This paper highlights the memristor bridge-based lowpass filter (LPF) and improved image processing algorithms along with a novel adaptive Gaussian filter for denoising image and a new Gaussian pyramid for scale invar...This paper highlights the memristor bridge-based lowpass filter (LPF) and improved image processing algorithms along with a novel adaptive Gaussian filter for denoising image and a new Gaussian pyramid for scale invariant feature transform (SIFT). First, a novel kind of LPF based on the memristor bridge is designed, whose cut-off frequency and other traits are demonstrated to change with different time and memristance. In light of the changeable parameter of the memristor bridge-based LPF, a new adaptive Gaussian filter and an improved SIFT algorithm are presented. Finally, experiment results show that the peak signalto- noise ratio (PSNR) of our denoising is bettered more than 2.77 dB compared to the corresponding of the traditional Gaussian filter, and our improved SIFT performances including the number of matched feature points and the percent of correct matches are higher than the traditional SIFT, which verifies feasibility and effectiveness of our algorithm.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
CR–RCm filters are widely used in nuclear energy spectrum measurement systems. The choice of parameters of a CR–RCm digital filter directly affects its performance in terms of energy resolution and pulse count rate ...CR–RCm filters are widely used in nuclear energy spectrum measurement systems. The choice of parameters of a CR–RCm digital filter directly affects its performance in terms of energy resolution and pulse count rate in digital nuclear spectrometer systems. A numerical recursive model of a CR differential circuit and RC integration circuit is derived, which shows that the shaping result of CR–RCm is determined by the adjustment parameter (k, it determines the shaping time of the shaper) and the integral number (m). Furthermore, the amplitude– frequency response of CR–RC^m is analyzed, which shows that it is a bandpass filter;the larger the shaping parameters (k and m), the narrower is the frequency band. CR–RC^m digital Gaussian shaping is performed on the actual sampled nuclear pulse signal under different shaping parameters. The energy spectrum of 137Cs is measured based on the LaBr3(Ce) detector under different parameters. The results show that the larger the shaping parameters (m and k), the closer the shaping result is to Gaussian shape, the wider is the shaped pulse, the higher is the energy resolution, and the lower is the pulse count rate. For the same batch of pulse signals, the energy resolution is increased from 3.8 to 3.5%, and the full energy peak area is reduced from 7815 to 6503. Thus, the optimal shaping parameters are m -3 and k -0.95. These research results can provide a design reference for the development of digital nuclear spectrometer measurement systems.展开更多
This paper presents a new data-driven model of length-pressure hysteresis of pneumatic artificial muscles(PAMs) based on Gaussian mixture models(GMMs). By ignoring the high-order dynamics, the hysteresis of PAMs is mo...This paper presents a new data-driven model of length-pressure hysteresis of pneumatic artificial muscles(PAMs) based on Gaussian mixture models(GMMs). By ignoring the high-order dynamics, the hysteresis of PAMs is modeled as a first-order nonlinear dynamical system based on GMMs, and inversion of the model is subsequently derived. Several verification experiments are conducted. Firstly, parameters of the model are identified under low-frequency triangle-wave pressure excitations.Then, pressure signals with different amplitudes, shapes and frequencies are applied to the PAM to test the prediction performance of the model. The proposed model shows advantages in identification efficiency and prediction precision compared with a generalized Prandtl–Ishlinskii(GPI) model and a modified generalized Prandtl–Ishlinskii(MGPI) model. Finally, the effectiveness of the inverse model is demonstrated by implementing the feedforward hysteresis compensation in trajectory tracking experiments.展开更多
We present a planar model system of a silica covered with a monolayer of nonlinear graphene to achieve a tunable Goos–H?nchen(GH) shift in the terahertz range. It is theoretically found that the transition between a ...We present a planar model system of a silica covered with a monolayer of nonlinear graphene to achieve a tunable Goos–H?nchen(GH) shift in the terahertz range. It is theoretically found that the transition between a negative shift and a large positive one can be realized by altering the intensity of incident light. Moreover, by controlling the chemical potential of graphene and the incident angle of light, we can further control the tunable GH shift dynamically. Numerical simulations for GH shifts based on Gaussian waves are in good agreement with our theoretical calculations.展开更多
The accelerated cosmic expansion could be due to dark energy within general relativity(GR), or modified gravity. Differentiating between them using both the expansion history and growth history has attracted considera...The accelerated cosmic expansion could be due to dark energy within general relativity(GR), or modified gravity. Differentiating between them using both the expansion history and growth history has attracted considerable attention. In the literature, the growth index γ has been found useful to distinguish these two scenarios. This work aims to consider the non-parametric reconstruction of the growth index γ as a function of redshift z from the latest observational data as of July 2018 via Gaussian processes. We found that f(R) theories and dark energy models within GR(especially ΛCDM) are inconsistent with the results in the moderate redshift range far beyond 3σ confidence level. A modified gravity scenario different from f(R) theories is favored. However, these results can also be due to other non-trivial possibilities in which dark energy models within GR(especially ΛCDM) and f(R) theories may still survive. In all cases, our results suggest that new physics is required.展开更多
