Resolving the outer ring of HD 38206 using ALMA and constraining limits on planets in the system

ABSTRACT HD 38206 is an A0V star in the Columba association, hosting a debris disc first discovered by IRAS. Further observations by Spitzer and Herschel showed that the disc has two components, likely analogous to the asteroid and Kuiper belts of the Solar system. The young age of this star makes it a prime target for direct imaging planet searches. Possible planets in the system can be constrained using the debris disc. Here, we present the first ALMA observations of the system’s Kuiper belt and fit them using a forward modelling MCMC approach. We detect an extended disc of dust peaking at around 180 au with a width of 140 au. The disc is close to edge on and shows tentative signs of an asymmetry best fit by an eccentricity of $0.25^{+0.10}_{-0.09}$. We use the fitted parameters to determine limits on the masses of planets interior to the cold belt. We determine that a minimum of four planets are required, each with a minimum mass of 0.64 MJ, in order to clear the gap between the asteroid and Kuiper belts of the system. If we make the assumption that the outermost planet is responsible for the stirring of the disc, the location of its inner edge and the eccentricity of the disc, then we can more tightly predict its eccentricity, mass, and semimajor axis to be $e_{\rm {p}}=0.34^{+0.20}_{-0.13}$, $m_{\rm {p}}=0.7^{+0.5}_{-0.3}\, \rm {\it M}_{\rm {J}}$, and $a_{\rm {p}}=76^{+12}_{-13}\, \rm {au}$.

Bayesian Connective Field Modeling: a Markov Chain Monte Carlo approach

The majority of neurons in the human brain process signals from neurons elsewhere in the brain. Connective Field (CF) modeling is a biologically-grounded method to describe this essential aspect of the brain’s circuitry. It allows characterizing the response of a population of neurons in terms of the activity in another part of the brain. CF modeling translates the concept of the receptive field (RF) into the domain of connectivity by assessing the spatial dependency between signals in distinct cortical visual field areas. Standard CF model estimation has some intrinsic limitations in that it cannot estimate the uncertainty associated with each of its parameters. Obtaining the uncertainty will allow identification of model biases, e.g. related to an over- or under-fitting or a co-dependence of parameters, thereby improving the CF prediction. To enable this, here we present a Bayesian framework for the CF model. Using a Markov Chain Monte Carlo (MCMC) approach, we estimate the underlying posterior distribution of the CF parameters and consequently, quantify the uncertainty associated with each estimate. We applied the method and its new Bayesian features to characterize the cortical circuitry of the early human visual cortex of 12 healthy participants that were assessed using 3T fMRI. In addition, we show how the MCMC approach enables the use of effect size (beta) as a data-driven parameter to retain relevant voxels for further analysis. Finally, we demonstrate how our new method can be used to compare different CF models. Our results show that single Gaussian models are favoured over differences of Gaussians (i.e. center-surround) models, suggesting that the cortico-cortical connections of the early visual system do not possess center-surround organisation. We conclude that our new Bayesian CF framework provides a comprehensive tool to improve our fundamental understanding of the human cortical circuitry in health and disease.Highlights□ We present and validate a Bayesian CF framework based on a MCMC approach.□ The MCMC CF approach quantifies the model uncertainty associated with each CF parameter.□ We show how to use effect size beta as a data-driven threshold to retain relevant voxels.□ The cortical connective fields of the human early visual system are best described by a single, circular symmetric, Gaussian.

Modeling the early phase of the Belgian COVID-19 epidemic using a stochastic compartmental model and studying its implied future trajectories

Following the onset of the ongoing COVID-19 pandemic throughout the world, a large fraction of the global population is or has been under strict measures of physical distancing and quarantine, with many countries being in partial or full lockdown. These measures are imposed in order to reduce the spread of the disease and to lift the pressure on healthcare systems. Estimating the impact of such interventions as well as monitoring the gradual relaxing of these stringent measures is quintessential to understand how resurgence of the COVID-19 epidemic can be controlled for in the future. In this paper we use a stochastic age-structured discrete time compartmental model to describe the transmission of COVID-19 in Belgium. Our model explicitly accounts for age-structure by integrating data on social contacts to (i) assess the impact of the lockdown as implemented on March 13, 2020 on the number of new hospitalizations in Belgium; (ii) conduct a scenario analysis estimating the impact of possible exit strategies on potential future COVID-19 waves. More specifically, the aforementioned model is fitted to hospital admission data, data on the daily number of COVID-19 deaths and serial serological survey data informing the (sero)prevalence of the disease in the population while relying on a Bayesian MCMC approach. Our age-structured stochastic model describes the observed outbreak data well, both in terms of hospitalizations as well as COVID-19 related deaths in the Belgian population. Despite an extensive exploration of various projections for the future course of the epidemic, based on the impact of adherence to measures of physical distancing and a potential increase in contacts as a result of the relaxation of the stringent lockdown measures, a lot of uncertainty remains about the evolution of the epidemic in the next months.

