Abstract: Optimal control theory allows us to choose control functions in a dynamical system to achieve a certain goal.
The theory generalizes that of the classical calculus of variations
and has found many applications in engineering, physics, economics, and life sciences. In 1996/97, motivated by
nonconservative physical processes in mechanics, the subject was extended to the case in which derivatives and integrals
are understood as fractional operators of arbitrary order.
In this talk, we begin with a brief survey of main results and techniques of the fractional variational calculus and fractional optimal control. We consider problems containing Caputo derivatives and review both indirect and direct methods. We end our talk giving emphasis to applications and to the direct approach, which allow us to model and investigate complex systems.
Abstract: The advent of the Internet Of Things has made a huge contribution to improving the human life from all aspects from Health to Industrial challenges.
With the widespread of such technology we have opened ourselves to bigger security challenges which are compromising the reasons why we have implemented IoT in the first place.
Combined with AI the IoT devices will be able to adapt and react and make decisions based on environmental changes as well as security risks and take adequate measures to self-heal. At the same time the number of hacking attacks will increase du to the use of AI which in the wrong hands can be used to block/compromise or send false status to the central application rendering the IoT device a weapon of damage rather than control.
Abstract: In the first part of this talk, we collect some definitions and preliminary results about fractional derivatives. Secondly, an SIR spatio-fractional time epidemic system involving the ABC (Atangana-Baleanu-Caputo) fractional time derivative is formulated with no-flux boundary conditions. Immunity is forced through vaccine distribution considered a control variable. Existence of an optimal control that minimizes the number of infected individuals and the costs associated with vaccination is proved. Then, necessary optimality conditions are obtained. Finally, numerical simulations verifying that the proposed control strategy provide significantly results are illustrated.
Cryptography is used to strengthen the security of financial institutions, online communication, and sensitive data.
However, most of the widely used cryptosystems will be completely broken once large quantum computers are commercially available.
As a consequence, for security reasons, there is a need to make information systems quantum resistant.
To this end, the National Institute of Standards and Technology (NIST) is organising an international competition to standardise post-quantum cryptographic schemes.
In this talk, we present the main mathematical techniques and hard problems that are used to build post quantum cryptosystems. This includes code-based cryptography, lattice cryptography and multivariate cryptography.
The hydrostatic approximation of the Navier-Stokes equations is a general nonlinear system
of PDEs model widely used in oceanography for the study of the circulation of water in large portions of oceans or lakes.
In this presentation, we will be interested in the analysis of certain variants of the steady-state of this model.
Some numerical simulations based on the hydrostatic approximation will also be shown.
La physique quantique est une branche fascinante du savoir.
Elle fournit un cadre de réflexions en dehors du sens commun capables d'apporter des interprétations des phénomènes à l'échelle infiniment petite du monde matériel.
Plusieurs disciplines sont fortement stimulées à la base de cette physique quantique dont nous citons à titre non exhaustif l'information quantique, la cryptographie ainsi que la géométrie non commutative.