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| - | Master thesis projects: 2007-2008 | + | ==== Empirical Correlation Matrices ==== |
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| - | ==== Scheduling and Information Theory for the Multiple Access Channel ==== | + | |
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| - | **Description:**\\ | + | **Description:**\\ |
| - | \\ In a multiple access system the transmitters are generally driven by independent sources generating bursty streams of packets. Information theory views multiple access as a question of combating noise and interference. The issue of bursty packet arrival is something to be dealt with appropriate source coding. On the other hand, network theory views multiple access as a question of resource allocation and distributed scheduling, but ignores the issues of noise and interference. So far, not much has been done to unify these two approaches [1]. A step in this direction is taken in [2], in this paper the authors derive a scheduling policy using an analogy between the capacity region of a multi-access channel and a multi-processor system. They show, under certain assumptions (infinite number of users, poisson arrivals), that the policy achieves an average delay close to the optimal one. | + | The estimation of correlations in a basket composed of 50 or more stocks is a major issue in finance, because of the high number of correlation coefficients (more than 1000) that need to be evaluated and the relatively small size of available time series. The idea of the project is to study various models that deal with this issue (among which the random matrix approach proposed in [1]), and to compare the performance of related investment strategies.\\ |
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| - | **Objective:** | + | |
| - | In this semester project, we propose to study the behavior of this strategy using different assumptions (e.g. average power constraint). The analysis will be done by running numerical simulations (using C programming or Matlab) and drawing simple theoretical models. \\ | + | **Prerequisites:**\\ |
| + | The student should be at ease with probability. Prior knowledge | ||
| + | of stochastic calculus is a plus.\\ | ||
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| - | **Prerequisites:** | ||
| - | \\ | + | **References:**\\ |
| - | **References:** | + | [1] M. Potters, J.-P. Bouchaud and L. Laloux, |
| + | "Financial Applications of Random Matrix Theory: Old Laces and New Pieces", | ||
| + | arXiv:physics/0507111\\ | ||
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| - | [1] A. Ephremides, B. hajek,"Information theory and communication networks: An unconsummated union", IEEE Trans. on Information Theory, vol.44, no 6, 1998, pp. 2416-2434. | + | **Supervisor:**\\ |
| - | [2] S. Bhaskaran, E. Telatar, D. Tse, "Job scheduling and multiple access", Dimacs Series in Discrete Mathematics and Theoretical Computer Science, 2003.\\ | + | Olivier Lévêque (LTHI) * Email: olivier.leveque#epfl.ch * Office: INR-132 * tel: 38112\\ |
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| - | **Contact:** | + | |
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| - | Stéphane Musy (LTHI) * Email: stephane.musy@epfl.ch * Office: INR-140 * tel: 3 6604\\ | + | |
| - | [[en:projects:2007-2008:mtp|back to master thesis projects]] | + | [[en:projects:masterthesis:mtp|back to master projects]] |