We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discu...We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.展开更多
In this paper,a data consistency condition(DCC)in Radon domain is re-derived from the perspective of Lie transformation group and compared with other two derivations.By carefully observing the proof procedure on the b...In this paper,a data consistency condition(DCC)in Radon domain is re-derived from the perspective of Lie transformation group and compared with other two derivations.By carefully observing the proof procedure on the basis of Lie transformation group,we may have a deeper insight on the essence of this DCC.Moreover,it may help determine whether there are the corresponding counterparts in both image and Radon domains.Following this line of thought,more data consistency conditions will possibly be explored in the future.This is definitely critical as data consistency conditions would be applied to the construction of algorithms for next-generation CT imaging.展开更多
Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solv...Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solving internal variables are given. It makes the rate-dependent model applicable no matter whether the consistency conditions can be satisfied or not.展开更多
A consistency condition is developed for computed tomography （CT） projection data acquired from a straight-line X-ray source trajectory. The condition states that integrals of normalized projection data along detect...A consistency condition is developed for computed tomography （CT） projection data acquired from a straight-line X-ray source trajectory. The condition states that integrals of normalized projection data along detector lines parallel to the X-ray path must be equal. The projection data is required to be untruncated only along the detector lines parallel to the X-ray path, a less restrictive requirement compared to Fourier conditions that necessitate completely untruncated data. The condition is implemented numerically on simple image functions, a discretization error bound is estimated, and detection of motion inconsistencies is demonstrated. The results show that the consistency condition may be used to quantitatively compare the quality of projection data sets obtained from different scans of the same image object.展开更多
Accurate attenuation correction is required in dedicated breast PET imaging systems for image artifact removal and quantitative studies. In this study, a method using only emission data based on consistency conditions...Accurate attenuation correction is required in dedicated breast PET imaging systems for image artifact removal and quantitative studies. In this study, a method using only emission data based on consistency conditions is proposed for attenuation correction in breast PET imaging systems. The consistency conditions are exploited to evaluate the accuracy of the estimated attenuation distribution and find the appropriate parameters that yield the most consistent attenuation distribution with the measured emission data. We have proved the validity of the method with experimental investigations and single-patient studies using a dedicated breast PET. The results show that the method is capable of accurately estimating the attenuation distribution of a uniform attenuator from the experimental data with various relatively low activities. The results also show that in single-patient studies, the method is robust for the irregular boundary of breast tissue and provides a distinct improvement in image quality.展开更多
The accuracy of attenuation correction in positron emission tomography scanners depends mainly on deriving the reliable 511-keV linear attenuation coefficient distribution in the scanned objects. In the PET/CT system,...The accuracy of attenuation correction in positron emission tomography scanners depends mainly on deriving the reliable 511-keV linear attenuation coefficient distribution in the scanned objects. In the PET/CT system, the linear attenu- ation distribution is usually obtained from the intensities of the CT image. However, the intensities of the CT image relate to the attenuation of photons in an energy range of 40 keV-140 keV. Before implementing PET attenuation correction, the intensities of CT images must be transformed into the PET 511-keV linear attenuation coefficients. However, the CT scan parameters can affect the effective energy of CT X-ray photons and thus affect the intensities of the CT image. Therefore, for PET/CT attenuation correction, it is crucial to determine the conversion curve with a given set of CT scan parameters and convert the CT image into a PET linear attenuation coefficient distribution. A generalized method is proposed for con- verting a CT image into a PET linear attenuation coefficient distribution. Instead of some parameter-dependent phantom calibration experiments, the conversion curve is calculated directly by employing the consistency conditions to yield the most consistent attenuation map with the measured PET data. The method is evaluated with phantom experiments and small animal experiments. In phantom studies, the estimated conversion curve fits the true attenuation coefficients accurately, and accurate PET attenuation maps are obtained by the estimated conversion curves and provide nearly the same correction results as the true attenuation map. In small animal studies, a more complicated attenuation distribution of the mouse is obtained successfully to remove the attenuation artifact and improve the PET image contrast efficiently.展开更多
A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as mea...A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.展开更多
In this thesis, the interal relations between about shear looking, zero energy mode and patch test are studied, and a reasonable method provided for building general element of thick and thin plate with effectual and ...In this thesis, the interal relations between about shear looking, zero energy mode and patch test are studied, and a reasonable method provided for building general element of thick and thin plate with effectual and realiable numerical solution.展开更多
This paper presents new definitions of stability of solutions to singular systems with delay, and establishes theorems on stability and instability. Then by discussing second order timervarying linear singular systems...This paper presents new definitions of stability of solutions to singular systems with delay, and establishes theorems on stability and instability. Then by discussing second order timervarying linear singular systems with delay, this paper obtains some results of stability and instability, and discovers bifurcation-likephenomenons on stability.展开更多
This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states ...This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states of minor agents are governed by linear forward stochastic differential equations(SDEs).The major agent is dominating as its state enters those of minor agents.On the other hand,all minor agents are individually negligible but their state-average affects the cost functional of major agent.The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies.We first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation(BFSDE)system.Next,we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method.Consequently,we obtain the decentralized strategies for major and minor agents which are proved to satisfy the-Nash equilibrium property.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11175077,11575075 and 11547156the Joint Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China under Grant No 20122136110002+1 种基金the Open Project Program of State Key Laboratory of Theoretical Physics of Institute of Theoretical Physics under Grant No Y4KF101CJ1the Project of Key Discipline of Theoretical Physics of Department of Education in Liaoning Province under Grant Nos 905035 and 905061
文摘We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.
