ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Cell-selective modulation of the neuromuscular system in Drosophila

The capacity for all living cells to sense and interact with their environment is a necessity for life. In highly evolved, eukaryotic species, like humans, signalling mechanisms are necessary to regulate the function and survival of all cells in the organism. Synchronizing systemic signalling systems at the cellular, organ and whole-organism level is a formidable task, and for most species requires a large number of signalling molecules and their receptors. One of the major types of signalling molecules used throughout the animal kingdom are modulatory substances (e.x. hormones and peptides). Modulators can act as chemical transmitters, facilitating communication at chemical synapses. There are hundreds of circulating modulators within the mammalian system, but the reason for so many remains a mystery. Recent work with the fruit fly, Drosophila melanogaster demonstrated the capacity for peptides to modulate synaptic transmission in a neuron-specific manner, suggesting that peptides are not simply redundant, but rather may have highly specific roles. Thus, the diversity of peptides may reflect cell-specific functions. The main objective of my doctoral thesis was to examine the extent to which neuromodulator substances and their receptors modulate synaptic transmission at a cell-specific level using D. melanogaster. Using three different modulatory substances, i) octopamine - a biogenic amine released from motor neuron terminals, ii) DPKQDFMRFa - a neuropeptide secreted into circulation, and iii) Proctolin - a pentapeptide released both from motor neuron terminals and into circulation, I was able to investigate not only the capacity of these various substances to work in a cell-selective manner, but also examine the different mechanisms of action and how modulatory substances work in concert to execute systemic functionality . The results support the idea that modulatory substances act in a circuit-selective manner in the central nervous system and in the periphery in order to coordinate and synchronize physiologically and behaviourally relevant outputs. The findings contribute as to why the nervous system encodes so many modulatory substances.