Nilesh Tripuraneni — Page 2

arXiv2015

A Linear-Time Particle Gibbs Sampler for Infinite Hidden Markov Models

Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In this paper, we present an infinite-state Particle Gibbs (PG) algorithm to resample state trajectories for the iHMM. The proposed algorithm uses an efficient proposal optimized for iHMMs and leverages ancestor sampling to suppress degeneracy of the standard PG algorithm. Our algorithm demonstrates significant convergence improvements on synthetic and real world data sets. Additionally, the infinite-state PG algorithm has linear-time complexity in the number of states in the sampler, while competing methods scale quadratically.

stat.ML↗

arXiv2010

Bulk Viscosity and Cavitation in Boost-Invariant Hydrodynamic Expansion

We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the dependence of the energy density as a function of proper time on the values of the shear viscosity, the bulk viscosity, and second order coefficients, confirming that large changes in the values of the latter have negligible effects. Varying the shear viscosity between zero and a few times s/(4 pi), with s the entropy density, has significant effects, as expected based on other studies. Introducing a nonzero bulk viscosity also has significant effects. In fact, if the bulk viscosity peaks near the crossover temperature Tc to the degree indicated by recent lattice calculations in QCD without quarks, it can make the fluid cavitate -- falling apart into droplets. It is interesting to see a hydrodynamic calculation predicting its own breakdown, via cavitation, at the temperatures where hadronization is thought to occur in ultrarelativistic heavy ion collisions.

hep-ph↗