People who inject drugs are an important population to study in order to reduce transmission of blood-borne illnesses including HIV and Hepatitis. In this paper we estimate the HIV and Hepatitis C prevalence among people who inject drugs, as well as the proportion of people who inject drugs who are female in Mauritius. Respondent driven sampling (RDS), a widely adopted link-tracing sampling design used to collect samples from hard-to-reach human populations, was used to collect this sample. The random walk approximation underlying many common RDS estimators assumes that each social relation (edge) in the underlying social network has an equal probability of being traced in the collection of the sample. This assumption does not hold in practice. We show that certain RDS estimators are sensitive to the violation of this assumption. In order to address this limitation in current methodology, and the impact it may have on prevalence estimates, we present a new method for improving RDS prevalence estimators using estimated edge inclusion probabilities, and apply this to data from Mauritius.

Miles Q. Ott Krista J. Gile Matthew T. Harrison Lisa G. Johnston Joseph W. Hogan

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined $\Upsilon(1S)$ and $\eta_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass.

Christine T. H. Davies Judd Harrison Ciaran Hughes Ronald R. Horgan Georg M. von Hippel Matthew Wingate

A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures (MFM). While inference in MFMs can be done with methods such as reversible jump Markov chain Monte Carlo, it is much more common to use Dirichlet process mixture (DPM) models because of the relative ease and generality with which DPM samplers can be applied. In this paper, we show that, in fact, many of the attractive mathematical properties of DPMs are also exhibited by MFMs---a simple exchangeable partition distribution, restaurant process, random measure representation, and in certain cases, a stick-breaking representation. Consequently, the powerful methods developed for inference in DPMs can be directly applied to MFMs as well. We illustrate with simulated and real data, including high-dimensional gene expression data.

Jeffrey W. Miller Matthew T. Harrison

Shallow water waves are a striking example of nonlinear hydrodynamics, giving rise to phenomena such as tsunamis and undular waves. These dynamics are typically studied in hundreds-of-meter-long wave flumes. Here, we demonstrate a chip-scale, quantum-enabled wave flume. The wave flume exploits nanometer-thick superfluid helium films and optomechanical interactions to achieve nonlinearities surpassing those of extreme terrestrial flows. Measurements reveal wave steepening, shock fronts, and soliton fission -- nonlinear behaviors long predicted in superfluid helium but never previously directly observed. Our approach enables lithography-defined wave flume geometries, optomechanical control of hydrodynamic properties, and orders of magnitude faster measurements than terrestrial flumes. Together, this opens a new frontier in hydrodynamics, combining quantum fluids and nanophotonics to explore complex wave dynamics at microscale.

Matthew T. Reeves Walter W. Wasserman Raymond A. Harrison Igor Marinkovic Nicole Luu Andreas Sawadsky Yasmine L. Sfendla Glen I. Harris Warwick P. Bowen Christopher G. Baker

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.

Jeffrey W. Miller Matthew T. Harrison

Predicting the $B_s^0-\bar{B}_s^0$ width difference $\Delta\Gamma_s$ relies on the heavy quark expansion and on hadronic matrix elements of $\Delta B=2$ operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators $R_{2,3}$ and linear combinations $\tilde{R}_{2,3}$ using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC ensembles of gauge field configuations with $2+1+1$ flavors of sea quarks with the HISQ discretization, including lattices with physically light up/down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first Standard Model determination of $\Delta\Gamma_s$ using lattice QCD results for all hadronic matrix elements through $\mathcal{O}(1/m_b)$. The main result of our calculations yields the $1/m_b$ contribution $\Delta \Gamma_{1/m_b} = -0.022(10)~\mathrm{ps}^{-1}$. Adding this to the leading order contribution, the Standard Model prediction is $\Delta \Gamma_s = 0.092(14)~\mathrm{ps}^{-1}$.

Christine T. H. Davies Judd Harrison G. Peter Lepage Christopher J. Monahan Junko Shigemitsu Matthew Wingate

We present the status of our ongoing calculation of the zero-recoil form factor for the semileptonic decay $\bar{B}^0\rightarrow D^{*+}l^-\bar{\nu}$ using lattice QCD with 2+1+1 flavours of highly improved staggered quarks in the sea (the MILC HISQ configurations) and using non-relativistic QCD for the bottom quark. We combine our result for $ F(1)$ with the latest HFAG average of $\eta_{EW} F(1)|V_{cb}|$ to get a preliminary value for $|V_{cb}|$.

Judd Harrison Christine Davies Matthew Wingate

Let $A$ be a commutative comodule algebra over a commutative bialgebra $H$. The group of invertible relative Hopf modules maps to the Picard group of $A$, and the kernel is described as a quotient group of the group of invertible grouplike elements of the coring $A\ot H$, or as a Harrison cohomology group. Our methods are based on elementary $K$-theory. The Hilbert 90 Theorem follows as a corollary. The part of the Picard group of the coinvariants that becomes trivial after base extension embeds in the Harrison cohomology group, and the image is contained in a well-defined subgroup $E$. It equals $E$ if $H$ is a cosemisimple Hopf algebra over a field.

S. Caenepeel T. Guedenon

We report magnetic susceptibility, specific heat, and neutron scattering measurements as a function of applied magnetic field and temperature to characterize the $S=1/2$ quasi-two-dimensional frustrated magnet piperazinium hexachlorodicuprate (PHCC). The experiments reveal four distinct phases. At low temperatures and fields the material forms a quantum paramagnet with a 1 meV singlet triplet gap and a magnon bandwidth of 1.7 meV. The singlet state involves multiple spin pairs some of which have negative ground state bond energies. Increasing the field at low temperatures induces three dimensional long range antiferromagnetic order at 7.5 Tesla through a continuous phase transition that can be described as magnon Bose-Einstein condensation. The phase transition to a fully polarized ferromagnetic state occurs at 37 Tesla. The ordered antiferromagnetic phase is surrounded by a renormalized classical regime. The crossover to this phase from the quantum paramagnet is marked by a distinct anomaly in the magnetic susceptibility which coincides with closure of the finite temperature singlet-triplet pseudo gap. The phase boundary between the quantum paramagnet and the Bose-Einstein condensate features a finite temperature minimum at $T=0.2$ K, which may be associated with coupling to nuclear spin or lattice degrees of freedom close to quantum criticality.

M. B. Stone C. Broholm D. H. Reich P. Schiffer O. Tchernyshyov P. Vorderwisch N. Harrison

The prototype of accreting, pulsating white dwarfs (GW Lib) underwent a large amplitude dwarf nova outburst in 2007. We used ultraviolet data from GALEX and ground-based optical photometry and spectroscopy to follow GW Lib for three years following this outburst. Several variations are apparent during this interval. The optical shows a superhump modulation in the months following outburst while a 19 min quasi-periodic modulation lasting for several months is apparent in the year after outburst. A long timescale (about 4 hr) modulation first appears in the UV a year after outburst and increases in amplitude in the following years. This variation also appears in the optical 2 years after outburst but is not in phase with the UV. The pre-outburst pulsations are not yet visible after 3 years, likely indicating the white dwarf has not returned to its quiescent state.

Eric Bullock Paula Szkody Anjum S. Mukadam Bernardo W. Borges Luciano Fraga Boris T. Gänsicke Thomas E. Harrison Arne Henden Jon Holtzman Steve B. Howell Warrick A. Lawson Stephen Levine Richard M. Plotkin Mark Seibert Matthew Templeton Johanna Teske Frederick J. Vrba