AVERAGING PROPERTIES AND SPREADING MODELS

Averaging and Climate Models

Lattice Structures and Spreading Models

We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices and countable lattices and all finite lattices.

Bagged Averaging of Regression Models

Linear regression and regression tree models are among the most known regression models used in the machine learning community and recently many researchers have examined their sufficiency in ensembles. Although many methods of ensemble design have been proposed, there is as yet no obvious picture of which method is best. One notable successful adoption of ensemble learning is the distributed s...

Mesoscale Averaging of Nucleation and Growth Models

The aim of this paper is to derive a general theory for the averaging of heterogeneous processes with stochastic nucleation and deterministic growth. We start by generalizing the classical Johnson-Mehl-Avrami-Kolmogorov theory based on the causal cone to hetereogeneous growth situations. Moreover, we relate the computation of the causal cone to a Hopf-Lax formula for Hamilton-Jacobi equations d...

Semilattice Structures of Spreading Models

Given a Banach space X, denote by SPw(X) the set of equivalence classes of spreading models of X generated by normalized weakly null sequences in X. It is known that SPw(X) is a semilattice, i.e., it is a partially ordered set in which every pair of elements has a least upper bound. We show that every countable semilattice that does not contain an infinite increasing sequence is order isomorphi...