Hyperparameters are important for machine learning algorithms since they directly control the behaviors of training algorithms and have a significant effect on the performance of machine learning models.Several techni...Hyperparameters are important for machine learning algorithms since they directly control the behaviors of training algorithms and have a significant effect on the performance of machine learning models.Several techniques have been developed and successfully applied for certain application domains.However,this work demands professional knowledge and expert experience.And sometimes it has to resort to the brute-force search.Therefore,if an efficient hyperparameter optimization algorithm can be developed to optimize any given machine learning method,it will greatly improve the efficiency of machine learning.In this paper,we consider building the relationship between the performance of the machine learning models and their hyperparameters by Gaussian processes.In this way,the hyperparameter tuning problem can be abstracted as an optimization problem and Bayesian optimization is used to solve the problem.Bayesian optimization is based on the Bayesian theorem.It sets a prior over the optimization function and gathers the information from the previous sample to update the posterior of the optimization function.A utility function selects the next sample point to maximize the optimization function.Several experiments were conducted on standard test datasets.Experiment results show that the proposed method can find the best hyperparameters for the widely used machine learning models,such as the random forest algorithm and the neural networks,even multi-grained cascade forest under the consideration of time cost.展开更多
Interstation travel speed is an important indicator of the running state of hybrid Bus Rapid Transit and passenger experience. Due to the influence of road traffic, traffic lights and other factors, the interstation t...Interstation travel speed is an important indicator of the running state of hybrid Bus Rapid Transit and passenger experience. Due to the influence of road traffic, traffic lights and other factors, the interstation travel speeds are often some kind of multi-peak and it is difficult to use a single distribution to model them. In this paper, a Gaussian mixture model charactizing the interstation travel speed of hybrid BRT under a Bayesian framework is established. The parameters of the model are inferred using the Reversible-Jump Markov Chain Monte Carlo approach (RJMCMC), including the number of model components and the weight, mean and variance of each component. Then the model is applied to Guangzhou BRT, a kind of hybrid BRT. From the results, it can be observed that the model can very effectively describe the heterogeneous speed data among different inter-stations, and provide richer information usually not available from the traditional models, and the model also produces an excellent fit to each multimodal speed distribution curve of the interstations. The causes of different speed distribution can be identified through investigating the Internet map of GBRT, they are big road traffic and long traffic lights respectively, which always contribute to a main road crossing. So, the BRT lane should be elevated through the main road to decrease the complexity of the running state.展开更多
Cluster-based channel model is the main stream of fifth generation mobile communications, thus the accuracy of clustering algorithm is important. Traditional Gaussian mixture model (GMM) does not consider the power in...Cluster-based channel model is the main stream of fifth generation mobile communications, thus the accuracy of clustering algorithm is important. Traditional Gaussian mixture model (GMM) does not consider the power information which is important for the channel multipath clustering. In this paper, a normalized power weighted GMM (PGMM) is introduced to model the channel multipath components (MPCs). With MPC power as a weighted factor, the PGMM can fit the MPCs in accordance with the cluster-based channel models. Firstly, expectation maximization (EM) algorithm is employed to optimize the PGMM parameters. Then, to further increase the searching ability of EM and choose the optimal number of components without resort to cross-validation, the variational Bayesian (VB) inference is employed. Finally, 28 GHz indoor channel measurement data is used to demonstrate the effectiveness of the PGMM clustering algorithm.展开更多
