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The black hole occupation fraction (focc) defines the fraction of galaxies that harbor central massive black holes (MBHs), irrespective of their accretion activity level. While it is widely accepted that focc is nearly 100% in local massive galaxies with stellar masses M⋆ ≳ 1010 M⊙, it is not yet clear whether MBHs are ubiquitous in less-massive galaxies. In this work, we present new constraints on focc based on over 20 yr of Chandra imaging data for 1606 galaxies within 50 Mpc. We employ a Bayesian model to simultaneously constrain focc and the specific accretion-rate distribution function, p(λ), where the specific accretion rate is defined as λ = LX/M⋆, where LX is the MBH accretion luminosity in the 2─10 keV range. Notably, we find that p(λ) peaks around 1028ergs−1M⊙−1 ; above this value, p(λ) decreases with increasing λ, following a power law that smoothly connects with the probability distribution of bona fide active galactic nuclei. We also find that the occupation fraction decreases dramatically with decreasing M⋆: in high-mass galaxies (M⋆ ≍ 1011−12 M⊙), the occupation fraction is >93% (a 2σ lower limit), and then declines to 66%−7%+8% (1σ errors) between M⋆ ≍ 109−10 M⊙, and to 33%−9%+13% in the dwarf galaxy regime between M⋆ ≍ 108−9 M⊙. Our results have significant implications for the normalization of the MBH mass function over the mass range most relevant for tidal disruption events, extreme mass ratio inspirals, and MBH merger rates that upcoming facilities are poised to explore. 

We study novel soliton glass frequency combs to a modified Lugiato-Lefever Equation (LLE) that include cross-phase modulation within a Fabry-Perot resonator. Soliton glasses are characterized by stable, spatially locked, phase-locked, and randomly spaced soliton pulses. 

Streams of intergalactic gas enriched by previous star formation were observed spiraling toward a massive galaxy. 

Biomarkers play an important role in early detection and intervention in Alzheimer’s disease (AD). However, obtaining effective biomarkers for AD is still a big challenge. In this work, we propose to use the worst transportation cost as a univariate biomarker to index cortical morphometry for tracking AD progression. The worst transportation (WT) aims to find the least economical way to transport one measure to the other, which contrasts to the optimal transportation (OT) that finds the most economical way between measures. To compute the WT cost, we generalize the Brenier theorem for the OT map to the WT map, and show that the WT map is the gradient of a concave function satisfying the Monge-Ampere equation. We also develop an efficient algorithm to compute the WT map based on computational geometry. We apply the algorithm to analyze cortical shape difference between dementia due to AD and normal aging individuals. The experimental results reveal the effectiveness of our proposed method which yields better statistical performance than other competiting methods including the OT. 

Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD). However, obtaining effective shape representations remains challenging. This paper proposes to use the Alexandrov polyhedra as surface-based shape signatures for cortical morphometry analysis. Given a closed genus-0 surface, its Alexandrov polyhedron is a convex representation that encodes its intrinsic geometry information. We propose to compute the polyhedra via a novel spherical optimal transport (OT) computation. In our experiments, we observe that the Alexandrov polyhedra of cortical surfaces between pathology-confirmed AD and cognitively unimpaired individuals are significantly different. Moreover, we propose a visualization method by comparing local geometry differences across cortical surfaces. We show that the proposed method is effective in pinpointing regional cortical structural changes impacted by AD. 

Abstract Weak emission-line quasars (WLQs) are a subset of type 1 quasars that exhibit extremely weak Lyα+ Nvλ1240 and/or Civλ1549 emission lines. We investigate the relationship between emission-line properties and accretion rate for a sample of 230 “ordinary” type 1 quasars and 18 WLQs atz< 0.5 and 1.5 <z< 3.5 that have rest-frame ultraviolet and optical spectral measurements. We apply a correction to the Hβ-based black hole mass (M_BH) estimates of these quasars using the strength of the optical Feiiemission. We confirm previous findings that WLQs’M_BHvalues are overestimated by up to an order of magnitude using the traditional broad-emission-line region size–luminosity relation. With thisM_BHcorrection, we find a significant correlation between Hβ-based Eddington luminosity ratios and a combination of the rest-frame Civequivalent width and Civblueshift with respect to the systemic redshift. This correlation holds for both ordinary quasars and WLQs, which suggests that the two-dimensional Civparameter space can serve as an indicator of accretion rate in all type 1 quasars across a wide range of spectral properties.