Arthur David Snider

An exact statistical method for comparing topographic maps, with any number of subjects and electrodes

SummaryStatistical methods for testing differences between neural images (e.g., PET, MRI or EEG maps) are problematic because they require (1) an untenable assumption of data sphericity and (2) a high subject to electrode ratio. We propose and demonstrate an exact and distribution-free method of significance testing which avoids the sphericity assumption and may be computed for any combination of electrode and subject numbers. While this procedure is rigorously rooted in permutation test theory, it is intuitively comprehensible. The sensitivity of the permutation test to graded changes in dipole location for systematically varying levels of signal/noise ratio, intersubject variability and number of subjects was demonstrated through a simulation of 70 different conditions, generating 5,000 different data sets for each condition. Data sets were simulated from a homogenous single-shell dipole model. For noise levels commonly encountered in evoked potential studies and for situations where the number of subjects was less than the number of electrodes, the permutation test was very sensitive to a change in dipole location of less than 0.75 cm. This method is especially sensitive to localized changes that would be “washed-out‘ by more traditional methods of analysis. It is superior to all previous methods of statistical analysis for comparing topographical maps, because the test is exact, there is no assumption of a multivariate normal distribution or of the correlation structure of the data requiring correction, the test can be tailored to the specific experimental hypotheses rather than allowing the statistical tests to limit the experimental design, and there is no limitation on the number of electrodes that can be simultaneously analyzed.

Charge conservation and the transcapacitance element: an exposition

A simple gedanken experiment is presented to demonstrate the violation of charge (and energy) conservation, as predicted by D.E. Ward (1981), J.J. Paulos and D.A. Antoniadis (1983), and D. Root and B. Hughes (1988), in the two-parameter nonlinear modeling of capacitance. The paradoxes are resolved through examination of a complete physical model of the capacitor. The role of the transcapacitive element in reestablishing charge conservation is explored in this context. Discussion of the software implementation of transcapacitance and its dual, transinductance, is also included. >

The Quest for the Optimum Longitudinal Fin Profile

The search for the optimal profile for a longitudinal fin has occupied a portion of the mathematics and engineering communities for almost 60 years. Heuristic and rigorous arguments have led to definitive answers only when the “length of arc” idealization is involved. This paper reviews the chronology of these research efforts and offers some counterexamples, with regard to the usual models, which indicate that fins of mathematically unbounded performance are theoretically (although not practically) achievable. The construction of such fins, in the practical limit, suggests some promising new horizons in extended-surface heal transfer.

Efficient optimization of certain functionals in a hypercube

A new computational method for solving the shallow-water equations has been developed. This method combines some of the recent developments of geophysical and computational fluid dynamics, like a semi-Lagrangian advection scheme, an adaptive mesh refinement based on a posteriori error estimation, parallelization on a local memory parallel computer, and iterative solution of the linear system derived from a finite element discretization. Dynamic load balancing has been applied in order to achieve high parallel efficiency.

Recent developments in the analysis and design of extended surface

Earlier papers by the authors developed a new set of parameters for characterizing heat transfer properties of single fins and fins in arrays of extended surface. The use of these parameters has facilitated the solutions to several interesting fin problems namely: a more careful characterization of one-dimensional flow configurations, a method for accomodating continuously distributed heat sources along the fin, a perturbating approach for the approximate computation of the parameters, and new insights into the precepts of the optimal fin shape. These developments are reported in this paper.

Resolving capacitor discrepancies between large and small signal FET models

A novel solution is presented for the well known capacitor discrepancy problem between large and small signal FET models. The discrepancy arises due to the two-parameter bias voltage dependence of the intrinsic FET model capacitances. The resolution is enabled by the proper choice of partial-integration constants associated with the transformation of a charge source in the large signal model to a capacitor in the small signal model.<<ETX>>

Math methods in transistor modeling: Condition numbers for parameter extraction

Condition numbers expressing the sensitivity of computed circuit element values to inaccuracies in S-parameter measurements are derived and evaluated for a standard small-signal MESFET model. The condition numbers shed light on the common difficulty experienced by transistor modelers in extracting accurate values for the input resistance. Other elements are also classified according to their sensitivity.

A General Extended Surface Analysis Method

An earlier paper by the authors presented an algorithm for analyzing certain arrays of extended surface, in terms of the heat transfer properties and geometries of the individual fins comprising the array. This paper identifies the subclass of arrays susceptible to such analysis as trees, in the graph theoretic sense, and extends the technique by deriving general equations for efficiently analyzing a perfectly arbitrary configuration of fins.

Mathematical Analysis of the Length-of-Arc Assumption

Abstract The observation by Maday in 1974 that the Schmidt-Duffin solution to the optimal fin profile problem was flawed due to neglect of the slant height factor led to a new solution—actually, a demonstration of the ill-posedness of the question—by Snider. The present article proves mathematically that omission of this factor leads inevitably to underestimation of the heat transfer capability of any fin. Additionally, a perturbation scheme for estimating the correction for this effect is derived for configurations with low generalized Biot numbers, and a revised assessment of the performance of the Schmidt fin is presented.

An Improved Estimate of the Accuracy of Trigonometric Interpolation

Utilizing the concept of aliasing, we are able to obtain a new estimate of the accuracy of trigonometric interpolation. For functions with K continuous derivatives, we show that the n-point sum gives approximation to order