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  • We describe a simple and effective technique, the Eigenvector Method for Umbrella Sampling (EMUS), for accurately estimating small probabilities and expectations with respect to a given target probability density. In EMUS, we apply the principle of stratified survey sampling to Markov chain Monte Carlo (MCMC) simulation: We divide the support of the target distribution into regions called strata, we use MCMC to sample (in parallel) from probability distributions supported in each of the strata, and we weight the data from each stratum to assemble estimates of general averages with respect to the target distribution. We demonstrate by theoretical results and computational examples that EMUS can be dramatically more efficient than direct Markov chain Monte Carlo when the target distribution is multimodal or when the goal is to compute tail probabilities. Read More
  • Circumplanetary disks regulate the late accretion to the giant planet and serve as the birthplace for satellites. Understanding their characteristics via simulations also helps to prepare for their observations. Here we study disks around 1, 3, 5, 10 $\mathrm{M_{Jup}}$ planets with three dimensional, global radiative hydrodynamic simulations with sub-planet peak resolution, and various planetary temperatures. We found that as the 1 $\mathrm{M_{Jup}}$ planet radiates away its formation heat, the circumplanetary envelope transitions to a disk between $T_p = 6000$ K and 4000 K. In the case of 3-10 $\mathrm{M_{Jup}}$ planets a disk always forms. The temperature profile of the circumplanetary disks is very steep, the inner 1/6th is over the silicate condensation temperature and the entire disk is above water freezing point, making satellite formation impossible in this early stage ($<$1 Myr). Satellites might form much later and first in the outer parts of the disk migrating inwards later on. Our disk masses are $1, 7, 20, 40 \times 10^{-3}\mathrm{M_{Jup}}$ for the 1, 3, 5, 10 $\mathrm{M_{Jup}}$ gas giants respectively, and we provide an empirical formula to estimate the subdisk masses based on the planet- and circumstellar disk mass. Our finding is that the cooler the planet, the lower the temperature of the subdisk, the higher the vertical influx velocities, and the planetary gap is both deeper and wider. We also show that the gaps in 2D and 3D are different. The subdisk eccentricity increases with planetary mass and violently interacts with the circumstellar disk, making satellite-formation less likely, if $\mathrm{M_p} \gtrsim 5 \mathrm{M_{Jup}}$. Read More
  • We study the transverse momentum distribution of hadrons within jets, where the transverse momentum is defined with respect to the standard jet axis. We consider the case where the jet substructure measurement is performed for an inclusive jet sample $pp\to\text{jet}+X$. We demonstrate that this observable provides new opportunities to study transverse momentum dependent fragmentation functions (TMDFFs) which are currently poorly constrained from data, especially for gluons. The factorization of the cross section is obtained within Soft Collinear Effective Theory (SCET), and we show that the relevant TMDFFs are the same as for the more traditional processes semi-inclusive deep inelastic scattering (SIDIS) and electron-positron annihilation. Different than in SIDIS, the observable for the in-jet fragmentation does not depend on TMD parton distribution functions which allows for a cleaner and more direct probe of TMDFFs. We present numerical results and compare to available data from the LHC. Read More
  • There is increasing observational and theoretical evidence for a tight correlation between the metallicity and total mass of accreted stellar halos for galaxies with Milky Way-like stellar masses. Using the Illustris cosmological hydrodynamical simulations, we explore this relationship for central galaxies spanning a broad range in dark matter halo masses. We find that there exists a general accreted metallicity-stellar mass relationship over 3 orders of magnitude in accreted stellar mass. This arises due to the accreted stellar metallicity being set by the dominant accreted progenitor, which also contributes the bulk of its stellar material. We show that the scatter in accreted metallicity at a fixed accreted stellar mass encodes information about the stellar mass of the dominant progenitor, while the density and metallicity gradients of the accreted stellar halo provides information about the time of accretion of the dominant progenitor. We demonstrate that the total accreted stellar metallicity and accreted stellar mass can be reconstructed from aperture measurements along the minor axis of edge-on disk galaxies. These correlations highlight the potential for observational studies of stellar halos to quantify our understanding of the most dominant events in the growth history of galaxies. We explore the implication of our models for our understanding of the accretion histories of the Milky Way, M31 and NGC 5128. In particular, a relatively late and massive accretion is favoured for M31; additionally, we provide a first estimate of the accreted stellar mass for NGC 5128. Read More
  • Let $X \subset \mathbb{P}^n$ be a general Fano complete intersection of type $(d_1,\dots, d_k)$. If at least one $d_i$ is greater than $2$, we show that $X$ contains rational curves of degree $e \leq n$ with balanced normal bundle. If all $d_i$ are $2$ and $n\geq 2k+1$, we show that $X$ contains rational curves of degree $e \leq n-1$ with balanced normal bundle. As an application, we prove a stronger version of the theorem of Z. Tian \cite{Tian}, Q. Chen and Y. Zhu \cite{ChenZhu} that $X$ is separably rationally connected by exhibiting very free rational curves in $X$ of optimal degrees. Read More
  • In this paper we present a methodology and discuss some implementation issues for a project on statistical/expert approach to data analysis and knowledge acquisition. We discuss some general assumptions underlying the project. Further, the requirements for a user-friendly computer assistant are specified along with the nature of tools aiding the researcher. Next we show some aspects of belief network approach and Dempster-Shafer (DST) methodology introduced in practice to system SEAD. Specifically we present the application of DS methodology to belief revision problem. Further a concept of an interface to probabilistic and DS belief networks enabling a user to understand the communication with a belief network based reasoning system is presented Read More