This paper serves to prove the thesis that a computational trick can open entirely new approaches to theory. We illustrate by describing such random matrix techniques as the stochastic operator approach, the method of ghosts and shadows, and the method of “Riccatti Diffusion/Sturm Sequences,” giving new insights into the deeper mathematics underneath random matrix theory.

To recover a sharp image from its blurry observation is the problem known as image deblurring. It frequently arises in imaging sciences and technologies, including optical, medical, and astronomical applications, and is crucial for allowing to detect important features and patterns such as those of a distant planet or some microscopic tissue. Mathematically, image deblurring is intimately conne...

Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuous-time computation. However, while special-case algorithms and devices are being developed, relatively little work exists on the general theory of continuous-time models of computation. In this paper, we survey the exist...

The main purpose of this paper is to examine some (potential) applications of quantum computation in AI and to review the interplay between quantum theory and AI. For the readers who are not familiar with quantum computation, a brief introduction to it is provided, and a famous but simple quantum algorithm is introduced so that they can appreciate the power of quantum computation. Also, a (quit...

The Linear Quadratic Gaussian Poisson (LQGP) problem denotes an optimal control problem with linear dynamics and quadratic costs with both Gaussian and Poisson noise disturbances. The LQGP problem provides a benchmark model with suucient complexity while permitting formal solutions for testing both theoretical and computational methods. The problem is examined in this paper.

Oscillatory integrals are present in many applications, and their numerical approximation is the subject of this paper. Contrary to popular belief, their computation can be achieved efficiently, and in fact, the more oscillatory the integral, the more accurate the approximation. We review several existing methods, including the asymptotic expansion, Filon method, Levin collocation method and nu...