Unlinking information from 4-manifolds

We generalise theorems of Cochran-Lickorish and Owens-Strle to the case of links with more than one component. This enables the use of linking forms on double branched covers, Heegaard Floer correction terms, and Donaldson's diagonalisation theorem to complete the table of unlinking numbers for nonsplit prime links with crossing number nine or less.Comment: 18 pages, 2 figures. V2: Improved exposition incorporating referee's suggestions. Accepted for publication in Bull. London Math. So

Concordance group of virtual knots

We study concordance of virtual knots. Our main result is that a classical knot K is virtually slice if and only if it is classically slice. From this we deduce that the concordance group of classical knots embeds into the concordance group of long virtual knots

Multivariable signatures, genus bounds and 0.50.5-solvable cobordisms

We refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the 4-genus having their origins in the Murasugi-Tristram inequality, and at the same time extends previously known results about concordance invariance of the signature to a bigger set of allowed variables. Finally, we show that the multivariable signature and nullity are also invariant under $0.5$-solvable cobordism.Comment: 41 pages, 3 figure

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure

Analysis of adhesive and repulsive functions of FLRT proteins in central nervous system development

Fibronectin-leucine-rich-repeat-transmembrane proteins (FLRTs) are a family of three single pass transmembrane proteins with extracellular leucine rich repeats and a short intracellular domain of largely unknown function. They are broadly expressed in the developing and adult nervous system as well as in other tissues. FLRTs have been implicated in a variety of different developmental processes mainly via two functions: as homophilic cell adhesion molecules, and as repulsive ligands for Unc5-positive cells. Furthermore, they can regulate cell adhesion via control of surface expression of C Cadherin and are involved in FGF signaling. Previously we found that all FLRTs are localized to synapses in the mouse brain and thus investigated a potential involvement of FLRTs in synapse formation. However, using different in vitro and in vivo approaches ranging from HEK293 cell-neuron coculture assays to ultrastructural analysis of synapse density in FLRT3 knock-out mouse brains, I did not find any evidence for an involvement of FLRTs in synapse development. This is in contrast to published results but can be explained by differences in the experimental approaches and timing of the experiments. In collaboration with structural biologists we solved the crystal structure of the FLRT and Unc5 extracellular domains and a complex of both, to gain insight into the structural basis of the adhesive and repulsive functions of FLRTs. We found that homophilic FLRT FLRT and heterophilic FLRT-Unc5 interactions both occur via the FLRT LRR domain but at distinct structural surfaces. Thus, the interactions can be uncoupled. Based on the structural results we developed FLRT and Unc5 glycosylation mutants that specifically inhibit FLRT-FLRT or FLRT-Unc5 interaction and validated them in vitro. I then used these mutants in in utero electroporation experiments to prove that the repulsive effect of Unc5D overexpression in radially migrating neurons that was discovered previously is indeed, at least partially, mediated by FLRT2. Furthermore I found that overexpression of FLRTs inhibits radial migration of cortical pyramidal neurons and this effect is dependent on FLRT-FLRT homophilic interaction and the FLRT intracellular domain but independent of FLRT-Unc5 binding. In summary, the work presented here provides new insights into adhesive and repulsive functions of the FLRT family of proteins in the regulation of cell migration during cortical development