SOME NOTATIONS AND REMARKS PARABOLIC EQUATIONS WITH ONE SPACE VARIABLE Equations with Power-Law Nonlinearities Equations with Exponential Nonlinearities Equations with Hyperbolic Nonlinearities Equations with Logarithmic Nonlinearities Equations with Trigonometric Nonlinearities Equations Involving Arbitrary Functions Nonlinear Schrodinger Equations and Related Equations PARABOLIC EQUATIONS WITH TWO OR MORE SPACE VARIABLES Equations with Two Space Variables Involving Power-Law Nonlinearities Equations with Two Space Variables Involving Exponential Nonlinearities Other Equations with Two Space Variables Involving Arbitrary Parameters Equations Involving Arbitrary Functions Equations with Three or More Space Variables Nonlinear Schrodinger Equations HYPERBOLIC EQUATIONS WITH ONE SPACE VARIABLE Equations with Power-Law Nonlinearities Equations with Exponential Nonlinearities Other Equations Involving Arbitrary Parameters Equations Involving Arbitrary Functions Equations of the Form wxy=F(x,y,w, wx, wy ) HYPERBOLIC EQUATIONS WITH TWO OR THREE SPACE VARIABLES Equations with Two Space Variables Involving Power-Law Nonlinearities Equations with Two Space Variables Involving Exponential Nonlinearities Nonlinear Telegraph Equations with Two Space Variables Equations with Two Space Variables Involving Arbitrary Functions Equations with Three Space Variables Involving Arbitrary Parameters Equations with Three Space Variables Involving Arbitrary Functions ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES Equations with Power-Law Nonlinearities Equations with Exponential Nonlinearities Equations Involving Other Nonlinearities Equations Involving Arbitrary Functions ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Equations with Three Space Variables Involving Power-Law Nonlinearities Equations with Three Space Variables Involving Exponential Nonlinearities Three-Dimensional Equations Involving Arbitrary Functions Equations with n Independent Variables EQUATIONS INVOLVING MIXED DERIVATIVES AND SOME OTHER EQUATIONS Equations Linear in the Mixed Derivative Equations Quadratic in the Highest Derivatives Bellman Type Equations and Related Equations SECOND-ORDER EQUATIONS OF GENERAL FORM Equations Involving the First Derivative in t Equations Involving Two or More Second Derivatives THIRD-ORDER EQUATIONS Equations Involving the First Derivative in t Equations Involving the Second Derivative in t Hydrodynamic Boundary Layer Equations Equations of Motion of Ideal Fluid (Euler Equations) Other Third-Order Nonlinear Equations FOURTH-ORDER EQUATIONS Equations Involving the First Derivative in t Equations Involving the Second Derivative in t Equations Involving Mixed Derivatives EQUATIONS OF HIGHER ORDERS Equations Involving the First Derivative in t and Linear in the Highest Derivative General Form Equations Involving the First Derivative in t Equations Involving the Second Derivative in t Other Equations SUPPLEMENTS: EXACT METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Classification of Second-Order Semilinear Partial Differential Equations in Two Independent Variables Transformations of Equations of Mathematical Physics Traveling-Wave Solutions and Self-Similar Solutions. Similarity Methods Method of Generalized Separation of Variables Method of Functional Separation of Variables Generalized Similarity Reductions of Nonlinear Equations Group Analysis Methods Differential Constraints Method Painleve Test for Nonlinear Equations of Mathematical Physics Inverse Scattering Method Conservation Laws Hyperbolic Systems of Quasilinear Equations REFERENCES INDEX

