Adaptive time-stepping methods based on the Monte Carlo Euler method for weak approximation of Itô stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading-order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or deterministic time steps are described. Numerical examples illustrate when stochastic and deterministic adaptive time steps are superior to constant time steps and when adaptive stochastic steps are superior to adaptive deterministic steps. Stochastic time steps use Brownian bridges and require more work for a given number of time steps. Deterministic time steps may yield more time steps but require less work; for example, in the limit of vanishing error tolerance, the ratio of the computational error and its computable estimate tends to 1 with negligible additional work to determine the adaptive deterministic time steps.

This dissertation addresses the problem of approximating, in floating-point arithmetic, all real roots (simple, clustered, and multiple) over the unit interval of polynomials in Bernstein...

We propose a parallel specialized language that ensures portable and cost-predictable implementations on parallel computers. The language is basically a first-order, recursion-less, strict functional language equipped with a collection of higher-order functions or skeletons. These skeletons apply on (nested) vectors and can be grouped in four classes: computation, reorganization, communication, and mask skeletons. The compilation process is described as a series of transformations and analyses leading to spmd-like functional programs which can be directly translated into real parallel code. The language restrictions enforce a programming discipline whose benefit is to allow a static, symbolic, and accurate cost analysis. The parallel cost takes into account both load balancing and communications, and can be statically evaluated even when the actual size of vectors or the number of processors are unknown. It is used to automatically select the best data distribution among a set of standard distributions. Interestingly, this work can be seen as a cross fertilization between techniques developed within the Fortran parallelization, skeleton, and functional programming communities.

v LIST OF FIGURES ix CHAPTER 1. INTRODUCTION 1 1.1 Short History of Neurocomputing ...................... 2 1.2 Basic Neural Network structure ....................... 4 1.3 Short History of Neural Network structure ................. 6 1.3.1 BASIC TYPES OF NEURON NETWORKS............. 7 1.3.2 OPTICAL IMPLEMENTATIONS OF NEURAL NETWORK . . . 9 1.4 Neural Network Learning Process ...................... 10 1.4.1 Error-Correction Learning . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 Hebbian Learning ........................... 11 1.4.3 Supervised Learning . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.4 Unsupervised Learning ........................ 12 1.4.5 Competitive Learning ......................... 12 1.4.6 Activation Function .......................... 12 1.5 Proposed Rapidly Trained Fiber Optic Neural Network .......... 15 1.6 Training Algorithm .............................. 17 1.7 Scope of the Dissertation Project ...................... 19 CHAPTER 2. RAPIDLY T...

. Tomographic techniques are successfully applied to obtain 4D images of the tropospheric refractivity in a local dense network of Global Positioning System (GPS) receivers. We show here how GPS data are processed to obtain the tropospheric slant wet delays and discuss the validity of the processing. These slant wet delays are the observables in the tomographic processing. We then discuss the inverse problem in 4D tropospheric tomography making extensive use of simulations to test the system and dene the resolution and the impact of noise. Finally, we use data from the Kilauea network in Hawaii for February 1st 1997 and a local 4x4x40 voxel grid on a region of 400 Km 2 and 15 Km in height to produce the corresponding 4D wet refractivity elds, which are then validated using forecast analysis from the European Center for Medium Range Weather Forecast (ECMWF). We conclude that tomographic techniques can be used to monitor the troposphere in time and space. 1 Introduction Tomographic...

The hypothesis that the variability in the discharge of cortical neurons results from balanced excitation and inhibition is analyzed. A method is presented for analyzing the integrate and re neural model with reversal potentials which enables the interspike interval distribution to be calculated in the Gaussian approximation. Results are presented for the perfect integrator model, for which a stable value of the membrane potential in the absence of the spiking mechanism exists. The results show close agreement with numerical simulations for large numbers of small amplitude inputs. The coecient of variation is consistently less than 1.0, as observed in cortical neurons. Key words: Integrate and re neurons, Reversal potentials, Perfect integrator, Interspike interval variability, First-passage time. 1 Introduction The origin of the variability in the discharge of cortical neurons is not well understood. An analysis of the coecient of variation in the spikes generated by an integrate an...

An explicit mixing parcel model (EMPM) has been developed and applied to study the effects of entrainment and fine scale mixing on in-cloud structure and droplet spectral evolution in cumulus clouds. In the EMPM, entrainment occurs in random discrete events, while turbulent mixing is simulated by a one-dimensional stochastic turbulent mixing model, the linear eddy model. Within the linear eddy model, molecular diffusion is treated directly by solving the 1D diffusion equation, while turbulent stirring (advection) is treated in a stochastic manner by random rearrangement events of the scalar field in the one-dimensional domain. Because the simulation is performed in a one-dimensional domain, all relevant length scales of the mixing process can be resolved. Two versions of the EMPM have been developed. The first involves an implicit microphysical calculation and subgrid-scale eddy diffusivity. Although the details of droplet distributions are not provided, the simulated results using this versio...

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de l'Ecole des Mines de Paris presentee par