Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the

Abstract. New medical imaging modalities offering multi-valued data, suchas phase contrast MRA and diffusion tensor MRI, require general representations for the development of automatized algorithms. In this paper we propose a unified framework for the registration of medical volumetric multi-valued data. The paper extends the usual concept of similarity in intensity (scalar) data to vector and tensor cases. A discussion on appropriate template selection and on the limitations of the template matching approach to incorporate the vector and tensor reorientation is also offered. Our approachto registration is based on a multiresolution scheme based on local matching of areas with a high degree of local structure and subsequent interpolation. Consequently we provide an algorithm to assess the amount of structure in generic multi-valued data by means of gradient and correlation computations. The interpolation step is carried out by means of the Kriging estimator that outperforms conventional polynomial methods for the interpolation of sparse vector fields. The feasibility of the approach is illustrated by results on synthetic and clinical data. 1

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this article. 2.1 Universal Kriging

Abstract. Geostatistics have become the dominant tool for probabilistic estimation of properties of heterogeneous formations at points where data are not available. Ordinary kriging, the starting point in development of other geostatistical techniques, has a number of serious limitations, chief among which is the intrinsic hypothesis of the (second order) stationarity of the underlying random field. Attempts to overcome this limitation have led to the development of ever more complex flavors of kriging. We pursue an opposite strategy that consists of finding the simplest possible technique that is adequate for the task of facies delineation. Guided by the principle of parsimony, we identify Nearest Neighbor classification (NNC) as a viable alternative to geostatistics among deterministic techniques. We demonstrate that when used for the purpose of facies delineation, the NNC, which has no fitting parameters and operational assumptions, outperforms indicator kriging, which has several parameters. 1.

this paper will be assumed to have mean zero. 2 2. Preliminaries. The proofs of the uniqueness results given in Section 3 require some simple manipulations with backshift-operator polynomial filters and their inverses as they apply to stationary time series. Here we establish the validity of these manipulations

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Abstract: This paper presents a novel class of self-organizing sensing agents that form a swarm and learn the static spatial process of interest through noisy measurements from neighbors for various global goals. The spatial phenomenon of interest is modeled by a Gaussian process. Each sensing agent maintains its own prediction of the Gaussian process based on measurements from neighbors. A set of biologically inspired navigation strategies are derived by exploiting the predictive posterior statistics. A unified way to prescribe a global goal for the group of agents so that a high-level behavior builds on a set of lowlevel simple behavior modules. As a result, collective mobility of agents emerges from a specified global goal. The proposed cooperatively learning control consists of motion coordination based on the recursive estimation of an unknown field of interest with measurement noise. The convergence properties of the proposed coordination algorithm for different situations and global goals are investigated by a simulation study. Keywords: Multi-agent systems; Estimation and filtering; Sensor networks; Gaussian processes. 1.

Reospective studies of disease often are limited by the resolution of the exposumeasurements. Forexmple, in atypical study of adverse health effects from contaminated groundwater, the number of wells sampled may range fron only a few to as many as several dozen, while the number of cases and controls may be in the hundreds or more. To derive individual estimates of exposure for wells that were not sampled, investigators must extrapolate. In this study, we compare three methods of extrapolating from a limited number of observations to estimate individual exposures. Using two naive models of groundwater contamination, we compare nearest neighbor interpolaion, inverse distance squared weighting, and kriging for estimating exposure based on alimited number of measurements. Our results show that although kriging isastatistcally optimal method, it is not markedly better than simpler interpolation algorithms, though it is considerably more complex to use. Aberrant well measurements and discontinuities are problematic for all methods. We provide some guidance in interpolating data and outline a more comprehensive comparison of methodology.