Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data.

Objective Magnetic resonance imaging (MRI), functional MRI (fMRI) and other neuroimaging techniques are routinely used in medical diagnosis, cognitive neuroscience or recently in brain decoding. They produce three- or four-dimensional scans reflecting the geometry of brain tissue or activity, which is highly correlated temporally and spatially. While there exist numerous theoretically guided methods for analyzing correlations in one-dimensional data, they often cannot be readily generalized to the multidimensional geometrically embedded setting.

Investigating structural and functional aspects of the brain's criticality in stroke.

This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for information transmission and responses to inputs. If structural damage could cause the critical point to disappear and thus make self-organized criticality unachievable, it would offer the theoretical explanation for the post-stroke impairment of brain function.

Matter-Driven Change of Spacetime Topology.

Using Monte Carlo computer simulations, we study the impact of matter fields on the geometry of a typical quantum universe in the causal dynamical triangulations (cdt) model of lattice quantum gravity. The quantum universe has the size of a few Planck lengths and the spatial topology of a three-torus. The matter fields are multicomponent scalar fields taking values in a torus with circumference δ in each spatial direction, which acts as a new parameter in the cdt model.

Comparison of eigeninference based on one- and two-point Green's functions.

We compare two methods of eigeninference from large sets of data. Our analysis points at the superiority of our eigeninference method based on one-point Green's functions and Padé approximants over a method based on fluctuations and two-point Green's functions. The first method is orders of magnitude faster than the second one; moreover, we found a source of potential instability of the second method and identified it as arising from the spurious zero and negative modes of the estimator for the variance operator of a certain multidimensional Gaussian distribution, inherent for that method.