A core calculus for the analysis and implementation of biologically inspired languages

The application of Concurrency Theory to Systems Biology is in its earliest stage of progress. The metaphor of cells as computing systems by Regev and Shapiro opened the employment of concurrent languages for the modelling of biological systems. Their peculiar characteristics led to the design of many bio-inspired formalisms which achieve higher faithfulness and specificity. In this thesis we present pi@, an extremely simple and conservative extension of the pi-calculus representing a keystone in this respect, thanks to its expressiveness capabilities. The pi@ calculus is obtained by the addition of polyadic synchronisation and priority to the pi-calculus, in order to achieve compartment semantics and atomicity of complex operations respectively. In its direct application to biological modelling, the stochastic variant of the calculus, Spi@, is shown able to model consistently several phenomena such as formation of molecular complexes, hierarchical subdivision of the system into compartments, inter-compartment reactions, dynamic reorganisation of compartment structure consistent with volume variation. The pivotal role of pi@ is evidenced by its capability of encoding in a compositional way several bio-inspired formalisms, so that it represents the optimal core of a framework for the analysis and implementation of bio-inspired languages. In this respect, the encodings of BioAmbients, Brane Calculi and a variant of P Systems in pi@ are formalised. The conciseness of their translation in pi@ allows their indirect comparison by means of their encodings. Furthermore it provides a ready-to-run implementation of minimal effort whose correctness is granted by the correctness of the respective encoding functions. Further important results of general validity are stated on the expressive power of priority. Several impossibility results are described, which clearly state the superior expressiveness of prioritised languages and the problems arising in the attempt of providing their parallel implementation. To this aim, a new setting in distributed computing (the last man standing problem) is singled out and exploited to prove the impossibility of providing a purely parallel implementation of priority by means of point-to-point or broadcast communication.

Parallel modeling of the electric field distribution in the brain

The term "Brain Imaging" identi�es a set of techniques to analyze the structure and/or functional behavior of the brain in normal and/or pathological situations. These techniques are largely used in the study of brain activity. In addition to clinical usage, analysis of brain activity is gaining popularity in others recent �fields, i.e. Brain Computer Interfaces (BCI) and the study of cognitive processes. In this context, usage of classical solutions (e.g. f MRI, PET-CT) could be unfeasible, due to their low temporal resolution, high cost and limited portability. For these reasons alternative low cost techniques are object of research, typically based on simple recording hardware and on intensive data elaboration process. Typical examples are ElectroEncephaloGraphy (EEG) and Electrical Impedance Tomography (EIT), where electric potential at the patient's scalp is recorded by high impedance electrodes. In EEG potentials are directly generated from neuronal activity, while in EIT by the injection of small currents at the scalp. To retrieve meaningful insights on brain activity from measurements, EIT and EEG relies on detailed knowledge of the underlying electrical properties of the body. This is obtained from numerical models of the electric �field distribution therein. The inhomogeneous and anisotropic electric properties of human tissues make accurate modeling and simulation very challenging, leading to a tradeo�ff between physical accuracy and technical feasibility, which currently severely limits the capabilities of these techniques. Moreover elaboration of data recorded requires usage of regularization techniques computationally intensive, which influences the application with heavy temporal constraints (such as BCI). This work focuses on the parallel implementation of a work-flow for EEG and EIT data processing. The resulting software is accelerated using multi-core GPUs, in order to provide solution in reasonable times and address requirements of real-time BCI systems, without over-simplifying the complexity and accuracy of the head models.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.