Modelling the Somantic Electrical Response of Hippocampal Pyramidal Neurons

A modeling study of hippocampal pyramidal neurons is described. This study is based on simulations using HIPPO, a program which simulates the somatic electrical activity of these cells. HIPPO is based on a) descriptions of eleven non-linear conductances that have been either reported for this class of cell in the literature or postulated in the present study, and b) an approximation of the electrotonic structure of the cell that is derived in this thesis, based on data for the linear properties of these cells. HIPPO is used a) to integrate empirical data from a variety of sources on the electrical characteristics of this type of cell, b) to investigate the functional significance of the various elements that underly the electrical behavior, and c) to provide a tool for the electrophysiologist to supplement direct observation of these cells and provide a method of testing speculations regarding parameters that are not accessible.

Parameter Estimation in Chaotic Systems

This report examines how to estimate the parameters of a chaotic system given noisy observations of the state behavior of the system. Investigating parameter estimation for chaotic systems is interesting because of possible applications for high-precision measurement and for use in other signal processing, communication, and control applications involving chaotic systems. In this report, we examine theoretical issues regarding parameter estimation in chaotic systems and develop an efficient algorithm to perform parameter estimation. We discover two properties that are helpful for performing parameter estimation on non-structurally stable systems. First, it turns out that most data in a time series of state observations contribute very little information about the underlying parameters of a system, while a few sections of data may be extraordinarily sensitive to parameter changes. Second, for one-parameter families of systems, we demonstrate that there is often a preferred direction in parameter space governing how easily trajectories of one system can "shadow'" trajectories of nearby systems. This asymmetry of shadowing behavior in parameter space is proved for certain families of maps of the interval. Numerical evidence indicates that similar results may be true for a wide variety of other systems. Using the two properties cited above, we devise an algorithm for performing parameter estimation. Standard parameter estimation techniques such as the extended Kalman filter perform poorly on chaotic systems because of divergence problems. The proposed algorithm achieves accuracies several orders of magnitude better than the Kalman filter and has good convergence properties for large data sets.

Electrical Design: A Problem for Artificial Intelligence Research

This report outlines the problem of intelligent failure recovery in a problem-solver for electrical design. We want our problem solver to learn as much as it can from its mistakes. Thus we cast the engineering design process on terms of Problem Solving by Debugging Almost-Right Plans, a paradigm for automatic problem solving based on the belief that creation and removal of "bugs" is an unavoidable part of the process of solving a complex problem. The process of localization and removal of bugs called for by the PSBDARP theory requires an approach to engineering analysis in which every result has a justification which describes the exact set of assumptions it depends upon. We have developed a program based on Analysis by Propagation of Constraints which can explain the basis of its deductions. In addition to being useful to a PSBDARP designer, these justifications are used in Dependency-Directed Backtracking to limit the combinatorial search in the analysis routines. Although the research we will describe is explicitly about electrical circuits, we believe that similar principles and methods are employed by other kinds of engineers, including computer programmers.

Nanocrystalline Ge Flash Memories: Electrical Characterization and Trap Engineering

Conventional floating gate non-volatile memories (NVMs) present critical issues for device scalability beyond the sub-90 nm node, such as gate length and tunnel oxide thickness reduction. Nanocrystalline germanium (nc-Ge) quantum dot flash memories are fully CMOS compatible technology based on discrete isolated charge storage nodules which have the potential of pushing further the scalability of conventional NVMs. Quantum dot memories offer lower operating voltages as compared to conventional floating-gate (FG) Flash memories due to thinner tunnel dielectrics which allow higher tunneling probabilities. The isolated charge nodules suppress charge loss through lateral paths, thereby achieving a superior charge retention time. Despite the considerable amount of efforts devoted to the study of nanocrystal Flash memories, the charge storage mechanism remains obscure. Interfacial defects of the nanocrystals seem to play a role in charge storage in recent studies, although storage in the nanocrystal conduction band by quantum confinement has been reported earlier. In this work, a single transistor memory structure with threshold voltage shift, Vth, exceeding ~1.5 V corresponding to interface charge trapping in nc-Ge, operating at 0.96 MV/cm, is presented. The trapping effect is eliminated when nc-Ge is synthesized in forming gas thus excluding the possibility of quantum confinement and Coulomb blockade effects. Through discharging kinetics, the model of deep level trap charge storage is confirmed. The trap energy level is dependent on the matrix which confines the nc-Ge.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.