Gaussian Boson sampling(GBS) provides a highly efficient approach to make use of squeezed states from parametric down-conversion to solve a classically hard-to-solve sampling problem. The GBS protocol not only signifi...Gaussian Boson sampling(GBS) provides a highly efficient approach to make use of squeezed states from parametric down-conversion to solve a classically hard-to-solve sampling problem. The GBS protocol not only significantly enhances the photon generation probability, compared to standard Boson sampling with single photon Fock states, but also links to potential applications such as dense subgraph problems and molecular vibronic spectra. Here, we report the first experimental demonstration of GBS using squeezed-state sources with simultaneously high photon indistinguishability and collection efficiency.We implement and validate 3-, 4- and 5-photon GBS with high sampling rates of 832, 163 and 23 kHz,respectively, which is more than 4.4, 12.0, and 29.5 times faster than the previous experiments.Further, we observe a quantum speed-up on a NP-hard optimization problem when comparing with simulated thermal sampler and uniform sampler.展开更多
The photoionization in the frame of the Ammosov-Delone-Krainov theory has been theoretically examined for noble gases,argon,krypton,and xenon,in an elliptically polarized laser field.We consider the intermediate range...The photoionization in the frame of the Ammosov-Delone-Krainov theory has been theoretically examined for noble gases,argon,krypton,and xenon,in an elliptically polarized laser field.We consider the intermediate range of the Keldysh parameter,γ~1,and analyze the influence of shifted ionization potential and temporal profile to eliminate disagreement between theoretical and experimental findings.By including these effects in the ionization rates,we solve rate equations in order to determine an expression for the ionization yield.The use of modified ionization potential shows that the ionization yields will actually decrease below the values predicted by original(uncorrected)formulas.This paper will discuss the causes of this discrepancy.展开更多
There are large amount of research papers on stochastic partial differential equations (SPDEs). This volume attempts to collect some recent progresses on some very special topics in this broad field. Our concentration...There are large amount of research papers on stochastic partial differential equations (SPDEs). This volume attempts to collect some recent progresses on some very special topics in this broad field. Our concentration will be the stochastic heat (wave) equations driven by Gaussian noises.展开更多
This article establishes the precise asymptoticsEum(t, x)(i →∞ or m →∞)for the stochastic heat equation■u/■t(t,x)=1/2△u(t,x)+u(t,x)■w/■t(t,x)with the time-derivative Gaussian noise ■u/■t(t,x)that is fractio...This article establishes the precise asymptoticsEum(t, x)(i →∞ or m →∞)for the stochastic heat equation■u/■t(t,x)=1/2△u(t,x)+u(t,x)■w/■t(t,x)with the time-derivative Gaussian noise ■u/■t(t,x)that is fractional in time and homogeneous in space.展开更多
In this work,we combined the model based reinforcement learning(MBRL)and model free reinforcement learning(MFRL)to stabilize a biped robot(NAO robot)on a rotating platform,where the angular velocity of the platform is...In this work,we combined the model based reinforcement learning(MBRL)and model free reinforcement learning(MFRL)to stabilize a biped robot(NAO robot)on a rotating platform,where the angular velocity of the platform is unknown for the proposed learning algorithm and treated as the external disturbance.Nonparametric Gaussian processes normally require a large number of training data points to deal with the discontinuity of the estimated model.Although some improved method such as probabilistic inference for learning control(PILCO)does not require an explicit global model as the actions are obtained by directly searching the policy space,the overfitting and lack of model complexity may still result in a large deviation between the prediction and the real system.Besides,none of these approaches consider the data error and measurement noise during the training process and test process,respectively.We propose a hierarchical Gaussian processes(GP)models,containing two layers of independent GPs,where the physically continuous probability transition model of the robot is obtained.Due to the physically continuous estimation,the algorithm overcomes the overfitting problem with a guaranteed model complexity,and the number of training data is also reduced.The policy for any given initial state is generated automatically by minimizing the expected cost according to the predefined cost function and the obtained probability distribution of the state.Furthermore,a novel Q(λ)based MFRL method scheme is employed to improve the policy.Simulation results show that the proposed RL algorithm is able to balance NAO robot on a rotating platform,and it is capable of adapting to the platform with varying angular velocity.展开更多
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equ...In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.展开更多
In this article,we consider the Parabolic Anderson Model with constant initial condition,driven by a space-time homogeneous Gaussian noise,with general covariance function in time and spatial spectral measure satisfyi...In this article,we consider the Parabolic Anderson Model with constant initial condition,driven by a space-time homogeneous Gaussian noise,with general covariance function in time and spatial spectral measure satisfying Dalang's condition.First,we prove that the solution (in the Skorohod sense) exists and is continuous in Lp(Ω).Then,we show that the solution has a modification whose sample paths are H(o)lder continuous in space and time,under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time).This improves similar results which were obtained in [6,10] under more restrictive conditions,and with sub-optimal exponents for H(o)lder continuity.展开更多
基金supported by the National Natural Science Foundation of China(61550110248).