Handbook of Nonlinear Partial Differential Equations

An evaluation of lattice Boltzmann schemes for porous medium flow simulation

Computer Controlled Systems: Theory and Design

Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root finding with noisy input information. As with all stochastic search algorithms, there are adjustable algorithm coefficients that must be specified, and that can have a profound effect on algorithm performance. It is known that choosing these coefficients according to an SA analog of the deterministic Newton-Raphson algorithm provides an optimal or near-optimal form of the algorithm. However, directly determining the required Hessian matrix (or Jacobian matrix for root finding) to achieve this algorithm form has often been difficult or impossible in practice. The paper presents a general adaptive SA algorithm that is based on a simple method for estimating the Hessian matrix, while concurrently estimating the primary parameters of interest. The approach applies in both the gradient-free optimization (Kiefer-Wolfowitz) and root-finding/stochastic gradient-based (Robbins-Monro) settings, and is based on the "simultaneous perturbation (SP)" idea introduced previously. The algorithm requires only a small number of loss function or gradient measurements per iteration-independent of the problem dimension-to adaptively estimate the Hessian and parameters of primary interest. Aside from introducing the adaptive SP approach, the paper presents practical implementation guidance, asymptotic theory, and a nontrivial numerical evaluation. Also included is a discussion and numerical analysis comparing the adaptive SP approach with the iterate-averaging approach to accelerated SA.

/pdf/adaptive-stochastic-approximation-by-the-simultaneous-32pbrvg1e5.pdf

Adaptive stochastic approximation by the simultaneous perturbation method

Real-time traffic signal control is an integral part of the urban traffic control system, and providing effective real-time traffic signal control for a large complex traffic network is an extremely challenging distributed control problem. This paper adopts the multiagent system approach to develop distributed unsupervised traffic responsive signal control models, where each agent in the system is a local traffic signal controller for one intersection in the traffic network. The first multiagent system is developed using hybrid computational intelligent techniques. Each agent employs a multistage online learning process to update and adapt its knowledge base and decision-making mechanism. The second multiagent system is developed by integrating the simultaneous perturbation stochastic approximation theorem in fuzzy neural networks (NN). The problem of real-time traffic signal control is especially challenging if the agents are used for an infinite horizon problem, where online learning has to take place continuously once the agent-based traffic signal controllers are implemented into the traffic network. A comprehensive simulation model of a section of the Central Business District of Singapore has been developed using PARAMICS microscopic simulation program. Simulation results show that the hybrid multiagent system provides significant improvement in traffic conditions when evaluated against an existing traffic signal control algorithm as well as the SPSA-NN-based multiagent system as the complexity of the simulation scenario increases. Using the hybrid NN-based multiagent system, the mean delay of each vehicle was reduced by 78% and the mean stoppage time, by 85% compared to the existing traffic signal control algorithm. The promising results demonstrate the efficacy of the hybrid NN-based multiagent system in solving large-scale traffic signal control problems in a distributed manner

/pdf/neural-networks-for-real-time-traffic-signal-control-3wiqqdm62w.pdf

Neural Networks for Real-Time Traffic Signal Control

Two-Dimensional Model of a Reaction-Bonded Aluminum Oxide Cylinder

Optimal jacketed tubular reactor operation: classic vs. flow reversal

The derivation of minimal bioreaction models is of primary importance to develop monitoring and control strategies of cell/microorganism culture production. These minimal bioreaction models can be obtained based on the selection of a basis of elementary flux modes (EFMs) using an algorithm starting from a relatively large set of EFMs and progressively reducing their numbers based on geometric and least-squares residual criteria. The reaction rates associated with the selected EFMs usually have complex features resulting from the combination of different activation, inhibition and saturation effects from several culture species. Multilayer perceptrons (MLPs) are used in order to undertake the representation of these rates, resulting in a hybrid dynamic model combining the mass-balance equations provided by the EFMs to the rate equations described by the MLPs. To further reduce the number of kinetic parameters of the model, pruning algorithms for the MLPs are also considered. The whole procedure ends up with reduced-order macroscopic models that show promising prediction results, as illustrated with data of perfusion cultures of hybridoma cell line HB-58.

/pdf/hybrid-dynamic-models-of-bioprocesses-based-on-elementary-1fq65thy.pdf

A. Vande Wouwer

Papers

Two-Dimensional Model of a Reaction-Bonded Aluminum Oxide Cylinder

Optimal jacketed tubular reactor operation: classic vs. flow reversal

Hybrid Dynamic Models of Bioprocesses Based on Elementary Flux Modes and Multilayer Perceptrons

Design of a confidence interval observer—Application to vehicle positioning

Parameter identification to enforce practical observability of nonlinear systems