MathMods :: Joint MSc

Sem3 UAQ-GSSI Social S.

uaq largegssi logo

Applications  @  UAQ - GSSI  30 ECTS credits

Mathematical models in social sciences

The specialization track “Mathematical models in social science” will take place at the University of L’Aquila in collaboration with the Gran Sasso Science Institute (GSSI) in 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. The crucial contribution of GSSI concerns with classical and modern topics in fluid dynamics and real analysis providing the student with a complementary expertise in advanced mathematical theory required in some of the other courses of this semester.

This track has three compulsory courses: “Advanced analysis” (in collaboration with GSSI), providing tools to deepen the understanding of advanced nonlinear models; “Mathematical fluid dynamics” (in collaboration with GSSI), 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.

Two optional sub-paths can be undertaken to complete the semester. The first one specialises the student on "modelling in life sciences", a subject sharing several methodologies with social science modeling, which has become a classic topic in modern applied mathematics. Such sub-path consists of the "Biomathematics" and "System biology" (in collaboration with the IASI-CNR institute) courses, both presenting mathematical a modeling approach via ODEs, PDEs, and multiscale modelling, in contexts arising from modern applications such as population biology, medicine, and genetics. The second sub-path is focused on "modelling in seismology", a topic of great interest for the UAQ team after the earthquake that struck the Abruzzo Region in 2009. A selection of topics mostly related with geo-dynamics and seismic wave propagation will be presented in the course "Modelling seismic wave propagation". The course "Time series and prediction" will complete this sub-path with additional expertise in statistical methods which are essential to analyse earthquake catalogues and seismic event sequences. The INGV (Italian Institute of Geophysics and Volcanology, the reference Italian public institution for seismic events) will offer its collaboration in the offer of this course. The group of Andrea Bertozzi at UCLA (associated partner) gives the opportunity for a master thesis on mathematical models for criminal behavior. The INGV will offer collaborations on research projects and thesis with impact on the seismical activity around the Abruzzo Region.

 

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

  • Advanced analysis 1 [6 credits]

    Advanced analysis 1

    • 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.

    Open this tab in a window
  • 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 is inspired to create models to reach a high level of efficiency across various sectors
in cities and communities, producing at the same time important impacts on the social cohesion.
The course will be coordinated by a mathematician but will taught by different actors from the area of ICT,
renewable energy, transport and logistics

    • Topics

       

      The course shall account for a set of multi-disciplinary concerns: elaboration of a general smart planning model; modeling and quantification of energy flows across main sectors. Intelligent energy distribution networks; ICT infrastructure design model (hybrid communication infrastructure); sustainable mobility (e.g.: via suitably adapted the classical first order models of Lighthill- Whitham-Richardson type and the second order of Aw-Rascle) and last-mile logistic; public building
monitoring and remote diagnosis; smart health.
Mathematical models for validation and large scale simulation.


    Open this tab in a window
  • Mathematical fluid dynamics [6 credits]

    Mathematical fluid dynamics

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

       

      This course is designed to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to the mathematical modeling of fluid dynamic type. At the end of the course the students will be able to perform a qualitative and quantitative analysis of solutions for particular fluid dynamics problems and to use concepts and mathematical techniques learned from this course for the analysis of other partial differential equations.

    • Topics

       

      Derivation of the governing equations: Euler and Navier-Stokes. Eulerian and Lagrangian description of fluid motion; examples of fluid flows. Vorticiy equation in 2D and 3D. Dimensional analysis: Reynolds number, Mach Number, Frohde number. From compressible to incompressible models. Existence of solutions for viscid and inviscid fluids.


    Open this tab in a window

Pick 1 sub-path

a) Modelling in Life Science

  • Biomathematics [6 credits]

    Biomathematics

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

      The aim of the course is to introduce the students to the theories and the techniques for atomistic simulations of molecular systems. At the end of the course the student will have basic concepts of the statistical mechanics and the mathematics necessary for molecular modelling as well as the tools to understand the connections between the techniques and the chemical and physical problems.

    • Topics

      ODE models. Single species population models. ODEs with delay. Dynamical systems. Multi species models: predator-prey, competition, mutualism. Models in epidemiology. SIR and XSI models. Modeling AIDS. Modelling reaction kinetics. Michaelis-Menten approach. Singular limits. PDE models. Diffusion equations. Nonlinear diffusion. Reaction diffusion equations. Threshold phenomena and travelling waves. Reaction diffusion systems. Turing instability. Models for chemotaxis. Blow-up of solutions. Models for structured populations.


    Open this tab in a window
  • Systems biology [6 credits]

    Systems biology

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

       

      Systems biology is an emerging research area, which aims to investigate mathematical models helping to understand the dynamic interactions occurring within and between cells. This course provides the mathematical tools to model and analyze gene transcription networks and focuses the attention on the case study of cell cycle modeling.

    • Topics

       

      Transcription networks. The rules of transcription: promoters and transcriptor factors, activators and repressors. Graph properties of a transcriptor network. ODE approach: dynamics of gene regulation. Network motifs emerging by comparison to randomized networks. Possible functions of network motifs in transcription networks. Methods to infer information from data: the state observer approach and application to gene transcription networks. Biological examples from the E. Coli. Cell cycle models: focus on the budding yeast. The G1/S transition: the critical size and the budding period. Heterogeneous population models and age/protein distribution functions.


    Open this tab in a window

 

b) Modelling in Seismology

  • Modelling seismic wave propagation [6 credits]

    Modelling seismic wave propagation

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

    Open this tab in a window
  • 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
      Estimatiom 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.


    Open this tab in a window
Home Program structure Semester 3 UAQ-GSSI Mathematical models in social sciences

Connect with us

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)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

University of Hamburg, Germany (UHH)

Department of Mathematics
Bundesstr. 55 20146 Hamburg - Germany

University of Nice - Sophia Antipolis, France (UNS)

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

Vienna Univ. of Technology, Austria (TUW)

Technische Universität Wien
Institute of Analysis & Scientific Computing
Wiedner Hauptstr. 8, 1040 Vienna - Austria

This web-site reflects the views only of the author, and the EU Commission cannot be held responsible for any use which may be made of the information contained therein.