文摘This paper highlights the memristor bridge-based lowpass filter (LPF) and improved image processing algorithms along with a novel adaptive Gaussian filter for denoising image and a new Gaussian pyramid for scale invariant feature transform (SIFT). First, a novel kind of LPF based on the memristor bridge is designed, whose cut-off frequency and other traits are demonstrated to change with different time and memristance. In light of the changeable parameter of the memristor bridge-based LPF, a new adaptive Gaussian filter and an improved SIFT algorithm are presented. Finally, experiment results show that the peak signalto- noise ratio (PSNR) of our denoising is bettered more than 2.77 dB compared to the corresponding of the traditional Gaussian filter, and our improved SIFT performances including the number of matched feature points and the percent of correct matches are higher than the traditional SIFT, which verifies feasibility and effectiveness of our algorithm.
基金an NSERC grant and a startup fund of University of Alberta.
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
基金National Natural Science Foundation of China (Nos. 11665001, 41864007)National Key R&D Project (No. 2017YFF0106503)+1 种基金China Scholarship Council (No. 201708360170)One Hundred People Sail in Jiangxi Province, Open-ended Foundation from the Chinese Engineering Research Center (No. HJSJYB2014-03).
文摘CR–RCm filters are widely used in nuclear energy spectrum measurement systems. The choice of parameters of a CR–RCm digital filter directly affects its performance in terms of energy resolution and pulse count rate in digital nuclear spectrometer systems. A numerical recursive model of a CR differential circuit and RC integration circuit is derived, which shows that the shaping result of CR–RCm is determined by the adjustment parameter (k, it determines the shaping time of the shaper) and the integral number (m). Furthermore, the amplitude– frequency response of CR–RC^m is analyzed, which shows that it is a bandpass filter;the larger the shaping parameters (k and m), the narrower is the frequency band. CR–RC^m digital Gaussian shaping is performed on the actual sampled nuclear pulse signal under different shaping parameters. The energy spectrum of 137Cs is measured based on the LaBr3(Ce) detector under different parameters. The results show that the larger the shaping parameters (m and k), the closer the shaping result is to Gaussian shape, the wider is the shaped pulse, the higher is the energy resolution, and the lower is the pulse count rate. For the same batch of pulse signals, the energy resolution is increased from 3.8 to 3.5%, and the full energy peak area is reduced from 7815 to 6503. Thus, the optimal shaping parameters are m -3 and k -0.95. These research results can provide a design reference for the development of digital nuclear spectrometer measurement systems.
基金the National Natural Science Foundation of China (Grant No. 91648104)Shanghai Rising-Star Program (Grant No. 17QA1401900).
文摘This paper presents a new data-driven model of length-pressure hysteresis of pneumatic artificial muscles(PAMs) based on Gaussian mixture models(GMMs). By ignoring the high-order dynamics, the hysteresis of PAMs is modeled as a first-order nonlinear dynamical system based on GMMs, and inversion of the model is subsequently derived. Several verification experiments are conducted. Firstly, parameters of the model are identified under low-frequency triangle-wave pressure excitations.Then, pressure signals with different amplitudes, shapes and frequencies are applied to the PAM to test the prediction performance of the model. The proposed model shows advantages in identification efficiency and prediction precision compared with a generalized Prandtl–Ishlinskii(GPI) model and a modified generalized Prandtl–Ishlinskii(MGPI) model. Finally, the effectiveness of the inverse model is demonstrated by implementing the feedforward hysteresis compensation in trajectory tracking experiments.
基金the National Natural Science Foundation of China under Grant No 11774252the Natural Science Foundation of Jiangsu Province under Grant No BK20161210+1 种基金the Qi ng Lan project, the ‘333' project under Grant No BRA2015353and the PAPD of Jiangsu Higher Education Institutions.
文摘We present a planar model system of a silica covered with a monolayer of nonlinear graphene to achieve a tunable Goos–H?nchen(GH) shift in the terahertz range. It is theoretically found that the transition between a negative shift and a large positive one can be realized by altering the intensity of incident light. Moreover, by controlling the chemical potential of graphene and the incident angle of light, we can further control the tunable GH shift dynamically. Numerical simulations for GH shifts based on Gaussian waves are in good agreement with our theoretical calculations.
