A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being int...A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators partial derivative(t) and its dual, creation operators partial derivative(t)*.展开更多
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency.Sometimes,it is difficult to model the governing equations of the hybrid...Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency.Sometimes,it is difficult to model the governing equations of the hybrid energy harvesting system precisely,especially under external excitation.Accompanied with machine learning,data-driven methods play an important role in discovering the governing equations from massive datasets.Recently,there are many studies of datadriven models done in aspect of ordinary differential equations and stochastic differential equations(SDEs).However,few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise(GWN).Thus,in this paper,a data-driven approach,with least square and sparse constraint,is devised to discover the governing equations of the systems from observed data.Firstly,the algorithm processing and pseudo code are given.Then,the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN,respectively.For harmonic excitation,all coefficients of the system can be simultaneously learned.For GWN,we approximate the drift term and diffusion term by using the Kramers-Moyal formulas,and separately learn the coefficients of the drift term and diffusion term.Cross-validation(CV)and mean-square error(MSE)are utilized to obtain the optimal number of iterations.Finally,the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.展开更多
In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended...In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.展开更多
Covert communication guarantees the security of wireless communications via hiding the existence of the transmission.This paper focuses on the first and second order asymptotics of covert communication in the AWGN cha...Covert communication guarantees the security of wireless communications via hiding the existence of the transmission.This paper focuses on the first and second order asymptotics of covert communication in the AWGN channels.The covertness is measured by the total variation distance between the channel output distributions induced with and without the transmission.We provide the exact expressions of the maximum amount of information that can be transmitted with the maximum error probability and the total variation less than any small numbers.The energy detection and the random coding are employed to prove our results.We further compare our results with those under relative entropy.The results show how many additional amounts of information can be transmitted covertly when changing the covertness constraint to total variation.展开更多
文摘A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators partial derivative(t) and its dual, creation operators partial derivative(t)*.
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12002089 and 11902081)roject of Science and Technology of Guangzhou(Grant No.202201010326)
文摘Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency.Sometimes,it is difficult to model the governing equations of the hybrid energy harvesting system precisely,especially under external excitation.Accompanied with machine learning,data-driven methods play an important role in discovering the governing equations from massive datasets.Recently,there are many studies of datadriven models done in aspect of ordinary differential equations and stochastic differential equations(SDEs).However,few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise(GWN).Thus,in this paper,a data-driven approach,with least square and sparse constraint,is devised to discover the governing equations of the systems from observed data.Firstly,the algorithm processing and pseudo code are given.Then,the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN,respectively.For harmonic excitation,all coefficients of the system can be simultaneously learned.For GWN,we approximate the drift term and diffusion term by using the Kramers-Moyal formulas,and separately learn the coefficients of the drift term and diffusion term.Cross-validation(CV)and mean-square error(MSE)are utilized to obtain the optimal number of iterations.Finally,the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.
基金supported by the National Natural Science Foundation of China(No.61401164,No.61201145,No.61471175)the Natural Science Foundation of Guangdong Province of China(No.2014A030310308)the Supporting Plan for New Century Excellent Talents of the Ministry of Education(No.NCET-13-0805)
文摘In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.
基金supported in part by the Natural Science Foundation of Xinjiang Uygur Autonomous Region under Grant 2022D01B184the National Natural Science Foundation of China under Grant 62301117,62131005.
文摘Covert communication guarantees the security of wireless communications via hiding the existence of the transmission.This paper focuses on the first and second order asymptotics of covert communication in the AWGN channels.The covertness is measured by the total variation distance between the channel output distributions induced with and without the transmission.We provide the exact expressions of the maximum amount of information that can be transmitted with the maximum error probability and the total variation less than any small numbers.The energy detection and the random coding are employed to prove our results.We further compare our results with those under relative entropy.The results show how many additional amounts of information can be transmitted covertly when changing the covertness constraint to total variation.