Effects of the Hubble parameter on the cosmic growth of the first quasars

ABSTRACT Supermassive black holes (SMBHs) play a crucial role in the evolution of galaxies and are currently detected up to $z$ ∼ 7.5. Theories describing black hole (BH) growth are challenged by how rapidly seeds with initial mass $M_\bullet \lesssim 10^5 \, {\rm M_\odot }$, formed at $z$ ∼ 20–30, grew to $M_\bullet \sim 10^9 \, {\rm M_\odot }$ by $z$ ∼ 7. Here we study the effects of the value of the Hubble parameter, H0, on models describing the early growth of BHs. First, we note that the predicted mass of a quasar at $z$ = 6 changes by $\gt 300{{\ \rm per\ cent}}$ if the underlying Hubble parameter used in the model varies from H0 = 65 to H0 = 74 km s−1Mpc−1, a range encompassing current estimates. Employing an MCMC approach based on priors from $z$ ≳ 6.5 quasars and on H0, we study the interconnection between H0 and the parameters describing BH growth: seed mass Mi and Eddington ratio fEdd. Assuming an Eddington ratio of fEdd = 0.7, in agreement with previous estimates, we find $H_0 = 73.6^{+1.2}_{-3.3}$ km s−1Mpc−1. In a second analysis, allowing all the parameters to vary freely, we find log (Mi/M⊙) > 4.5 (at 95 per cent CL), $H_0 = 74^{+1.5}_{-1.4}$ km s−1Mpc−1 and $f_{\rm Edd}=0.77^{+0.035}_{-0.026}$ at 68 per cent CL. Our results on the typical Eddington ratio are in agreement with previous estimates. Current values of the Hubble parameter strongly favour heavy seed formation scenarios, with $M_i \gtrsim 10^4 \, {\rm M_\odot }$. In our model, with the priors on BH masses of quasars used, light seed formation scenarios are rejected at ∼3σ.

Inferring key epidemiological parameters and transmission dynamics of COVID-19 based on a modified SEIR model

This study aims to establish a model-based framework for inferring key transmission characteristics of the newly emerging outbreak of the coronavirus disease 2019 (COVID-19), especially the epidemic dynamics under quarantine conditions. Inspired by the shifting therapeutic levels and capacity at different stages of the COVID-19 pandemic, we propose a modified SEIR model with a two-phase removal rate of quarantined hosts undergoing continuously tunable transition. We employ the Markov Chain Monte Carlo (MCMC) approach for inferring and forecasting the epidemiological dynamics from the publicly available surveillance reports. The effectiveness of a short-term prediction is illustrated by adopting the data sets from 10 demographic regions including Chinese mainland and South Korea. In the surveillance period, the average R0 ranges from 1.74 to 3.28, and the median of the mean latent period does not exceed 10 days across the surveillance regions.

Specification and estimation of network formation and network interaction models with the exponential probability distribution

We model network formation and interactions under a unified framework by considering that individuals anticipate the effect of network structure on the utility of network interactions when choosing links. There are two advantages of this modeling approach: first, we can evaluate whether network interactions drive friendship formation or not. Second, we can control for the friendship selection bias on estimated interaction effects. We provide microfoundations of this statistical model based on the subgame perfect equilibrium of a two‐stage game and propose a Bayesian MCMC approach for estimating the model. We apply the model to study American high school students' friendship networks using the Add Health dataset. From two interaction variables, GPA and smoking frequency, we find that the utility of interactions in academic learning is important for friendship formation, whereas the utility of interactions in smoking is not. However, both GPA and smoking frequency are subject to significant peer effects.