**Social Physics (SocioPhysics)**

Social physics or sociophysics is a field of science which uses mathematical tools inspired by physics to understand the behavior of human crowds. In a modern commercial use, it can also refer to the analysis of social phenomena with big data. Social physics is closely related to econophysics which uses physics methods to describe economics.

https://www.datasciencecentral.com/profiles/blogs/the-upcoming-revolution-in-predictive-analytics-and-data-science … **Accumulated Total Derivative Effects Plot**

Interpreting a nonparametric regression model with many predictors is known to be a challenging problem. There has been renewed interest in this topic due to the extensive use of machine learning algorithms and the difficulty in understanding and explaining their input-output relationships. This paper develops a unified framework using a derivative-based approach for existing tools in the literature, including the partial-dependence plots, marginal plots and accumulated effects plots. It proposes a new interpretation technique called the accumulated total derivative effects plot and demonstrates how its components can be used to develop extensive insights in complex regression models with correlated predictors. The techniques are illustrated through simulation results. … **DN-ResNet**

A deep learning approach to blind denoising of images without complete knowledge of the noise statistics is considered. We propose DN-ResNet, which is a deep convolutional neural network (CNN) consisting of several residual blocks (ResBlocks). With cascade training, DN-ResNet is more accurate and more computationally efficient than the state of art denoising networks. An edge-aware loss function is further utilized in training DN-ResNet, so that the denoising results have better perceptive quality compared to conventional loss function. Next, we introduce the depthwise separable DN-ResNet (DS-DN-ResNet) utilizing the proposed Depthwise Seperable ResBlock (DS-ResBlock) instead of standard ResBlock, which has much less computational cost. DS-DN-ResNet is incrementally evolved by replacing the ResBlocks in DN-ResNet by DS-ResBlocks stage by stage. As a result, high accuracy and good computational efficiency are achieved concurrently. Whereas previous state of art deep learning methods focused on denoising either Gaussian or Poisson corrupted images, we consider denoising images having the more practical Poisson with additive Gaussian noise as well. The results show that DN-ResNets are more efficient, robust, and perform better denoising than current state of art deep learning methods, as well as the popular variants of the BM3D algorithm, in cases of blind and non-blind denoising of images corrupted with Poisson, Gaussian or Poisson-Gaussian noise. Our network also works well for other image enhancement task such as compressed image restoration. … **Frobenius Coin Problem**

The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations. For example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set. The Frobenius number exists as long as the set of coin denominations has no common divisor greater than 1. There is an explicit formula for the Frobenius number when there are only two different coin denominations, x and y: xy – x – y. If the number of coin denominations is three or more, no explicit formula is known; but, for any fixed number of coin denominations, there is an algorithm computing the Frobenius number in polynomial time (in the logarithms of the coin denominations forming an input). No known algorithm is polynomial time in the number of coin denominations, and the general problem, where the number of coin denominations may be as large as desired, is NP-hard. …

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Nov 2020

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