There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

The adoption of a reconfigurable intelligent surface (RIS) for downlink multi-user communication from a multi-antenna base station is investigated in this paper. We develop energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements subject to individual link budget guarantees for the mobile users. This leads to non-convex design optimization problems for which to tackle we propose two computationally affordable approaches, capitalizing on alternating maximization, gradient descent search, and sequential fractional programming. Specifically, one algorithm employs gradient descent for obtaining the RIS phase coefficients, and fractional programming for optimal transmit power allocation. Instead, the second algorithm employs sequential fractional programming for the optimization of the RIS phase shifts. In addition, a realistic power consumption model for RIS-based systems is presented, and the performance of the proposed methods is analyzed in a realistic outdoor environment. In particular, our results show that the proposed RIS-based resource allocation methods are able to provide up to 300% higher energy efficiency in comparison with the use of regular multi-antenna amplify-and-forward relaying.

Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication

Erratum to “MRI Heating Reduction for External Fixation Devices Using Absorption Material”

The reduced basis method is a model-order reduction technique that converts the original system equations into smaller ones using a reduced basis set. This basis set is usually derived from a set of solutions of the system equation with different values of control parameters. If the system model changes affinely with the parameter values, a reduced-order model can be derived. In this abstract, we apply the reduced basis method to method of moments for quasi-periodic array modeling. With this method, a new basis set for a single element is constructed through an offline process. Because of the similarities among elements, the number of basis functions for each element can be much less than directing modeling from geometrical mesh. Numerical example shows that both the computational and memory efficiency is improved compared with direct modeling using method of moments.

Application of the reduced basis method to ID quasi-periodic array modeling

In this paper, we propose the physics-informed supervised residual learning (PISRL) which is a general framework for electromagnetic forward modeling based on deep learning. PISRL is designed to solve a system of linear matrix equations and not limited to a specific electromagnetic problem. Stationary and non-stationary iterative PISRL neural networks (SIPISRLNN and NSIPISRLNN) are designed based on the mathematical connection between residual neural network (ResNet)[1] and stationary or non-stationary iterative methods. With convolutional neural network mapping residuals and modifications, SIPISRLNN and NSIPISRLNN can improve the approximated solutions via iterative process, which mimics the procedure of solving linear equations by stationary and non-stationary iterative methods. The generalities of SIPISRLNN and NSIPISRLNN are validated by solving different types of volume integral equations (VIEs) with non-lossy and lossy scatterers. In numerical results of non-lossy scatterers, the mean squared errors (MSEs) of SIPISRLNN and NSIPISRLNN finally converge below $3.152 \times 10^{-4}$ and $4.8925 \times 10^{-7}$; in results of lossy scatterers, the MSEs converge below $1.2775 \times 10^{-4}$ and $1.567 \times 10^{-7}$. The generalization abilities of SIPISRLNN and NSIPISRLNN are verified by testing them on the data sets of contrast shapes and different incident frequencies that are unseen during the training process.

Physics-informed Supervised Residual Learning for 2D Electromagnetic Forward Modeling

Joint 2D inversion of AMT and seismic traveltime data with deep learning constraint

Based on Huygens' principle, the equivalence principle algorithm can decompose a large computational domain into several subdomains and model electromagnetic phenomenon efficiently. This paper analyses the numerical projection error of the equivalence principle operator (EPO), i.e., the error of the scattered equivalent currents on the equivalence surfaces projected from the currents inside the surface. Numerical studies show that the accuracy of the equivalent magnetic current on the equivalence surface and its far field radiation depend on the shape of the scatterer, and the error convergence rate is usually faster for spherical equivalence surfaces than cubic ones. Therefore, properly choosing the shape of equivalence surfaces according to the shape of the inside scatterers and the position of the observers can improve the accuracy of the equivalence principle algorithm.

Fan Yang

Papers

Erratum to “MRI Heating Reduction for External Fixation Devices Using Absorption Material”

Application of the reduced basis method to ID quasi-periodic array modeling

Physics-informed Supervised Residual Learning for 2D Electromagnetic Forward Modeling

Joint 2D inversion of AMT and seismic traveltime data with deep learning constraint

Study on projection error of equivalence principle algorithm