scholarly journals A new approach to observational cosmology using the scattering transform

2020 ◽  
Vol 499 (4) ◽  
pp. 5902-5914
Author(s):  
Sihao Cheng (程思浩) ◽  
Yuan-Sen Ting (丁源森) ◽  
Brice Ménard ◽  
Joan Bruna

ABSTRACT Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with convolutional neural networks (CNNs) but requiring neither training nor tuning. It generates a compact set of coefficients, which can be used as robust summary statistics for non-Gaussian information. It is especially suited for fields presenting localized structures and hierarchical clustering, such as the cosmological density field. To demonstrate its power, we apply this estimator to a cosmological parameter inference problem in the context of weak lensing. On simulated convergence maps with realistic noise, the scattering transform outperforms classic estimators and is on a par with the state-of-the-art CNN. It retains advantages of traditional statistical descriptors, has provable stability properties, allows to check for systematics, and importantly, the scattering coefficients are interpretable. It is a powerful and attractive estimator for observational cosmology and the study of physical fields in general.

Atmosphere ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 248
Author(s):  
Nan Chen ◽  
Xiao Hou ◽  
Qin Li ◽  
Yingda Li

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simple information criterion is developed to assess the model error in imperfect models. This effective information criterion takes into account the information in both the equilibrium statistics and the temporal autocorrelation function, where the latter is written in the form of the spectrum density that permits the quantification via information theory. This information criterion facilitates the study of model reduction, stochastic parameterizations, and intermittent events. In the second part of this article, a new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT). This new approach makes use of a Gaussian Mixture (GM) to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response, as is widely used in the quasi-Gaussian (qG) FDT. Testing examples show that this GM FDT outperforms qG FDT in various strong non-Gaussian regimes.


2004 ◽  
Vol 14 (1) ◽  
pp. 193-198 ◽  
Author(s):  
P. Coullet ◽  
C. Riera ◽  
C. Tresser

2013 ◽  
Vol 27 (23) ◽  
pp. 1350120 ◽  
Author(s):  
HONG-CHUN YUAN ◽  
YE-JUN XU ◽  
LEI CHEN ◽  
XUE-FEN XU

We adopt a new approach, thermo entangled representation, to study time evolution of density operator in thermal environment. We then investigate the analytical expressions of Wigner function (WF) evolution of arbitrary number excited coherent states (ECSs) and excited even (odd) coherent states (EECSs, EOCSs) in thermal environment, respectively. In addition, their nonclassicality is numerically discussed by exploring the negativity of WF with decay time in thermal channel, respectively. It is found that WF loses its non-Gaussian nature and becomes Gaussian after long times.


In real world applications, Speech recognition system have grown due its significance in various online and offline applications such as security, robotic application, speech translator etc. These systems are widely used now-a-days where acquisition of signal is performed using various instruments which causes noise, source mixing and other impurities which affects the performance of speech recognition system. In this work, issue of source mixing in original speech signal is addressed which causes performance degradation. In order to overcome this we propose a new approach which utilizes non-negative matrix factorization modelling. This method utilizes scattering transform by applying wavelet filter bank and pyramid scattering to estimate the source and minimization of unwanted signals. After estimation the signals or sources, source separation algorithm is implemented using optimization process based on the training and testing method. Proposed approach is compared with other existing method by computing performance measurement matrices which shows the better performance


2021 ◽  
pp. 2150483
Author(s):  
Weifang Weng ◽  
Zhenya Yan

In this paper, the general triple-pole multi-soliton solutions are proposed for the focusing modified Korteweg–de Vries (mKdV) equation with both nonzero boundary conditions (NZBCs) and triple zeros of analytical scattering coefficients by means of the inverse scattering transform. Furthermore, we also give the corresponding trace formulae and theta conditions. Particularly, we analyze some representative reflectionless potentials containing the triple-pole multi-dark-anti-dark solitons and breathers. The idea can also be extended to the whole mKdV hierarchy (e.g. the fifth-order mKdV equation, and third-fifth-order mKdV equation) with NZBCs and triple zeros of analytical scattering coefficients. Moreover, these obtained triple-pole solutions can also be degenerated to the triple-pole soliton solutions with zero boundary conditions.


Author(s):  
HW Cheng ◽  
JY Tao ◽  
X Chen ◽  
Y Jiang

We describe efforts to improve the accuracy of fatigue damage estimation methods of narrowband non-Gaussian random loading. The available analytical solutions are reviewed and briefly summarized, and the reasons for the occurrence of computational errors during nonlinear transformation-based methods are determined. The computational errors are mainly due to inconsistencies in the statistical moments above fourth order. A new approach is proposed for the evaluation of rainflow fatigue damage. This approach avoids the problem of transformation-based methods and provides accurate estimation for fatigue damage of narrowband leptokurtic non-Gaussian random loading. Additionally, the applicability of the proposed method to Gaussian random loading is investigated. Finally, two examples are carried out and comparisons are made to more commonly used methods to demonstrate the capabilities and brevity of the proposed algorithm.


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