The reionization of intergalactic hydrogen has received intense theoretical scrutiny over the past two decades. Here, we approach the process formally as a percolation process and phase transition. Using semi-numeric simulations, we demonstrate that an infinitely-large ionized region abruptly appears at an ionized fraction of ~0.1 and quickly grows to encompass most of the ionized gas: by an ionized fraction of 0.3, nearly ninety percent of the ionized material is part of this region. Throughout most of reionization, nearly all of the intergalactic medium is divided into just two regions, one ionized and one neutral, and both infinite in extent. We also show that the discrete ionized regions that exist before and near this transition point follow a near-power law distribution in volume, with equal contributions to the total filling factor per logarithmic interval in size up to a sharp cutoff in volume. These qualities are generic to percolation processes, with the detailed behavior a result of long-range correlations in the underlying density field. These insights will be crucial to understanding the distribution of ionized and neutral gas during reionization and provide precise meaning to the intuitive description of reionization as an "overlap" process.

A key physical quantity during reionization is the size of H II regions. Previous studies found a characteristic bubble size which increases rapidly during reionization, with apparent agreement between simulations and analytic excursion set theory. Using four different methods, we critically examine this claim. In particular, we introduce the use of the watershed algorithm - widely used for void finding in galaxy surveys - which we show to be an unbiased method with the lowest dispersion and best performance on Monte Carlo realizations of a known bubble size probability density function (PDF).We find that a friends-of-friends algorithm declares most of the ionized volume to be occupied by a network of volume-filling regions connected by narrow tunnels. For methods tuned to detect the volume-filling regions, previous apparent agreement between simulations and theory is spurious, and due to a failure to correctly account for the window function of measurement schemes. The discrepancy is already obvious from visual inspection. Instead, H II regions in simulations are significantly larger (by factors of 10-1000 in volume) than analytic predictions. The size PDF is narrower, and evolves more slowly with time, than predicted. It becomes more sharply peaked as reionization progresses. These effects are likely caused by bubble mergers, which are inadequately modelled by analytic theory. Our results have important consequences for high-redshift 21 cm observations, the mean free path of ionizing photons, and the visibility of Lya emitters, and point to a fundamental failure in our understanding of the characteristic scales of the reionization process.

The ionizing background of cosmic hydrogen is an important probe of the sources and absorbers of ionizing radiation in the post-reionization universe. Previous studies show that the ionization rate should be very sensitive to changes in the source population: as the emissivity rises, absorbers shrink in size, increasing the ionizing mean free path and, hence, the ionizing background. By contrast, observations of the ionizing background find a very flat evolution from z~2-5, before falling precipitously at z~6. We resolve this puzzling discrepancy by pointing out that, at z~2-5, optically thick absorbers are associated with the same collapsed halos that host ionizing sources. Thus, an increasing abundance of galaxies is compensated for by a corresponding increase in the absorber population, which moderates the instability in the ionizing background. However, by z~5-6, gas outside of halos dominates the absorption, the coupling between sources and absorbers is lost, and the ionizing background evolves rapidly. Our halo based model reproduces observations of the ionizing background, its flatness and sudden decline, as well as the redshift evolution of the ionizing mean free path. Our work suggests that, through much of their history, both star formation and photoelectric opacity in the universe track halo growth.

In endothelial cells, two type I receptors of the transforming growth factor β (TGF-β) family, ALK1 and ALK5, coordinate to regulate embryonic angiogenesis in response to BMP9/10 and TGF-β. Whereas TGF-β binds to and activates ALK5, leading to Smad2/3 phosphorylation and inhibition of endothelial cell proliferation and migration, BMP9/10 and TGF-β also bind to ALK1, resulting in the activation of Smad1/5. SnoN is a negative regulator of ALK5 signaling through the binding and repression of Smad2/3. Here we uncover a positive role of SnoN in enhancing Smad1/5 activation in endothelial cells to promote angiogenesis. Upon ligand binding, SnoN directly bound to ALK1 on the plasma membrane and facilitated the interaction between ALK1 and Smad1/5, enhancing Smad1/5 phosphorylation. Disruption of this SnoN-Smad interaction impaired Smad1/5 activation and up-regulated Smad2/3 activity. This resulted in defective angiogenesis and arteriovenous malformations, leading to embryonic lethality at E12.5. Thus, SnoN is essential for TGF-β/BMP9-dependent biological processes by its ability to both positively and negatively modulate the activities of Smad-dependent pathways.

Arteriovenous malformations (AVMs) are abnormal connections of vessels that shunt blood directly from arteries into veins. Rupture of brain AVMs (bAVMs) can cause life-threatening intracranial bleeding. Even though the majority of bAVM cases are sporadic without a family history, some cases are familial. Most of the familial cases of bAVMs are associated with a genetic disorder called hereditary hemorrhagic telangiectasia (HHT). The mechanism of bAVM formation is not fully understood. The most important advances in bAVM basic science research is the identification of somatic mutations of genes in RAS-MAPK pathways. However, the mechanisms by which mutations of these genes lead to AVM formation are largely unknown. In this review, we summarized the latest advance in bAVM studies and discussed some pathways that play important roles in bAVM pathogenesis. We also discussed the therapeutic implications of these pathways.

In endothelial cells, two type I receptors of the transforming growth factor β (TGF-β) family, ALK1 and ALK5, coordinate to regulate embryonic angiogenesis in response to BMP9/10 and TGF-β. Whereas TGF-β binds to and activates ALK5, leading to Smad2/3 phosphorylation and inhibition of endothelial cell proliferation and migration, BMP9/10 and TGF-β also bind to ALK1, resulting in the activation of Smad1/5. SnoN is a negative regulator of ALK5 signaling through the binding and repression of Smad2/3. Here we uncover a positive role of SnoN in enhancing Smad1/5 activation in endothelial cells to promote angiogenesis. Upon ligand binding, SnoN directly bound to ALK1 on the plasma membrane and facilitated the interaction between ALK1 and Smad1/5, enhancing Smad1/5 phosphorylation. Disruption of this SnoN-Smad interaction impaired Smad1/5 activation and up-regulated Smad2/3 activity. This resulted in defective angiogenesis and arteriovenous malformations, leading to embryonic lethality at E12.5. Thus, SnoN is essential for TGF-β/BMP9-dependent biological processes by its ability to both positively and negatively modulate the activities of Smad-dependent pathways.