Saturation is (μ, κ)-transferable in T if and only if there is an expansion T1 of T with |T1| = |T | such that if M is a μ-saturated model of T1 and |M | ≥ κ then the reduct M ↾ L(T ) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (א0, λ)-transferable or (κ(T ), λ)-transferable for all λ. Further if for...

For Gibbsian systems of particles in R a, we investigate large deviations of the translation invariant empirical fields in increasing boxes. The particle interaction is given by a superstable, regular pair potential. The large deviation principle is established for systems with free or periodic boundary conditions and, under a stronger stability hypothesis on the potential, for systems with tem...

The Dirichlet form given by the intrinsic gradient on Poisson space is associated with a Markov process consisting of a countable family of interacting diiusions. By considering each diiusion as a particle with unit mass, the randomly evolving connguration can be thought of as a Radon measure valued diiusion. The quasi-sure analysis of Dirichlet forms is used to nd exceptional sets for this Mar...

We prove a version of Hrushovski's 1989 results on almost orthogonal regular types in the context of simple and superstable nitary abstract elementary classes: from a certain expression of `non-orthogonality' we can conclude the existence of a group acting on the geometry obtained on the set of realizations of a regular Lascar strong type, and if we rule out the presence of a non-classical grou...

Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for finite subgroups G of general linear groups. In the root system case, the recurrent and superstable configurations are identified explicitly and are related to ...

Origin of chaos in a simple two-dimensional map model replicating the spiking and spikingbursting activity of real biological neurons is studied. The map contains one fast and one slow variable. Individual dynamics of fast subsystem of the map is characterized by two types of possible attractors: stable fixed point (replicating silence) and superstable limit cycle (replicating spikes). Coupling...