An atomic cross-chain swap is a distributed coordination task where multiple parties exchange assets across multiple blockchains, for example, trading bitcoin for ether. An atomic swap protocol guarantees (1) if all parties conform to the protocol, then all swaps take place, (2) if some coalition deviates from the protocol, then no conforming party ends up worse off, and (3) no coalition has an incentive to deviate from the protocol. A cross-chain swap is modeled as a directed graph D, whose vertexes are parties and whose arcs are proposed asset transfers. For any pair (D,L), where D=(V,A) is a strongly-connected directed graph and L⊂V a feedback vertex set for D, we give an atomic cross-chain swap protocol for D, using a form of hashed timelock contracts, where the vertexes in L generate the hashlocked secrets. We show that no such protocol is possible if D is not strongly connected, or if D is strongly connected but L is not a feedback vertex set.

How does the Brain give rise to the Mind? How do neurons and synapses, molecules and genes, ​​evolution and development, give rise to behavior and cognition, language and intelligence? Despite lightning progress in recording and molecular technology and a deluge of experimental data, we do not seem to get closer to an answer. This is a talk about admiring and appreciating the problem, and proposing a new approach based on a recognized but little studied intermediate level of Brain computation carried out by the synchronous firing of large and highly interconnected sets of neurons called assemblies. We show that assemblies give rise to a novel computational system, and we speculate that they may instrument higher cognitive functions, such as language and math.

A dynamic graph algorithms is a data structure that maintains a property of a graph while it is modified by edge insertions and deletions. The last few years have seen exciting new developments in dynamic graph algorithms, namely strong conditional lower bounds and dynamic algorithm based on the primal-dual approach.