Dear Editor,This letter presents a latent-factorization-of-tensors(LFT)-incorporated battery cycle life prediction framework.Data-driven prognosis and health management(PHM)for battery pack(BP)can boost the safety and...Dear Editor,This letter presents a latent-factorization-of-tensors(LFT)-incorporated battery cycle life prediction framework.Data-driven prognosis and health management(PHM)for battery pack(BP)can boost the safety and sustainability of a battery management system(BMS),which relies heavily on the quality of the measured BP data like the voltage(V),current(I),and temperature(T).展开更多
In this paper,we present a Deep Neural Network(DNN)based framework that employs Radio Frequency(RF)hologram tensors to locate multiple Ultra-High Frequency(UHF)passive Radio-Frequency Identification(RFID)tags.The RF h...In this paper,we present a Deep Neural Network(DNN)based framework that employs Radio Frequency(RF)hologram tensors to locate multiple Ultra-High Frequency(UHF)passive Radio-Frequency Identification(RFID)tags.The RF hologram tensor exhibits a strong relationship between observation and spatial location,helping to improve the robustness to dynamic environments and equipment.Since RFID data is often marred by noise,we implement two types of deep neural network architectures to clean up the RF hologram tensor.Leveraging the spatial relationship between tags,the deep networks effectively mitigate fake peaks in the hologram tensors resulting from multipath propagation and phase wrapping.In contrast to fingerprinting-based localization systems that use deep networks as classifiers,our deep networks in the proposed framework treat the localization task as a regression problem preserving the ambiguity between fingerprints.We also present an intuitive peak finding algorithm to obtain estimated locations using the sanitized hologram tensors.The proposed framework is implemented using commodity RFID devices,and its superior performance is validated through extensive experiments.展开更多
The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor...The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor(QGT),another important concept in the field of quantum geometry.The DWZC is Hermitian with respect to the two integer indices,just like the original Hermitian WZC.Based on the symmetric logarithmic derivative operator,we propose a mixed-state quantum geometric tensor.Using the symmetric properties of the DWZC,we find that the real part of the QGT is connected to the real part of the DWZC and the square of eigenvalue differences of the density matrix,whereas the imaginary part can be given in terms of the imaginary part of the DWZC and the cube of the eigenvalue differences.For density matrices with full rank or no full rank,the QGT can be given in terms of real and imaginary parts of the DWZC.展开更多
We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are...We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ＂Y＂ type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.展开更多
In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance grav...In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance gravity anomalies and gravity gradient tensors. We discuss the effect of Gaussian white noise on the improved small sub-domain filtering method, as well as analyze the effect of window size on geological body edge recognition at different extension directions. Model experiments show that the improved small sub-domain filtering method is less affected by noise, filter window size, and geological body edge direction so it can more accurately depict geological body edges than the conventional small sub-domain filtering method. It also shows that deeply buried body edges can be well delineated through increasing the filter window size. In application, the enhanced gravity anomalies and calculated gravity gradient tensors of the Hulin basin show that the improved small sub-domain filtering can recognize more horizontal fault locations than the conventional method.展开更多
We have determined approximate average rates of deformation in the Qinghai_Tibet plateau and its margins from the GPS data for last 10 years and the moment tensors from earthquakes between 1900 and 1999.We also determ...We have determined approximate average rates of deformation in the Qinghai_Tibet plateau and its margins from the GPS data for last 10 years and the moment tensors from earthquakes between 1900 and 1999.We also determined the strain rate (seismic strain rate) associated with the seismic deformation using 254 M w ≥5.0 earthquakes,and estimated the shortening and extension rates for every block in the area as well.We also estimated the strain rate (geodetic strain rate)by 80 GPS sites’ velocity vectors and analyzed characteristic of kinematics by two kinds of strain rates and discussed earthquake potential in the area.As a result,the deformation rates from seismic moment tensors and from GPS velocities are basically agreed with each other.It is feasible to analyze seismic risk by comparing geodetic strain rate with seismic strain rate based on the opinion that strain energy will be released through earthquake.It is concluded that there is no strong earthquake potential (>M7) in the Qinghai_Tibet plateau and its margins,but there is earthquake potential (>M5) in middle Tibet in a few years.展开更多
