocampal differences between pa...Diffusion kurtosis imaging can be used to assess pathophysiological changes in tissue structure and to diagnose central nervous system diseases. However, its sensitivity in assessing hippocampal differences between patients with Alzheimer’s disease and those with amnestic mild cognitive impairment has not been characterized. Here, we examined 20 individuals with Alzheimer’s disease (11 men and 9 women, mean 73.2 ± 4.49 years), 20 with amnestic mild cognitive impairment (10 men and 10 women, mean 71.55 ± 4.77 years), and 20 normal controls (11 men and 9 women, mean 70.45 ± 5.04 years). We conducted diffusion kurtosis imaging, using a 3.0 T magnetic resonance scanner, to compare hippocampal differences among the three groups. The results demonstrated that the right hippocampal volume and bilateral mean kurtosis were remarkably smaller in individuals with Alzheimer’s disease compared with those with amnestic mild cognitive impairment and normal controls. Further, the mean kurtosis was lower in the amnestic mild cognitive impairment group compared with the normal control group. The mean diffusion in the left hippocampus was lower in the Alzheimer’s disease group than in the amnestic mild cognitive impairment and normal control groups, while the mean diffusion in the right hippocampus was lower in the Alzheimer’s disease group than in the normal control group. Fractional anisotropy was similar among the three groups. These results verify that bilateral mean kurtosis and mean diffusion are sensitive to the diagnosis of Alzheimer’s disease and amnestic mild cognitive impairment. This study was approved by the Ethics Review Board of Affiliated Sixth People’s Hospital of Shanghai Jiao Tong University, China on May 4, 2010 (approval No. 2010(C)-6).展开更多
Some in vitro experiments have shown that erythropoietin （EPO） increases resistance to apoptosis and facilitates neuronal survival follow- ing cerebral ischemia. However, results from in vivo studies are rarely repo...Some in vitro experiments have shown that erythropoietin （EPO） increases resistance to apoptosis and facilitates neuronal survival follow- ing cerebral ischemia. However, results from in vivo studies are rarely reported. Perfusion-weighted imaging （PWI） and diffusion-weighted imaging （DWI） have been applied successfully to distinguish acute cerebral ischemic necrosis and penumbra in living animals; therefore, we hypothesized that PWI and DWI could be used to provide imaging evidence in vivo for the conclusion that EPO could reduce apoptosis in brain areas injured by cerebral ischemia/reperfusion. To validate this hypothesis, we established a rat model of focal cerebral ischemia/ reperfusion injury, and treated with intra-cerebroventricular injection of EPO （5,000 U/kg） 20 minutes before injury. Brain tissue in the ischemic injury zone was sampled using MRI-guided localization. The relative area of abnormal tissue, changes in PWI and DWI in the ischemic injury zone, and the number of apoptotic cells based on TdT-mediated dUTP-biotin nick end-labeling （TUNEL） were assessed. Our findings demonstrate that EPO reduces the relative area of abnormally high signal in PWI and DWI, increases cerebral blood volume, and decreases the number of apoptotic cells positive for TUNEL in the area injured by cerebral ischemia/reperfusion. The experiment pro- vides imaging evidence in vivo for EPO treating cerebral ischemia/reperfusion injury.展开更多
We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward utilities.We,also,consider their continuum limit which gives rise to a ...We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward utilities.We,also,consider their continuum limit which gives rise to a forward mean field game with unbounded controls in both the drift and volatility terms.Furthermore,we allow for general(time monotone)preferences,thus departing from the homothetic case,the only case so far analyzed.We produce explicit solutions for the optimal policies,the optimal wealth processes and the game values,and also provide representative examples for both the finite and the mean field game.展开更多
We study R^(d)-valued mean-field stochastic differential equations with a diffusion coefficient that varies in a discontinuous manner on the L_(p)-norm of the process.We establish the existence of a unique global stro...We study R^(d)-valued mean-field stochastic differential equations with a diffusion coefficient that varies in a discontinuous manner on the L_(p)-norm of the process.We establish the existence of a unique global strong solution in the presence of a robust drift,while also investigating scenarios where the presence of a global solution is not assured.展开更多
