Sem 3 UAQ Life&Social

Sem 3 UAQ Life&Social

Applications  @  UAQ  30 ECTS credits

Mathematical models in life and social sciences

The curriculum proposed by L'Aquila (UAQ) partner, "Mathematical Models in Life and Social Sciences", aims to lead the student to newly developed mathematical modelling approaches, with the daring purpose of realizing smart and health communities. Over the past years at UAQ there has been a remarkable improvement of the research activity of the involved teaching staff in the target topics. In particular, UAQ has a strong collaboration with the Imperial College of London (UK) on mathematical modelling in bio-fluid-mechanics and biomechanical models arising from medicine; with DAMTP, University of Cambridge (UK), in the area of transport models in biology and ecology; with many other research institutions, private and public companies in the field of traffic models. Additionally, the contribution of the Associated Partner IASI (CNR) goes in the direction of applications to biosciences: it arises from a well established collaboration between UAQ and the Italian National Research Council (CNR).
The aim of the proposed curriculum has also strong social impact for the Abruzzi Region and L'Aquila, which have been heavily struck by the 2009 earthquake. Following a proposal submitted by the IT and the Mathematical Modelling research areas of UAQ, in 2011 the Italian Ministry of Research and Education (MIUR) approved the establishing of an important research centre in L'Aquila, the Gran Sasso Science Institute (GSSI), and the inclusion of Mathematical Modelling among its research topics . Moreover, the recent OECD – University of Groningen Forum "Abruzzo 2030: on the wings of L'Aquila" has maintained that mathematical modelling can help the rebuilding of the city of L'Aquila in the shape of a smart community.

 

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

Advanced analysis I [6 credits]

  • 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.

Biomathematics [6 credits]

  • 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.

Mathematical models for collective behaviour [6 credits]

  • 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.

Systems biology [6 credits]

  • 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.

Computer modelling and simulations of biomolecules [6 credits]

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

     

    The objective of the present course is to establish the foundations of the mathematical modelling of biological macromolecules. Students will learn the basics of the molecular structures of the molecules of life such as DNA and proteins. They will be also introduced to the mathematical methods underlying the statistical mechanics, the modelling, and the computational strategies of computer simulations of biomolecules. A practical approach to the atomistic simulations will be done through computer tutorials and exercises.

  • Topics

     

    Introduction to structural biology of proteins and nucleic acids. Molecular modelling of biomolecules. Introduction to Lagrangian and Hamiltonian mechanics. Statistical mechanics in the microcanonical and canonical ensembles. The basic algorithms of molecular dynamics simulations. Long
    range interactions. Static and dynamical properties. Monte Carlo methods.
    Practice of computer simulations of liquids and proteins using free software in linux environment.

Italian Language and Culture for Foreigners (level A2) [3 credits]

  • ECTS credits 3
  • Semester 1
  • University University of L'Aquila
  • Objectives

     

    Students will reach an elementary level of both written and spoken Italian (A2 level according to CEFR).

  • Books

     

    -Nuovo Espresso 1, Alma Edizioni, ISBN: 9788861823181

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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)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

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

Gdansk University of Technology, Poland (GUT)

Department of Solid State Physics, G. Narutowicza 11/12, 80-952 Gdansk, Poland

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

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