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Memristor bridge-based low pass filter for image processing 预览
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作者 YU Yongbin YANG Nijing +1 位作者 YANG Chenyu NYIMA Tashi 《系统工程与电子技术:英文版》 SCIE EI CSCD 2019年第3期448-455,共8页
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
关键词 MEMRISTOR BRIDGE LOW-PASS FILTER (LPF) adaptive GAUSSIAN FILTER image denoising GAUSSIAN pyramid
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巧用Gaussian软件学原子轨道 预览
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作者 王炎 赵江川 《吕梁学院学报》 2019年第2期71-73,共3页
用Gaussian软件,搭建并优化了原子结构;用Gauss View显示了不同类型原子轨道的特征,便于学生进行直观地理解,为学习原子结构抽象知识打开了一扇全新的窗口.
关键词 GAUSSIAN 原子轨道 直观显示
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SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS 预览
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作者 胡耀忠 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期874-914,共41页
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
关键词 GAUSSIAN random field GAUSSIAN noise STOCHASTIC partial differential EQUATION (stochastic heat equation) Feynman-Kac FORMULA for the solution Feynman- Kac FORMULA for the moments of the solution chaos expansion hypercontractivity moment bounds HOLDER CONTINUITY joint HOLDER CONTINUITY asymptotic behaviour Trotter-Lie FORMULA Skorohod integral
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量子化学软件在大学无机化学教学中的应用 预览
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作者 李明明 《科教文汇》 2019年第17期70-71,共2页
大学无机化学的教学内容较为抽象,难以被学生所接受,尤其是物质结构等方面的内容。当前学生的学习方式与传统模式相比发生了翻天覆地的变化,传统教学模式也难以激发学生对无机化学的学习兴趣。因此,寻找一种更为科学合理的无机化学教学... 大学无机化学的教学内容较为抽象,难以被学生所接受,尤其是物质结构等方面的内容。当前学生的学习方式与传统模式相比发生了翻天覆地的变化,传统教学模式也难以激发学生对无机化学的学习兴趣。因此,寻找一种更为科学合理的无机化学教学方法对于大学无机化学教学工作来说至关重要。本文通过查阅大量相关文献资料,分析了量子化学软件在物质结构、化学反应等方面的重要作用,总结了Gaussian软件可以有效解决无机化学教学工作中分子结构难理解的问题,将抽象的化学知识宏观地表现出来,以提升大学无机化学的教学质量,提高学生的学习效率。 展开更多
关键词 量子化学软件 GAUSSIAN 无机化学 教学
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Optimal parameter choice of CR–RCm digital filter in nuclear pulse processing 预览
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作者 Huai-Qiang Zhang Zhuo-Dai Li +1 位作者 Bin Tang He-Xi Wu 《核技术:英文版》 SCIE CAS CSCD 2019年第7期42-46,共5页
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
关键词 CR-RCm digital filter NUCLEAR PULSE signal GAUSSIAN SHAPING Energy resolution
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Modeling and compensation of hysteresis for pneumatic artificial muscles based on Gaussian mixture models
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作者 XU JiHao XIAO MuBang DING Ye 《中国科学:技术科学英文版》 SCIE EI CAS CSCD 2019年第7期1094-1102,共9页
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
关键词 HYSTERESIS MODELING HYSTERESIS COMPENSATION pneumatic artificial muscles (PAMs) GAUSSIAN MIXTURE model (GMM)
Tunable Bistability in the Goos–H?nchen Effect with Nonlinear Graphene
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作者 刘彬彬 马普娟 +2 位作者 於文静 徐亚东 高雷 《中国物理快报:英文版》 SCIE CAS CSCD 2019年第6期33-36,共4页
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
关键词 GOOS controlling GAUSSIAN SHIFT can our GH It
Non-parametric reconstruction of growth index via Gaussian processes
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作者 Zhao-Yu Yin Hao Wei 《中国科学:物理学、力学、天文学英文版》 SCIE EI CAS CSCD 2019年第9期110-119,共10页
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
关键词 COSMOLOGY DARK energy modified GRAVITY growth index GAUSSIAN processes
Hyperparameter Optimization for Machine Learning Models Based on Bayesian Optimization 预览
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作者 Jia Wu Xiu-Yun Chen +3 位作者 Hao Zhang Li-Dong Xiong Hang Lei Si-Hao Deng 《电子科技学刊:英文版》 CAS CSCD 2019年第1期26-40,共15页
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
关键词 BAYESIAN OPTIMIZATION GAUSSIAN process hyperparameter OPTIMIZATION MACHINE LEARNING
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Modeling Interstation Travel Speed of Hybrid Bus Rapid Transit within A Bayesian Framework 预览
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作者 Ji-hua Hu Jia-xian Liang 《智能城市应用》 2019年第5期33-45,共13页
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
关键词 BAYESIAN HYBRID BRT RJMCMC interstation TRAVEL speed GAUSSIAN MIXTURE model
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Clustering in the Wireless Channel with a Power Weighted Statistical Mixture Model in Indoor Scenario 预览