BACKGROUND： Previous studies regarding primary progressive aphasia （PPA） have focused on progressive, non-fluent aphasia. Little information is available with regard to the use of diffusion tensor imaging compared ...BACKGROUND： Previous studies regarding primary progressive aphasia （PPA） have focused on progressive, non-fluent aphasia. Little information is available with regard to the use of diffusion tensor imaging compared with conventional magnetic resonance imaging for the detection of subtle structural abnormalities. OBJECTIVE： To investigate and localize brain abnormalities in a Chinese patient with semantic dementia. DESIGN, TIME AND SETTING： A concurrent, non-randomized, case-controlled, neuroimaging, clinical trial was performed at the Department of Radiology, West China Hospital of Sichuan University in March 2009. PARTICIPANTS： One 75-year-old male patient, who was diagnosed with semantic dementia, and 21 age- and gender-matched healthy volunteers were recruited for the study. METHODS： Diffusion tensor imaging was used to determine mean diffusion （MD） and fractional anisotropy （FA） in the brains of the patient and the 21 healthy subjects. Voxel-based analysis of MD and FA values was performed using statistical parametric mapping. MAIN OUTCOME MEASURES： MD and FA value maps differences between patient and controls. RESULTS： MD was significantly increased in both cerebra, but was predominant on the left side and expanded to outside of the language-related region. Reduced MD was not detected in any of the brains. FA was shown to be decreased in the corpus callosum, but was increased in the basal ganglia. CONCLUSION： The present study provided clear in vivo magnetic imaging evidence of diffuse brain involvement in semantic dementia. Increases in MD were greater than in FA when brain diffusion alterations were detected, which suggested that MD could be a better marker of disease progression.展开更多
Under different temperatures and concentrations, the diffusion of Vitamin C （VC） in water solution was exam- ined by molecular dynamics simulation. The diffusion coefficients were calculated based on the Einstein eq...Under different temperatures and concentrations, the diffusion of Vitamin C （VC） in water solution was exam- ined by molecular dynamics simulation. The diffusion coefficients were calculated based on the Einstein equation. The influences of temperature, concentration, and simulation time on the diffusion coefficient were discussed. The results showed that at higher temperature and lower concentration the normal diffusions appear relatively late, but the linear range of mean square displacement curves continues longer than that at lower temperature and higher concentration. At the same temperature, the normal diffusion time increases and the diffusion coefficient decreases as the simulation concentration increases. These simulation results are in good agreement with experiments. Analyses of the pair correlation functions of the simulation systems showed that hydrogen bonds are mainly formed be- tween the hydrogen atoms of VC molecules and oxygen atoms of H20 molecules, rather than between the O atoms of VC molecules and H atoms of H20 molecules. The diffusion coefficient is higher as the interaction between water molecules and VC molecules is stronger when VC concentration is lower. The water in the model systems affects the diffusion of VC molecules by the short-range repulsion of O（H20）-O（H20） pairs and the non-bond interaction of H（H20）-H（H20） pairs. The short-range repulsion of O（H20）-O（H20） pairs is greater when VC concentration is higher, the diffusion of VC is weaker. The greater the non-bond interaction of H（H20）-H（H20） pairs is, the higher the VC diffusion is. It is expected that this study can provide a theoretical direction for the experiments on the mass transfer of VC in water solution.展开更多
In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditio...In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.展开更多
Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such type...Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.展开更多
The periodic one-dimensional hopping model is useful for studying the motion of microscopic particles in the thermal noise environment. Based on the explicit formulations of mean velocity, mean first passage time and ...The periodic one-dimensional hopping model is useful for studying the motion of microscopic particles in the thermal noise environment. Based on the explicit formulations of mean velocity, mean first passage time and effective diffusion constant, a general N internal states or even infinite internal states model can be approximated by a one state model that retains the basic properties of the original process. This effective description aids the analysis of biochemical and biophysical problems. This effective description also implies that, to some extent, many processes can be well described by simple two-state models, or even one-state models.展开更多
