In connection with the so-called Hurwitz action of homeomorphisms in ramified covers we define a groupoid, which we call a ramification groupoid of the 2sphere, constructed as a certain path groupoid of the universal ramified cover of the 2-sphere with finitely many marked-points. Our approach to ramified covers is based on cosheaf spaces, which are closely related to Fox’s complete spreads. A ...

The original formulation of SharedPlans (Grosz and Sidner, 1990a) was developed to provide a model of collaborative planning in which it was not necessary for one agent to have intentions-to toward an act of a di erent agent. Unlike other contemporaneous approaches (Searle, 1990), this formulation provided for two agents to coordinate their activities without introducing any notion of irreducib...

Let R be a discrete valuation ring with fraction field K, uniformizer π and residue field k of characteristic p > 0. Let XK be a flat K-scheme of finite type endowed with a faithful action of a finite group scheme G. Given an R-model X to which the action extends, it may happen that the reduced action on the special fibre acquires a kernel, especially if p divides |G|. Typically, this happens i...

Let U( ) be the enveloping algebra of a semi-simple Lie algebra . Very little is known about the nature of AutU( ). However, if G is a finite subgroup of AutU( ) then very general results of Lorenz-Passman and of Montgomery can be used to relate SpecU( ) to SpecU( ). As noted by Alev-Polo one may read off the Dynkin diagram of from SpecU( ) and they used this to show that U( ) could not be agai...

Joyal’s theory of combinatorial species provides a rich and elegant framework for enumerating combinatorial structures by translating structural information into algebraic functional equations. We also extend the theory to incorporate information about “structural” group actions (i.e. those which commute with the label permutation action) on combinatorial species, using the Γ-species of Henders...

Many public-key cryptosystems depend on the difficulty of solving a few specific problems such as finding the prime factorization of a composite number and the discrete logarithm problem. While the existing systems depending on the hardness of these problems are considered secure, there is still deep concern about the security of these systems. Shor [8]invented a fast algorithm for prime factor...

In this paper we investigate the possible states of knowledge among a group of individuals and their relations to decision making. A travelling salesman found himself spending the night at home with his wife when one of his trips was accidentally cancelled. The two of them were sound asleep, when in the middle of the night there was a loud knock at the front door. The wife woke up with a start ...