In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of ...In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.展开更多
One of the major factors inhibiting the construction of deep underground projects is the risk posed by rockbursts.A study was conducted on the access tunnel of the Shuangjiangkou hydropower station to determine the ev...One of the major factors inhibiting the construction of deep underground projects is the risk posed by rockbursts.A study was conducted on the access tunnel of the Shuangjiangkou hydropower station to determine the evolutionary mechanism of microfractures within the surrounding rock mass during rockburst development and develop a rockburst warning model.The study area was chosen through the combination of field studies with an analysis of the spatial and temporal distribution of microseismic(MS)events.The moment tensor inversion method was adopted to study rockburst mechanism,and a dynamic Bayesian network(DBN)was applied to investigating the sensitivity of MS source parameters for rockburst warnings.A MS multivariable rockburst warning model was proposed and validated using two case studies.The results indicate that fractures in the surrounding rock mass during the development of strain-structure rockbursts initially show shear failure and are then followed by tensile failure.The effectiveness of the DBN-based rockburst warning model was demonstrated using self-validation and K-fold cross-validation.Moment magnitude and source radius are the most sensitive factors based on an investigation of the influence on the parent and child nodes in the model,which can serve as important standards for rockburst warnings.The proposed rockburst warning model was found to be effective when applied to two actual projects.展开更多
In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie...In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.展开更多
A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pat...A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pattern analysis system(TIPAS).It can be represented by a high-dimensional and incomplete(HDI)tensor whose entries are mostly unknown.Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN.A latent factorization-of-tensors(LFT)model proves to be highly efficient in extracting such knowledge from an HDI tensor,which is commonly achieved via a stochastic gradient descent(SGD)solver.However,an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs.To address this issue,this work proposes a proportional-integralderivative(PID)-incorporated LFT model.It constructs an adjusted instance error based on the PID control principle,and then substitutes it into an SGD solver to improve the convergence rate.Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models,the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.展开更多
The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold ...The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.展开更多
In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKH...In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKHrpqsllll创串C, defined by: A(ei, ej, ek, es)=ijksa, where the (aijks)s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions rpqsllll哪?(( is not a Banach algebra under schur product.展开更多
The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always ...The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.展开更多
This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm ...This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l1-norm is used to exploit the impulse noise. Then, this optimization problem is solved by some augmented-Lagrangian-based algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.展开更多
In this paper, we have proposed an upper bound for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which is called the Brauer upper bound:■where■ As applications, a bound on the Z...In this paper, we have proposed an upper bound for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which is called the Brauer upper bound:■where■ As applications, a bound on the Z-spectral radius of uniform hypergraphs is presented.展开更多
I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection st...I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the connection is true for this tensor connection through its output method using a small bit of tensor calculus and mostly number theory.展开更多
The explicit representations for tensorial Fourier expansion of 3_D crystal orientation distribution functions (CODFs) are established. In comparison with that the coefficients in the mth term of the Fourier expansion...The explicit representations for tensorial Fourier expansion of 3_D crystal orientation distribution functions (CODFs) are established. In comparison with that the coefficients in the mth term of the Fourier expansion of a 3_D ODF make up just a single irreducible mth_order tensor, the coefficients in the mth term of the Fourier expansion of a 3_D CODF constitute generally so many as 2m+1 irreducible mth_order tensors. Therefore, the restricted forms of tensorial Fourier expansions of 3_D CODFs imposed by various micro_ and macro_scopic symmetries are further established, and it is shown that in most cases of symmetry the restricted forms of tensorial Fourier expansions of 3_D CODFs contain remarkably reduced numbers of mth_order irreducible tensors than the number 2m+1 . These results are based on the restricted forms of irreducible tensors imposed by various point_group symmetries, which are also thoroughly investigated in the present part in both 2_ and 3_D spaces.展开更多
