A SVM bases AI design for interactive gaming

Interactive gaming requires automatic processing on large volume of random data produced by players on spot, such as shooting, football kicking, boxing etc. In this paper, we describe an artificial intelligence approach in processing such random data for interactive gaming by using a one-class support vector machine (OC-SVM). In comparison with existing techniques, our OC-SVM based interactive gaming design has the features of: (i): high speed processing, providing instant response to the players: (i) winner selection and control by one parameter, which can be pre-designed and adjusted according to the game design needs, i.e. level of difficulties: Experiments on numerical simulation support that the proposed design is robust to random noise, accurate in picking up winning data, and convenient for all interactive gaming design

Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions

The global classical solution to the incompressible Navier-Stokes-Fourier equation with small initial data in the whole space is constructed through a zero Knudsen number limit from the solutions to the Boltzmann equation with general collision kernels. The key point is the uniform estimate of the Sobolev norm on the global solutions to the Boltzmann equation.Comment: 21 page

The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

Let $(X,d,\mu)$ be a $RCD^\ast(K, N)$ space with $K\in mathbb{R}$ and $N\in [1,\infty)$. Suppose that $(X,d)$ is connected, complete and separable, and \supp \mu=X. We prove that the Li-Yau inequality for the heat flow holds true on $(X,d,\mu)$ when $K\ge 0$. A Baudoin-Garofalo inequality and Harnack inequalities for the heat flows are established on $(X,d,\mu)$ for general $K\in \mathbb{R}$. Large time behaviors of heat kernels are also studied.Comment: 31 pages, J. Math. Pures Appl., to appea