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Doctoral training program in Applied Mathematics

Objectives assigned to doctoral training     

1. Description of the training (Research axes):     

Doctoral training is sponsored by the research teams of the LaMOS research unit, whose axes are described below by key words:           

1. a) Team N°1: MCO (Cybernetic Methods and Optimization)

Decision-making process in a competitive or cooperative environment, Mathematical programming, multi-criteria decision-making methods, game theory, financial mathematics, futures market, negotiation problems, clustering, bin-packing, industrial organization, transport networks, Adhoc networks, network security.         

1. b) Team N°2: SR2 (Systems with Reminders and Networks)

Queues with callbacks, Priority, Vacations, negative arrivals, Petri nets, Approximation methods, Strong stability, Performance evaluation, Stochastic comparison, stochastic decomposition     

1. c) Team N°3: CSQ (Statistical Quality Control)

        Statistical Methods, Non-Parametric Estimation.     

1. d) Team N°4: PA2 (Random Processes and Applications)

Markov chains; Disturbance terminals; Strong stability; Entropy approach; Development in Taylor series, risk models, inventory management, QDB models,…           

1. e) Team N°5: FSE2 (Reliability of Electro-Energetic Systems)

Electrical reliability, Mechanical reliability, Graph Theory, Performance evaluation, industrial systems (mechanical, computer, electrical engineering, electronics, telecommunications)     

1. f) Team N°6: OCO (Optimization and Optimal Control)

Mathematical programming, Optimization, Optimal control.     

2. Objectives related to the training of trainers:

The evolution of the number of students in the IT and operational research fields requires a strengthening (in terms of staff) of the teaching teams for quality training. Moreover, on the qualitative side, the evolution of computer science and information and decision support systems require continuous updating of knowledge in these areas. The seminars for doctoral students will be used primarily for doctoral students, but also for teaching teams to learn about the latest developments in science in fields related to the themes of doctoral training: Decision-making methods and their applications (transport, computer and communication networks, inventory management, reliability systems, etc.)     

3. Research related objectives:

 The objectives are those of the research projects selected within the framework of doctoral training, in addition to the contribution to the training of doctoral students and the promotion of the research work of the research unit through publications and international and national communications. To this list are added the following objectives:     

• Find new modeling tools that take into account as many parameters as possible describing complex systems in order to assess their current performance and to predict others in the future in the event of a variation in these parameters.
• Provide theoretical and practical means that allow us to obtain a better quality of service from these different complex systems.
• The development of new models and methods to improve, evaluate and optimize the performance of wireless channel access techniques and to optimally manage existing resources using well-adapted protocols.
• The choice of the adequate protocol which can be done according to several criteria. The simultaneous consideration of these criteria brings us back to the resolution of a multi-criteria problem. Moreover, taking into account several users (stations) wishing to transmit data highlights an interaction situation that can be modeled by game theory.
• Proposal of opportunistic routing protocols for mesh networks / VANETs. These protocols must efficiently explore the network and search for the best available paths in terms of QoS.
• Machine learning: In the presence of data, artificial intelligence methods in general and machine learning in particular can be very effective in managing bandwidth (wireless channel).
• Design statistical and valid techniques for data collection,
• Develop statistical methods for statistical inference from collected data
• Improve statistical models for future use based on these experiences.
• Development of new efficient algorithms for learning SVMs and their applications in various sectors, such as: health, economy and industry.
• Proposal of a new method for determining the efficient frontier in mean-variance portfolio management via parametric programming.
• Study the problems of bi-matrix Bayesian games and their application in finance and insurance, as well as in the field of computer security.
• Obtaining theoretical results on estimation, approximation and modeling in insurance, finance and networks allowing to answer real problems.
• Assist businesses and insurance companies in the decision-making process to avoid major losses and certain ruin.
• Better network management and security.
• Development of appropriate computer applications.