In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODF...In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODFs), which are scalar functions defined on the unit sphere and the rotation group, respectively. Recently it has been becoming clearer and clearer that concepts of ODF and CODF play a dominant role in various micromechanically_based approaches to mechanical and physical properties of heterogeneous materials. The theory of group representations shows that a square integrable ODF can be expanded as an absolutely convergent Fourier series of spherical harmonics and these spherical harmonics can further be expressed in terms of irreducible tensors. The fundamental importance of such irreducible tensorial coefficients is that they characterize the macroscopic or overall effect of the orientation distribution of the size, shape, phase, position of the material constitutions and defects. In Part (Ⅰ), the investigation about the irreducible tensorial Fourier expansions of ODFs defined on the N_dimensional (N_D) unit sphere is carried out. Attention is particularly paid to constructing simple expressions for 2_ and 3_D irreducible tensors of any orders in accordance with the convenience of arriving at their restricted forms imposed by various point_group (the synonym of subgroup of the full orthogonal group) symmetries. In the continued work -Part (Ⅱ), the explicit expression for the irreducible tensorial expansions of CODFs is established. The restricted forms of irreducible tensors and irreducible tensorial Fourier expansions of ODFs and CODFs imposed by various point_group symmetries are derived.展开更多
A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of...A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.展开更多
This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector ident...This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.展开更多
文摘Dear Editor,This letter presents a latent-factorization-of-tensors(LFT)-incorporated battery cycle life prediction framework.Data-driven prognosis and health management(PHM)for battery pack(BP)can boost the safety and sustainability of a battery management system(BMS),which relies heavily on the quality of the measured BP data like the voltage(V),current(I),and temperature(T).
基金supported in part by the U.S.National Science Foundation(NSF)under Grants ECCS-2245608 and ECCS-2245607。
文摘In this paper,we present a Deep Neural Network(DNN)based framework that employs Radio Frequency(RF)hologram tensors to locate multiple Ultra-High Frequency(UHF)passive Radio-Frequency Identification(RFID)tags.The RF hologram tensor exhibits a strong relationship between observation and spatial location,helping to improve the robustness to dynamic environments and equipment.Since RFID data is often marred by noise,we implement two types of deep neural network architectures to clean up the RF hologram tensor.Leveraging the spatial relationship between tags,the deep networks effectively mitigate fake peaks in the hologram tensors resulting from multipath propagation and phase wrapping.In contrast to fingerprinting-based localization systems that use deep networks as classifiers,our deep networks in the proposed framework treat the localization task as a regression problem preserving the ambiguity between fingerprints.We also present an intuitive peak finding algorithm to obtain estimated locations using the sanitized hologram tensors.The proposed framework is implemented using commodity RFID devices,and its superior performance is validated through extensive experiments.
基金Project supported by Quantum Science and Technology–National Science and Technology Major Project(Grant No.2024ZD0301000)the National Natural Science Foundation of China(Grant No.12305031)+1 种基金the Hangzhou Joint Fund of the Natural Science Foundation of Zhejiang Province,China(Grant No.LHZSD24A050001)the Science Foundation of Zhejiang Sci-Tech University(Grant Nos.23062088Y and 23062153-Y)。
文摘The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor(QGT),another important concept in the field of quantum geometry.The DWZC is Hermitian with respect to the two integer indices,just like the original Hermitian WZC.Based on the symmetric logarithmic derivative operator,we propose a mixed-state quantum geometric tensor.Using the symmetric properties of the DWZC,we find that the real part of the QGT is connected to the real part of the DWZC and the square of eigenvalue differences of the density matrix,whereas the imaginary part can be given in terms of the imaginary part of the DWZC and the cube of the eigenvalue differences.For density matrices with full rank or no full rank,the QGT can be given in terms of real and imaginary parts of the DWZC.
基金supported by the Scientific Research Starting Foundation of HoHai University,China(2084/40801136)the Fundamental Research Funds for the Central Universities(No.2009B12514)
文摘We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ＂Y＂ type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.
