A Statistical Framework for Domain Shape Estimation in Stokes Flows

We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this "uncertainty" can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov Chain Monte Carlo (MCMC) algorithms designed to resolve infinite dimensional statistical quantities

Reinstatement of methamphetamine seeking in male and female rats treated with modafinil and allopregnanolone

Background Sex differences in methamphetamine (METH) use (females>males) have been demonstrated in clinical and preclinical studies. This experiment investigated the effect of sex on the reinstatement of METH-seeking behavior in rats and to determine whether pharmacological interventions for METH-seeking behavior vary by sex. Treatment drugs were modafinil (MOD), an analeptic, and allopregnanolone (ALLO), a neuroactive steroid and progesterone metabolite. Method Male and female rats were trained to self-administer i.v. infusions of METH (0.05mg/kg/infusion). Next, rats self-administered METH for a 10-day maintenance period. METH was then replaced with saline, and rats extinguished lever-pressing behavior over 18 days. A multi-component reinstatement procedure followed where priming injections of METH (1 mg/kg) were administered at the start of each daily session, preceded 30 min by MOD (128 mg/kg, i.p.), ALLO (15 mg/kg, s.c.), or vehicle treatment. MOD was also administered at the onset of the session to determine if it would induce the reinstatement of METH-seeking behavior. Results Female rats had greater METH-induced reinstatement responding compared to male rats following control treatment injections. MOD (compared to the DMSO control) attenuated METH-seeking behavior in male and female rats; however, ALLO only reduced METH-primed responding in females. MOD alone did not induce the reinstatement of METH-seeking behavior. Conclusions These results support previous findings that females are more susceptible to stimulant abuse compared to males and ALLO effectively reduced METH-primed reinstatement in females. Further, they illustrate the utility of MOD as a potential agent for prevention of relapse to METH use in both males and females

Embracing Uncertainty in "Small Data" Problems: Estimating Earthquakes from Historical Anecdotes

We apply the Bayesian inversion process to make principled estimates of the magnitude and location of a pre-instrumental earthquake in Eastern Indonesia in the mid 19th century, by combining anecdotal historical accounts of the resultant tsunami with our modern understanding of the geology of the region. Quantifying the seismic record prior to modern instrumentation is critical to a more thorough understanding of the current risks in Eastern Indonesia. In particular, the occurrence of such a major earthquake in the 1850s provides evidence that this region is susceptible to future seismic hazards on the same order of magnitude. More importantly, the approach taken here gives evidence that even "small data" that is limited in scope and extremely uncertain can still be used to yield information on past seismic events, which is key to an increased understanding of the current seismic state. Moreover, sensitivity bounds indicate that the results obtained here are robust despite the inherent uncertainty in the observations

On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of SARS-CoV-2 across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology

The impact of a hybrid social marketing intervention on inequities in access, ownership and use of insecticide-treated nets

BACKGROUND: An ITN intervention was initiated in three predominantly rural districts of Eastern Province, Zambia, that lacked commercial distribution and communication infrastructures. Social marketing techniques were used for product and message development. Public sector clinics and village-based volunteers promoted and distributed subsidized ITNs priced at $2.5 per net. A study was conducted to assess the effects of the intervention on inequities in knowledge, access, ownership and use of ITNs. METHODS: A post-test only quasi-experimental study design was used to compare intervention and comparison districts. A total of 2,986 respondents were interviewed. Survey respondents were grouped into four socio-economic (SES) categories: low, medium-low, medium and high. Knowledge, access, ownership and use indicators are compared. Concentration index scores are calculated. Interactions between intervention status and SES help determine how different SES groups benefited from the intervention. RESULTS: Although overall use of nets remained relatively low, post-test data show that knowledge, access, ownership and use of mosquito nets was higher in intervention districts. A decline in SES inequity in access to nets occurred in intervention districts, resulting from a disproportionately greater increase in access among the low SES group. Declines in SES inequities in net ownership and use of nets were associated with the intervention. The largest increases in net ownership and use occurred among medium and high SES categories. CONCLUSION: Increasing access to nets among the poorest respondents in rural areas may not lead to increases in net use unless the price of nets is no longer a barrier to their purchase