We consider an optimal control problem which serves as a mathematical model for several problems in economics and management.The problem is the minimization of a continuous constrained functional governed by a linear ...We consider an optimal control problem which serves as a mathematical model for several problems in economics and management.The problem is the minimization of a continuous constrained functional governed by a linear parabolic diffusion-advection equation controlled in a coefficient in advection part.The additional constraint is non-negativity of a solution of state equation.We construct and analyze several mesh schemes approximating the formulated problem using finite difference methods in space and in time.All these approximations keep the positivity of the solutions to mesh state problem,either unconditionally or under some additional constraints to mesh steps.This allows us to remove corresponding constraint from the formulation of the discrete problem to simplify its implementation.Based on theoretical estimates and numerical results,we draw conclusions about the quality of the proposed mesh schemes.展开更多
A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrins...A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrinsic partial differentialequation for updating the position vector of evolving family of plane curves. A curvecan be evolved in the normal direction by a combination of fourth order terms relatedto the intrinsic Laplacian of the curvature, second order terms related to the curva-ture, first order terms related to anisotropy and by a given external velocity field. Theevolution is numerically stabilized by an asymptotically uniform tangential redistri-bution of grid points yielding the first order intrinsic advective terms in the governingsystem of equations. By using a semi-implicit in time discretization it can be numer-ically approximated by a solution to linear penta-diagonal systems of equations (inpresence of the fourth order terms) or tri-diagonal systems (in the case of the secondorder terms). Various numerical experiments of plane curve evolutions, including, inparticular, nonlinear, anisotropic and regularized backward curvature flows, surfacediffusion and Willmore flows, are presented and discussed.展开更多
基金supported by the Shanghai Municipal Education Commission-Gaofeng Clinical Medicine in China,No.2016427(to YHL)the Clinical Science and Technology Innovation Project of Shanghai Shen Kang Hospital Development Center in China,No.SHDC22015038(to YHL)the Shanghai Municipal Science and Technology Commission Medical Guide Project in China,No.16411968900(to YHL)
文摘Diffusion kurtosis imaging can be used to assess pathophysiological changes in tissue structure and to diagnose central nervous system diseases. However, its sensitivity in assessing hippocampal differences between patients with Alzheimer’s disease and those with amnestic mild cognitive impairment has not been characterized. Here, we examined 20 individuals with Alzheimer’s disease (11 men and 9 women, mean 73.2 ± 4.49 years), 20 with amnestic mild cognitive impairment (10 men and 10 women, mean 71.55 ± 4.77 years), and 20 normal controls (11 men and 9 women, mean 70.45 ± 5.04 years). We conducted diffusion kurtosis imaging, using a 3.0 T magnetic resonance scanner, to compare hippocampal differences among the three groups. The results demonstrated that the right hippocampal volume and bilateral mean kurtosis were remarkably smaller in individuals with Alzheimer’s disease compared with those with amnestic mild cognitive impairment and normal controls. Further, the mean kurtosis was lower in the amnestic mild cognitive impairment group compared with the normal control group. The mean diffusion in the left hippocampus was lower in the Alzheimer’s disease group than in the amnestic mild cognitive impairment and normal control groups, while the mean diffusion in the right hippocampus was lower in the Alzheimer’s disease group than in the normal control group. Fractional anisotropy was similar among the three groups. These results verify that bilateral mean kurtosis and mean diffusion are sensitive to the diagnosis of Alzheimer’s disease and amnestic mild cognitive impairment. This study was approved by the Ethics Review Board of Affiliated Sixth People’s Hospital of Shanghai Jiao Tong University, China on May 4, 2010 (approval No. 2010(C)-6).
