We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characteriza...We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass;they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of 展开更多
Optical coherence tomography(OCT)provides significant advantages of high resolution(approaching the histopathology level)realtime imaging of tsess without use of contrast agents.Based on these advantages,the microstru...Optical coherence tomography(OCT)provides significant advantages of high resolution(approaching the histopathology level)realtime imaging of tsess without use of contrast agents.Based on these advantages,the microstructural features of tumors can be visualized and detected intra-operatively.However,it is still not clinically accepted for tumor margin delin-eation due to poor specificity and accuracy.In contrast,Raman spectroscopy(RS)can obtain tissue information at the molecular level,but does not provide real-time inaging capability.Therefore,combining OCT and RS could provide synergy.To this end,we present a tissue analysis and dassification method using both the slope of OCT intensity signal Vs depth and the principle components from the RS spectrum as the indicators for tissuse characterization.The goal of this study was to understand prediction accuracy of OCT and combined OCT/RS method for dassification of optically similar tisues and organs.Our pilot experiments were performed on mouse kidneys,livers,and small intestines(SIs).The prediction accuracy with five-fold cross validation of the method has been evaluated by the support vector machine(SVM)method.The results demonstrate that tissue characterization based on the OCT/RS method was superior compared to using OCT structural information alone.This combined OCT/RS method is potentially useful as a noninvasive optical biopsy technique for rapid and automatic tissue characterization during surgery.展开更多
Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key proper...Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and展开更多
文摘We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass;they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of
基金supported in part by the grants to Kirill Larin from NIH 1R01EY022362,1R01HL120140,U54HG006348,and DOD PRJ71Tsupported by grants to Wei-Chuan Shih from NSF CAREER Award (CBET-1151154)+1 种基金NASA Early Career Faculty Grant (NNX12AQ44G)Gulf of Mexico Research Initiative (GoMRI-030).
文摘Optical coherence tomography(OCT)provides significant advantages of high resolution(approaching the histopathology level)realtime imaging of tsess without use of contrast agents.Based on these advantages,the microstructural features of tumors can be visualized and detected intra-operatively.However,it is still not clinically accepted for tumor margin delin-eation due to poor specificity and accuracy.In contrast,Raman spectroscopy(RS)can obtain tissue information at the molecular level,but does not provide real-time inaging capability.Therefore,combining OCT and RS could provide synergy.To this end,we present a tissue analysis and dassification method using both the slope of OCT intensity signal Vs depth and the principle components from the RS spectrum as the indicators for tissuse characterization.The goal of this study was to understand prediction accuracy of OCT and combined OCT/RS method for dassification of optically similar tisues and organs.Our pilot experiments were performed on mouse kidneys,livers,and small intestines(SIs).The prediction accuracy with five-fold cross validation of the method has been evaluated by the support vector machine(SVM)method.The results demonstrate that tissue characterization based on the OCT/RS method was superior compared to using OCT structural information alone.This combined OCT/RS method is potentially useful as a noninvasive optical biopsy technique for rapid and automatic tissue characterization during surgery.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)(Grant No.RGPIN-2019-04276)。
文摘Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and
