Autocorrelation functions and spectral densities for plastic microstrain in crystals

1981 ◽  
Vol 17 (2) ◽  
pp. 196-199
Author(s):  
L. V. Kuksa
Keyword(s):  
Spectral Densities ◽  
Autocorrelation Functions ◽  
Plastic Microstrain

Heat Transfer of Thin Fins With Stochastic Root Temperature

1969 ◽  
Vol 91 (1) ◽  
pp. 129-134 ◽  
Author(s):  
H. M. Hung
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Computational Experiments ◽  
Spectral Densities ◽  
Root Temperature ◽  
Convergence Problem ◽  
Autocorrelation Functions ◽  
Numerical Examples ◽  
Power Spectral ◽  
Power Spectral Densities

An analysis of the temperature distribution of straight and circular fins with stochastic root temperature is presented. The response autocorrelation functions and power spectral densities of temperatures with stationary Gaussian excitation temperatures are obtained. These excitations include purely stochastic and Markoff processes. Several numerical examples are studied. Graphical results are given. The convergence problem in computational experiments is found to be not very severe.

Transformation of non-Gaussian random processes, signals and noise in the nonlinear differential systems by the method of cumulative functions

2018 ◽  
Vol 15 (1) ◽  
pp. 84-93
Author(s):  
V. I. Volovach ◽  
V. M. Artyushenko
Keyword(s):  
Spectral Characteristics ◽  
Random Processes ◽  
Spectral Densities ◽  
Differential Systems ◽  
Non Gaussian ◽  
Nonlinear Differential Systems

Reviewed and analyzed the issues linked with the torque and naguszewski cumulant description of random processes. It is shown that if non-Gaussian random processes are given by both instantaneous and cumulative functions, it is assumed that such processes are fully specified. Spectral characteristics of non-Gaussian random processes are considered. It is shown that higher spectral densities exist only for non-Gaussian random processes.

scholarly journals Gaussian processes with skewed Laplace spectral mixture kernels for long-term forecasting

2021 ◽  
Author(s):  
Kai Chen ◽  
Twan van Laarhoven ◽  
Elena Marchiori
Keyword(s):  
Gaussian Processes ◽  
Multivariate Time Series ◽  
Heavy Tail ◽  
Lottery Ticket ◽  
Spectral Densities ◽  
Heavy Tailed ◽  
Long Term Forecasting ◽  
The Time Domain ◽  
Spectral Mixture

AbstractLong-term forecasting involves predicting a horizon that is far ahead of the last observation. It is a problem of high practical relevance, for instance for companies in order to decide upon expensive long-term investments. Despite the recent progress and success of Gaussian processes (GPs) based on spectral mixture kernels, long-term forecasting remains a challenging problem for these kernels because they decay exponentially at large horizons. This is mainly due to their use of a mixture of Gaussians to model spectral densities. Characteristics of the signal important for long-term forecasting can be unravelled by investigating the distribution of the Fourier coefficients of (the training part of) the signal, which is non-smooth, heavy-tailed, sparse, and skewed. The heavy tail and skewness characteristics of such distributions in the spectral domain allow to capture long-range covariance of the signal in the time domain. Motivated by these observations, we propose to model spectral densities using a skewed Laplace spectral mixture (SLSM) due to the skewness of its peaks, sparsity, non-smoothness, and heavy tail characteristics. By applying the inverse Fourier Transform to this spectral density we obtain a new GP kernel for long-term forecasting. In addition, we adapt the lottery ticket method, originally developed to prune weights of a neural network, to GPs in order to automatically select the number of kernel components. Results of extensive experiments, including a multivariate time series, show the beneficial effect of the proposed SLSM kernel for long-term extrapolation and robustness to the choice of the number of mixture components.

scholarly journals On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

2020 ◽  
Vol 15 (1) ◽  
pp. 258-265
Author(s):  
Yu Zhou ◽  
Daoguang Mu ◽  
Xinfeng Dong
Keyword(s):  
Sufficient Conditions ◽  
Sum Of Squares ◽  
Basic Component ◽  
Necessary And Sufficient Conditions ◽  
Autocorrelation Functions ◽  
Walsh Spectrum ◽  
Cryptographic Algorithms ◽  
Necessary And Sufficient ◽  
Relationship Of

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

scholarly journals Comments on Kinetic Equation for Autocorrelation Functions

1969 ◽  
Vol 10 (6) ◽  
pp. 964-974 ◽  
Author(s):  
P. Résibois ◽  
J. Brocas ◽  
G. Decan
Keyword(s):  
Kinetic Equation ◽  
Autocorrelation Functions
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