Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.

An algebraic curve is defined as the zero set of a polynomial in two variables. Algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics. The main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data. Usually, arguments against using algebraic curves involve references to mathematicians Wilkinson (see [1] chapter 7) and Runge (see [3] chapter 4). The first goal of this article is to understand the stability issue of algebraic curve tting. Then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed, and its properties are investigated. The fitting algorithm is of sufficient stability for very fast position-invariant shape recognition, position estimation, and shape tracking, based on invariants and new representations. Among appropriate applications are shape-based indexing into image databases.

The problem of minimizing a multivariate function is recurrent in many disciplines as Physics, Mathematics, Engeneering and, of course, Computer Science. Both deterministic and nondeterministic algorithms have been devised to perform this task. It is common practice to use the nondeterministic algorithms when the function to be minimized is not smooth or depends on binary variables, as in the case of combinatorial optimization. In this paper we describe a simple nondeterministic algorithm which is based on the idea of adaptive noise, and that proved to be particularly effective in the minimization of a class of multivariate, continuous valued, smooth functions, associated with some recent extension of regularization theory by Poggio and Girosi (1990).

The typical subroutines that compute sin(z) and exp(z) bear little resemblance to our mathematical knowledge of these functions: they are composed of concrete arithmetic expressions that include many mysterious numerical constants. Instead of programming these subroutines conventionally, we can express their construction using symbolic ideas such as periodicity and Taylor series. Such an approach has many advantages: the code is closer to the mathematical basis of the function, less vulnerable to errors, and is trivially adaptable to various precisions.

Motivated by the goal of establishing stochastic and information theoretic foundations for the study of intelligence and synthesis of intelligent machines, this thesis probes several topics relating to hidden state stochastic models. Finite Growth Models (FGM) are introduced. These are nonnegative functionals that arise from parametrically-weighted directed acyclic graphs and a tuple observation that affects these weights. Using FGMs the parameters of a highly general form of stochastic transducer can be learned from examples, and the particular case of stochastic string edit distance is developed. Experiments are described that illustrate the application of learned string edit distance to the problem of recognizing a spoken word given a phonetic transcription of the acoustic signal. With FGMs one may direct learning by criteria beyond simple maximum-likelihood. The MAP (maximum a posteriori estimate) and MDL (minimum description length) are discussed along with the application to cau...

We present a rapid and accurate method of calibrating seismic systems using a random binary calibration signal and cross-spectral techniques. The complex transfer function obtained from the cross spectrum is least-squares fit to the ratio of two polynomials in s ( s-- i~) whose degrees are determined by a linear systems analysis. This provides a compact representation of the system fre-quency response. We demonstrate its application to two seismic systems, the IDA and SRO seismometers. This method yields calibrations to an accuracy of better than 1 per cent in amplitude and 1 ° in phase. 1.

ABSTRACr This paper develops techniques for equivalent circuit analysis of tight epithelia by alternating-current impedance measurements, and tests these techniques on rabbit urinary bladder. Our approach consists of measuring transepithelial impedance, also measuring the DC voltage-divider ratio with a microelectrode, and extracting values of circuit parameters by computer fit of the data to an equivalent circuit model. We show that the commonly used equivalent circuit models of epithelia give significant misfits to the impedance data, because these models (so-called "lumped models") improperly represent the distributed resistors associated with long and narrow spaces such as lateral intercellular spaces (LIS).We develop a new "distributed model " of an epithelium to take account of these structures and thereby obtain much better fits to the data. The extracted parameters include the resistance and capacitance ofthe apical and basolateral cell membranes, the series resistance, and the ratio of the cross-sectional area to the length ofthe LIS. The capacitance values yield estimates of real area ofthe apical and basolateral membranes. Thus, impedance analysis can yield morphological information (configuration of the LIS, and real membrane areas) about a living tissue, independently of electron microscopy. The effects of transport-modifying agents such as amiloride and nystatin can be related to their effects on particular circuit elements by extracting parameter values from impedance runs before and during application of the agent. Calculated parameter values have been validated by independent electrophysiological and morphological measurements.

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