基金supported by the Scientific Research Starting Foundation of HoHai University, China (No. 2084/40801136)the Fundamental Research Funds for the Central Universities (No.2009B12514).
文摘In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance gravity anomalies and gravity gradient tensors. We discuss the effect of Gaussian white noise on the improved small sub-domain filtering method, as well as analyze the effect of window size on geological body edge recognition at different extension directions. Model experiments show that the improved small sub-domain filtering method is less affected by noise, filter window size, and geological body edge direction so it can more accurately depict geological body edges than the conventional small sub-domain filtering method. It also shows that deeply buried body edges can be well delineated through increasing the filter window size. In application, the enhanced gravity anomalies and calculated gravity gradient tensors of the Hulin basin show that the improved small sub-domain filtering can recognize more horizontal fault locations than the conventional method.
文摘We have determined approximate average rates of deformation in the Qinghai_Tibet plateau and its margins from the GPS data for last 10 years and the moment tensors from earthquakes between 1900 and 1999.We also determined the strain rate (seismic strain rate) associated with the seismic deformation using 254 M w ≥5.0 earthquakes,and estimated the shortening and extension rates for every block in the area as well.We also estimated the strain rate (geodetic strain rate)by 80 GPS sites’ velocity vectors and analyzed characteristic of kinematics by two kinds of strain rates and discussed earthquake potential in the area.As a result,the deformation rates from seismic moment tensors and from GPS velocities are basically agreed with each other.It is feasible to analyze seismic risk by comparing geodetic strain rate with seismic strain rate based on the opinion that strain energy will be released through earthquake.It is concluded that there is no strong earthquake potential (>M7) in the Qinghai_Tibet plateau and its margins,but there is earthquake potential (>M5) in middle Tibet in a few years.
基金Supported by the National Natural Science Foundation of China (10971224)the Hebei Natural ScienceFoundation (07M003)
文摘In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.
基金funding support from the National Natural Science Foundation of China(Grant No.42177143 and 51809221)the Science Foundation for Distinguished Young Scholars of Sichuan Province,China(Grant No.2020JDJQ0011).
文摘One of the major factors inhibiting the construction of deep underground projects is the risk posed by rockbursts.A study was conducted on the access tunnel of the Shuangjiangkou hydropower station to determine the evolutionary mechanism of microfractures within the surrounding rock mass during rockburst development and develop a rockburst warning model.The study area was chosen through the combination of field studies with an analysis of the spatial and temporal distribution of microseismic(MS)events.The moment tensor inversion method was adopted to study rockburst mechanism,and a dynamic Bayesian network(DBN)was applied to investigating the sensitivity of MS source parameters for rockburst warnings.A MS multivariable rockburst warning model was proposed and validated using two case studies.The results indicate that fractures in the surrounding rock mass during the development of strain-structure rockbursts initially show shear failure and are then followed by tensile failure.The effectiveness of the DBN-based rockburst warning model was demonstrated using self-validation and K-fold cross-validation.Moment magnitude and source radius are the most sensitive factors based on an investigation of the influence on the parent and child nodes in the model,which can serve as important standards for rockburst warnings.The proposed rockburst warning model was found to be effective when applied to two actual projects.
基金Supported by the Scientific Research Foundation for Science&Technology Innovation Talent Team of the Intelligent Computing and Monitoring of Guizhou Province(Grant No.QJJ[2023]063)the Science and Technology Program of Guizhou Province(Grant Nos.ZK[2023]025+4 种基金QKHZC[2023]372ZK[2022]031)the National Natural Science Foundation of China(Grant No.12161013)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022KYYB08)the Doctoral Research Start-Up Fund of Guiyang University(Grant No.GYU-KY-2024).
文摘In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.
