A computational method for the coupled solution of reaction–diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk–surface reaction–diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk–surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane

Evidence against the Detectability of a Hippocampal Place Code Using Functional Magnetic Resonance Imaging

Individual hippocampal neurons selectively increase their firing rates in specific spatial locations. As a population, these neurons provide a decodable representation of space that is robust against changes to sensory- and path-related cues. This neural code is sparse and distributed, theoretically rendering it undetectable with population recording methods such as functional magnetic resonance imaging (fMRI). Existing studies nonetheless report decoding spatial codes in the human hippocampus using such techniques. Here we present results from a virtual navigation experiment in humans in which we eliminated visual- and path-related confounds and statistical limitations present in existing studies, ensuring that any positive decoding results would represent a voxel-place code. Consistent with theoretical arguments derived from electrophysiological data and contrary to existing fMRI studies, our results show that although participants were fully oriented during the navigation task, there was no statistical evidence for a place code

A point mass in an isotropic universe: III. The region R≤2mR\leq 2m

McVittie's solution of Einstein's field equations, representing a point mass embedded into an isotropic universe, possesses a scalar curvature singularity at proper radius $R=2m$. The singularity is space-like and precedes, in the expanding case, all other events in the space-time. It is shown here that this singularity is gravitationally weak, and the possible structure of the region $R\leq 2m$ is investigated. A characterization of this solution which does not involve asymptotics is given.Comment: Revtex, 11pp. To appear in Class.Quant.Grav. Paper II appeared as Class. Quant. Grav. 16 (1999) 122

Expansion-induced contribution to the precession of binary orbits

We point out the existence of new effects of global spacetime expansion on local binary systems. In addition to a possible change of orbital size, there is a contribution to the precession of elliptic orbits, to be added to the well-known general relativistic effect in static spacetimes, and the eccentricity can change. Our model calculations are done using geodesics in a McVittie metric, representing a localized system in an asymptotically Robertson-Walker spacetime; we give a few numerical estimates for that case, and indicate ways in which the model should be improved.Comment: revtex, 7 pages, no figures; revised for publication in Classical and Quantum Gravity, with minor changes in response to referees' comment

The Gamma Ray Pulsar Population

We apply a likelihood analysis to pulsar detections, pulsar upper limits, and diffuse background measurements from the OSSE and EGRET instruments on the Compton Gamma Ray Observatory to constrain the luminosity law for gamma-ray pulsars and some properties of the gamma-ray pulsar population. We find that the dependence of luminosity on spin period and dipole magnetic field is much steeper at OSSE than at EGRET energies (50-200 keV and >100 MeV, respectively), suggesting that different emission mechanisms are responsible for low- and high-energy gamma-ray emission. Incorporating a spin-down model and assuming a pulsar spatial distribution, we estimate the fraction of the Galactic gamma-ray background due to unidentified pulsars and find that pulsars may be an important component of the OSSE diffuse flux, but are most likely not important at EGRET energies. Using measurements of the diffuse background flux from these instruments, we are able to place constraints on the braking index, initial spin period, and magnetic field of the Galactic pulsar population. We are also able to constrain the pulsar birthrate to be between 1/(25 yr) and 1/(500 yr). Our results are based on a large gamma-ray beam, but they do not scale in a simple way with beam size. With our assumed beam size, the implied gamma-ray efficiency for the EGRET detections is no more than 20%. We estimate that about 20 of the 169 unidentified EGRET sources are probably gamma-ray pulsars. We use our model to predict the pulsar population that will be seen by future gamma-ray instruments and estimate that GLAST will detect roughly 750 gamma-ray pulsars as steady sources, only 120 of which are currently known radio pulsars.Comment: 32 pages, including figures. submitted to Ap

Haemoglobin unfolding studies at the liquid-liquid interface

The electrochemical behaviour of haemoglobin denatured using different concentrations of urea was investigated at the liquid|liquid interface. The reverse peak current varied with the concentration of urea, allowing the building of the unfolding curve, which compares well with UV-Vis absorbance results. Thermodynamic parameters, such as the change in free energy of folding in water, , and the index of the compactness of the protein, m, were extracted from the experimental data. The work here presents a simple electrochemical method for the study of protein unfolding by electrochemistry at the liquid | liquid interface

Detection of Contact Binaries Using Sparse High Phase Angle Lightcurves

We show that candidate contact binary asteroids can be efficiently identified from sparsely sampled photometry taken at phase angles >60deg. At high phase angle, close/contact binary systems produce distinctive lightcurves that spend most of the time at maximum or minimum (typically >1mag apart) brightness with relatively fast transitions between the two. This means that a few (~5) sparse observations will suffice to measure the large range of variation and identify candidate contact binary systems. This finding can be used in the context of all-sky surveys to constrain the fraction of contact binary near-Earth objects. High phase angle lightcurve data can also reveal the absolute sense of the spin.Comment: 4 pages, 4 figures, 1 table. Accepted for publication in ApJ

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds : application to a model of cell migration and chemotaxis

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane

Macular Pigment and Visual Function in Patients With Glaucoma: The San Diego Macular Pigment Study.

PurposeAlthough recent studies have shown that macular pigment (MP) is significantly lower in glaucoma patients, this relationship merits further investigation.MethodsThis cross-sectional study included 85 glaucoma patients and 22 controls. All subjects had standard automated perimetry (SAP) and retinal nerve fiber layer (RNFL) thickness measurements. Intake of lutein (L) and zeaxanthin (Z) was estimated using a novel dietary screener. The Heidelberg Spectralis dual-wavelength autofluorescence (AF) technology was employed to study the relationship between MP and glaucoma. The association between MP volume and glaucoma was investigated using linear regression models accounting for potential confounding factors.ResultsGlaucoma patients had significantly worse SAP mean deviation (MD) and lower RNFL thickness in the study eye compared to control subjects (P < 0.001 for both). MP (volume) was comparable between groups (P = 0.436). In the univariable model, diagnosis of glaucoma was not associated with MP volume (R2 = 1.22%; P = 0.257). Dietary intake of L and Z was positively and significantly related to MP in the univariable (P = 0.022) and multivariable (P = 0.020) models.ConclusionsThese results challenge previous studies that reported that glaucoma is associated with low MP. Dietary habits were found to be the main predictor of MP in this sample. Further research is merited to better understand the relationship between glaucoma, MP, and visual performance in these patients