a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

We study the block-coordinate forward–backward algorithm in which blocks are updated a random and possibly parallel manner, according to arbitrary probabilities. The allows different stepsizes along block-coordinates fully exploit smoothness properties of objective function. In convex case an infinite dimensional setting, we establish almost sure weak convergence iterates asymptotic rate o(1/n)...

A cylindrical coordinate colour space (lightness, saturation/chroma, hue) is derived from an opponent colour space in the RGB space. It is shown how cylindrical coordinate colour models widely used in the literature are related to or can be reduced to the derived model, thereby contributing to creating a unified cylindrical coordinate colour model. In particular, the widely used saturation expr...

In this paper, a unified beam theory is developed and applied to study the buckling response of two types of functionally graded sandwich beams. In the first type (Type A), the sandwich beam has a hardcore whereas in the second type (Type B), the sandwich beam has a softcore. In both the type of beams, face sheets are made up of functionally graded material. The material properties of face shee...

Network coordinate systems, such as GNP and Vivaldi, provide virtual positions for networked hosts, which enable the hosts to connect to nearby peers, find the closest server, or organize themselves in a topologically-aware manner. Current network coordinate systems, however, only use latency to compute the positions, leaving out an important network metric—namely bandwidth. In this paper, we p...

This paper concerns asynchrony in iterative processes, focusing on gradient descent and tatonnement, a fundamental price dynamic. Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process, although distributed and asynchronous variants have been studied since the 1980s. Coordinate d...

Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms...

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. Recently, the efficiency of the block coordinate descent (BCD) type methods has been empirically illustrated for DNN training. The main idea of BCD is to decompose the highly composite and nonconvex DNN training problem into several almost separable simple subproblems. However, t...