Multispecies virial expansions

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs

Logarithmic and complex constant term identities

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamovic and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove complex and logarithmic constant term identities for the root system G_2.Comment: 26 page

A review of diagnostic and functional imaging in headache

The neuroimaging of headache patients has revolutionised our understanding of the pathophysiology of primary headaches and provided unique insights into these syndromes. Modern imaging studies point, together with the clinical picture, towards a central triggering cause. The early functional imaging work using positron emission tomography shed light on the genesis of some syndromes, and has recently been refined, implying that the observed activation in migraine (brainstem) and in several trigeminal-autonomic headaches (hypothalamic grey) is involved in the pain process in either a permissive or triggering manner rather than simply as a response to first-division nociception per se. Using the advanced method of voxel-based morphometry, it has been suggested that there is a correlation between the brain area activated specifically in acute cluster headache — the posterior hypothalamic grey matter — and an increase in grey matter in the same region. No structural changes have been found for migraine and medication overuse headache, whereas patients with chronic tension-type headache demonstrated a significant grey matter decrease in regions known to be involved in pain processing. Modern neuroimaging thus clearly suggests that most primary headache syndromes are predominantly driven from the brain, activating the trigeminovascular reflex and needing therapeutics that act on both sides: centrally and peripherally

Transformation model and constraints cause bias in statistics on deformation fields

Abstract. This work investigates the effects of nonrigid transformation model and deformation constraints on the results of deformation-based morphometry (DBM) studies. We evaluate three popular registration algorithms: a B-spline algorithm with several different constraint terms, Thirion’s demons algorithm, and a curvature PDE-based algorithm. All algorithms produced virtually identical overlaps of corresponding structures, but the underlying deformation fields were very different, and the Jacobian determinant values within homogeneous structures varied dramatically. In several cases, we observed bi-modal distributions of Jacobians within a region that violate the assumption of gaussianity that underlies many statistical tests. Our results demonstrate that, even with perfect overlap of corresponding structures, the statistics of Jacobian values are affected by bias due to design elements of the particular nonrigid registration. These findings are not limited to DBM, but also apply to voxel-based morphometry to the extent that it includes a Jacobian-based correction step (“modulation”).