Fisher-KPP dynamics in diffusive Rosenzweig-MacArthur and Holling-Tanner models

We prove the existence of traveling fronts in diffusive Rosenzweig-MacArthur and Holling-Tanner population models and investigate their relation with fronts in a scalar Fisher-KPP equation. More precisely, we prove the existence of fronts in a Rosenzweig-MacArthur predator-prey model in two situations: when the prey diffuses at the rate much smaller than that of the predator and when both the predator and the prey diffuse very slowly. Both situations are captured as singular perturbations of the associated limiting systems. In the first situation we demonstrate clear relations of the fronts with the fronts in a scalar Fisher-KPP equation. Indeed, we show that the underlying dynamical system in a singular limit is reduced to a scalar Fisher-KPP equation and the fronts supported by the full system are small perturbations of the Fisher-KPP fronts. We obtain a similar result for a diffusive Holling-Tanner population model. In the second situation for the Rosenzweig-MacArthur model we prove the existence of the fronts but without observing a direct relation with Fisher-KPP equation. The analysis suggests that, in a variety of reaction-diffusion systems that rise in population modeling, parameter regimes may be found when the dynamics of the system is inherited from the scalar Fisher-KPP equation

Evolution of star clusters on eccentric orbits

We study the evolution of star clusters on circular and eccentric orbits using direct $N$-body simulations. We model clusters with initially $N=8{\rm k}$ and $N=16{\rm k}$ single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same $N$ on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semi-major axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the Galactic mass profile. From both sets of simulations we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.Comment: 7 pages, 8 figures, accepted for publication in the Monthly Notices of the Royal Astronomical Societ

3D Anisotropic Hybrid Network: Transferring Convolutional Features from 2D Images to 3D Anisotropic Volumes

While deep convolutional neural networks (CNN) have been successfully applied for 2D image analysis, it is still challenging to apply them to 3D anisotropic volumes, especially when the within-slice resolution is much higher than the between-slice resolution and when the amount of 3D volumes is relatively small. On one hand, direct learning of CNN with 3D convolution kernels suffers from the lack of data and likely ends up with poor generalization; insufficient GPU memory limits the model size or representational power. On the other hand, applying 2D CNN with generalizable features to 2D slices ignores between-slice information. Coupling 2D network with LSTM to further handle the between-slice information is not optimal due to the difficulty in LSTM learning. To overcome the above challenges, we propose a 3D Anisotropic Hybrid Network (AH-Net) that transfers convolutional features learned from 2D images to 3D anisotropic volumes. Such a transfer inherits the desired strong generalization capability for within-slice information while naturally exploiting between-slice information for more effective modelling. The focal loss is further utilized for more effective end-to-end learning. We experiment with the proposed 3D AH-Net on two different medical image analysis tasks, namely lesion detection from a Digital Breast Tomosynthesis volume, and liver and liver tumor segmentation from a Computed Tomography volume and obtain the state-of-the-art results

Probing the missing baryons with the Sunyaev-Zel'dovich effect from filaments

Observations of galaxies and galaxy clusters in the local universe can account for only $\sim\,10\%$ of the total baryon content. Cosmological simulations predict that the `missing baryons' are spread throughout filamentary structures in the cosmic web, forming a low-density gas with temperatures of $10^5-10^7\,\!$K. We search for this warm-hot intergalactic medium (WHIM) by stacking the Planck Compton $y$-parameter map of the thermal Sunyaev-Zel'dovich (tSZ) effect for 1,002,334 pairs of CMASS galaxies from the Sloan Digital Sky Survey. We model the contribution from the galaxy halo pairs assuming spherical symmetry, finding a residual tSZ signal at the 2.9\mbox{\sigma} level from a stacked filament of length $10.5\,h^{-1}\,\rm Mpc$ with a Compton parameter magnitude $y=(0.6\pm0.2)\times10^{-8}$. We consider possible sources of contamination and conclude that bound gas in haloes may contribute only up to $20\%$ of the measured filamentary signal. To estimate the filament gas properties we measure the gravitational lensing signal for the same sample of galaxy pairs; in combination with the tSZ signal, this yields an inferred gas density of $\rho_{\rm b}=(5.5\pm 2.9)\times\bar{\rho_{\rm b}}$ with a temperature $T=(2.7\pm 1.7) \times 10^6\,$K. This result is consistent with the predicted WHIM properties, and overall the filamentary gas can account for $11\pm 7\%$ of the total baryon content of the Universe. We also see evidence that the gas filament extends beyond the galaxy pair. Averaging over this longer baseline boosts the significance of the tSZ signal and increases the associated baryon content to $28\pm 12\%$ of the global value.Comment: 13 pages, 8 figures; accepted for publication in A&

Keck/Palomar Cosmic Web Imagers (KCWI/PCWI) Reveal an Enormous Lyα\alpha Nebula in an Extremely Overdense QSO Pair Field at z=2.45z=2.45

Enormous Ly$\alpha$ nebulae (ELANe) represent the extrema of Ly$\alpha$ nebulosities. They have detected extents of $>200$ kpc in Ly$\alpha$ and Ly$\alpha$ luminosities $>10^{44}$ erg s$^{-1}$. The ELAN population is an ideal laboratory to study the interactions between galaxies and the intergalactic/circumgalactic medium (IGM/CGM) given their brightness and sizes. The current sample size of ELANe is still very small, and the few $z\approx2$ ELANe discovered to date are all associated with local overdensities of active galactic nuclei (AGNs). Inspired by these results, we have initiated a survey of ELANe associated with QSO pairs using the Palomar and Keck Cosmic Web Imagers (PCWI/KCWI). In this letter, we present our first result: the discovery of ELAN0101+0201 associated with a QSO pair at $z=2.45$. Our PCWI discovery data shows that, above a 2-$\sigma$ surface brightness of $1.2\times10^{-17}$ \sbunit, the end-to-end size of ELAN0101+0201 is $\gtrsim 232$ kpc. We have conducted follow-up observations using KCWI, resolving multiple Ly$\alpha$ emitting sources within the rectangular field-of-view of $\approx 130\times165$ projected kpc$^2$, and obtaining their emission line profiles at high signal-to-noise ratios. Combining both KCWI and PCWI, our observations confirm that ELAN0101+0201 resides in an extremely overdense environment. Our observations further support that a large amount of cool ($T\sim10^4$K) gas could exist in massive halos (M$\gtrsim10^{13}$M$_\odot$) at $z\approx2$. Future observations on a larger sample of similar systems will provide statistics of how cool gas is distributed in massive overdensities at high-redshift and strongly constrain the evolution of the intracluster medium (ICM).Comment: Submitted to Astrophysical Journal Letter, 9 pages, 4 figures, Comments Welcom