Some characterizations of spheres and elliptic paraboloids II

We show some characterizations of hyperspheres in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with intrinsic and extrinsic properties such as the $n$-dimensional area of the sections cut off by hyperplanes, the $(n+1)$-dimensional volume of regions between parallel hyperplanes, and the $n$-dimensional surface area of regions between parallel hyperplanes. We also establish two characterizations of elliptic paraboloids in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional volume of regions between parallel hyperplanes. For further study, we suggest a few open problems.Comment: 10 page

A Method of Experimentally Probing Transeverse Momentum Dependent Distributions

We calculate the double spin asymmetry A_LL(x, y, z, P_hT) of pi^0 production with the spectator model and the model based on the factorization ansatz. We also calculate the double spin asymmetry for the integration over the range of (x,y,z) for the setups of the experiments of COMPASS, HERMES, and JLab. We find that the results are characteristically dependent on the model used. Therefore, we suggest that the measurements of the double spin asymmetry provides a method of experimentally probing the transeverse momentum dependent distributions.Comment: 10 pages, 31 figure

Baseline CNN structure analysis for facial expression recognition

We present a baseline convolutional neural network (CNN) structure and image preprocessing methodology to improve facial expression recognition algorithm using CNN. To analyze the most efficient network structure, we investigated four network structures that are known to show good performance in facial expression recognition. Moreover, we also investigated the effect of input image preprocessing methods. Five types of data input (raw, histogram equalization, isotropic smoothing, diffusion-based normalization, difference of Gaussian) were tested, and the accuracy was compared. We trained 20 different CNN models (4 networks x 5 data input types) and verified the performance of each network with test images from five different databases. The experiment result showed that a three-layer structure consisting of a simple convolutional and a max pooling layer with histogram equalization image input was the most efficient. We describe the detailed training procedure and analyze the result of the test accuracy based on considerable observation.Comment: 6 pages, RO-MAN2016 Conferenc