8613420
Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition
This is the fourth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we describe a finite element approximation for this system on locally refined grids. This adaptive approximation is based on a mixed finite element method for the elliptic pressure equation and a Galerkin finite element method for the degenerate parabolic saturation equation. Both discrete stability and sharp a priori error estimates are established for this approximation. Iterative techniques of domain decomposition type for solving it are discussed, and numerical results are presented.
5311208
Domain decomposition algorithms for mixed methods for second-order elliptic problems
Domain decomposition algorithms for mixed finite element methods for linear second-order elliptic problems in R 2 and R 3 are developed. A convergence theory for two-level and multilevel Schwarz methods applied to the algorithms under consideration is given. It is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems. Numerical experiments are presented to illustrate the present techniques.
11820934
Computing Lyapunov exponents based on the solution expression of the variational system
A simple discrete QR algorithm based on a solution expression of the variational equation of a dynamical system is presented for computing the Lyapunov exponents of n-dimensional continuous dynamical systems. The developed numerical scheme of study is based on a time integration using a constant time-step fourth-order Adams–Bashforth method. Numerical results are presented for a Lorenz system with known Lyapunov exponents, and higher dimensional dynamical systems. The algorithm proposed to compute the Lyapunov exponents is found to be robust, computationally efficient, and stable for a sufficiently small step-size h.
62617805
Improved rate control for MPEG-4 video transport over wireless channel
Video streaming over wireless channel is challenging due to a number of factors such as limited bandwidth and loss sensitivity. In this paper, we develop a novel rate control algorithm for MPEG-4 video coding. Unlike traditional rate control schemes, we jointly consider the encoding complexity variation and buffer variation as well as human visual properties to optimize the rate control efficiency. We also analyze the sensitivity of a macroblock (MB) as a result of bit errors and calculate its error sensitivity metric. This metric is used in unequal error protection (UEP) of the MB. Simulation results show that proposed approach can improve the decoded picture quality in wireless video coding and transmission.
6847311
On the Complexity of Rocchio's Similarity-Based Relevance Feedback Algorithm
In this paper, we prove for the first time that the learning complexity of Rocchio's algorithm is O(d + d2(log d + log n)) over the discretized vector space {0,...,n–1}d, when the inner product similarity measure is used. The upper bound on the learning complexity for searching for documents represented by a monotone linear classifier (q,0) over {0,...,n–1}d can be improved to O(d + 2k(n–1)(log d + log(n–1))), where k is the number of nonzero components in q. An Ω((d2)log n) lower bound on the learning complexity is also obtained for Rocchio's algorithm over {0,...,n–1}d. In practice, Rocchio's algorithm often uses fixed query updating factors. When this is the case, the lower bound is strengthened to 2$^{{\it \Omega}(d)}$ over the binary vector space {0,1}d. In general, if the query updating factors are bounded by O(nc) for some constant c≥ 0, an ${\it \Omega}(n^{d-1-c}/(n-1))$ lower bound is obtained over {0,...,n–1}d.
18029622
The Bounded Injury Priority Method and the Learnability of Unions of Rectangles
Abstract We develop a bounded version of the finite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain {0, …, n − 1}d with only equivalence queries. Applying this method, we show three main results: 1. (1)The class of unions of rectangles is polynomial time learnable for constant dimension d. 2. (2)The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable. 3. (3)The class of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses.
52859343
Towards rate-distortion tradeoff in real-time color video coding
In this paper, we address to the key problem in real-time video coding, the rate-distortion tradeoff. We found that the distribution of the integer transform coefficients in H.264 color video coding can be approximated by Laplacian distribution but the rate-distortion characteristics should be modelled for the luminance and chrominance components separately. So we propose separable rate-distortion models for color video coding. The feedback from the encoder buffer is analyzed by a control-theoretic adaptation approach. To achieve smooth video quality and satisfy the delay constraints in real-time applications, a novel rate distortion tradeoff controller is employed. Simulations results demonstrate that the proposed approach can achieve smooth video quality without sacrificing overall quality while efficiently utilize the bandwidth without buffer overflow or underflow.