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作者 Yupeng Li Jianhua Zhang +1 位作者 Pan Tang Lei Tian 《中国通信:英文版》 SCIE CSCD 2019年第7期83-95,共13页
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
关键词 channel MULTIPATH CLUSTERING mmWave Gaussian mixture model EXPECTATION MAXIMIZATION VARIATIONAL Bayesian INFERENCE
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烷基环己苯异硫氰酸液晶材料太赫兹波吸收 预览
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作者 阎昊岚 程雅青 +4 位作者 王凯礼 王雅昕 陈洋玮 袁秋林 马恒 《物理学报》 SCIE EI CAS CSCD 北大核心 2019年第11期212-219,共8页
基于密度泛函理论,利用Gaussian09程序包,通过Opt+Freq优化结构,以B3LYP/6-311g基组对4-(trans-4-n-alkylcyclohexyl) isothiocyanatobenzenes (CHBT) 16种液晶分子在0.1—5.0 THz波段的吸收进行研究,提出了通过考察分子转动惯量和质量... 基于密度泛函理论,利用Gaussian09程序包,通过Opt+Freq优化结构,以B3LYP/6-311g基组对4-(trans-4-n-alkylcyclohexyl) isothiocyanatobenzenes (CHBT) 16种液晶分子在0.1—5.0 THz波段的吸收进行研究,提出了通过考察分子转动惯量和质量重心偏移对太赫兹吸收的影响方法.计算结果表明,随着分子烷基链上碳原子数目增加,分子的转动惯量和重心的偏移将对太赫兹波的吸收产生影响.在0.1—5.0 THz波段, 3—7个碳原子的分子吸收相对较强.以此为参照,减少和增加烷基链上的碳原子数目都会降低分子对太赫兹波的吸收.在0.3—3.0 THz范围内,将计算结果与10种有实验数据的分子进行了对比.结果发现,低频波段计算结果与实验测量相比存在差异,其中吸收峰位置的差异可能来源于氢键.比较吸收强度的相对大小值,发现实验测量与计算结果较为一致,表明吸收强度来源于偶极子振动、转动吸收,展现了计算模拟的积极意义.研究结果可对相关分子的设计与合成提供有用的建议. 展开更多
关键词 液晶 太赫兹 烷基链 高斯
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Experimental Gaussian Boson sampling
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作者 Han-Sen Zhong Li-Chao Peng +15 位作者 Yuan Li Yi Hu Wei Li Jian Qin Dian Wu Weijun Zhang Hao Li Lu Zhang Zhen Wang Lixing You Xiao Jiang Li Li Nai-Le Liu Jonathan P.Dowling Chao-Yang Lu Jian-Wei Pan 《科学通报:英文版》 SCIE EI CSCD 2019年第8期511-515,共5页
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
关键词 QUANTUM information BOSON sampling GAUSSIAN BOSON sampling SQUEEZED state QUANTUM ADVANTAGE QUANTUM APPROXIMATE optimization
基于LoG算子的常规镜下细胞计数图像 预览
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作者 李政浩 《电子技术与软件工程》 2019年第18期70-71,共2页
本文将基于Lo G算子,对镜下细胞图像进行预处理与边缘提取;随后便能够使用细胞边缘模板,对处理后的图像卷积,进而更好地实现视野范围内,细胞计数的需求。
关键词 LOG算子 GAUSSIAN LAPLACE 边缘 检测 细胞计数
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Ellipticity-dependent ionization yield for noble atoms
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作者 Hristina Delibasicf Violeta Petrovic 《中国物理B:英文版》 SCIE EI CAS CSCD 2019年第8期73-78,共6页
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
关键词 ELLIPTICAL polarization ponderomotive potential STARK effect Gaussian laser pulse
PREFACE 预览
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作者 胡耀忠 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期627-628,共2页
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
关键词 PREFACE RESEARCH PAPERS GAUSSIAN NOISES
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PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE 预览
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作者 李贺宇 陈夏 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期629-644,共16页
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
关键词 STO chastic HEA t equation t ime-deriva tive Gaussian noise BROWNIAN MOT ion Feynman-Kac representation Schilder's large deviation
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Balance Control of a Biped Robot on a Rotating Platform Based on Efficient Reinforcement Learning 预览
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作者 Ao Xi Thushal Wijekoon Mudiyanselage +1 位作者 Dacheng Tao Chao Chen 《自动化学报:英文版》 CSCD 2019年第4期938-951,共14页
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
关键词 BIPED robot GAUSSIAN processes(GP) REINFORCEMENT learning TEMPORAL DIFFERENCE
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ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE 预览
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作者 胡耀忠 刘阳辉 Samy TINDEL 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期669-690,共22页
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
关键词 Stochastic heat equation general Gaussian noise L^2 SOLUTION SUFFICIENT and necessary condition Wong-Zakai approximation pathwise SOLUTION HOLDER CONTINUITY BESOV space
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HOLDER CONTINUITY FOR THE PARABOLIC ANDERSON MODEL WITH SPACE-TIME HOMOGENEOUS GAUSSIAN NOISE 预览
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作者 Raluca M BALAN Lluis Q UER-SARDANYONS 宋健 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期717-730,共14页
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
关键词 GAUSSIAN noise STOCHASTIC partial differential equations Malliavin CALCULUS
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