基金the National Natural Science Foundation of China (Grant Nos. 11575022, and 11175016).
文摘The accelerated cosmic expansion could be due to dark energy within general relativity(GR), or modified gravity. Differentiating between them using both the expansion history and growth history has attracted considerable attention. In the literature, the growth index γ has been found useful to distinguish these two scenarios. This work aims to consider the non-parametric reconstruction of the growth index γ as a function of redshift z from the latest observational data as of July 2018 via Gaussian processes. We found that f(R) theories and dark energy models within GR(especially ΛCDM) are inconsistent with the results in the moderate redshift range far beyond 3σ confidence level. A modified gravity scenario different from f(R) theories is favored. However, these results can also be due to other non-trivial possibilities in which dark energy models within GR(especially ΛCDM) and f(R) theories may still survive. In all cases, our results suggest that new physics is required.
基金the National Natural Science Foundation of China under Grant No.61503059.
文摘Hyperparameters are important for machine learning algorithms since they directly control the behaviors of training algorithms and have a significant effect on the performance of machine learning models.Several techniques have been developed and successfully applied for certain application domains.However,this work demands professional knowledge and expert experience.And sometimes it has to resort to the brute-force search.Therefore,if an efficient hyperparameter optimization algorithm can be developed to optimize any given machine learning method,it will greatly improve the efficiency of machine learning.In this paper,we consider building the relationship between the performance of the machine learning models and their hyperparameters by Gaussian processes.In this way,the hyperparameter tuning problem can be abstracted as an optimization problem and Bayesian optimization is used to solve the problem.Bayesian optimization is based on the Bayesian theorem.It sets a prior over the optimization function and gathers the information from the previous sample to update the posterior of the optimization function.A utility function selects the next sample point to maximize the optimization function.Several experiments were conducted on standard test datasets.Experiment results show that the proposed method can find the best hyperparameters for the widely used machine learning models,such as the random forest algorithm and the neural networks,even multi-grained cascade forest under the consideration of time cost.
基金prepared based on Science and technology planning project of Guangdong province of China in 2017(No.2017B010111007)the National Natural Science 16 Foundation of China(No.41271181).
文摘Interstation travel speed is an important indicator of the running state of hybrid Bus Rapid Transit and passenger experience. Due to the influence of road traffic, traffic lights and other factors, the interstation travel speeds are often some kind of multi-peak and it is difficult to use a single distribution to model them. In this paper, a Gaussian mixture model charactizing the interstation travel speed of hybrid BRT under a Bayesian framework is established. The parameters of the model are inferred using the Reversible-Jump Markov Chain Monte Carlo approach (RJMCMC), including the number of model components and the weight, mean and variance of each component. Then the model is applied to Guangzhou BRT, a kind of hybrid BRT. From the results, it can be observed that the model can very effectively describe the heterogeneous speed data among different inter-stations, and provide richer information usually not available from the traditional models, and the model also produces an excellent fit to each multimodal speed distribution curve of the interstations. The causes of different speed distribution can be identified through investigating the Internet map of GBRT, they are big road traffic and long traffic lights respectively, which always contribute to a main road crossing. So, the BRT lane should be elevated through the main road to decrease the complexity of the running state.
基金National Science and Technology Major Program of the Ministry of Science and Technology (No.2018ZX03001031)Key program of Bei jing Municipal Natural Science Foundation (No. L172030)+2 种基金Beijing Municipal Science & Technology Commission Project (No. Z171100005217001)Key Project of State Key Lab of Networking and Switching Technology (NST20170205)National Key Technology Research and Development Program of the Ministry of Science and Technology of China (NO. 2012BAF14B01).
文摘Cluster-based channel model is the main stream of fifth generation mobile communications, thus the accuracy of clustering algorithm is important. Traditional Gaussian mixture model (GMM) does not consider the power information which is important for the channel multipath clustering. In this paper, a normalized power weighted GMM (PGMM) is introduced to model the channel multipath components (MPCs). With MPC power as a weighted factor, the PGMM can fit the MPCs in accordance with the cluster-based channel models. Firstly, expectation maximization (EM) algorithm is employed to optimize the PGMM parameters. Then, to further increase the searching ability of EM and choose the optimal number of components without resort to cross-validation, the variational Bayesian (VB) inference is employed. Finally, 28 GHz indoor channel measurement data is used to demonstrate the effectiveness of the PGMM clustering algorithm.
