MathMods :: Joint MSc

Sem3 UAB Stochastic

Sem3 UAB Stochastic

Applications  @  UAB  30 ECTS credits

Stochastic modelling and optimisation

From the curriculum of the Barcelona (UAB) partner, "Stochastic Modelling and Optimisation", students will learn how to model real systems in which randomness plays a significant role, and how to deal with situations in which a best alternative is sought among many feasible possibilities. Sometimes, both these features are present. Frequently, the best solution of a complex optimisation problem is impossible to be found exactly, and the realistic goal is to seek a suboptimal solution that can be attained in a reasonable time. Also, the random elements of a system are often introduced intentionally so as to disregard features which would make the model too complicated. One of the main objectives is to highlight this sort of compromise when it comes to solving a real world problem. Competence in designing algorithms and using existing standard software in these fields is essential. But at the same time we will try to ensure that the students get as solid as possible a theoretical background. After this semester, the students should be able to: join industrial R+D departments or laboratories, where the modelling of experimental data or the improvement of products and processes are the goal; enrol in general engineering consulting enterprises; or pursue studies in mathematics applied to finance, econometrics, networking, logistics, etc.

 

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

  • Combinatorial optimisation [6 credits]

    Combinatorial optimisation

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      To study the paradigmatic problems (routing, networking, scheduling, etc) that lead to discrete and combinatorial optimisation models, and that are intrinsically difficult in practice due to its high input size. To introduce the modern metaheuristics for approximating the solutions of such problems.

    • Topics

       

      Combinatorial Algorithms. Computational Complexity. Genetic Algorithms. Simulated Annealing. Ant Colony Optimisation. Neural networks in optimisation. Scheduling Problems.

    • Books

       

      G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, M. Protasi, "Complexity and Approximation".
      Springer Verlag, 1999.

      Sniedovich, M. (2006), "Dijkstra’s algorithm revisited: the dynamic
      programming connexion Journal of Control and Cybernetics/ *35* (3): 599–620.

      Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L,
      "Introduction to Algorithms" (first edition ed.). MIT Press and McGraw-Hill.

      Judea Pearl, "Heuristics: Intelligent Search Strategies for Computer
      Problem Solving", Addison-Wesley Pub (Sd) 1984.


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  • Probability and stochastic processes [6 credits]

    Probability and stochastic processes

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      The main goal is to provide powerful tools to deal with the analysis and numerical simulations of stochasticity both for systems affected by external noise or by internal noise. Applications to ecological or biological systems will be discussed in detail.

    • Topics

       

      Probability spaces. Stochastic processes. Markov processes. Microscopic description with stochastic differential equations. Mesoscopic description with the master equation and diffusions. Anomalous diffusions. Simulation of stochastic processes. 

    • Prerequisites

       

      Basic properties of measures, the integral with respect to Lebesgue measure, Lebesgue measure, sigma-algebras.

    • Books

       

      [1] R.M. Dudley. Real Analysis and Probability. Cambridge studies in advanced mathematics 74, 2002.
      [2] E. Hewitt and K. Stromberg, Real and Abstract Analysis. 1991. Springer.
      [3] W. Feller. An Introduction to Probability Theory and Its Applications. John Wiley & Sons, Inc, 1968.
      [4] P.G. Hoel, S.C. Port and C.J. Stone. Introduction to Probability Theory. Houghton Miin Company, 1971.
      [5] H.-H. Kuo. Introduction to Stochastic Integration. Springer, 2006.
      [6] D.C. Montgomery and G.C. Runger. Applied Statistics and Probability for Engineers. John Wiley & Sons, Inc., 2003.
      [7] S.H. Ross. Introduction to Probability Models. Academic Press, 2007.
      [8] H.L. Royden. Real Analysis. Third Edition. 1988. Prentice-Hall. Inc.
      [9] M. Sanz i Solé. Probabilitats. 1999. Universitat de Barcelona.
      [10] A.N. Shiryaev. Probability. 2000. Springer.
      [11] D. Williams. Probability with Martingales. Cambridge Mathematical Textbooks, 1991.


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  • Workshop of mathematical modelling [6 credits]

    Workshop of mathematical modelling

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      In-depth analysis of case studies, practice of working team dynamics, and development of presentation abilities. The problems will be illustrative of several application fields as well as of the different types of model. The case studies will not necessarily fit only into the category of stochastic or optimisation models.

    • Topics

       

      Mathematical modelling is a problem-driven task. Its methodology is quite generic and revolves around the so-called mathematical modelling cycle: 1: Analysis, simplification, representation; 2: Mathematical treatment; 3: Interpretation; 4: Validation, error estimation, refinement. The main activity of the workshop is a project to be developed by the students, organised in teams. The project tries to simulate the situation of an interdisciplinary team that has been hired by a company. Besides, the workshop could include also some talks about general ideas, techniques and illustrative examples.


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Pick 2 units from

  • Data visualisation and modelling [6 credits]

    Data visualisation and modelling

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      To learn the methodologies of data simulation, bootstrapping and permutation testing, that allow a fast solution to complex statistical models without deep knowledge of classical statistical topics. Introduce Bayesian networks as graphical structures for representing probabilistic relationships among many variables and for doing inference.

    • Topics

       

      Introduction to the R language. Permutation tests. Jackknife. Parametric and non-parametric bootstrap. Causal networks and inference in Bayesian networks. Learning Bayesian network parameters.


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  • Parallel programming [6 credits]

    Parallel programming

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      To identify the difficulties related to parallel programming. To apply an adequate methodology for the development of parallel applications. To understand the different approaches: shared memory, message passing. To evaluate parallel application performance and tune for performance improving.

    • Topics

       

      Introduction to parallelisation. Programming in the C language. OpenMP programming. CUDA. MPI programming.


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  • Research and innovation [6 credits]

    Research and innovation

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      The aim of this module is to widen the perception of the student concerning the landscape of applications of scientific modelling. It will be based on short courses and talks on specific topics.

    • Topics

       

      There are two type of activities in this module: A) Three mini-courses on topics that can be of direct applications (example: Numerical Weather Forecasting), methodology oriented (example: Metaheuristics in Search), or of instrumental nature (example: Open Access Data). B) One-hour talks by specialists in the areas of Complex Systems, Engineering Modelling, Mathematical Modelling, and Data Science, coming from research centers and private big companies.


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  • Simulation of logistic systems [6 credits]

    Simulation of logistic systems

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      To study the simulation techniques as a tool to draw conclusions when the real systems cannot be checked directly, or modelled more precisely, or when the output measures of interest are too hard to compute. Common problems in industrial logistics is the driving applied theme.

    • Topics

       

      Introduction to flexible manufacturing. Modelling of systems oriented to discrete events: Petri nets and coloured Petri nets. Statistical models for simulation. Simulation of systems oriented to discrete events. Management of shared resources. Heuristic techniques.

    • Books

      N.Viswanadham,Y. Narahari. Performance Modeling of Automated Manufacturing Systems. Prentice Hall, 1992.


      Merkuryev, Merkureva, Guasch, Piera: Simulation-Based Case Studies in Logistics: Education and AppliedResearch. Springer London. 2009.


      M.A. Piera, T.Guasch, J. Casanovas, J.J. Ramos. Cómo Mejorar la Logística de su Empresa Mediante la Simulación. Ed. Diaz De Santos. 2006.


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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

Hamburg University of Technology, Germany (TUHH)

Institute of Mathematics
Schwarzenberg-Campus 3, Building E-10
D-21073 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

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