Fast interval-valued statistical modeling of interconnect and effective capacitance
Correlated interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite intervals to approximate the essential mass of a probability density function (pdf) as it moves through numerical operators; the resulting compact interval-valued solution can be easily interpreted as a statistical distribution and efficiently sampled. This paper first describes improved interval-valued algorithms for asymptotic wave evaluation (AWE)/passive reduced-order interconnect macromodeling algorithm (PRIMA) model order reduction for tree-structured interconnect circuits with correlated resistance, inductance, and capacitance (RLC) parameter variations. By moving to a much faster interval-valued linear solver based on path-tracing ideas, and making more optimal tradeoffs between interval- and scalar-valued computations, the delay statistics roughly 10/spl times/ faster than classical Monte Carlo (MC) simulation, with accuracy to within 5% can be extracted. This improved interval analysis strategy is further applied in order to build statistical effective capacitance (C/sub eff/) models for variational interconnect, and show how to extract statistics of C/sub eff/ over 100/spl times/ faster than classical MC simulation, with errors less than 4%.

title: Pre-routing estimation of shielding for RLC signal integrity
abstract: The formula-based K/sub eff/ model is a figure of merit for inductive coupling, and has been used to solve the simultaneous shield insertion and net ordering (SINO) and simultaneous signal and power routing (SPR) problems. The authors first show that the K/sub eff/ model has a high fidelity compared to the SPICE-computed noise under an accurate RLC circuit model. We then develop simple yet accurate formulae to estimate numbers of shields needed by optimal SINO solutions under the K/sub eff/ model. Extensive experiments show that our pre-routing estimation has errors less than 10% compared to solutions given by detailed SINO algorithms. These formulae can be used effectively as a pre-routing congestion estimation for layout planning and synthesis.

title: Interval-valued reduced order statistical interconnect modeling
abstract: We show how recent advances in the handling of correlated interval representations of range uncertainty can be used to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in RLC parameters as sets of correlated intervals, and show how classical model order reduction methods - AWE and PRIMA - can be re-targeted to compute interval-valued, rather than scalar-valued reductions. By applying a statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show the technique can predict mean delay with errors between 5-10%, for correlated RLC parameter variations up to 35%.

title: A Neural Network Approach to Real-Time Pattern Recognition
abstract: This paper presents a new neural network approach to real-time pattern recognition on a given set of binary (or bipolar) sample patterns. The perceptive neuron of a binary pattern is defined and constructed as a binary neuron with a neighborhood perceptive field. Letting its hidden units be the respective perceptive neurons of the patterns, a three-layer forward neural network is constructed to recognize these patterns with minimum error probability in a noisy environment. The theoretical and simulation analyses show that the network is effective for pattern recognition and can be under strict real-time constraints.

title: The specification and implementation of a virtual university software system
abstract: Distance learning is one of the interesting research topics of distributed computing. This paper discusses a joint research project between the University of Aizu in Japan and Tamkang University in Taiwan. A software system supporting virtual university operations is proposed. The software architecture is designed based on three criteria of virtual university operations: administration, awareness and assessment. Specifications of each tools in the system are proposed, with some implementation details and solutions being discussed. We also point out some interesting research directions in the realization of a virtual university.

title: Rough Asymptotics of Forward-Backward Stochastic Differential Equations
abstract: This note is concerned with the asymptotic behavior of adapted solutions to forward-backward SDEs when the forward diffusion contains small noises. We prove the sample path Large Deviation Principle (LDP) for the adapted solutions to the FBSDEs under appropriate conditions stated in terms of a certain type of convergence of the solutions to the associated quasilinear PDEs. As an application we apply the LDP results to a problem of rare event simulation. We provide a necessary condition for the existence of an asymptotically efficient estimator amongst the class of importance sampling estimators.

title: A One-Bit-Matching Learning Algorithm for Independent Component Analysis
abstract: Independent component analysis (ICA) has many practical applications in the fields of signal and image processing and several ICA learning algorithms have been constructed via the selection of model probability density functions. However, there is still a lack of deep mathematical theory to validate these ICA algorithms, especially for the general case that super- and sub-Gaussian sources coexist. In this paper, according to the one-bit-matching principle and by turning the de-mixing matrix into an orthogonal matrix via certain normalization, we propose a one-bit-matching ICA learning algorithm on the Stiefel manifold. It is shown by the simulated and audio experiments that our proposed learning algorithm works efficiently on the ICA problem with both super- and sub-Gaussian sources and outperforms the extended Infomax and Fast-ICA algorithms.

title: Non-parametric Statistical Tests for Informative Gene Selection
abstract: This paper presents two non-parametric statistical test methods, called Kolmogorov-Smirnov (KS) and U statistic test methods, respectively, for informative gene selection of a tumor from microarray data, with help of the theory of false discovery rate. To test the effectiveness of these non-parametric statistical test methods, we use the support vector machine (SVM) to construct a tumor diagnosis system (i.e., a binary classifier) based on the identified informative genes on the colon and leukemia data. It is shown by the experiments that the constructed tumor diagnosis system with both the KS and U statistic test methods can reach a good prediction accuracy on both the colon and leukemia data sets.