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A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by strong…
We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those…
We present a theoretical background for the data analysis of the gravitational-wave signals from spinning neutron stars for Earth-based laser interferometric detectors. We introduce a detailed model of the signal including both the…
By default neural networks are not robust to changes in data distribution. This has been demonstrated with simple image corruptions, such as blurring or adding noise, degrading image classification performance. Many methods have been…
In the field of gamma-ray astronomy, irregular and noisy datasets make difficult the characterization of light-curve features in terms of statistical significance while properly accounting for trial factors associated with the search for…
We study compressible MHD turbulence, which holds key to many astrophysical processes, including star formation and cosmic ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid we use wavelet…
In interstellar medium studies, separating ordered and random velocity or magnetic fields is essential for interpreting turbulence in both simulations and observations. We investigate how the choice of averaging scale affects the…
Emission from the interstellar medium can be a significant contaminant of measurements of the intensity and polarization of the cosmic microwave background (CMB). For planning CMB observations, and for optimizing foreground-cleaning…
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
Usual modal analysis techniques are based on the Fourier transform. Due to the Delta T . Delta f limitation, they perform poorly when the modal overlap mu exceeds 30%. A technique based on a high-resolution analysis algorithm and an…
An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having…
In this paper, we design mother wavelets for the 1D continuous wavelet transform with some optimality properties. An optimal mother wavelet here is one that has an ambiguity function with minimal spread in the continuous coefficient space…
Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable…
In mixture experiments with noise variables or process variables that can not be controlled, investigate and try to control the variability of the response variable is very important for quality improvement in industrial processes. Thus,…
Global stability analysis and direct numerical simulation (DNS) are performed to study boundary layer flows with an isolated roughness element. Wall-attached cuboids with aspect ratios $\eta=1$ and $\eta=0.5$ are investigated for fixed…
A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy…
Variational system identification is a new formulation of maximum likelihood for estimation of parameters of dynamical systems subject to process and measurement noise, such as aircraft flying in turbulence. This formulation is an…
Unsupervised clustering of wafer map defect patterns is challenging because the appearance of certain defect patterns varies significantly. This includes changing shape, location, density, and rotation of the defect area on the wafer. We…
Cloud detection is a specialized application of image recognition and object detection using remotely sensed data. The task presents a number of challenges, including analyzing images obtained in visible, infrared and multi-spectral…