文摘Some in vitro experiments have shown that erythropoietin （EPO） increases resistance to apoptosis and facilitates neuronal survival follow- ing cerebral ischemia. However, results from in vivo studies are rarely reported. Perfusion-weighted imaging （PWI） and diffusion-weighted imaging （DWI） have been applied successfully to distinguish acute cerebral ischemic necrosis and penumbra in living animals; therefore, we hypothesized that PWI and DWI could be used to provide imaging evidence in vivo for the conclusion that EPO could reduce apoptosis in brain areas injured by cerebral ischemia/reperfusion. To validate this hypothesis, we established a rat model of focal cerebral ischemia/ reperfusion injury, and treated with intra-cerebroventricular injection of EPO （5,000 U/kg） 20 minutes before injury. Brain tissue in the ischemic injury zone was sampled using MRI-guided localization. The relative area of abnormal tissue, changes in PWI and DWI in the ischemic injury zone, and the number of apoptotic cells based on TdT-mediated dUTP-biotin nick end-labeling （TUNEL） were assessed. Our findings demonstrate that EPO reduces the relative area of abnormally high signal in PWI and DWI, increases cerebral blood volume, and decreases the number of apoptotic cells positive for TUNEL in the area injured by cerebral ischemia/reperfusion. The experiment pro- vides imaging evidence in vivo for EPO treating cerebral ischemia/reperfusion injury.
文摘We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward utilities.We,also,consider their continuum limit which gives rise to a forward mean field game with unbounded controls in both the drift and volatility terms.Furthermore,we allow for general(time monotone)preferences,thus departing from the homothetic case,the only case so far analyzed.We produce explicit solutions for the optimal policies,the optimal wealth processes and the game values,and also provide representative examples for both the finite and the mean field game.
文摘We study R^(d)-valued mean-field stochastic differential equations with a diffusion coefficient that varies in a discontinuous manner on the L_(p)-norm of the process.We establish the existence of a unique global strong solution in the presence of a robust drift,while also investigating scenarios where the presence of a global solution is not assured.
文摘BACKGROUND： Previous studies regarding primary progressive aphasia （PPA） have focused on progressive, non-fluent aphasia. Little information is available with regard to the use of diffusion tensor imaging compared with conventional magnetic resonance imaging for the detection of subtle structural abnormalities. OBJECTIVE： To investigate and localize brain abnormalities in a Chinese patient with semantic dementia. DESIGN, TIME AND SETTING： A concurrent, non-randomized, case-controlled, neuroimaging, clinical trial was performed at the Department of Radiology, West China Hospital of Sichuan University in March 2009. PARTICIPANTS： One 75-year-old male patient, who was diagnosed with semantic dementia, and 21 age- and gender-matched healthy volunteers were recruited for the study. METHODS： Diffusion tensor imaging was used to determine mean diffusion （MD） and fractional anisotropy （FA） in the brains of the patient and the 21 healthy subjects. Voxel-based analysis of MD and FA values was performed using statistical parametric mapping. MAIN OUTCOME MEASURES： MD and FA value maps differences between patient and controls. RESULTS： MD was significantly increased in both cerebra, but was predominant on the left side and expanded to outside of the language-related region. Reduced MD was not detected in any of the brains. FA was shown to be decreased in the corpus callosum, but was increased in the basal ganglia. CONCLUSION： The present study provided clear in vivo magnetic imaging evidence of diffuse brain involvement in semantic dementia. Increases in MD were greater than in FA when brain diffusion alterations were detected, which suggested that MD could be a better marker of disease progression.
基金This work was financially supported by open projectfrom the Key Laboratory of Genetic Breeding and Aquaculture Biology of Freshwater Fisher, Ministry of Agriculture, China （No. BZ2007-06） and the Natural Science Foundation of Jiangsu province, Higher Educa- tion Institution of China （No. 08KJD240003）.