基金supported in part by the National Natural Science Foundation of China(61772493)the CAAI-Huawei MindSpore Open Fund(CAAIXSJLJJ-2020-004B)+4 种基金in part by the Natural Science Foundation of Chongqing of China(cstc2019jcyjjq X0013)in part by the Pioneer Hundred Talents Program of Chinese Academy of Sciencesin part by the Deanship of Scientific Research(DSR)at King Abdulaziz UniversityJeddahSaudi Arabia(FP-165-43)。
文摘A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pattern analysis system(TIPAS).It can be represented by a high-dimensional and incomplete(HDI)tensor whose entries are mostly unknown.Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN.A latent factorization-of-tensors(LFT)model proves to be highly efficient in extracting such knowledge from an HDI tensor,which is commonly achieved via a stochastic gradient descent(SGD)solver.However,an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs.To address this issue,this work proposes a proportional-integralderivative(PID)-incorporated LFT model.It constructs an adjusted instance error based on the PID control principle,and then substitutes it into an SGD solver to improve the convergence rate.Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models,the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.
文摘The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.
文摘In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKHrpqsllll创串C, defined by: A(ei, ej, ek, es)=ijksa, where the (aijks)s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions rpqsllll哪?(( is not a Banach algebra under schur product.
基金Project supported by the National Natural Science Foundation of China(Nos.11271221,11771244,11571178,and 11771405)
文摘The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.
文摘This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l1-norm is used to exploit the impulse noise. Then, this optimization problem is solved by some augmented-Lagrangian-based algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.
基金Supported by the High-Level Innovative Talents of Guizhou ProvinceScience and Technology Fund Project of GZInnovative Talent Team in Guizhou Province(Grant Nos.Zun Ke He Ren Cai[2017]8,Qian Ke He J Zi LKZS[2012]08,Qian Ke HE Pingtai Rencai[2016]5619.)
文摘In this paper, we have proposed an upper bound for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which is called the Brauer upper bound:■where■ As applications, a bound on the Z-spectral radius of uniform hypergraphs is presented.
文摘I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the connection is true for this tensor connection through its output method using a small bit of tensor calculus and mostly number theory.
文摘The explicit representations for tensorial Fourier expansion of 3_D crystal orientation distribution functions (CODFs) are established. In comparison with that the coefficients in the mth term of the Fourier expansion of a 3_D ODF make up just a single irreducible mth_order tensor, the coefficients in the mth term of the Fourier expansion of a 3_D CODF constitute generally so many as 2m+1 irreducible mth_order tensors. Therefore, the restricted forms of tensorial Fourier expansions of 3_D CODFs imposed by various micro_ and macro_scopic symmetries are further established, and it is shown that in most cases of symmetry the restricted forms of tensorial Fourier expansions of 3_D CODFs contain remarkably reduced numbers of mth_order irreducible tensors than the number 2m+1 . These results are based on the restricted forms of irreducible tensors imposed by various point_group symmetries, which are also thoroughly investigated in the present part in both 2_ and 3_D spaces.
文摘In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODFs), which are scalar functions defined on the unit sphere and the rotation group, respectively. Recently it has been becoming clearer and clearer that concepts of ODF and CODF play a dominant role in various micromechanically_based approaches to mechanical and physical properties of heterogeneous materials. The theory of group representations shows that a square integrable ODF can be expanded as an absolutely convergent Fourier series of spherical harmonics and these spherical harmonics can further be expressed in terms of irreducible tensors. The fundamental importance of such irreducible tensorial coefficients is that they characterize the macroscopic or overall effect of the orientation distribution of the size, shape, phase, position of the material constitutions and defects. In Part (Ⅰ), the investigation about the irreducible tensorial Fourier expansions of ODFs defined on the N_dimensional (N_D) unit sphere is carried out. Attention is particularly paid to constructing simple expressions for 2_ and 3_D irreducible tensors of any orders in accordance with the convenience of arriving at their restricted forms imposed by various point_group (the synonym of subgroup of the full orthogonal group) symmetries. In the continued work -Part (Ⅱ), the explicit expression for the irreducible tensorial expansions of CODFs is established. The restricted forms of irreducible tensors and irreducible tensorial Fourier expansions of ODFs and CODFs imposed by various point_group symmetries are derived.
文摘A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.
文摘This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.
