The rise of the Internet and the ubiquity of electronic devices has deeply changed our way of life. Many face to face and paper transactions have nowadays digital counterparts: home banking, e- commerce, e-voting, etc. The security of such transactions is ensured by the means of cryptographic protocols. While historically the main goals of protocols were to ensure confidentiality and authentication the situation has changed. The ability of people to stay connected constantly combined with ill-conceived systems seriously threatens people’s privacy. E-voting protocols need to guarantee privacy of votes, while ensuring transparency of the voting process; RFID and mobile telephone protocols have to guarantee that people cannot be traced. Moreover due to viruses and malware, personal computers and mobile phones must not be considered anymore to be trustworthy; yet they have to be used to execute protocols that need to achieve security goals. To detect flaws, prove the security of protocols and propose new design principles the Spooc project will develop solid foundations and practical tools to analyze and formally prove security properties that ensure the privacy of users as well as techniques for executing protocols on untrusted platforms. We will - develop foundations and practical tools for specifying and formally verifying new security properties, in particular privacy properties; - develop techniques for the design and automated analysis of protocols that have to be executed on untrusted platforms; - apply these methods in particular to novel e-voting protocols, which aim at guaranteeing strong security guarantees without need to trust the voter client software. The Spooc project will significantly advance formal verification of security protocols and contribute to the development of a rich framework that provides techniques and tools to analyze and design security protocols guaranteeing user’s privacy and relaxing trust assumptions on the execution platforms.

Neurological disorders such as epilepsy (affecting about 5 MILL people worldwide) are associated with deviations from the optimal network structure and dynamics. Epilepsy surgery (costing 1000-3000 EUR per surgery in EU countries) consists in the removal of the minimum amount of tissue needed to stop seizure propagation, but it is only successful in aprox. 2/3 of the cases. Analyses of brain network structure, and computational studies simulating seizure dynamics over it, have related aspects of the patients' brain network (e.g. hub distribution, excitability) with surgery outcome. However, results are not always replicable, and have not been able to surpass the current clinical standard. In the MENTE (which stands for "mind" in Spanish) project, I will explicitly consider the previously neglected effect of high-order (HO) brain structure on seizure dynamics and epilepsy surgery. I will characterize the HO brain structure of epilepsy patients (via Topological Data Analysis), in relation to surgery outcome. I will then create a HO computational model of seizure dynamics, by extending pairwise multiscale (MS) neuronal models of ictal activity. I will study the emergent behavior of the system via theoretico-computational analysis to characterize the healthy-to-ictal transition. Finally, I will fit the model to intracranial EEG data of ictal activity, and use it to model epilepsy surgery, with the goal of predicting surgery outcome and finding alternative resection strategies (smaller of with better outcome), to reduce the societal and economical burden of epilepsy. MENTE will validate the role of HO coupling on brain activity and promote the theoretico-computational modeling, analysis and application to neuroscience of network dynamics including HO and MS coupling. The fellowship will strengthen mine and the host's expertise these topics, and allow me develop my academic career to the point of scientific maturity.

Waves propagating through a complex medium provide a non-invasive way to probe its interior structures. In ambient noise imaging, the input data are the cross-correlation of the stochastic wavefields. To reconstruct the properties of the medium, the waveform inversion is formulated as an optimization problem involving a misfit function whose convexity plays a critical role in the achievable spatial resolution of the inversion results, especially in the absence of a priori information about the medium. Current inversions are often limited by computational cost, cross-talk between the physical quantities, and the use of single-scattering approximations. Project INCORWAVE proposes to create a new mathematical and computational framework for nonlinear inversion of full waveform cross-correlation. Two specific problems are considered: first, for the reconstruction of geophysical visco-elasticity tensors with applications to Earth's subsurface monitoring; secondly, for the reconstruction of three-dimensional flows in the Sun to characterize the poorly understood properties of deep solar convection. To improve the convexity of misfit functions, the inversion procedure of project INCORWAVE will follow a hierarchical progression which is established by selecting subsets of input data, unknown parameters, and frequencies. The choice of each of these subsets, as well as the associated misfit function, is controlled by criteria in form of convergence estimates. Indispensable to meaningful inversion is accurate modeling operators that describe the physics under consideration and that are adapted to the treatment of real data. For the reconstruction of the elasticity tensor, the project will develop a solver in terms of P- and S-potentials for heterogeneous media. A 3D global Sun vector-wave solver is created for the inversion of the convection component of the solar flow that does not bear symmetry.