A generalized spatiotemporal covariance model for stationary background in analysis of MEG data

Using a noise covariance model based on a single Kronecker product of spatial and temporal covariance in the spatiotemporal analysis of MEG data was demonstrated to provide improvement in the results over that of the commonly used diagonal noise covariance model. In this paper we present a model that is a generalization of all of the above models. It describes models based on a single Kronecker product of spatial and temporal covariance as well as more complicated multi-pair models together with any intermediate form expressed as a sum of Kronecker products of spatial component matrices of reduced rank and their corresponding temporal covariance matrices. The model provides a framework for controlling the tradeoff between the described complexity of the background and computational demand for the analysis using this model. Ways to estimate the value of the parameter controlling this tradeoff are also discussedComment: 4 pages, EMBS 2006 conferenc

The Theory of Dynamical Random Surfaces with Extrinsic Curvature

We analyze numerically the critical properties of a two-dimensional discretized random surface with extrinsic curvature embedded in a three-dimensional space. The use of the toroidal topology enables us to enforce the non-zero external extension without the necessity of defining a boundary and allows us to measure directly the string tension. We show that a phase transition from the crumpled phase to the smooth phase observed earlier for a spherical topology appears also for a toroidal surface for the same finite value of the coupling constant of the extrinsic curvature term. The phase transition is characterized by the vanishing of the string tension. We discuss the possible non-trivial continuum limit of the theory, when approaching the critical point. Numerically we find a value of the critical exponent \n to be between .38 and .42. The specific heat, related to the extrinsic curvature term seems not to diverge (or diverge slower than logarithmically) at the critical point.Comment: figures available as postscript files on request. 28 pages plus figure