Characterising Computational Devices with Logical Systems

In this thesis we shall present and develop the concept of a theory machine. Theory machines describe computation via logical systems, providing an overarching formalism for characterising computational systems such as Turing machines, type-2 machines, quantum computers, infinite time Turing machines, and various physical computation devices. Notably we prove that the class of finite problems that are computable by a finite theory machine acting in first-order logic is equal to the class Turing machine computable problems. Whereas the class infinite problems that are computable by a finite first-order theory machine is equal to the class type-2 machine computable problems. A key property of a theory machine computation is that it does not have to occur in a causally ordered manner. A consequence of this fact is that the class of problems that are computable by finite first-order theory machine in polynomial resources is equal to $NP \cap co-NP$. Since there are problems which appear to lie in $NP \cap co-NP \setminus P$ that are efficiently solvable by a quantum computer (such as the factorisation problem), this gives weight to the argument that there is an atemporal/non-causal component to the apparent speed-up offered by quantum computers

Physical Computation, P/poly and P/log*

In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities in polynomial time are equivalent to P/poly. We then extend our framework to describe how measurement and transformation times may vary depending on their input. Finally we describe two classes of classical "physical" computation systems in this new framework whose computational capabilities in polynomial time are equivalent to P/poly and P/log*

The potential of liquid marbles for biomedical applications: a critical review

Liquid marbles (LM) are freestanding droplets covered by micro/nanoparti- cles with hydrophobic/hydrophilic properties, which can be manipulated as a soft solid. The phenomenon that generates these soft structures is regarded as a different method to generate a superhydrophobic behavior in the liquid/ solid interface without modifying the surface. Several applications for the LM have been reported in very different fields, however the developments for bio- medical applications are very recent. At first, the LM properties are reviewed, namely shell structure, LM shape, evaporation, floatability and robustness. The different strategies for LM manipulation are also described, which make use of magnetic, electrostatic and gravitational forces, ultraviolet and infrared radiation, and approaches that induce LM self-propulsion. Then, very distinc- tive applications for LM in the biomedical field are presented, namely for diagnostic assays, cell culture, drug screening and cryopreservation of mam- malian cells. Finally, a critical outlook about the unexplored potential of LM for biomedical applications is presented, suggesting possible advances on this emergent scientific area. The authors acknowledge funding from the European Research Council grant agreement ERC-2012-ADG 20120216-321266 for project ComplexiTE. N. M. Oliveira acknowledges the financial support from Portuguese Foundation for Science and Technology - FCT (Grant SFRH/BD/73172/2010), from the financial program POPH/FSE from QREN.info:eu-repo/semantics/publishedVersio