Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Sources of Productivity Growth in Health Services: A Case Study of Queensland Public Hospitals

Improving the performance of health sector is one of the most popular issues in Queensland, Australia. This paper contributes to this important policy debate by examining the efficiency of health facilities in Queensland using the Malmquist Productivity Index (MPI). This method is selected because it is suitable for the multi-input, multi-output, and not-for-profit natures of public health services. In addition, with the availability of panel data we can decompose productivity growth into useful components, including technical efficiency changes, technological changes and scale changes. The results revealed an average of 1.6 per cent of growth in total factor productivity (TFP) among Queensland public hospitals in the study period. The main component contribute to the modest improvement of TFP during the period was catching-up at an average of 1.0 per cent. SFA estimates suggest that the number of nurses is the most influential determinant of output.Public health services, productivity growth, Queensland

Joint dynamic probabilistic constraints with projected linear decision rules

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically