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This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. The first part of the text is concerned with basic backstepping control of freeway traffic using the Aw-Rascle-Zhang (ARZ) second-order PDE model. It begins by illustrating a basic control problem suppressing traffic with stop-and-go oscillations downstream of ramp metering before turning to the more challenging case for traffic upstream of ramp metering. The authors demonstrate how to design state observers for the purpose of stabilization using output-feedback control. Experimental traffic data are then used to calibrate the ARZ model and validate the boundary observer design. Because large uncertainties may arise in traffic models, adaptive control and reinforcement learning methods are also explored in detail. Part II then extends the conventional ARZ model utilized until this point in order to address more complex traffic conditions: multi-lane traffic, multi-class traffic, networks of freeway segments, and driver use of routing apps. The final chapters demonstrate the use of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and to optimize flow through a bottleneck. In order to make the text self-contained, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is included. Traffic Congestion Control by PDE Backstepping is ideal for control theorists working on control of systems modeled by PDEs and for traffic engineers and applied scientists working on unsteady traffic flows. It will also be a valuable resource for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.

Agent-based modelling in economics Lynne Hamill and Nigel Gilbert, Centre for Research in Social Simulation (CRESS), University of Surrey, UK New methods of economic modelling have been sought as a result of the global economic downturn in 2008. This unique book highlights the benefits of an agent-based modelling (ABM) approach. It demonstrates how ABM can easily handle complexity: heterogeneous people, households and firms interacting dynamically. Unlike traditional methods, ABM dus not require people or firms to optimise or economic systems to reach equilibrium. ABM offers a way to link micro foundations directly to the macro situation. Key features: -Introduces the concept of agent-based modelling and shows how it differs from existing approaches.-Provides a theoretical and methodological rationale for using ABM in economics, along with practical advice on how to design and create the models.-Each chapter starts with a short summary of the relevant economic theory and then shows how to apply ABM.-Explores both topics covered in basic economics textbooks and current important policy themes; unemployment, exchange rates, banking and environmental issues.-Describes the models in pseudocode, enabling the reader to develop programs in their chosen language.-Supported by a website featuring the NetLogo models described in the book. Agent-based Modelling in Economics provides students and researchers with the skills to design, implement, and analyze agent-based models. Third year undergraduate, master and doctoral students, faculty and professional economists will find this book an invaluable resource.

This book treats three planning problems arising in public railway transportation planning: line planning, timetabling, and delay management, with the objective to minimize passengers' travel time. While many optimization approaches simplify these problems by assuming that passengers' route choice is independent of the solution, this book focuses on models which take into account that passengers will adapt their travel route to the implemented planning solution. That is, a planning solution and passengers' routes are determined and evaluated simultaneously. This work is technically deep, with insightful findings regarding complexity and algorithmic approaches to public transportation problems with integrated passenger routing. It is intended for researchers in the fields of mathematics, computer science, or operations research, working in the field of public transportation from an optimization standpoint. It is also ideal for students who want to gain intuition and experience in doing complexity proofs and designing polynomial-time algorithms for network problems. The book models line planning, timetabling, and delay management as combined design and routing problems on networks. In a complexity analysis, the border between NP-hard and polynomially solvable problems is illustrated. Based on that, the insights gained are used to develop solution approaches for the considered problems. Besides integer programming formulations, a heuristic method iterating planning and routing steps is proposed to solve the problems.

This book provides a complete framework of long-term financial forecasts in a practical and accessible way, helping finance professionals include uncertainty in their planning and budgeting process. With thorough coverage of financial statement simulation models and clear, concise implementation instruction, it guides readers through the entire projection plan development process. Readers learn the tools, techniques, and special considerations that increase accuracy and smooth the workflow, and develop a more robust analysis process that improves financial strategy. You will develop long-term projection plans using Excel; use appropriate models to develop a more proactive strategy; apply risk and uncertainty projections more accurately; master the Excel Scenario Manager, Sensitivity Analysis, Monte Carlo Simulation, and more. --

Three models of relative mass flows of water and sugar concerning crystallizing and centrifuging of A massecuite are presented. The input data for the calculation of particular flow volumes were the dry substance content wDS and sucrose content wS values measured in them during the sugarbeet campaign in one Polish beet sugar factory. These values, along with authors' own knowledge and technological charts, provided the authors with the basis for the development of a mathematical model making possible the determination of appropriate, relative mass flows (sugar mass flow was accepted as the reference value) in a station for crystallizing and centrifuging of A massecuite. Then, an external balance model was developed to check the accuracy of the measured and of the calculated data. This model was provided with reliable data to develop a neural model. The developed and trained artificial neural network allowed for the simulation of relative water and sugar mass flows in an installation for crystallizing and centrifuging A massecuite. The results were satisfactory and the neural model developed was found to have a practical application in the simulation of the influence of particular sugar and water mass flows on the work of this installation.

The topic of this book is the development of pricing formulae for European style derivatives on assets with mean-reverting behavior, especially commodity derivatives. For this class of assets, convenience yield effects lead to mean-reversion under the risk-neutral measure. Mean-reversion in the log-price process is combined with other stochastic factors such as stochastic volatility, jumps in the underlying and the price process and a stochastic target level as well as with deterministic seasonality effects. Another focus is on numerical algorithms to calculate the Fourier integral as well as to integrate systems of ordinary differential equations

"Attempts by ecologists to establish models for predicting the growth of a population or the fluctuations of a natural resource can be confounded by environmental heterogeneity. Spatio-Temporal Heterogeneity explores a range of available statistical methods to help ecologists in the attempt to unravel complexities, demonstrating how to place these changes into an understandable statistical framework. It addresses several key questions, including how to interpret the parameters of statistical models in relation to the biological and environmental realities, how to design a study to collect the best sample data and how to avoid pitfalls in modelling, design, statistical assessment and interpretation. Dutilleul uses a variety of examples to facilitate understanding, from plant ecology, earth and atmospheric sciences, animal biology, forestry and limnology. The accompanying CD-ROM contains MATLAB and SAS codes to aid analyses"--

Abstract
In this paper, we analyse the simplest possible three-dimensional model of endogenous growth to account for the relationship between financial intermediation and economic growth. In our setting, households maximize an interim utility function and firms maximize profit. Households can save money only through banks which offer firms investment loans. We show that under very general assumptions, investments realized by firms depend not only on savings accumulated by banks but also on financial intermediation technology ϕ(θ). Using mathematical methods of dynamical systems, we found stationary states of the system and study their stability.

Classical game theory is one of the basic methods of scientific analysis of political phenomena. The models developed on this basis are used in the studies of electoral and legislative behaviour, in the analysis of processes of forming political coalitions, and in the analysis of issues related to democratization, national security and armed conflicts. Evolutionary game theory has developed from classical game theory. This theory is referred to in this article, which presents selected possibilities of using single-population evolutionary models in studies of political violence transmission. On the basis of the analysis of two population variants, the article describes the changes in the prevalence of selected behavioural traits and answers the questions regarding the asymptotic states of evolutionary processes and their stability. The study uses Hawk–Dove and Hawk–Dove–Retaliator type games. The calculations were carried out using the R program.