文摘Under different temperatures and concentrations, the diffusion of Vitamin C （VC） in water solution was exam- ined by molecular dynamics simulation. The diffusion coefficients were calculated based on the Einstein equation. The influences of temperature, concentration, and simulation time on the diffusion coefficient were discussed. The results showed that at higher temperature and lower concentration the normal diffusions appear relatively late, but the linear range of mean square displacement curves continues longer than that at lower temperature and higher concentration. At the same temperature, the normal diffusion time increases and the diffusion coefficient decreases as the simulation concentration increases. These simulation results are in good agreement with experiments. Analyses of the pair correlation functions of the simulation systems showed that hydrogen bonds are mainly formed be- tween the hydrogen atoms of VC molecules and oxygen atoms of H20 molecules, rather than between the O atoms of VC molecules and H atoms of H20 molecules. The diffusion coefficient is higher as the interaction between water molecules and VC molecules is stronger when VC concentration is lower. The water in the model systems affects the diffusion of VC molecules by the short-range repulsion of O（H20）-O（H20） pairs and the non-bond interaction of H（H20）-H（H20） pairs. The short-range repulsion of O（H20）-O（H20） pairs is greater when VC concentration is higher, the diffusion of VC is weaker. The greater the non-bond interaction of H（H20）-H（H20） pairs is, the higher the VC diffusion is. It is expected that this study can provide a theoretical direction for the experiments on the mass transfer of VC in water solution.
文摘In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.
基金supported by the Office of Vice Chancellor for Research and Graduate Education(VCRGE)at University of Wisconsin-Madisonthe Office of Naval Research Grant ONR MURI N00014-16-1-2161+1 种基金the Center for Prototype Climate Modeling(CPCM)at New York University Abu Dhabi Research InstituteNUS Grant R-146-000-226-133
文摘Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.
基金the National Natural Science Foundation of China(Grant No. 10701029)
文摘The periodic one-dimensional hopping model is useful for studying the motion of microscopic particles in the thermal noise environment. Based on the explicit formulations of mean velocity, mean first passage time and effective diffusion constant, a general N internal states or even infinite internal states model can be approximated by a one state model that retains the basic properties of the original process. This effective description aids the analysis of biochemical and biophysical problems. This effective description also implies that, to some extent, many processes can be well described by simple two-state models, or even one-state models.
基金Shuhua Zhang was supported by the National Basic Research Program(No.2012CB955804)the Major Research Plan of the National Natural Science Foundation of China(No.91430108)+2 种基金the Natural Science Foundation of China(No.11771322)the Major Program of Tianjin University of Finance and Economics(No.ZD1302)Alexander Lapin was supported by Russian Foundation of Basic Researches(No.16-01-00408)and by program”1000 Talents”of China.
文摘We consider an optimal control problem which serves as a mathematical model for several problems in economics and management.The problem is the minimization of a continuous constrained functional governed by a linear parabolic diffusion-advection equation controlled in a coefficient in advection part.The additional constraint is non-negativity of a solution of state equation.We construct and analyze several mesh schemes approximating the formulated problem using finite difference methods in space and in time.All these approximations keep the positivity of the solutions to mesh state problem,either unconditionally or under some additional constraints to mesh steps.This allows us to remove corresponding constraint from the formulation of the discrete problem to simplify its implementation.Based on theoretical estimates and numerical results,we draw conclusions about the quality of the proposed mesh schemes.
基金This work was supported by grants:VEGA 1/0269/09,APVV-0351-07,APVV-RPEU-0004-07(K.Mikula and M.Balazovjech)and APVV-0247-06(D.Sevcovic).
文摘A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrinsic partial differentialequation for updating the position vector of evolving family of plane curves. A curvecan be evolved in the normal direction by a combination of fourth order terms relatedto the intrinsic Laplacian of the curvature, second order terms related to the curva-ture, first order terms related to anisotropy and by a given external velocity field. Theevolution is numerically stabilized by an asymptotically uniform tangential redistri-bution of grid points yielding the first order intrinsic advective terms in the governingsystem of equations. By using a semi-implicit in time discretization it can be numer-ically approximated by a solution to linear penta-diagonal systems of equations (inpresence of the fourth order terms) or tri-diagonal systems (in the case of the secondorder terms). Various numerical experiments of plane curve evolutions, including, inparticular, nonlinear, anisotropic and regularized backward curvature flows, surfacediffusion and Willmore flows, are presented and discussed.
