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This is our 2020 curriculum. For the new structure, valid as of the 2021 intake, click here

Sem3 UAQ Agent-Based for 2020 intake

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Applications  @  UAQ  30 ECTS credits

Agent-based modelling and transport phenomena

The specialization track “Agent-based modelling and transport phenomena” will take place at the University of L’Aquila. The proposed curriculum covers newly developed mathematical modelling approaches, aiming at realizing practical solutions for smart and healthy communities. UAQ has longstanding collaborations with the Imperial College of London (UK) and with the University of Muenster (Germany) on many-agent modelling and mean-field limits in several branches of social sciences such as opinion formation, emergence of collective motion, and the social behaviour of largely crowded communities (the latter also in collaboration with the Universities of Catania and Ferrara, in Italy); the UAQ team has a longstanding expertise on "nonlocal aggregation models", an emerging subject in applied mathematical research with applications in particular to the modelling of criminal behaviour in urban areas. Important achievements have been also carried out at UAQ in the area of nonlinear conservation laws with applications to traffic modeling and population dynamics.

This track has three compulsory courses: “Advanced analysis” , providing tools to deepen the understanding of advanced nonlinear models; “Mathematical fluid dynamics”, featuring advanced analytical methods on classical and modern fluid-dynamical theories; “Mathematical model for collective behavior”, presenting a selection of topics in the modeling of collective motion in social sciences and of transport modeling in real world applications, particularly in urban and behavioural sciences.

The last two courses, "Biomathematics" and "System biology" (in collaboration with the IASI-CNR institute), specialise the student on "modelling in life sciences", which has become a classic topic in modern applied mathematics. Both of them present mathematical and modeling approach via ODEs, PDEs, and multiscale modelling, in contexts arising from modern applications such as population biology, medicine, and genetics.

 

Below you can find information about the subjects for this semester.

  • Advanced analysis [6 credits]

    Advanced analysis

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      The main objectives of the course are as follows: to provide knowledge of mathematical methods that are widely used by researchers in the area of Applied Mathematics; to apply this knowledge to a variety of topics, including the basic equations of mathematical physics and some current research topics about nonlinear equations (traffic flow, gas dynamics, fluid dynamics).

    • Topics

       

      Measure and integration theory. Functions of bounded variation. Distributions theory. Fourier transform. Sobolev spaces. Application to the study of partial differential equations: elliptic equations of second order, parabolic equations of second order, hyperbolic systems of first-order equations, nonlinear conservation laws. An outline of semigroup theory.


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  • Mathematical models for collective behaviour [6 credits]

    Mathematical models for collective behaviour

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      The course will cover some mathematical models currently used in the analysis of collective phenomena, such as vehicular and pedestrian traffic, flocking phenomena. Emphasis will be given to the mathematical treatment of specific problems coming from real world applications.

    • Topics

       

      Macroscopic traffic models: LWR model, fundamental diagrams. The Riemann problem. Point-type constraints (the "Toll gate" problem). Second order models for traffic flow: Aw-Rascle model, shocks description, instabilities near vacuum. Basics on the theory of systems of conservation laws. Junction of roads, networks. Distribution rules along the roads, optimization of the flux. Solution to the Riemann problem at a junction. Pedestrian flow: normal and panic situation. Macroscopic models, conservation of "mass", eikonal equation. The Hughes model for pedestrian flow; in one space dimension: curve of turning points, Rankine-Hugoniot conditions. Macroscopic models for pedestrian flow that include: knowledge of a preferred path, discomfort from walking along walls, tendency of avoiding high densities of pedestrian in a neighborhood (nonlocal term of convolution type), angle of vision, obstacle in the domain. Introduction to the theory of flocking. Cucker-Smale model for flocking, conservation of moment and decay of the kinetic energy. Asymptotic flocking. Singular communication rate. The kinetic limit. Introduction to synchronization: Kuramoto model, basic properties.


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  • Mathematics for decision making [6 credits]

    Mathematics for decision making

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      The goal of this course is to describe some mathematical models of strategic interaction among rational decision-makers.

      We provide knowledge of the main mathematical tools of nonlinear and set-valued analysis which are crucial for studying the existence and the stability of the solutions of particular equilibrium problems such as variational and quasi-variational inequalities and non-cooperative games.

    • Topics

       

      We cover aspects of pure mathematics such as continuity notions and fixed point theorems for set-valued maps (Browder, Kakutani, Fan-Glicksberg) and we study the the existence of solutions for problems arising in behavioral and social science, among which Nash equilibria and Ky Fan minimax inequalities.


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  • Time series and prediction [6 credits]

    Time series and prediction

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      The course is an introduction to Time Series Analysis and Forecasting. The level is the first-year graduate in Mathematics with a prerequisite knowledge of basic inferential statistical methods. The aim of the course is to present important concepts of time series analysis (Stationarity of stochastic processes, ARIMA models, forecasting etc.). At the end of the course, the student should be able to select an appropriate ARIMA model for a given time series.

    • Topics

       

      Stochastic processes (some basic concepts). Stationary stochastic processes. Autocovariance and autocorrelation functions. Ergodicity of a stationary stochastic process. Estimation of moment functions of a stationary process. ARIMA models. Estimation of ARIMA models. Building ARIMA models. Forecasting from ARIMA models

    • Books

       

      Time Series Analysis Univariate and Multivariate Methods, 2nd Edition, W. W. Wei, 2006, Addison Wesley.
      Time Series Analysis, J. Hamilton, 1994, Princeton University Press.
      Time Series Analysis and Its Applications with R Examples, Shumway, R. and Stoffer, D., 2006, Springer.
      Introduction to Time Series and Forecasting. Second Edition, P. Brockwell and R. Davis, 2002, Springer.


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  • Workshop on mathematical models in social dynamics [6 credits]

    Workshop on mathematical models in social dynamics

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila

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Pick 1 sub-path

a) Modelling in Life Science

 

b) Modelling in Seismology

Home Structure for 2020 intake Sem3 UAQ Agent-Based for 2020 intake

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Our partners' addresses

University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

University of Hamburg , Germany (UHH)

Department of Mathematics
Bundesstr. 55
20146 Hamburg - Germany

University of Côte d'Azur, Nice - France (UCA)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2