generic convolution integral  (Genovis Inc)

Journal: Journal of Applied Crystallography

Article Title: Deconvoluting Patterson

doi: 10.1107/S1600576725006569

Figure Lengend Snippet: Comparing electron density with its autocorrelation function demonstrates that P ( u ) reveals the interatomic distances. The centrosymmetric nature of the interatomic distance vector map (Patterson map) in contrast to the electron density map becomes obvious. We also discover that, as a result of the convolution, the Patterson peaks are twice as broad as the electron density peaks ( cf . purple arrows).

Article Snippet: Briefly, in the generic convolution integral (using as the convolution operator) for two different functions f ( r ) and g ( r ), we replace g ( r ) with g (− r ) which changes the second integrand to g ( r + u ) and the convolution into a correlation: Next, we substitute ρ for both g and f (same function, thus ‘auto’ in correlation).

Techniques: Plasmid Preparation

Journal: Nature Communications

Article Title: Digital-analog hybrid matrix multiplication processor for optical neural networks

doi: 10.1038/s41467-025-62586-0

Figure Lengend Snippet: a Simulation setup. An image “Chelsea” from the scikit-image dataset is convolved with a Prewitt operator (vertical edge detection). We explore the noise tolerance of both the analog and the hybrid optical computing systems by adding additive white Gaussian noise to the weights and examining the system’s performance by investigating the noise distribution of the outputs. b performance of the analog and hybrid computing schemes in terms of RMSE with different SNRs. The following results are obtained at an SNR of 25 dB. c , f Processed and reconstructed images by the analog and hybrid computing systems, respectively. d , g Distribution of expected pixel values against the processed pixel values (both normalized), for the analog and hybrid computing systems, respectively. Insets show the corresponding processed images. Noisy pixels can be clearly observed in the image processed using analog computing. e , h Noise distribution of the analog and hybrid computing systems, respectively. Analog computing reveals a Gaussian noise distribution with a standard deviation of 0.027, corresponding to a numerical precision of 3.6 bits. The HOP shows a greatly improved noise distribution thanks to the introduction of logic levels and decisions based on thresholding.

Article Snippet: An image “Chelsea” from the scikit-image dataset is processed using the 3 × 3 Prewitt convolution operator for horizontal edge detection.

Techniques: Standard Deviation