Sem 3 UAB Stochastic

Sem 3 UAB Stochastic

Applications  @  UAB  30 ECTS credits

Stochastic modelling and optimization

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.

Probability and Stochastic Processes [6 credits]

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

     

    This is a course in basic stochastic processes. Many systems evolve over time with an inherent amount of randomness. The purpose of this course is to develope and analyse probability models that capture the features of the system under study to predict the short and long term effects that this randomness will have on the system under consideration.

  • Topics

     

    Bernoulli Processess, random walks; Discrete-time Markov chains; Reneval theory; Poisson point processes; Brownian motion

  • 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.

Data Visualisation and Modeling [6 credits]

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

     

    This 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 course provides the basic tools of the analysis of a time series in the time domain.

  • Topics

     

    Smoothing and filtering of time series; Stationary processes; ARIMA Models I; ARIMA Models II; Diagnostic checking and forecasting; Categorical and discrete time series.

  • Books

    P.J. Brockwell, R.A. Davis (2002): "Introduction to Time Series and Forecasting". Second Edition. Springer.

    P.J. Brockwell, R.A. Davis (1991): "Time Series. Theory and Methods". Springer-Verlag.

    N. H. Chan (2002): "Time Series. Applications to Finance". Wiley.

    Shumway, Robert H (2006). "Time Series Analysis and its Applications: with Rexamples". Springer Series in Statistics.

    Bloomfield, P. (2000). "Fourier Analysis of Time Series", Wiley.

    Brockwell, P. J. and Davis, R. A. (1996) "Introduction to Time Series and Forecasting", Springer, Berlin.

    Brockwell, P. J. and Davis, R. A. (1991) "Time Series: Theory and Methods", 2nd. Edit., Springer, Berlin.

Combinatorial optimisation [6 credits]

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

     

    This course is an introduction to Combinatorial Optimisation at the first-year graduate level. We will also cover and review some important aspects of Linear and Integer Optimisation at the start

  • Topics

     

    Linear Optimisation, Integer Optimisation, Graph and Network Optimisation, Complexity Theory and Heuristics

  • 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.

Simulation of Logistic Systems [6 credits]

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

     

    This subject seeks to introduce the decision making activity in the production and logistic field. This subject will introduce the students to analyze the cause-effect relationship between the elements that determine system behavior, and design mechanism to avoid the propagation of perturbation through the whole system.

  • Topics

     

    Introduction to Flexible manufacturing systems; Discrete event system modeling; Statistic models in simulation; Discrete event system simulation and decision making in the logistic field.

  • 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.

Workshop of Mathematical Modelling [6 credits]

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

     

    The Mathematical Modelling Workshop is aimed and analyzing and solving real-world problems by means of mathematics. It has a very practical and interdisciplinary character

  • Topics

     

    The main part of the workshop is a project to be developed by the students, organised in teams. Besides, the workshop will include also a few lessons about general ideas and techniques, as well as about illustartive examples.

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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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