Mathematical analysis of a model for the growth of the bovine corpus luteum

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2).\ud \ud In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system.\ud \ud We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, p5. We find that weak (low p5) or strong (high p5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of p5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Constraint Damping in First-Order Evolution Systems for Numerical Relativity

A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST system first-order, are given modified evolution equations designed to drive constraint violations toward zero. The algebraic structure of the new system is investigated, showing that the modifications preserve the hyperbolicity of the fundamental and constraint evolution equations. The evolution of the constraints for pertubations of flat spacetime is completely analyzed, and all finite-wavelength constraint modes are shown to decay exponentially when certain adjustable parameters satisfy appropriate inequalities. Numerical simulations of a single Schwarzschild black hole are presented, demonstrating the effectiveness of the new constraint-damping modifications.Comment: 11 pages, 5 figure

How Many Templates for GW Chirp Detection? The Minimal-Match Issue Revisited

In a recent paper dealing with maximum likelihood detection of gravitational wave chirps from coalescing binaries with unknown parameters we introduced an accurate representation of the no-signal cumulative distribution of the supremum of the whole correlator bank. This result can be used to derive a refined estimate of the number of templates yielding the best tradeoff between detector's performance (in terms of lost signals among those potentially detectable) and computational burden.Comment: submitted to Class. Quantum Grav. Typing error in eq. (4.8) fixed; figure replaced in version

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem

An X-ray and Optical Investigation of the Environments Around Nearby Radio Galaxies

Investigations of the cluster environment of radio sources have not shown a correlation between radio power and degree of clustering. However, it has been demonstrated that extended X-ray luminosity and galaxy clustering do exhibit a positive correlation. This study investigates a complete sample of 25 nearby (z less than 0.06) radio galaxies which are not cataloged members of Abell clusters. The environment of these radio galaxies is studied in both the X-ray and the optical by means of the ROSAT All-Sky Survey (RASS), ROSAT pointed observations, and the Palomar optical Digitized Sky Survey (DSS). X-ray luminosities and extents are determined from the RASS, and the DSS is used to quantify the degree of clustering via the spatial two-point correlation coefficient, Bgg. Of the 25 sources, 20 are greater than sigma detections in the X-ray and 11 possessed Bgg's significantly in excess of that expected for an isolated galaxy. Adding the criterion that the X-ray emission be resolved, 10 of the radio galaxies do appear to reside in poor clusters with extended X-ray emission suggestive of the presence of an intracluster medium. Eight of these galaxies also possess high spatial correlation coefficients. Taken together, these data suggest that the radio galaxies reside in a low richness extension of the Abell clusters. The unresolved X-ray emission from the other galaxies is most likely associated with AGN phenomena. Furthermore, although the sample size is small, it appears that the environments of FR I and FR II sources differ. FR I's tend to be more frequently associated with extended X-ray emission (10 of 18), whereas FR II's are typically point sources or non-detections in the X-ray (none of the 7 sources exhibit extended X-ray emission).Comment: 28 page postscript file including figures and tables, plus one landscape table and 5 GIF figure

A new super-soft X-ray source in the Small Magellanic Cloud: Discovery of the first Be/white dwarf system in the SMC?

The Small Magellanic Cloud (SMC) hosts a large number of Be/X-ray binaries, however no Be/white dwarf system is known so far, although population synthesis calculations predict that they might be more frequent than Be/neutron star systems. XMMUJ010147.5-715550 was found as a new faint super-soft X-ray source (SSS) with a likely Be star optical counterpart. We investigate the nature of this system and search for further high-absorbed candidates in the SMC. We analysed the XMM-Newton X-ray spectrum and light curve, optical photometry, and the I-band OGLE III light curve. The X-ray spectrum is well represented by black-body and white dwarf atmosphere models with highly model-dependent temperature between 20 and 100 eV. The likely optical counterpart AzV 281 showed low near infrared emission during X-ray activity, followed by a brightening in the I-band afterwards. We find further candidates for high-absorbed SSSs with a blue star as counterpart. We discuss XMMUJ010147.5-715550 as the first candidate for a Be/white dwarf binary system in the SMC.Comment: 6 pages, 4 figures, accepted by A&

State-dependent Jastrow correlation functions for 4He nuclei

We calculate the ground-state energy for the nucleus 4He with V4 nucleon interactions, making use of a Jastrow description of the corresponding wavefunction with state-dependent correlation factors. The effect related to the state dependence of the correlation is quite important, lowering the upper bound for the ground-state energy by some 2 MeV.Comment: 10 pages, REVTeX, to be published in J. Phys. G: Nucl. Part. Phy