基金the National Natural Science Foundation of China(91836303,11674308,and 11525419)the Chinese Academy of Sciences,the National Fundamental Research Program(2018YFA0306100)the Anhui Initiative in Quantum Information Technologies.
文摘Gaussian Boson sampling(GBS) provides a highly efficient approach to make use of squeezed states from parametric down-conversion to solve a classically hard-to-solve sampling problem. The GBS protocol not only significantly enhances the photon generation probability, compared to standard Boson sampling with single photon Fock states, but also links to potential applications such as dense subgraph problems and molecular vibronic spectra. Here, we report the first experimental demonstration of GBS using squeezed-state sources with simultaneously high photon indistinguishability and collection efficiency.We implement and validate 3-, 4- and 5-photon GBS with high sampling rates of 832, 163 and 23 kHz,respectively, which is more than 4.4, 12.0, and 29.5 times faster than the previous experiments.Further, we observe a quantum speed-up on a NP-hard optimization problem when comparing with simulated thermal sampler and uniform sampler.
基金Project supported by the Science Foundation from the Serbian Ministry of Education,Science and Technological Development(Grant No.171020).
文摘The photoionization in the frame of the Ammosov-Delone-Krainov theory has been theoretically examined for noble gases,argon,krypton,and xenon,in an elliptically polarized laser field.We consider the intermediate range of the Keldysh parameter,γ~1,and analyze the influence of shifted ionization potential and temporal profile to eliminate disagreement between theoretical and experimental findings.By including these effects in the ionization rates,we solve rate equations in order to determine an expression for the ionization yield.The use of modified ionization potential shows that the ionization yields will actually decrease below the values predicted by original(uncorrected)formulas.This paper will discuss the causes of this discrepancy.
文摘There are large amount of research papers on stochastic partial differential equations (SPDEs). This volume attempts to collect some recent progresses on some very special topics in this broad field. Our concentration will be the stochastic heat (wave) equations driven by Gaussian noises.
基金the “1000 Talents Plan” from Jilin University, Jilin Province and Chinese Government, and by the Simons Foundation (244767).
文摘This article establishes the precise asymptoticsEum(t, x)(i →∞ or m →∞)for the stochastic heat equation■u/■t(t,x)=1/2△u(t,x)+u(t,x)■w/■t(t,x)with the time-derivative Gaussian noise ■u/■t(t,x)that is fractional in time and homogeneous in space.
文摘In this work,we combined the model based reinforcement learning(MBRL)and model free reinforcement learning(MFRL)to stabilize a biped robot(NAO robot)on a rotating platform,where the angular velocity of the platform is unknown for the proposed learning algorithm and treated as the external disturbance.Nonparametric Gaussian processes normally require a large number of training data points to deal with the discontinuity of the estimated model.Although some improved method such as probabilistic inference for learning control(PILCO)does not require an explicit global model as the actions are obtained by directly searching the policy space,the overfitting and lack of model complexity may still result in a large deviation between the prediction and the real system.Besides,none of these approaches consider the data error and measurement noise during the training process and test process,respectively.We propose a hierarchical Gaussian processes(GP)models,containing two layers of independent GPs,where the physically continuous probability transition model of the robot is obtained.Due to the physically continuous estimation,the algorithm overcomes the overfitting problem with a guaranteed model complexity,and the number of training data is also reduced.The policy for any given initial state is generated automatically by minimizing the expected cost according to the predefined cost function and the obtained probability distribution of the state.Furthermore,a novel Q(λ)based MFRL method scheme is employed to improve the policy.Simulation results show that the proposed RL algorithm is able to balance NAO robot on a rotating platform,and it is capable of adapting to the platform with varying angular velocity.
基金an NSERC grant and a startup fund of University of AlbertaS. Tindel is supported by the NSF grant DMS1613163.
文摘In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
基金a grant from the Natural Sciences and Engineering Research Council of Canada, and the second author is supported by the grant MTM2015-67802P.
文摘In this article,we consider the Parabolic Anderson Model with constant initial condition,driven by a space-time homogeneous Gaussian noise,with general covariance function in time and spatial spectral measure satisfying Dalang's condition.First,we prove that the solution (in the Skorohod sense) exists and is continuous in Lp(Ω).Then,we show that the solution has a modification whose sample paths are H(o)lder continuous in space and time,under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time).This improves similar results which were obtained in [6,10] under more restrictive conditions,and with sub-optimal exponents for H(o)lder continuity.