基金supported in partby Shaanxi Provincial Natural Science Foundation of China(No.2023-JC-YB-521)by National Natural Science Foundation of China(NSFC)(No.12475313)+1 种基金Excellent Youth Fund of Shandong Natural Science Foundation(ZR2024YQ066)by Xi'an Science and Technology Program of China(No.23GXFW0065).
文摘In this paper,a data consistency condition(DCC)in Radon domain is re-derived from the perspective of Lie transformation group and compared with other two derivations.By carefully observing the proof procedure on the basis of Lie transformation group,we may have a deeper insight on the essence of this DCC.Moreover,it may help determine whether there are the corresponding counterparts in both image and Radon domains.Following this line of thought,more data consistency conditions will possibly be explored in the future.This is definitely critical as data consistency conditions would be applied to the construction of algorithms for next-generation CT imaging.
基金the National Natural Science Foundation of China(No.59739180)the Foundation of National Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology(No.9701)
文摘Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solving internal variables are given. It makes the rate-dependent model applicable no matter whether the consistency conditions can be satisfied or not.
基金Supported in part by NIH R01 (Nos.CA120540 and EB000225)the Illinois Department of Public Health Ticket for the CureGrant. E.Y. Sidky was supported in part by a Career Development Award from NIH SPORE (No.CA125183-03)
文摘A consistency condition is developed for computed tomography （CT） projection data acquired from a straight-line X-ray source trajectory. The condition states that integrals of normalized projection data along detector lines parallel to the X-ray path must be equal. The projection data is required to be untruncated only along the detector lines parallel to the X-ray path, a less restrictive requirement compared to Fourier conditions that necessitate completely untruncated data. The condition is implemented numerically on simple image functions, a discretization error bound is estimated, and detection of motion inconsistencies is demonstrated. The results show that the consistency condition may be used to quantitatively compare the quality of projection data sets obtained from different scans of the same image object.
基金Supported by National Natural Science Foundation of China(81101070)
文摘Accurate attenuation correction is required in dedicated breast PET imaging systems for image artifact removal and quantitative studies. In this study, a method using only emission data based on consistency conditions is proposed for attenuation correction in breast PET imaging systems. The consistency conditions are exploited to evaluate the accuracy of the estimated attenuation distribution and find the appropriate parameters that yield the most consistent attenuation distribution with the measured emission data. We have proved the validity of the method with experimental investigations and single-patient studies using a dedicated breast PET. The results show that the method is capable of accurately estimating the attenuation distribution of a uniform attenuator from the experimental data with various relatively low activities. The results also show that in single-patient studies, the method is robust for the irregular boundary of breast tissue and provides a distinct improvement in image quality.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.81101070 and 81101175)
文摘The accuracy of attenuation correction in positron emission tomography scanners depends mainly on deriving the reliable 511-keV linear attenuation coefficient distribution in the scanned objects. In the PET/CT system, the linear attenu- ation distribution is usually obtained from the intensities of the CT image. However, the intensities of the CT image relate to the attenuation of photons in an energy range of 40 keV-140 keV. Before implementing PET attenuation correction, the intensities of CT images must be transformed into the PET 511-keV linear attenuation coefficients. However, the CT scan parameters can affect the effective energy of CT X-ray photons and thus affect the intensities of the CT image. Therefore, for PET/CT attenuation correction, it is crucial to determine the conversion curve with a given set of CT scan parameters and convert the CT image into a PET linear attenuation coefficient distribution. A generalized method is proposed for con- verting a CT image into a PET linear attenuation coefficient distribution. Instead of some parameter-dependent phantom calibration experiments, the conversion curve is calculated directly by employing the consistency conditions to yield the most consistent attenuation map with the measured PET data. The method is evaluated with phantom experiments and small animal experiments. In phantom studies, the estimated conversion curve fits the true attenuation coefficients accurately, and accurate PET attenuation maps are obtained by the estimated conversion curves and provide nearly the same correction results as the true attenuation map. In small animal studies, a more complicated attenuation distribution of the mouse is obtained successfully to remove the attenuation artifact and improve the PET image contrast efficiently.
基金Project(71001079)supported by the National Natural Science Foundation of China
文摘A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.
文摘In this thesis, the interal relations between about shear looking, zero energy mode and patch test are studied, and a reasonable method provided for building general element of thick and thin plate with effectual and realiable numerical solution.
文摘This paper presents new definitions of stability of solutions to singular systems with delay, and establishes theorems on stability and instability. Then by discussing second order timervarying linear singular systems with delay, this paper obtains some results of stability and instability, and discovers bifurcation-likephenomenons on stability.
基金support partly by RGC Grant 502412,15300514,G-YL04.ZWu acknowledges the Natural Science Foundation of China(61573217),111 project(B12023)the National High-level personnel of special support program and the Chang Jiang Scholar Program of Chinese Education Ministry.
文摘This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states of minor agents are governed by linear forward stochastic differential equations(SDEs).The major agent is dominating as its state enters those of minor agents.On the other hand,all minor agents are individually negligible but their state-average affects the cost functional of major agent.The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies.We first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation(BFSDE)system.Next,we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method.Consequently,we obtain the decentralized strategies for major and minor agents which are proved to satisfy the-Nash equilibrium property.
