A note on the motion of an ocean bacterium in a linear shear flow

This paper treats a simple model, which can be exactly solved, motivated by the back-and-forth motion of ocean bacteria. In particular, the probability is determined that a bacterium moving randomly along a fluid line through the origin in a linear shear flow hits the origin before time

TOPOGRAPHIC ROSSBY WAVES ABOVE A RANDOM ARRAY OF SEA-MOUNTAINS

The barotropic potential vorticity equation or topographic wave equation is not linear in topography: the solution structure for topography formed from a sum of obstacles is not the sum of solutions for the obstacles in isolation, even when these individual solutions have identical frequencies. This paper considers the mechanism by which normal modes of oscillation above one mountain are modified by interactions with its neighbours. Exact explicit solutions for the normal modes above a pair of circular seamountains show that the interactions between the mountains rapidly approaches the large-separation approximation obtained by considering solely the first reflection of the disturbance of one mountain at the other. For mountains of one diameter separation at the closest point, the approximation is accurate to within 1%. Perhaps surprisingly, coupling between two identical mountains is weak and resonance occurs between mountains and dales of equal and opposite height. The accurate approximate solutions enable consideration of the effects on a mountain of an infinite set of randomly distributed neighbours. The ensembleaveraged frequency for a mountain of given height is determined in terms of the area fraction of the other mountains. The idea of an effective topography is introduced for the ensemble-averaged stream function: it is that (non-random) topography generating a stream function identical to the ensemble-averaged stream function. This differs markedly from the ensemble-averaged topography. The explicit form of the effective topography is derived for a set of right circular cylinders

SLOW ENERGY-TRANSFER BETWEEN REGIONS SUPPORTING TOPOGRAPHIC WAVES

In a recent paper (Jansons & Johnson 1988) the authors discuss topographic Rossby waves over a random array of seamounts. It is noted that resonance is possible between a hill and an equal and opposite dale but such resonances are mentioned only briefly due to the small likelihood of correctly matched topography in the ocean. The present paper considers the resonances in detail showing how the normal modes formed by frequency splitting at resonance can be combined to give modes that slowly transfer energy from one region supporting topographic waves, across a region where such weaves are evanescent, to another region supporting waves. In addition to the simplest case of a hill—dale pair for which an exact energy-transferring mode is obtained, transferring modes are given for a three-hill system, for two hills near a coastal boundary, and for two-basin lakes. The analysis is simplified and the results generalized by extensive use of the invariance of the governing equation under conformal mappings. A transferring mode is given for a dale in a random array of seamounts showing energy leaking slowly from the dale to large distances and returning, with the rate of leakage depending on the area fraction of seamounts. It is concluded that although resonances and transferring modes are not likely to be important in random arrays on infinite planes, they are relevant to numerical models, which are necessarily restricted to finite domains, to coastal seamount chains, and to multi-basin lakes

Using high angular resolution diffusion imaging data to discriminate cortical regions

Brodmann's 100-year-old summary map has been widely used for cortical localization in neuroscience. There is a pressing need to update this map using non-invasive, high-resolution and reproducible data, in a way that captures individual variability. We demonstrate here that standard HARDI data has sufficiently diverse directional variation among grey matter regions to inform parcellation into distinct functional regions, and that this variation is reproducible across scans. This characterization of the signal variation as non-random and reproducible is the critical condition for successful cortical parcellation using HARDI data. This paper is a first step towards an individual cortex-wide map of grey matter microstructure, The gray/white matter and pial boundaries were identified on the high-resolution structural MRI images. Two HARDI data sets were collected from each individual and aligned with the corresponding structural image. At each vertex point on the surface tessellation, the diffusion-weighted signal was extracted from each image in the HARDI data set at a point, half way between gray/white matter and pial boundaries. We then derived several features of the HARDI profile with respect to the local cortical normal direction, as well as several fully orientationally invariant features. These features were taken as a fingerprint of the underlying grey matter tissue, and used to distinguish separate cortical areas. A support-vector machine classifier, trained on three distinct areas in repeat 1 achieved 80-82% correct classification of the same three areas in the unseen data from repeat 2 in three volunteers. Though gray matter anisotropy has been mostly overlooked hitherto, this approach may eventually form the foundation of a new cortical parcellation method in living humans. Our approach allows for further studies on the consistency of HARDI based parcellation across subjects and comparison with independent microstructural measures such as ex-vivo histology

Characterization of Functional and Structural Integrity in Experimental Focal Epilepsy: Reduced Network Efficiency Coincides with White Matter Changes

BACKGROUND: Although focal epilepsies are increasingly recognized to affect multiple and remote neural systems, the underlying spatiotemporal pattern and the relationships between recurrent spontaneous seizures, global functional connectivity, and structural integrity remain largely unknown. METHODOLOGY/PRINCIPAL FINDINGS: Here we utilized serial resting-state functional MRI, graph-theoretical analysis of complex brain networks and diffusion tensor imaging to characterize the evolution of global network topology, functional connectivity and structural changes in the interictal brain in relation to focal epilepsy in a rat model. Epileptic networks exhibited a more regular functional topology than controls, indicated by a significant increase in shortest path length and clustering coefficient. Interhemispheric functional connectivity in epileptic brains decreased, while intrahemispheric functional connectivity increased. Widespread reductions of fractional anisotropy were found in white matter regions not restricted to the vicinity of the epileptic focus, including the corpus callosum. CONCLUSIONS/SIGNIFICANCE: Our longitudinal study on the pathogenesis of network dynamics in epileptic brains reveals that, despite the locality of the epileptogenic area, epileptic brains differ in their global network topology, connectivity and structural integrity from healthy brains