Interval-valued statistical modeling of oxide chemical-mechanical polishing
Technology-oriented tools provide the raw data needed to optimize the fabrication process itself, and to predict problematic variational impacts on silicon design. Unfortunately, even in these physics-oriented tools, statistically uncertain quantities appear as crucial inputs. To date, Monte Carlo techniques have been the dominant solution method. We suggest an alternative in which uncertainties are represented as correlated intervals, and interval-valued computations replace the standard scalar operations in the numerical algorithm for the tool. We use an oxide chemical-mechanical polishing tool as an example, and show how to "retrofit" workable statistical models on top of the original algorithm. Accuracies to within /spl sim/1-10% of Monte Carlo simulation, and speedups of /spl sim/10-100X can be achieved, depending on whether we choose a formulation which emphasizes accuracy, or efficiency.

title: Probabilistic interval-valued computation: toward a practical surrogate for statistics inside CAD tools
abstract: Interval methods offer a general, fine-grain strategy for modeling correlated range uncertainties in numerical algorithms. We present a new, improved interval algebra that extends the classical affine form to a more rigorous statistical foundation. Range uncertainties now take the form of confidence intervals. In place of pessimistic interval bounds, we minimize the probability of numerical "escape"; this can tighten interval bounds by 10times, while yielding 10-100times speedups over Monte Carlo. The formulation relies on three critical ideas: liberating the affine model from the assumption of symmetric intervals; a unifying optimization formulation; and a concrete probabilistic model. We refer to these as probabilistic intervals, for brevity. Our goal is to understand where we might use these as a surrogate for expensive, explicit statistical computations. Results from sparse matrices and graph delay algorithms demonstrate the utility of the approach, and the remaining challenges

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: Fast interval-valued statistical modeling of interconnect and effective capacitance
abstract: 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: A Real Trading Model based Price Negotiation Agents
abstract: Sim proposed a market-driven negotiation agent model that makes adjustable amounts of concession by reacting to different market situations and trading constraints, and it was improved with an enhanced market-driven strategy by taking opponent eagerness into consideration. In both Sim's original model and improved model, however, it was implied that a negotiation agent has same behaviors and actions to all trading partners referring to a same trading issue. It is not quite true in a real world trading negotiation. Based on both models, this paper proposes a real trading model based price negotiation agents that take each trading partner as an individual with different strategies and actions. Moreover, negotiation actions between a negotiation agent and a trading partner are kept in secret and unknown to others

title: An Information Criterion for Informative Gene Selection
abstract: It is important in bioinformatics research and applications to select or discover informative genes of a tumor from microarray data. However, most of the existing methods are based on models which assume that the gene expressions are normal distributed, which is often violated in practice. In this paper, we propose an information criterion for informative gene selection by ranking the genes with the Kullback-Leiber discrimination information of two probability distributions of the expression levels on the tumor and normal (or another type of tumor) samples. We use support vector machine (SVM) to construct the tumor diagnosis system using certain top informative genes. The experiments on two well-known data sets (colon data and leukemia data) show that the information criterion can make the tumor diagnosis system reach 94.4% and 100% correctness rate of diagnosis on these two datasets, respectively.

title: A Dangerous Location Aware System for Assisting Kids Safety Care
abstract: This system focuses on a location-aware computing application and environment which provide preemptive information on dangerous locations in the kid's surroundings; i.e., the system alerts a kid on the move of the possible dangers whenever he/she is near accident prone areas. Using satellite-based GPS position sensing, this system can gradually learn and remember about the different locations that a kid routinely visits and/or passes by in his daily life, based on space-oriented contexts. The full set of system functionalities, including the map display, requires a graphical user interface. This location based services (LBSs) can compute the serious situations and alert kids to avoid dangerous situations. Our research can simulate the virtual environment as hyperspaces for kids safety care

title: A Shopping Negotiation Agent That Adapts to User Preferences
abstract: This paper describes a shopping negotiation agent that can adapt user preferences and automatically negotiate with its counter party on behalf of a user it represents. The agent is built on a basis of the proposed negotiation model, the enhanced extended Bazaar model, which is a sequence of decision making model of negotiation with exploiting common knowledge, public information, and game theory. Since different users can have different preferences, it is important for the agent to have adaptation to different user preferences. This can be achieved by acquiring user preferences, tracing user's behavior on Web and mapping the behavior to a set of the preference parameters, creating the negotiation model class, and generating an instance negotiation model object with new/updated preference parameters.

title: On the correct convergence of the EM algorithm for Gaussian mixtures
abstract: It is well-known that the EM algorithm generally converges to a local maximum likelihood estimate. However, there have been many evidences to show that the EM algorithm can converge correctly to the true parameters as long as the overlap of Gaussians in the sample data is small enough. This paper studies this correct convergence problem asymptotically on the EM algorithm for Gaussian mixtures. It has been proved that the EM algorithm becomes a contraction mapping of the parameters within a neighborhood of the consistent solution of the maximum likelihood when the measure of average overlap among Gaussians in the original mixture is small enough and the number of samples is large enough. That is, if the initial parameters are set within the neighborhood, the EM algorithm will always converge to the consistent solution, i.e., the expected result. Moreover, the simulation results further demonstrate that this correct convergence neighborhood becomes larger as the average overlap becomes smaller.